Download MPhil Thesis - Final - Suzanne Knight

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THE SEARCH FOR
SUBSTELLAR COMMON PROPER MOTION
COMPANIONS TO WHITE DWARFS
Suzanne Knight
B.Maths (Hons) & B.Sc.
Thesis submitted for the degree of
Master of Philosophy
at the University of Leicester
X-Ray & Observational Group
Department of Physics & Astronomy
University of Leicester
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July 2015
© Suzanne Knight 2015
This thesis is copyright and no quotation from it may be published
without proper acknowledgment.
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Abstract(
A large sample of white dwarfs within the solar neighbourhood has been examined to
search for resolved common proper motion companions. The luminosity of these
white dwarfs make them ideal candidates for detecting low mass objects such as
brown dwarfs and gas giant planets. !
Theoretical predictions generally agree that a star will consume and destroy close-in,
low mass planets as it ascends the red giant and asymptotic giant branch evolutionary
tracks, but larger mass objects and those further out will survive.!
A substellar companion detected around a white dwarf would prove that it could
survive the final stages of stellar evolution and place constraints on the frequency of
planetary systems around their progenitors.!
Ultra cool brown dwarfs are particularly interesting due to their scarcity and offer a
unique opportunity to test properties predicted for them by atmospheric models. They
provide a crucial link between the colder gas giant planets and hotter T spectral type
brown dwarfs that can be imaged orbiting nearby stars.!
Possible companions were identified from the reduction and analysis of archived
Spitzer data. Their masses and temperatures were determined using their apparent
magnitudes and the COND evolutionary models.
The results present evidence of the detection of potential companions to five white
dwarfs; four of these companions have masses within the range associated with giant
planets. It is inferred that < 15% of white dwarfs have unresolved companions with
masses between 5 - 13 MJup while < 8% of white dwarfs have companions with
masses above the deuterium burning limit (~ 13 MJup). Also, the search could detect
companions with effective temperatures in the range of 300 - 450 K (later Y spectral
type) for < 45% of the white dwarf targets. Future work should confirm these objects
and extend the search to other white dwarfs taken from the Spitzer Data Archive.
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Acknowledgements(
I wish to thank my supervisor Dr. Matthew Burleigh and Dr. Sarah Casewell for their
guidance during this brief project and to the staff of the Physics and Astronomy
Department for the opportunity to study and work at Leicester University. I have had
the privilege to get to know many and I have been grateful for their help and advice
on many occasions. I've also enjoyed the company of many PhD students and
postdoctoral researchers during this time and have appreciated their valuable support.!
To my friends, family and former work colleagues who have stood beside me on this
long road of discovery, I would have never been able to do this journey without you.!
Finally, eternal gratitude goes to the Universe for its infinite wisdom, patience and
guidance. As Plato once remarked, “Astronomy compels the soul to look upward, and
leads us from this world to another”. The truth of these words in essence, continues to
serve us well.!
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Table(Of(Contents(
Abstract(.................................................................................................................................(i(
Acknowledgements(..........................................................................................................(ii(
List(Of(Tables(.......................................................................................................................(v(
List(Of(Figures(....................................................................................................................(vi(
Chapter(1(?(Introduction(.................................................................................................(1(
1.1 - White Dwarfs ................................................................................................. 4!
1.2 - Brown Dwarfs ................................................................................................ 9!
1.3 - Aims Of The Project .................................................................................... 14!
Chapter(2(–(Imaging(Surveys(For(Substellar(Companions(To(White(Dwarfs
(...............................................................................................................................................(16(
2.1 - History .......................................................................................................... 16!
2.2 - A Search For Resolved Brown Dwarf And Massive Planetary Companions
To White Dwarfs With Spitzer ............................................................................. 19!
Chapter(3(–(The(Search(For(Common(Proper(Motion(Companions(................(26(
3.1 - Data Reduction ............................................................................................. 26!
3.2 - Results .......................................................................................................... 39!
Chapter(4(–(Completeness(Limits(And(IFMR(Of(Observations(..........................(47(
4.1 - Completeness Limits .................................................................................... 47!
4.2 - Calculating Limits On Companion Masses.................................................. 48!
4.2.1 - Summary .............................................................................................. 48!
4.2.2 - The Initial Final Mass Relation ............................................................ 49!
4.2.3 - COND Evolutionary Models ................................................................ 49!
4.2.4 - The Projected Separation Of Companion To A White Dwarf ............. 61!
4.3 - Results .......................................................................................................... 61!
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Chapter(5(–(Conclusion(And(Future(Work(...............................................................(66(
References(.........................................................................................................................(68(
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List(Of(Tables(
2.1 - Spitzer details of the observations for the sampled white dwarfs ............... 21
3.1 - Photometric information for the sampled white dwarfs............................... 36
4.1 - Stellar parameters derived for the sampled white dwarfs ............................ 57
4.2 - Results for the 23 equatorial and northern hemisphere white dwarfs
taken from the DODO Survey ..................................................................... 60
4.3 - Results for possible substellar companions to sampled white dwarfs ........ 62
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List(Of(Figures(
1.1 - Evolution of low and intermediate mass stars in the H-R Diagram............... 4
1.2 - The Carbon-Nitrogen-Oxygen Cycle ............................................................. 5
3.1 - Spitzer basic calibrated data (BCD) image ................................................. 27
3.2 - Example of a PSP mosaic image in GAIA data reduction ........................... 28
3.3 - Example of a PRF mosaic image in GAIA data reduction .......................... 30
3.4 - Example of a final combined epoch image in GAIA data reduction ........... 31
3.5 - Scatter error plots in RA and magnitude for WD0806-661 &
WD0101+048 ............................................................................................... 35
Proper motion diagrams for objects in the the field:
3.6 - WD0806-661 & WD0101+048.................................................................... 39
3.7 - WD0552-041 & WD1055-072..................................................................... 40
3.8 - WD1943+163 &WD2311-068..................................................................... 41
Completeness limit plots for both epochs for:
4.1 - WD0806-661 & WD0101+048.................................................................... 50
4.2 - WD0552-041 & WD1055-072..................................................................... 51
4.3 - WD1943+163 & WD2311-068.................................................................... 52
4.4 - WD0009+501 & WD2539-434 ................................................................... 53
4.5 - WD0912+536 & WD1031-114 ................................................................... 54
4.6 - WD1121+216 & WD1257+278 .................................................................. 55
4.7 - WD1609+135 & WD1900+705 ................................................................... 56
Cumulative completeness limit plots for the sampled white dwarfs:
4.8 - Unresolved companion mass ...................................................................... 63
4.9 - Unresolved companion temperature ............................................................ 64
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Chapter(1(=(Introduction(
“The universe is a pretty big place. If it's just us, seems like an awful waste of space.”
Carl Sagan, Contact.
In the past number of years, an increasing number of planets detected by transit and
radial velocity surveys (Borucki et al. 2011; Mayor et al. 2011) have given credence
to the quest of finding life elsewhere in the universe 1. The NASA Kepler Mission for
example, was designed to use the transit method to search for terrestrial planets near
habitable zones of late main-sequence parent stars (Borucki et al. 2010; Koch et al.
2010). To date, it has successfully confirmed over 1,000 planets as diverse as hot
Jupiters, super-Earths and circumbinary planets. Precise transit measurements and
mass determination from radial velocity measurements have enabled detections of
these planets in both the reflected (optical) and emitted (infrared) regimes providing
valuable insight into the study of exoplanetary composition and atmospheres.
The focus of these surveys now extends to the fate of planetary systems once their
host stars evolve off the main sequence. An effective method in finding indirect
evidence for the presence of planets is to search for remnants of planetary systems
around these post-main sequence stars. Theoretical studies have shown that a fraction
of planets can survive the red giant stage of their host star (Nordhaus et al. 2010;
Mustill & Villaver 2012) however the long-term evolution is complex and may result
in planet ejections or collisions (Debes & Sigurdsson 2002).
In recent years, studies have also begun to explore the possibility of habitable planets
around brown dwarfs (Bolmont et al. 2011) and white dwarfs. These objects are
relatively small and dim so their transits are more readily detectable than for main
sequence stars (Faedi et al. 2009; Agol 2011).
Brown dwarfs are objects that are not massive enough to produce the central pressures
necessary to fuse hydrogen into helium, yet it is thought that they are able to support a
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NASA’s Astrobiology’s quest to ‘follow the water’ in the search for the right places
elsewhere in the universe that might be hospitable for life.
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habitable zone since their slow contraction converts gravitational energy, the
dominant source of energy into heat (Burrows et al. 1997; Baraffe et al. 2003).
Surveys, such as the Wide Infrared Survey Explorer (WISE) and the Spitzer Space
Telescope, have found hundreds of these objects (Mainzer et al. 2011; Kirkpatrick et
al. 2011), opening the possibility of detecting planets in orbit around brown dwarfs.
While post main sequence evolution pose barriers to close planetary companions for
white dwarfs, giant planets have nevertheless been detected, such as the confirmed ~
2.5 MJup planetary companion at a distance ~ 43 AU from its primary located in the
2M1207 system (Sigurdsson et al. 2003; Chauvin et al. 2005; Zhou et al. 2012).
With an effective temperature (Teff) ≤ 6000 K, cool white dwarfs are promising hosts
of planets in the habitable zone (Fossati et al. 2012). While atmospheres of white
dwarfs should be relatively free of heavy elements (Zuckerman et al. 2003),
observational evidence supports white dwarfs hosting metal-rich disks (Gänsicke et
al. 2006; Girven et al 2012; Kilic et al. 2012; Xu & Jura 2012) or having disks
contaminated by accreted material and water from extrasolar asteroids, planetesimals
or perhaps from a tidally disrupted rocky planet within the roche limit of the white
dwarf (e.g. Jura 2003; Gänsicke et al. 2012; Barstow et al. 2014). Such disruption near
a white dwarf may lead to the formation of low-mass planets in tight orbits (i.e. at a
few solar radii) around the star (Bear et al. 2015).
A number of extrasolar planets have also been discovered around giant stars using the
radial velocity technique, e.g., HD 13189 (Hatzes et al. 2005). These stars have
entered the Red Giant Branch (RGB) phase or Asymptotic Giant Branch (AGB) phase
(Section 1.1) and hence reinforce the notion that planets can survive the final stages of
stellar evolution).
During the AGB phase, the main sequence progenitor will have reached its maximum
radius and lose most of its mass. Consequently, the orbital radius of the planet will not
evolve and increase due to the host star’s mass loss (Villaver & Livio, 2007).
However, if the red giant envelope expands beyond the orbital radius of the planet, the
interaction between the planet and the envelope will cause a reduction of the planet’s
orbital radius.
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Lovis & Mayor (2007) and Johnson et al. (2007) suggest that intermediate mass stars
rather than lower mass stars are more likely to host extrasolar companions of all
masses.
Furthermore variable white dwarfs with stability in pulse period and phase offers an
opportunity in the detection of lower mass planets at large orbital separations
(Mullally et al. 2009). By studying polluted white dwarfs, we can therefore obtain
invaluable measures of the bulk composition of these planets (e.g., Klein et al. 2010).
The conditions for the onset of planetary formation is also thought to apply to where
circumstellar disks have been detected around brown dwarf candidates (Apai et al.
2005).
Direct imaging of planets in comparison to the radial velocity and transit techniques is
much more problematic. Due to their close proximity as well as their smaller size and
dimness compared to the brighter parent stars, these planets are often lost in the star’s
glare and are difficult to resolve. There have been attempts during the past decade to
directly observe likely candidates. For example, 2M1207b is a companion to the
brown dwarf 2M1207A and is located at a distance of ≤ 40 AU to the primary
(Chauvin et al. 2004; Mamajek et al. 2005). Subsequent observations by the Hubble
Space Telescope and the VLT have confirmed that the faint object has a planetary
mass of ~ 5MJup (Chavin et al. 2005).
Burleigh et al. (2002) have proposed that planetary companions in wide (> 5 AU)
orbits around main sequence stars between 1 - 8!M⨀ !in mass are the best candidates
for direct imaging detection. Jovian planets in particular, will survive the late stages of
stellar evolution and be located in larger orbits 2 thus avoiding the red giant envelope
of the star. Furthermore, infrared-imaging of hot, young massive white dwarfs ( >
0.6!M⨀ ) that have the shortest overall system age should enable resolution and
detection of > 3 MJup companions using existing telescopes.
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The orbits of planets which do not interact directly with the red giant will simply expand by
a maximum factor main sequence progenitor mass /white dwarf mass (Jeans 1924).
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1.1(=(White(Dwarfs(
The first infrared excess around a white dwarf (G29-38) 3 was discovered more than
25 years ago (Zuckerman & Becklin 1987). Since 2005, primarily thanks to the
Spitzer Space Telescope (Werner et al. 2004), significant progress has been made in
this field of study.
White dwarfs are remnants representing the final stage of stellar evolution on the
Hertzsprung-Russell (H-R) diagram (Figure 1.1) for main sequence stars having initial
masses between 0.7 - 8.0 M⨀ (Weidemann 2000; Weidemann & Koester 1983).
Figure 1.1 – Evolution of low (1!M⨀ ), intermediate (5!M⨀ ) and high (25!M⨀ ) mass
stars in the H-R diagram. Places where dredge ups phases are indicated along the
AGB where thermal pulses begin. From Iben (1991).
These stars have convective cores and burn hydrogen during the main sequence via
means of the Carbon-Nitrogen-Oxygen (CNO) cycle (Figure 1.2). One of the main
outcomes of the CNO cycle is the conversion of almost all central !"C into !"N.
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Now attributed to a dust disk. Many more such disks have been found indicating planetary
systems may still exist at these stars.
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The main sequence phase of evolution ends when hydrogen in a star’s core is
exhausted. Due to the absence of hydrogen burning, there is no longer thermal
pressure from nuclear fusion to counteract the force of gravity, thus initiating the star
to contract on a Kevin-Helmholtz timescale. Gravitational potential is released
causing the luminosity to increase slightly. As the core’s radius decrease, the effective
temperature of the surrounding matter increases sufficiently to cause hydrogen to
continue burning in a shell around the core. The ignition of the shell is rapid, the
cooler overlaying envelope outside the shell begins to expand, absorbing some of the
energy released by the shell.
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!"
C!+! !H!→! !"N!+!!!+!1.95!MeV!!
N!!→!! !"C!+!! ! !+!!! !+!2.22!MeV!!
C!!+! !H →! !"N!+!!!+!7.54!MeV!
N!!+! !H →! !"O!+!!!+!7.35!MeV!
O!!→!! !"N!+!! ! !+!!! !+!2.75!MeV!!
N!!+! !H →! !"! + !H! +!4.96!MeV!
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Figure!1.2!5!The!Carbon5Nitrogen5Oxygen!Cycle!Equations.!
The core’s mass continues to increase as more helium is introduced from the hydrogen
burning shell (Prialnik, 2000).
At this stage, the star migrates off the main sequence and redward towards the Red
Giant branch (RGB). During this transformation, which occurs on relatively short
timescales (Hurley et al. 2000), the core temperature and luminosity increase along
with a marked increase in the star’s radius, causing the surface to cool to an effective
temperature of ≤ 3500 K (corresponding to an early M spectral type). The radiation
pressure from the shell burning forces the outer diffuse (red giant) envelope of the star
to expand, reaching distances between 20 R ⨀ and 300 R ⨀ ! Hurley!et!al. 2000 !to
conserve the gravitational potential energy.
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As the star climbs the RGB, convection is now the dominant energy transport
mechanism in the envelope. Before it starts to burn helium, the nearly adiabatic
temperature gradient associated with the envelope’s convection zone extends deep
within the stellar interior. Consequently, the star experiences the first dredge-up of
nuclear processed materials from the CNO process to its surface. The photospheric
abundance of carbon and nitrogen is thus altered ( !"C and !"O!are reduced, !"N is
increased).
The hydrogen burning shell consumes the hydrogen at the base of the envelope,
producing helium that contributes to the core’s increasing mass and temperature but
no expansion. For stars having masses ≤ 2.0 M⨀ , the core contracts, gets hotter and
denser and becomes more electron-degenerate (Herwig 2005). When the temperature
and density are high enough to ignite helium in the degenerate core and surrounding
shell (via the triple-! process), the energy released further raises the central
temperature. However, the core cannot expand due to the degeneracy and so raises the
burning rate. This results in runway nuclear burning known as a core helium flash
(Iben & Renzini 1983). Higher mass RGB stars (> 2.0 M⨀ ) in comparison, have hotter
but less dense cores. At these masses, there is no degeneracy and the core helium is
ignited gently.
When the core helium is depleted, another phase of core contraction and envelope
expansion begins. The star again increases in luminosity and cools, becoming a
second-ascent red giant, moving this time parallel to the RGB track, towards the
Asymptotic Giant Branch (AGB). Depending on the initial mass of the star, its radius
is 300!– 1500 R ⨀ (Hurley et al. 2000). The core now consists mainly of carbon and
oxygen from the conversion of helium and is surrounded by a newly formed thick
helium shell and an outer existing hydrogen shell. For stellar masses greater than
4.0!M⨀ , there is a second dredge-up phase whereby the helium and nitrogen content of
the envelope increase (Herwig 2005).
Thermal pulsing and intermittent flashes of the helium shell occur because of its close
proximity to the hydrogen shell. The periodic ignition of the hydrogen shell causes
deposits helium ash onto the helium layer below. The mass of the helium layer
increases and the star becomes degenerate. In the third dredge up phase, carbon rich
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material is periodically brought up to the surface. The star contracts before the
hydrogen shell is reignited for another phase of hydrogen burning.
The AGB phase is terminated when the star dissipates the less tightly bound envelope
in a mass loss designated as a superwind during thermal pulsing (Wachter et al. 2002).
The now exposed hydrogen and helium shells are extinguished, revealing a hot,
central core that quickly fades into a white dwarf. The exact proportions of carbon and
oxygen in the core are unknown because of uncertainties in the nuclear rates of helium
burning (Fontaine et al. 2001). The outer layers of the star, ionized by the high
temperature of the central star, are ejected into the surrounding ISM and become
visible as a planetary nebula.
Several properties of white dwarf stars can be found directly from observations. For
example, analysis of their energy distribution and the H or He lines in their optical and
ultraviolet spectra, determine their effective temperature: Teff which ranges from ≤
150000 K for the hottest stars to ≥ 4000 K for the coolest degenerate dwarfs. The
strength and width of these spectral features are sensitive to the density of particles in
the atmosphere, which is controlled by the surface gravity (log g). The average surface
gravity of white dwarf stars is log g ∼ 8 (cm s-2), compared to log g ∼ 4.4 for our Sun.
Their luminosity reflects the large range of observed effective temperatures (L
T4eff): the faintest are L ≤ 10-4.7 !L⨀ (Bergeron et al. 2001) while those entering the
cooling sequence typically have L between 102! – 103!L⨀ . Although white dwarfs can
have an initial mass less than 8!M⨀ , their mass distribution is strongly peaked, with a
FWHM of ~ 0.15!M⨀ , around ~ 0.59!M⨀ (Fontaine et al. 2001; Kepler et al. 2007).
Their average density is an incredible ~ 106 g cm-3.
It is generally believed that the immediate progenitors of most white dwarfs are nuclei
of planetary nebulae, born in the form of hot, collapsed objects and are themselves the
products of intermediate and low mass main sequence evolution and cool over time.
The thermal pressure in a star’s interior maintained by the energy produced by nuclear
processes is absent in the white dwarf. When the star’s material no longer undergoes
nuclear fusion, it is not supported against gravitational collapse by heat generated by
fusion but rather by electron degeneracy pressure. This pressure is a quantummechanical effect arising from the Pauli-Exclusion principle and is responsible for
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maintaining hydrostatic equilibrium in white dwarfs. The density of electrons is
described by Fermi-Dirac statistics as electrons having ½ integral spin. Due to the
Pauli Exclusion principle, two electrons in an atom cannot occupy the same quantum
bound state, i.e. having the same momentum ( ! = p) and spin, and so are in shells of
different energies. As electron density increases, the electrons will have less
uncertainty in their position but have higher uncertainty in their momentum and are
forced into higher momentum states. With higher energies, the electrons cannot be
pushed closer together. Degenerate electrons are excellent conductors of heat and so
can thermalize the interior of the star efficiently (Fontaine et al. 2001). The generated
pressure and the restriction on the number density at each state is the source of
electron degeneracy pressure that is independent of temperature.
Fowler (1926) showed that this pressure could support a white dwarf against
gravitational collapse, maintaining hydrostatic equilibrium in a white dwarf. By
equating the gravitational potential energy with the electron degeneracy pressure, the
inverse mass-radius relationship R ∝ M !!/! !is inferred for a degenerate object. Thus a
more massive white dwarf is expected to be smaller in its radius, a feature that is not
observed in main sequence stars. Furthermore, this mass is limited above (~ 1.44
M⨀ 4) at which hydrostatic equilibrium cannot be maintained and the star starts to
collapse (Chandrasekhar, 1931). Stars greater than this mass will become neutron stars
or black holes.
Radiation escaping from a white dwarf originates from its atmosphere that is usually
dominated by hydrogen and contains less than 10-14 of the star’s mass. The majority of
known white dwarfs have hydrogen dominated atmospheres and are classified ‘DA’
stars 5. Approximately 25% of these stars’ atmospheres are polluted by calcium or
other metals (Zuckerman et al. 2003), hence these stars are classified as DAZs. Given
their rather short gravitational settling time scales (between 10−2 and 106 years;
Dupuis et al. 1992), the metals need to be replenished continually by a nearby source
such as a debris disk (Dupuis et al. 1992), the interstellar medium (Koester & Wilken
2006) or even asteroids (Von Hippel et al. 2007). The presence of metal lines in DAZ
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For a composition of pure He.
DA stars are so-called due to their degeneracy and similarity to ‘A’ spectral type stars with
respect to H and He and exhibit Balmer hydrogen lines only.
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type stars may yet prove to be a significant marker in the detection of planetary
systems.
The remaining known white dwarfs are non-DA types with atmospheres dominated by
elements other than hydrogen. ‘DB’ stars for example, have a rich helium atmosphere
with an underlying carbon-oxygen core containing most of the mass. Rarer DQ white
dwarfs in comparison show a more complex spectra comprising of molecular carbon
and hydrocarbon. Their existence accounts for the DB gap, an interval of effective
temperature between 30000 K and 45000 K, in which no helium-atmospheric object
has been found. Finally, DZ stars are cool white dwarfs that display trace elements
other than carbon. They have a helium-dominated atmosphere, but the gas is too cool
for the helium lines to be detected.
White dwarf evolution is not driven by the initial metal content of the progenitor star,
due to the strong gravity of the white dwarf atmospheres (Salaris et al. 2010; Althaus
et al 2015). However, the level of metallicity a progenitor has could play a key role in
determining the chemical composition and consequently the cooling time (as well as
the initial-to-final-mass relation) of the white dwarf itself. For example, progenitors
with very low metallicity (Z=0.0001) will result in white dwarfs with masses ≤
0.6!M⨀ having thicker H envelopes compared to those with solar metallicity
progenitors. This leads to intense hydrogen burning shells compared to their solar
counterparts and delayed cooling time (Miller Bertolami et al. 2013).
1.2(=(Brown(Dwarfs(
Hydrogen provides the first source of thermonuclear power to the stars. Main
sequence stars more massive than our Sun, rapidly consume this fuel within short
timescales. For example, a 10!M⨀ star that is approximately 3000 times luminous than
our Sun will have a lifetime ≤ 30 million years. Our Sun in comparison with its
dramatically lower rate of power generation, takes ~ 9 billion years to burn through its
smaller reservoir of hydrogen. The trend of slower power generation by smaller stars
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continues down to the common ! solar mass stars, which are expected to burn their
fuel in about 100 billion years. Below a critical ass (~!0.072!M⨀ !or 75 MJup), the
thermonuclear fusion of hydrogen becomes impossible. The objects immediately
below this critical mass are called “brown dwarfs”.
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These are substellar mass objects (SMO) with masses ranging 13 - 75 MJup (0.012 !0.072!M⨀ ) are technically “failed stars” – although they are composed of hydrogen,
helium, and trace amounts of metals, they are too low mass to support the fusion of
hydrogen but those with a mass greater than 13 MJup (Saumon et al 1996; Burrows et
al. 2001) can fuse deuterium (Saumon et al 1996; Burrows et al. 2001) or lithium for
masses ≥ 65 MJup during formation.
Observational evidence suggests that brown dwarfs form in the same molecular cloud
as normal stars. However, to overcome thermal pressure, brown dwarfs must form out
of the highest density regions of these clouds. From its spectrum, the brown dwarf
appears to be simply an exceedingly cool star and yet in their inability to produce
significant amounts of energy from nuclear reactions is more analogous to planetary
behavior rather than a star. This underlies the fundamental physical difference
between a brown dwarf and a star: unlike a star, a brown dwarf does not need
thermonuclear fusion to hold itself up. The same degenerate electron pressure that
holds up the degenerate dwarfs and planets such as Saturn and Jupiter halts the
shrinkage of a brown dwarf before its core temperature reaches the thermonuclear
range.
With the advent of a new phase of discovery of brown dwarfs (and substellar objects
in general), their origins have challenged the scientific community into re-evaluating
what constitutes planets and stars. One school of thought is that brown dwarfs should
be defined similarly to that of stars (based on interior physics). One intuitive
difference between stars and planets is that stars experience nuclear fusion, whereas
planets do not. A star will stabilize its luminosity for a period of time by hydrogen
burning and derives all of its luminosity from fusion during the main sequence phase.
The highest-mass brown dwarf by contrast, is never able to stabilize its luminosity or
temperature since it has gravitational contraction as at least a small part of its
luminosity source. It is brightest when it is born and continuously dims and cools (at
the surface) with time. Unlike stars, over sufficiently long periods of time, brown
dwarfs become cool enough to allow the formation of methane molecules in their
atmospheres.
The existence of brown dwarfs was first suggested by astronomers in the 1960s
studying the formation and evolution of very low mass stars. Kumar (1963) attempted
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to determine the nature of an object that formed like a star but was of too low mass to
support fusion. The term “brown dwarf” was coined by Jill Tarter (1975) to describe
SMOs using brown as an approximate colour, but astronomers had to wait 20 years
before the announcements of the first brown dwarf GL 229B (Oppenheimer et al.
1995) and the first extrasolar giant planet, EGP1 (Mayor and Queloz 1995).
Brown dwarfs arise from the disks around forming stars or from the contraction and
fragmentation of giant molecular clouds in the interstellar medium. The latter
mechanism is also responsible for producing some other objects with true masses
below 13 MJup. Distinguishing brown dwarfs from these objects, one thought is that
brown dwarfs should be heavier than this mass threshold for core fusion of any
element to occur. A planet in the traditional view (based on our own solar system) is
formed differently via core accretion in a circumstellar debris disk and does not
undergo core fusion, thus having a mass much smaller than this threshold. The
standard working definition of a planet under Resolution 5A of the 26th IAU General
Assembly pertains only to applicable objects (not withstanding Pluto 6) in our solar
system and excludes extrasolar planets which are not tidally locked to their host star
and have wider eccentric orbits. The term “extrasolar planet” has therefore been
loosely applied to a variety of objects and there have been several attempts to resolve
what actually constitutes a planet. For example, Marcy and Butler (2000) define a
planet as “an object that has mass between that of Pluto and the deuterium burning
threshold and that forms in orbit around an object that can generate energy by nuclear
reactions”. The IAU definition has been extended to include the criteria for the
minimum mass/size required for an extrasolar object to be considered a planet, and yet
in essence it makes the distinction between extrasolar planets located at the higher
mass end range and the lower mass limit brown dwarfs even more difficult. The
difference between the formation of binary stellar companions and planets can be
attributed to the lack of a need for stars or brown dwarfs to first form a rock/ice core,
yet no current method exists to determine whether the object had such an initial core
(Basri 2000). Formation in a disk does not by itself differentiate star from planet
formation, as well as orbital eccentricity or separation. Giant planets can form both by
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Pluto was ‘demoted’ to a dwarf planet by the IAU having failed on the third qualification of
the newly approved official definition. The debate to reinstate its planetary status is still on
going amongst the scientific and general communities.
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gas accretion onto a rocky core and by more direct forms of gravitational collapse in
gaseous disks (Boss 1997). The requirement that a planet be found orbiting a star no
longer applies in the case when several giant planets form in a system, and one or
more are ejected by orbital interactions and end up as freely floating objects.
Subsequent searches have revealed that it is more probable to find a planet rather than
a brown dwarf as a companion to a solar-type star in the brown dwarf mass range (e.g.
Janson et al. 2011; Bonnefroy et al. 2013). These issues highlight the dilemma
regarding brown dwarf-planet distinction (see Mannings et al. 2000 for a detailed
discussion).
The most basic empirical characterization of a brown dwarf is its spectral
classification that is determined from the pattern of absorption features in its
spectrum. A relevant division between stars and brown dwarfs is by the temperature
range where the strength of Titanium Oxide (TiO) absorption lines in stellar
atmospheres weakens and absorption lines of metal hydrides (e.g. CrH, FeH)
strengthen instead. Late M spectral type stars (Teff > 2000 K) are characterized by the
formation of dust. In the optical regime, TiO and VO molecular bands become
saturated then weaken and are characterized by strong water vapor absorption in the
near infrared. They give way to cooler objects that show none of the hallmark features
evident in the M spectral type dwarfs (e.g. GD 165B 7). The designation of a new L
spectral class suggested by Kirkpatrick (1998) and Martin et al. (1997) is used to
distinguish these low mass objects. However, it is not taken in the literal context to
correspond exactly to the mass based definitions of stars, planets and brown dwarfs. In
other words, not all L spectral type stars are brown dwarfs.
Young massive brown dwarfs begin as late M spectral type objects before they cool
and evolve into L spectral type objects. In this temperature range (Teff between 1,400
K and 2,000 K), their spectrum is dominated by absorption bands of water (H2O). For
even cooler temperatures (500 ≤ Teff ≤ 1500 K), objects are classified as T spectral
type “methane” brown dwarfs so-called due to the appearance of H- and K-band CH4
absorption bands in their spectra (Burgasser et al. 2002; Geballe et al. 2002). Methane
is not a factor in stars, but it is a distinguishing feature of giant planets such as Jupiter
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
7
Faint and very red companion discovered (Becklin & Zuckerman 1988) and was argued to
be a possible brown dwarf (Kirpatrick et al. 1999). M ≤ 0.072 M⨀ and Teff ≤ 1900 K.
!
12
and Saturn. They are also marked by the absence of alkalines and hydrides as well as
the presence of water vapor. In their atmospheres, dust grains deposit below the
photosphere.
Two companions with estimated spectral types ≥ T10 were found by Luhman et al.
(2011) and Liu (2011) around white dwarfs WD0806-661 and CFBDSIRJ1458+1013
respectively. Subsequent discoveries by Cushing et al. (2011) and Kirkpatrick et al.
(2012); Tinney et al. (2012) constituted the first similarly type objects found by the
Wide Infrared Survey Explorer (WISE) satellite. These objects have been designated
as the new ultra cool Y spectral type dwarfs corresponding to Teff < 500 K. They
show very red optical/ near-infrared to mid-infrared colours, i.e. they emit most of
their fluxes in the infrared compared to the late T spectral type dwarfs. They provide a
standard reference for future classification of similar objects at these wavelengths.
The spectral sequence described above can be thought of as an evolutionary sequence
of a brown dwarf that cools over time. As the lower mass object starts off with less
thermal energy from gravitational contraction, ambiguity exists between its
temperature and luminosity and so its mass and age which must be measured
independently.
It is interesting to note that the temperature and gravity of young late M, T and L
spectral type objects are not unlike that of extrasolar hot “Jupiter” planets found at
close separations to their host star. Observations of optical and near-infrared
transmission spectra of these planets have also identified water vapor and methane in
their atmospheres (Tinetti et al. 2007; Swain et al. 2008) as also seen in the
atmospheres of free-floating brown dwarfs of L and T spectral types. Giant planets
located at larger separations than our solar system equivalents will have Teff < 500 K a
temperature range which corresponds to the Y spectral type. Also, Y spectral type
masses are estimated to be a few times the mass of Jupiter and hence their gravity will
be similar to these planets. It is not unreasonable to assume that the study of the
atmospheres of free-floating Y dwarfs will be beneficial to understanding the
composition and properties of extrasolar planets that will be discovered in future
searches.
!
13
Not all ultra cool objects are brown dwarfs, but depending on their temperature and
age, they may be also very low mass stars or planetary mass objects. The Li
spectroscopic test which detects the presence of atomic lithium at 6708 Å is a useful
tool to distinguish the sub stellar nature of ultra cool dwarfs. The element is destroyed
at temperatures of 2.5 x 10! - 3 x 10! K within the interior of the stars and brown
dwarfs (Chabrier & Barraffe 2000). Cooler, late M spectral type objects preserve Li
and hence are likely brown dwarfs. For later dwarf sequences, the test becomes
unreliable since lithium is in molecular form and cannot be identified by the strong
presence of that atomic line (Lodders 1999; Burrows, Marley & Sharp 2000).
Determination of L and T spectral type dwarfs is achieved more easily from other
spectral features.
Higher mass main-sequence stars produce higher mass (but smaller radius) white
dwarfs making them ideal candidates for direct detection searches particularly in
space and ranging to mid-infrared wavelengths. While the flux from a white dwarf
decreases with increasing wavelength, flux from a brown dwarf or a planet increases,
so that a companion can be detected as an excess flux from the star at certain
wavelengths. Regardless of their formation, brown dwarfs are brighter and more
massive than planets, and thus enabling for easier detection. It is not unusual for
surveys that begin with the search for extrasolar planets to unintentionally find brown
dwarfs.
1.3(=(Aims(Of(The(Project(
This dissertation continues the search, as surveyed by Burleigh (2009) and Luhman
(2004) using the Spitzer Space Telescope, for spatially resolved T and sub-T spectral
type brown dwarfs and other massive planetary-mass companions via common proper
motion to their primaries. The selected stars are confined to the solar neighbourhood
and they tend to show large proper motions. By imaging the field around a target
white dwarf at two epochs separated by a sufficient interval of time, the proper motion
of a white dwarf can be measured and compared to any motions exhibited by stars in
that field. Proper motion is often used when the radial velocity becomes difficult to
measure due to the white dwarf’s wide, pressure broadened line profiles and intrinsic
faintness. Proper-motion searches for companions have been used for many years to
identify low-mass objects (see, e.g., van Biesbroeck 1961) and offer a less biased way
!
14
of finding low mass companions than colour based surveys. It is noted that local white
dwarf population is only complete to within 13 pc and a significant number of the
local white dwarfs are still to be discovered (Giammichele et al. 2012). Furthermore,
in terms of lower contrast and older ages, white dwarf companions provide a unique
opportunity to obtain detection limits of lower mass objects (e.g. < 10 MJup as
obtained by the Spitzer Space Telescope; Farihi et al. 2008) in previously unexplored
region of parameter space. They are also pivotal to the testing models of planetary and
post main-sequence evolution and helping to understand the fate of our solar system.
In Chapter 2, the attention will turn to a brief discussion on the surveys of brown
dwarfs including the Burleigh mid-infrared survey of 87 white dwarfs. Chapter 3 will
focus on this project’s investigation for possible companions for a sample of 52 white
dwarfs taken from Burleigh’s survey. The description of the detection technique and
the results of possible companion detection will be presented in this chapter. In
Chapter 4, the sensitivity limits that provide theoretical upper mass limits for
undetected substellar companions will be found using a similar method employed by
Hogan et al. (2009). The linear initial-final mass relation (IFMR; Dobbie et al. 2006)
which connects the properties of a white dwarf with those of its main-sequence
progenitor is applied to calculate the main-sequence progenitor mass (MMS). The total
age of the system can thus be inferred from the sum of its cooling time and the main
sequence lifetime of this progenitor. Using this age together with ‘COND’
evolutionary models for giant planets and brown dwarfs and the limiting sensitivities,
the theoretical mass and temperature can be determined for potential companions
found in Chapter 3. These values will then be compared to previous work (e.g., Hogan
et al. 2009). Finally, the conclusion of this project and discussion of future work will
be detailed in Chapter 5.
!
15
Chapter(2(–(Imaging(Surveys(For(Substellar(Companions(
To(White(Dwarfs(
!
“A journey of a thousand miles begins with a single step.”
Lao-tzu, The Way of Lao-tzu, Chinese philosopher (604 BC - 531 BC).
2.1(=(History(
Searches for substellar companions to white dwarfs focus on exploiting the lower
contrast between star and companion when compared to a much brighter main
sequence star. Large-scale near-infrared surveys of white dwarfs are ideal for the
search and study of these objects because they are brightest at these wavelengths.
Direct imaging, unlike its radial velocity and transit counterparts, can reveal Jupitersized objects in wide orbits (> 5AU), enable detailed characterization of planetary
atmospheres, and is a key step towards imaging earth-like planets.
The first search for low mass substellar companions to white dwarfs was conducted by
Probst (1983), in which the measurement of IR magnitudes of ~ 100 white dwarfs for
excess emission did not result in the detection of any substellar companions. A larger
near-IR imaging survey of over 371 white dwarf primaries (Zuckerman & Becklin
1987; Farihi et al. 2005) detected two brown dwarf candidates. GD165B (Becklin &
Zuckerman 1988), with a mass of 75MJup, was later to become the prototype for a new
spectral class of cool stars and brown dwarfs, the L dwarfs (Kirkpatrick et al. 1999).
They also identified GD1400B (73 - 83 MJup; Farihi & Christopher 2004; Dobbie et al.
2005) which is as massive as GD165B.
The first unambiguous confirmed detection and image of a brown dwarf is GJ229B, a
warm (Teff ≤ 950K; e.g, Allard et al. 1996) T spectral type companion to the M1/M2
(Jenkins et al. 2009) spectral type red dwarf Gliese 229 (Byrne et al. 1985), located 19
light-years from Earth in the constellation Lepus. It has an angular separation of 7.8”
(Nakajima et al. 1995) to the host star and an estimated mass of ~ 50 MJup (Reid et al.
2000). Interestingly, a sub-saturnian mass planet candidate has been recently
!
16
announced in a much closer-in orbit around GJ229 (Tuomi et al. 2014) from radial
velocity measurements. Given the proximity to the Sun, the orbit of GL 229Ab might
be fully characterized by the GAIA space-astrometry mission or via direct imaging.
More recent imaging searches for objects of planetary mass revealed a companion to
the ≤ 25 MJup brown dwarf member of the TW Hydrae association 2MASSW
J1207334 −393254 (2M1207) with a mass of ~ 5 MJup (Chauvin et al. 2004, 2005;
Song et al. 2006) or perhaps as high as ~ 8 MJup as suggested by Mohanty et al. 2007.
However, Lodato et al. (2005) argue that 2M1207b is not a bona fide planet and more
likely formed as a binary brown dwarf system, since the core accretion model, thought
to be the most likely formation mechanism for gas giant planets like those in the Solar
System, is unable to account for the formation of 2M1207b.
The HR 8799 planetary system was the first directly imaged multi-planetary system
(Marois et al. 2008). Along with Fomalhaut and β Pic, it is also the only imaged
system with companion mass ratios and separations reasonably close to the giant
planets in the Solar System (e.g. Lagrange et al. 2009, 2010). The discovery of the one
or more planets b, c & d orbiting HR 8799 was reported by Marois et al. (2008) and
from other studies on the Hubble Space and Suburu Telescopes taken prior to 2008
(e.g. Lafreniere et al. 2009; Fukagawa et al. 2009). The young age of HR 8799 and the
low luminosities of these co-moving companions, suggest that the companions have
planetary masses and are not brown dwarfs; the only similar object known is the
planetary mass companion to the brown dwarf 2M1207. Recently, Marois et al. (2010)
imaged a fourth planet – HR 8799e. The formation of the HR 8799 planets is
consistent with either resulting instabilities in a massive protoplanetary disk, which
may form objects with masses above 5 MJup or through core accretion (Rafikov 2005;
Marois et al. 2008). Thus, the question of whether they are bona fide planets or brown
dwarfs (e.g Moro-Martın et al. 2010) has been subject to significant debate.
Jovian companions to a white dwarf should survive the red giant branch (RGB) and
asymptotic giant branch (AGB) phases of stellar evolution (Burleigh et al. 2002). As
the white dwarf progenitor expands to a few hundred solar radii in size, it experiences
significant mass loss. Planets that are located in an orbit within the expanding red
giant’s envelope will evaporate or accrete mass and migrate inwards to become a
close companion to the white dwarf (Livio & Soker 1984). On the other hand,
!
17
outward migration occurs for planets that are initially located farther out from the red
giant envelope. In the latter scenario, mass is lost from the central star and the orbits
!
expand by a maximum factor ! !" (Jeans 1924) for the given progenitor mass (M!" )
!"
and known (M!" ) mass of the white dwarf.
The successful detection and resolution of a planetary companion to white dwarf is
thus favoured towards a massive (i.e. ≥ 3 MJup; Burleigh et al. 2002) Jovian object
with a large projected separation to a nearby white dwarf (Burleigh et al. 2002). The
white dwarf cooling age and progenitor main sequence lifetime determines the system
age of the white dwarf. This age in turn when combined with the distance to the white
dwarf and the magnitude of these companions allows their masses to be determined
from evolutionary models for giant gas planets (Baraffe et al. 2003).
Various surveys have indicated that brown dwarf companions to white dwarfs are
nevertheless rare at any separation, for example for L spectral type white dwarfs this
value is ≥ 0.4 ± 0.3% (Steele at al. 2011). The Degenerate Objects around Degenerate
Objects (DODO) survey (Burleigh et al. 2008; Hogan et al. 2009, 2011) was initiated
to search for wide, spatially resolved brown dwarf and planetary mass companions to
white dwarfs via direct ground based imaging. The detection of such companions in
orbit around a white dwarf enables spectroscopic investigation of very low mass
objects cooler (< 500 K) and older (> few Gyr) than found around young stars like
2M1207 and HR8799 8. In addition, it also provides constraints on models for the
evolution of planets and planetary systems during the final stages of stellar evolution
(e.g. Debes et al. 2002).
Hogan et al. (2009) have found that ≤ 5% of white dwarfs have L, T or Y substellar
companions with effective temperatures ≥ 500 K which are below the coolest known
brown dwarfs and having typical projected physical separations of ≤ 200 AU.
Furthermore, ≤ 9% white dwarfs have companions with masses ≥ 10 MJup. The survey
also places limits on planetary-mass and ultra-cool substellar objects around some
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
8
For example, WD0806-661B is a recently identified common proper motion companion to
the white dwarf WD 0806-661 and is one of the faintest and coolest known brown dwarfs
with Teff = 300K – 345K (Luhman et al. 2011). It is likely to have a Y spectral type and an
estimated mass of 6–9 MJup (Luhman et al. 2012). I discuss this object further in Chapters 3
and 4.
!
!
18
famous nearby white dwarfs e.g. van Mannen’s star (≥ 10 ± 2 MJup ; Burleigh et al.
2008).
2.2(=(A(Search(For(Resolved(Brown(Dwarf(And(Massive(Planetary(
Companions(To(White(Dwarfs(With(Spitzer(
The Spitzer Space Telescope is the largest infrared observatory ever launched to
observe in wavelengths ranging from 3 µm to 180 µm. It has a 0.85m f/12 mirror
constructed of light beryllium and provides diffraction-limited performance at
wavelengths of 6.5 µm and longer.
Photometric observations are obtained with the Infrared Array Camera (IRAC, 1.213 ′′
pixel-1; Fazio et al. 2004) on board the Spitzer Space Telescope (Werner et al. 2004).
This camera produces images from four channels with FWHM = 1.6′′ - 1.9′′ from 3.6
µm to 8.0 µm.
An infrared imaging survey for companions to white dwarfs in the solar
neighbourhood (i.e. ≤ 30 pc) is suitable for identifying cool companion brown dwarfs
and gas giants because of the ability to partially or totally resolve these companions
from the primaries. Also, nearby white dwarfs are also more likely to have large
proper motions to background stars, and thus require a smaller baseline between
multi-epoch observations to distinguish any co-moving companions. The age
measured for a primary can be adopted for its companion, a parameter that would
otherwise be difficult or impossible to measure for isolated brown dwarfs.
IRAC Channel 2 deep imaging observations for 52 infrared-bright white dwarfs
located within 20 pc were taken primarily from the Spitzer Data Archive Cycle 2
epoch program 60161 (Burleigh 2009) and previous programs (with differing field of
views) as listed in Table 2.1. The median system age (main sequence progenitor
lifetime plus the white dwarf cooling age) of each target was ≤ 1.6 Gyr. The average
epoch difference between the data was ≤ 5 years. The data was downloaded from the
public archive as Basic Calibrated Data (BCD) that has been reduced and flux
calibrated with the Spitzer Science Centre pipeline (version S18.24). Each image was
acquired at the 4.5 µm band which offers the best spatial resolution and sensitivity to
cool brown dwarfs. For example, theoretical spectra of brown dwarf stars and massive
!
19
planets show a peak around 4-5µm between absorption bands of methane and water
(Burrows et al. 2003).
Using a 30s frame time with 20 point dithers in the cycling pattern, the second epoch
(program 60161) images had a total exposure time of ~ 536 s. The field of view was
the same for these later epoch images i.e., covering ~ 7.4′ x ~ 7.4′ which was centered
on each white dwarf target. In contrast, the first epoch images that were taken shortly
after Spitzer Telescope’s launch were irregular in shape and showed noticeable noise
degradation of the field (e.g. star bleeds) particularly towards the centre and along the
image borders. Some images were incomplete had different fields of view. Such
irregularities have to be taken into account when measuring the size of the search area
for common proper motion companions as well as the limiting magnitude (and
completeness limits) for that field.
The IRAC images have also been corrected for instrumental artifacts and then later
combined into mosaics using the MOPEX package (Makovoz & Khan 2005). Refer to
Chapter 3 for a detailed explanation of this procedure. Up-to-date information on the
photometry and absolute calibration of IRAC data is given at
http://ssc.spitzer.caltech.edu/irac.
!
20
!
Table 2.1 – Spitzer details of the observations for sampled white dwarfs
WD
WD0009+501
RA
(J2000)
hms
01 02 14.80
DEC
(J2000)
°'"
+50 25 21.4
WD0038-226
00 41 26.09
-22 21 04.2
WD0101+048
01 03 49.93
+05 04 30.5
WD0115+159
01 18 00.09
+16 10 20.6
WD0126+101
01 29 24.25
+10 23 01.4
WD0133-116
01 36 13.60
-11 20 32.2
WD0141-675
01 43 00.99
-67 18 30.3
WD0148+641
01 51 51.40
+64 26 11.0
WD0208+396
02 11 20.85
+39 55 21.5
WD0231-054
02 34 07.76
-05 11 39.3
WD0552-041
05 55 09.53
-04 10 07.1
WD0612+177
06 15 18.68
+17 43 40.2
21
!
Observation
Start Date & Time
Observation
End Date & Time
Program
ID
Principal
Investigator
2004-12-15 23:08:51
2009-08-22 01:05:55
2004-11-26 00:16:04
2009-08-18 16:33:05
2004-12-16 21:43:51
2009-08-22 06:12:06
2005-01-16 00:41:00
2009-08-22 03:57:49
2005-01-16 00:46:40
2009-08-22 04:12:53
2004-12-15 12:10:21
2009-08-25 13:45:41
2004-11-26 14:58:51
2009-08-14 00:50:37
2005-09-19 16:30:53
2010-02-22 00:18:39
2005-01-17 20:35:32
2009-09-15 23:43:48
2005-01-17 02:18:08
2009-08-30 16:49:57
2005-02-25 05:26:10
2009-11-07 20:43:46
2005-03-26 11:32:49
2009-11-02 16:14:19
2004-12-15 23:12:16
2009-08-22 01:21:31
2004-11-26 00:19:33
2009-08-18 16:49:27
2004-12-16 21:47:17
2009-08-22 06:27:03
2005-01-16 00:44:24
2009-08-22 04:12:53
2005-01-16 00:50:03
2009-08-22 04:27:58
2004-12-15 12:13:47
2009-08-25 14:00:38
2004-11-26 15:02:19
2009-08-14 01:05:52
2005-09-19 16:47:16
2010-02-22 01:04:14
2005-01-17 22:27:09
2009-09-16 00:00:06
2005-01-17 02:21:32
2009-08-30 17:05:00
2005-02-25 05:31:38
2009-11-07 21:01:51
2005-03-26 11:39:18
2009-11-02 16:29:33
2313
60161
2313
60161
2313
60161
2313
60161
2313
60161
2313
60161
2313
60161
20567
60020
3655
60161
2313
60161
2313
60161
2313
60161
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Zinnecker, Hans
Whitney, Barbara A
Debes, John H
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
!
Table 2.1 (continued)
WD
WD0732-427
RA
(J2000)
hms
07 33 37.84
DEC
(J2000)
°'"
-42 53 58.2
WD0738-172
07 40 20.79
-17 24 49.1
WD0752-676
07 53 08.38
-67 47 32.2
WD0806-661
08 06 53.56
-66 18 16.3
WD0839-327
08 41 32.56
-32 56 34.9
WD0851-246
08 53 57.79
-24 46 57.2
WD0912+536
09 15 56.23
+53 25 24.9
WD1031-114
10 33 42.76
-11 41 38.3
WD1053-550
10 55 13.63
-55 19 05.9
WD1055-072
10 57 35.14
-07 31 23.2
WD1105-048
11 07 59.95
-05 09 25.9
22
!
Observation
Start Date & Time
Observation
End Date & Time
Program
ID
Principal
Investigator
2004-12-16 19:44:20
2009-12-04 14:39:18
2005-10-31 02:02:18
2009-12-04 14:12:05
2004-12-15 05:24:02
2009-08-24 00:20:35
2004-12-15 05:29:12
2009-08-24 00:02:54
2004-12-16 16:22:23
2010-01-06 08:55:18
2007-05-07 02:25:31
2010-01-06 09:13:11
2004-11-21 18:12:50
2009-12-03 18:46:17
2004-12-17 13:13:21
2010-02-20 04:48:18
2005-06-10 12:30:47
2009-08-18 22:00:09
2004-12-18 06:25:37
2010-02-27 17:29:37
2004-12-18 06:20:15
2010-02-27 17:53:19
!
2004-12-16 19:47:44
2009-12-04 14:54:03
2005-10-31 02:06:13
2009-12-04 14:28:11
2004-12-15 05:27:26
2009-08-24 00:35:09
2004-12-15 05:32:36
2009-08-24 00:20:35
2004-12-16 16:25:47
2010-01-06 09:13:11
2007-05-07 02:44:24
2010-01-06 09:28:29
2004-11-21 18:16:18
2009-12-03 19:01:21
2004-12-17 13:16:45
2010-02-20 05:04:44
2005-06-10 12:34:11
2009-08-18 22:15:14
2004-12-18 06:29:0
2010-02-27 17:44:44
2004-12-18 06:23:39
2010-02-27 18:08:34
2313
60161
20567
60161
2313
60161
2313
60161
2313
60161
30208
60161
2313
60161
2313
60161
2313
60161
2313
60161
2313
60161
Kuchner, Marc J
Burleigh, Matt R
Zinnecker, Hans
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kilic, Mukremin
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
!
Table 2.1 (continued)
WD
WD1105-048
RA
(J2000)
hms
11 07 59.95
DEC
(J2000)
°'"
-05 09 25.9
WD1121+216
11 24 12.97
+21 21 35.6
WD1124-293
11 27 09.29
-29 40 12.0
WD1204-136
12 06 56.28
-13 53 53.1
WD1208+576
12 11 29.27
+57 24 17.4
WD1257+278
12 59 46.66
+27 34 04.1
WD1609+135
16 11 25.61
+13 22 17.8
WD1615-154
16 17 55.25
-15 35 52.4
WD1637+335
16 39 27.82
+33 25 22.3
WD1655+215
16 57 09.86
+21 26 48.7
WD1840-111
18 42 58.08
-11 08 52.8
WD1900+705
19 00 10.25
+70 39 51.2
23
!
Observation
Start Date & Time
Observation
End Date & Time
Program
ID
Principal
Investigator
2004-12-18 06:20:15
2010-02-27 17:53:19
2004-12-17 06:25:20
2010-02-19 09:15:22
2005-06-10 11:24:39
2010-03-08 16:50:39
2005-06-10 10:19:51
2010-03-08 16:30:01
2004-11-19 19:37:53
2010-01-12 19:25:43
2005-06-13 03:18:04
2010-03-14 14:16:37
2005-07-23 18:32:05
2009-08-31 13:04:49
2005-03-25 20:15:50
2009-09-09 23:36:56
2005-03-27 07:30:11
2009-08-22 14:45:13
2005-03-31 08:34:08
2009-08-31 13:35:41
2005-05-09 23:21:04
2009-10-30 14:12:31
2004-10-29 13:42:54
2009-08-21 21:38:09
2004-12-18 06:23:39
2010-02-27 18:08:34
2004-12-17 06:28:44
2010-02-19 09:32:44
2005-06-10 11:49:25
2010-03-08 17:03:59
2005-06-10 10:46:01
2010-03-08 16:43:21
2004-11-19 20:03:13
2010-01-12 19:40:10
2005-06-13 05:09:33
2010-03-14 14:31:46
2005-07-23 18:59:25
2009-08-31 13:20:14
2005-03-25 20:21:39
2009-09-09 23:50:21
2005-03-27 07:35:34
2009-08-22 14:59:46
2005-03-31 08:40:23
2009-08-31 13:51:18
2005-05-09 23:24:28
2009-10-30 14:27:52
2004-10-29 13:46:21
2009-08-21 21:53:37
2313
60161
2313
60161
3548
60161
3548
60161
3548
60161
3655
60161
20567
60161
2313
60161
2313
60161
2313
60161
2313
60161
2313
60161
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Zuckerman, Ben
Burleigh, Matt R
Zuckerman, Ben
Burleigh, Matt R
Zuckerman, Ben
Burleigh, Matt R
Debes, John H
Burleigh, Matt R
Zinnecker, Hans
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
!
Table 2.1 (continued)
WD
WD1943+163
RA
(J2000)
hms
19 45 31.76
DEC
(J2000)
°'"
+16 27 38.8
WD2034-532
20 38 16.84
-53 04 25.4
WD2039-682
20 44 21.47
-68 05 21.3
WD2047+372
20 49 06.71
+37 28 14.1
WD2105-820
21 13 15.88
-81 49 10.1
WD2115-560
21 19 36.52
-55 50 14.2
WD2117+539
21 18 56.27
+54 12 41.2
WD2126+734
21 26 57.69
+73 38 44.5
WD2130-047
21 33 34.84
-04 32 24.1
WD2136+828
21 33 43.29
+83 03 32.5
WD2140+207
21 42 41.00
+20 59 58.2
WD2149+021
21 52 25.38
+02 23 19.6
24
!
Observation
Start Date & Time
Observation
End Date & Time
Program
ID
Principal
Investigator
2004-10-29 13:18:40
2009-10-30 08:11:24
2005-10-20 22:06:24
2009-11-03 02:29:48
2005-09-15 21:30:00
2009-11-08 20:37:54
2004-11-25 18:55:55
2009-08-22 14:00:17
2005-03-31 12:59:00
2009-09-01 11:13:47
2005-06-10 13:39:03
2009-11-11 01:54:51
2004-11-23 20:10:52
2009-08-22 00:19:49
2004-11-23 07:51:54
2009-08-31 19:42:27
2004-11-27 05:53:58
2009-12-04 06:20:34
2004-11-21 18:45:37
2009-10-04 23:19:58
2004-11-24 08:14:13
2009-12-21 00:39:18
2004-11-26 09:35:09
2009-12-09 00:34:52
2004-10-29 13:22:08
2009-10-30 08:30:07
2005-10-20 22:09:48
2009-11-03 02:47:54
2005-09-15 21:33:24
2009-11-08 20:55:18
2004-11-25 18:59:22
2009-08-22 14:17:20
2005-03-31 13:06:27
2009-09-01 11:29:02
2005-06-10 13:42:28
2009-11-11 02:09:25
2004-11-23 20:14:20
2009-08-22 00:37:31
2004-11-23 07:55:21
2009-08-31 19:59:18
2004-11-27 05:57:26
2009-12-04 06:35:40
2004-11-21 18:49:06
2009-10-04 23:36:48
2004-11-24 08:17:41
2009-12-21 00:57:00
2004-11-26 09:38:37
2009-12-09 00:50:14
2313
60161
2313
60161
2313
60161
2313
60161
2313
60161
2313
60161
2313
60161
2313
60161
2313
60161
2313
60161
2313
60161
2313
60161
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
!
!
Table 2.1 (continued)
WD
WD2216-657
RA
(J2000)
hms
22 19 48.48
DEC
(J2000)
°'"
-65 29 18.4
WD2246+223
22 49 05.56
+22 36 31.9
WD2311-068
23 14 25.19
-06 32 47.8
WD2316-173
23 19 35.44
-17 05 28.4
WD2326+049
23 28 47.62
+05 14 54.2
WD2359-434
00 02 10.75
-43 09 55.6
!
25
!
Observation
Start Date & Time
Observation
End Date & Time
Program
ID
Principal
Investigator
2005-06-12 16:04:50
2009-11-07 18:04:51
2004-11-26 10:25:54
2009-08-22 13:35:57
2005-11-27 15:43:11
2009-08-19 14:02:49
2004-11-25 23:22:22
2009-12-20 23:20:17
2004-11-26 10:54:11
2009-08-19 14:46:14
2004-11-26 00:37:33
2009-08-19 13:07:18
2005-06-12 16:08:15
2009-11-07 18:20:15
2004-11-26 10:29:22
2009-08-22 13:50:35
2005-11-27 16:10:37
2009-08-19 14:18:34
2004-11-25 23:25:50
2009-12-20 23:40:22
2004-11-26 10:57:40
2009-08-19 15:01:38
2004-11-26 00:41:01
2009-08-19 13:22:25
2313
60161
2313
60161
20567
60161
2313
60161
2313
60161
2313
60161
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Zinnecker, Hans
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Kuchner, Marc J
Burleigh, Matt R
Chapter(3(–(The(Search(For(Common(Proper(Motion(
Companions(
3.1(–(Data(Reduction(
Infrared data obtained from the IRAC imager on the Spitzer Telescope is reduced and
analyzed using the MOPEX (Mosaicking and Point Source Extraction) online GUI
package developed at the Spitzer Science Centre for Astronomical Imaging. A typical
MOPEX task for data reduction consists of combining a stack of Spitzer data FITS
images into a mosaic and doing point-source photometry and looking at the residuals.
This process must be repeated for each white dwarf (and associated epoch observation)
in the sample.
In the first step of the overlap pipeline, an additive correction using the PMASK bad
pixel mask, which flags any permanently damaged pixels in the instrument arrays, is
first applied to each frame in the input image stack to minimize pixel differences in the
overlap regions and to bring them to a common background level (i.e offset-corrected
images). Frames are then interpolated to a common grid using a Fiducial Image Frame
(FIF) based on the World Coordinate System (WCS) information from each of the basic
calibrated data (BCD) image headers (Figure 3.1). They are also corrected for geometric
distortion and updated to include outlier detection information before a co-added
scheme is applied (that is, using the default of the average of input pixels) to create a
single mosaic. Interpolated uncertainty images and coverage maps are also processed in
a similar approach.
For crowded fields, point source detection, extraction and profile fitting (PSF) on the
mosaic image is performed using APEX, the inbuilt Astronomical Point source
EXtractor for MOPEX (Makovz & Marleau, 2005). Since mosaic generation does not
involve outlier rejection, the APEX Single Frame pipeline is appended to the end of a
MOSAIC pipeline with the previously generated mosaic file, Spitzer coverage maps and
uncertainty images as input to the pipeline.
A background subtraction (DETECT MEDFILTER module) is initiated on both
mosaicked and co-added images in order to prepare for point source detection. The ratio
of the image signal to the noise is calculated (GAUSSNOISE module) using data
!
26
uncertainties for PRF-fitted SNR default option ‘YES, WITH GAIN’
(USE_PHOTERR_FOR_SNR=2) specified in the Apex single Frame Settings. The
Output is saved as a signal to noise ratio (SNR) image while noise estimation results are
added to the final extract table as the SNR.
!
Figure 3.1 – A basic calibrated data (BCD) image from Spitzer that is used as input to
the mosaic creation, as seen in the Graphical Astronomical and Image Analysis Tool
(GAIA).
Source Extraction is a multi-step process carried out to give a single position and flux
density estimate for each detected source. Initial point source detection is done on the
co-added mosaic images. Subsequent non-linear matched filtering (POINT SOURCE
PROBABILITY module) reduces fluctuations in background noise and enhances source
contributions as well as increasing the signal-to-noise ratio of faint point sources in coadded images. The output produced is a series of point source probability (PSP) images
(Figure 3.2).
Image segmentation, a repetitive process of separating objects from the sky background,
accepts pixel clusters greater than a user-specified threshold defined in terms of a robust
estimate of background fluctuation in the filtered, background subtracted image. For
each cluster, a higher threshold is determined and is based on mean pixel value and the
!
27
standard deviation of the pixel values within the cluster. However the disadvantage is
that many faint sources close to brighter sources will be undetected. To overcome this
problem, clusters may be split if they contain peak pixels with values greater than the
user specified number of adjacent pixels. The centroids of final clusters are calculated
and stored in a list of position estimates for the point sources.
Figure 3.2 – An example of a Point Source Probability (PSP) image as shown in GAIA.
In general, mosaic images have variable coverage so when a constant pixel value
threshold is applied the mosaic has a variable effective threshold. Areas of higher
coverage will have higher threshold in terms of the SNR of the detected point sources.
This is resolved when the Spitzer supplied coverage map is applied to attenuate the
mosaic undergoing segmentation, that is, the input image is multiplied by the square
root of the coverage prior to segmentation.
A second background subtraction is performed on the mosaicked image for the purpose
of point source fitting (EXRACT MED FILTER module). The value of each pixel in an
image can be considered as the sum of a background signal and light from objects of
interest. A fast fitting algorithm, analogous to that used by the SExtractor program
(Bertin & Arnouts 1996), is used to estimate the localized background level of each
!
28
designated area within the image grid in order to construct a background map. This map
is then subtracted from the image.
Final point source positions and photometry estimation is done for point sources in the
detection listing. Input mosaic data is fitted with a Point Response Function (PRF) or an
array-position dependent map to determine flux and refine the mosaic position of a
point source (Figure 3.3). For Spitzer data, standard PRFs for each IRAC channel are
used for this purpose. Default FITTING AREA X and FITTING AREA Y parameters
set in the SOURCE ESTIMATE module override the FIT RADIUS process to estimate
the size of the fitting area for each detection. An input PRF map identifies areas of
constant PRF and matches each fitting area in the mosaic W j to the map. Given that the
number of degrees of freedom (dof) is equal to the number of all the good pixels in the
fitting areas minus the number of fitting parameters and χ2 is minimized for the first
point source, then the goodness-of-fit is the ratio χ 2 /dof . If this ratio is less than the
Chi Threshold default parameter value, the fitting is successful and the program will
continue fitting in order to improve the results until either the number of iterations
exceed the MAX N Success parameter value or χ 2 is less than MINIMIZE FTOL
SUCCESS toleration parameter value set in the module.
Passive de-blending is an essential part of point source extraction. It occurs when the
above fitting is done simultaneously on the background-subtracted mosaic containing
point sources deemed in close proximity to each other so that their PRFs overlap and
hence belonging to the same blend.
For sources detected in a field, the amount of flux in each source must be determined.
This flux has contributions from both the source and the background in the original
rather than background subtracted mosaic image. It is then used to calculate the
magnitude of each source. The aperture photometry module in APEX counts the flux by
placing an annulus around the source, which has a specified inner radius (in pixels)
centred on that source and outer radius that is typically twice of the inner radius. The
background measurement is thus estimated from the region between the inner and outer
radii. Finally, it is subtracted from the total measurement to determine source only flux.
!
29
Figure 3.3 – The mosaic is fitted with a point source response function (PRF) as shown
in GAIA.
The output of APEX is a standard IPAC formatted table of all sources detected in the
final combined mosaic (SELECT DETECT module) on which selection is based on the
default MOPEX criteria (Figure 3.4). For example, those sources having SNR > 6 and
whether passive, active or no de-blending has been performed on the source. Extracted
information gives the position (in both RA and DEC and pixel coordinates), fluxes and
uncertainties determined for point source and from the aperture photometry for each
object.
Once the APEX extract table has been generated for each epoch, the next step is to
match field objects, in particular the white dwarf, between the first and second epoch
mosaics for identification purposes and subsequent proper motion determination.
Spurious distortion effects caused by optical aberrations in the image results in a white
dwarf rarely being positioned on the same pixels in each epoch, so its motion between
the two epoch images depends on field position. If there are a sufficiently large number
of background reference stars, both epoch mosaics can be well matched and the
distortions can be removed. However, using fewer background reference stars in the
matching process often tends to reduce the limits of the astrometric accuracy involved.!
!
30
Figure 3.4 – The final combined epoch mosaic as shown in GAIA. As can be seen, it is over
layered with objects taken from the APEX extract table that have been identified in the UCAC4 all
sky catalogue (Finch et al. 2014). The distance can be measured (in arc minutes) between a target
white dwarf (lower left) and its common proper motion companion (upper right).
For each epoch observation, celestial coordinates are converted to decimal degrees.
Magnitude is derived from flux using the Zero Point (Zp) and an aperture correction for
the instrument calibration of the relevant channel using equation (3.1):!
Mag = 2.5 log (!
!"
!!"#$∗!"#$%&$#'($$#)%*(+ 1!106
!)
Equation (3.1)!
The difference in RA (Δα) and DEC (Δδ) coordinates in decimal degrees between any
two objects with coordinates (α1, δ1) and (α2, δ2) may be calculated as follows:!
Δδ = (δ2 −δ1)
Equation (3.2)!
Δα = (α2 −α1)
Equation (3.3)!
The angular separation ! between them is derived using equation (3.4):
Cos ! = cos (90° - δ1) cos (90° - δ2) + sin (90° - δ1) sin (90° - δ2) cos Δα Equation (3.4)
!
31
Objects including the white dwarf selection in the first epoch image are considered
‘matched’ to the closest object in the second epoch image if their separation is ≤ 0.02
square degrees (a larger search area to account for the time lapse between epochs) and
their magnitudes differ by less than 1 mag. Objects that are situated ≤ 0.01 square
degrees and with brighter than expected for typical brown dwarfs are deemed as
astrometric reference stars which can be used to minimize the effects of non-linear
distortion within the epoch image. !
A customized FORTRAN program utilizes several STARLINK SLALIB software
library (sla_*) routines to perform plate reduction and proper motion calculation for the
X and Y pixel positions of objects. The process described below was originally
developed by Casewell et al. 2007, in the search of Pleiades brown dwarfs, and is
suitable for this survey as well.
An iterative RMS fitting of a linear model (Sla_FITXY routine) is applied to relate the
measured positions between reference stars and sourced X and Y coordinates. For each
epoch, a listing of input X and Y pixel coordinates of non-moving reference stars
generated by the previous matching step, is read into the program. Each 1x pixel value
is adjusted by an average of all 1 x pixel values so as to make the RMS fit to the data
more robust. A transform between the two epoch images (for example due to
differences in pixel scale) involves six coefficients, namely the zero points modelling
the squash and shear of axes (i.e. non-perpendicularity, in degrees), origin, scale and
orientation parameters of the fit. Objects having RMS residuals greater than 3 times
than the scaled median of absolute deviation of the reference star residuals (s) are
discarded to remove any fast moving objects, cosmic rays or other contributors that
could cause a bad fit to the data.
Given coefficients a through e and f, the sla_PXY routine transforms the measured
second epoch coordinates [Xm,Ym] into expected coordinates [Xe,Ye] through the
following relationships:
!
!! = ! + !!! + !!!
Equation (3.5)
!! = ! + !!! + !!!
Equation (3.6)
32
Sign reversals of the coefficients are taken into account to ensure a best model fit. The
RMS value to the fit is the difference between [Xe,Ye] coordinates and the average
adjusted first epoch coordinates. Furthermore, RMS residuals for X and Y are simply
the median of first epoch RMS values multiplied by a scaling factor of 1.48 (usually a
standard between σ and the RMS value) (Leys et al. 2013).
After routine convergence, the linear fit is decomposed by sla_DCMPF and
sla_XY2XY routines into its constituent parameters and the second epoch coordinates
are translated into first epoch coordinate system (i.e. X* and Y*). The final coefficients
are written to an output file. Relative proper motion, in RA (µα) and DEC (µδ)
components (in degrees), is the scaled difference between the first epoch measured and
the newly translated coordinates:
µtα = CD1_1X* + CD1_2Y*
Equation (3.7)
µtδ = CD2_1X* + CD2_2Y*
Equation (3.8)
where CD1_1, CD1_2, CD2_1 and CD2_2 are elements, from the coordinate transform (CD)
matrix from FITS header of the first epoch image, corresponding to plate scale and
rotation respectively.
The resulting motion in RA is divided by the time difference in the Julian dates between
the two epoch observations (which was approximately 5 years in this case) and then
converted to milli-arcseconds per year (mas/yr). To account for the spherical nature of
the coordinates, it is finally multiplied by cos δ.
Perl program PM_ALL.pl, uses the RMS fit values previously obtained and the pixel
errors for the translated coordinates in X or Y direction, to determine the displaced
measurement error in that direction. For example, in the X direction this becomes:
Error (X) = !! !"" ! + !! !"" ! + !"#! !
Equation (3.10)
where !! !"" and !! !"" are the pixel errors.
The final step in the detection of companions involves verifying objects that have been
identified in the MOPEX extract and lie within the 1σ and 3σ common proper motion
!
33
scatter distribution relative to the sample white dwarf. The reasoning as offered by
Neuhäuser & Schmidt (2012), is that for an object to be considered a companion, both
the star and object are required to show the same or at least very similar proper motion
(within a few mas/yr) given the orbital motion of the star and its companion, inclination
and eccentricity. If the companion and the white dwarf exhibit the same proper motion,
we would therefore expect a co-moving companion rather than a non-moving
background star.
Actual measurement values and errors depend on the accuracy of the documented
proper motion of the white dwarf, the number of field sources with a good SNR, the
quality of the images for each epoch, and the time baseline between epochs. Spurious
sources, taken to be objects that are located around the edges of the final stacked image,
have high proper motion in only one direction, is saturation from a nearby star due to
the longer exposed image or are cosmic rays are discounted. By trial and error, SNR >
25 per pixel was chosen to remove many spurious sources and to minimize the error
corresponding to the object’s magnitude (Figure 3.5). Visual inspection of the
remaining sources on the GAIA mosaic image was also done to further discount known
catalogued galactic objects.
Proper motion sources for the white dwarf sample are obtained from literature and
verified against SIMBAD and VizieR utilizing proper motion catalogues such as the
UCAC4 Catalogue (Zacharias et al. 2012), the PPMXL Catalogue (Roeser et al.
2010), the UKIDSS- DR6 Galactic Plane Survey (Lucas et al. 2008) and the DENSE
25 pc sample project (Sion et al. 2014). These references together with other
photometric data are listed in Table 3.1. This search has detected five possible
companions to the white dwarf sample. Figures 3.6 through 3.8 show proper
motions of all objects in the field of selected white dwarfs. The 1σ and 3σ scatter
distributions for these motions, represented by blue dashed circles, have been
included to indicate motion limits of the associated white dwarf. A discussion of the
results follows in the next section.
!
34
!
!
Figure 3.5 - Scatter plots showing a non-linear increase in the error in RA for increasing magnitude for selected white dwarfs. The white dwarf
magnitude is designated in red while the magnitude for the possible companion is shown in green.
!
35!
!
!
!
!
Table 3.1 – Photometric information for the sampled white dwarfs
WD
WD0009+501
WD0038-226
WD0101+048
WD0115+159
WD0126+101
WD0133-116
WD0141-675
WD0148+641
WD0208+396
WD0231-054
WD0243-026
WD0552-041
WD0612+177
WD0732-427
WD0738-172
WD0752-676
WD0806-661
WD0839-327
WD0851-246
WD0912+536
SIMBAD Name
Spectral Type
Distance (pc)
LHS 1038
LHS 1126
G1-45
LHS 1227
G2-40
G271-106
LHS 145
G244-36
GJ 86 B
GD 31
LHS 1442
LP 658-2
G104-27
GJ 2062
L745-46A
BPM 4729
L93-7
L532-81
LHS 2068
G195-19
DAH7.6
DQpec9.3
DA6.4
DQ5.6
DA5.8
DA4.0
DA7.8
DA5.6
DAZ6.9
DA3.7
DAZ7.4
DZ10.0
DA1.9
DA3.2
DAZ6.6
DA8.8
DQ4.9
DA5.5
DA4.0
DCP7
11.03
9.05 (0.10)
21.32
15.40
23.0
31.0
9.73 (0.67)
17.8 (0.7)
16.7 (1.0)
22.7
21.2 (2.3)
6.45 (0.08)
43.0
36.0
8.90 (0.21)
7.89
19.2 (0.6)
8.87 (0.77)
10.3 (0.2)
Proper Motion (mas/yr)
µαcosδ
µδ
-488 (2.6)
-549.6 (2.6)
-366.6
-449.5
344.3
219.2
40 (33.3)
604.3 (24.5)
-128
-387
453.6
-119.9
-329.9
-996.8
237
-159
1029.5 (4.1)
-499.5 (4.1)
249.1
92.3
223.5
-485.4
535.9
- 2315
-58
-356
138.6
645.3
1146.8
-538.1
1466.6
-1506.7
292.6
-270
-984
1261.7
157.1 (7.2)
-318.2 (7.2)
-1091
-1127
References 9
1,11
1,5,12
1,12
1,11
1,2,12
1,2,12
1,5,12
1,5,12
1,5,13
1,12
1,5,12
1,5,12
2,12
1,2,12
1,5,12
1,14
1,5,12
1,5,12
2,11
1,5
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
9!!References – 1) Sion et al. 2014 2) Gianninas et al. 2011 3) Pancino et al. 2012 4) Skiff, 2014 5) Giammichele, et al. 2012, ApJS, 199, 2 6) Gudennvar et al.
2012 7) Pickles et al. 2010 8) Bakos et al. 2002 9) Farihi et al. 2005 10) Bergeron et al. 2011 11) Smart 2013 12) 12) Zacharias et al. 2012 13) Zacharias et al.
2004a 14) Roeser et al. 2010 15) Cutri et al. 2013 16) Stauffer et al. 2010 17) Ivanov 2008 18) Zacharias et al. 2004b
!
36!
!
!
Table 3.1 (continued)
WD
SIMBAD Name
Spectral Type
Distance (pc)
WD1031-114
WD1053-550
WD1055-072
WD1105-048
WD1204-136
WD1208+576
WD1615-154
WD1637+335
WD1655+215
WD1840-111
WD1900+705
WD1943+163
WD2034-532
WD2039-682
WD2047+372
WD2105-820
WD2115-560
WD2117+539
WD2126+734
WD2130-047
WD2136+828
WD2140+207
EGGR 70
LTT 4013
LHS 2333
G163-50
EC 12043_1337
LHS 2522
LTT 6487
G180-65
LHS 3254
G155-34
GW+70 8247
G 142-50
BPM 26944
LTT 8190
G210-36
L24-52
BPM 27273
G231-40
G261-43
GD 233
GJ836.2
LHS 3703
DA2.0
DA3.4
DA6.8
DA3.5
DA4.4
DAZ8.6
DA1.7
DA4.9
DAB5.4
DA4.9
DAP4.2
DA2.5
DB4
DA3.1
DA3.6
DA4.7
DA6
DA3.6
DA3.8
DB4
DA2.8
DQ6.1
37
40
12.2 (0.5)
24.2
45
20.4 (1.9)
12.2
27
23.3 (1.7)
21
13.0 (0.4)
47
35
19.6 (0.9)
17.3 (0.7)
17.1 (2.6)
26.5 (1.0)
19.7 (0.7)
21.2 (0.8)
50
26.0
12.5 (0.5)
Proper Motion (mas/yr)
µαcosδ
µδ
-347.7 (8.0)
-29.8 (8.0)
-13.1 (32.5)
-3.7 (32.5)
-822.4
91.2
-63.1 (8.0)
-440 (8.0)
-303
-44
410.6 (4.0)
-364.9 (4.0)
169.5 (8.0)
-164 (8.0)
26
-467
-139 (92)
-573 (98)
246
-255
80.3 (4.0)
505.3 (4.0)
-30.7
-291.2
84.7
-176
187.4
-228.9
161.0
146.9
286
-430
-113.2
-79
-85.1 (1.8)
192.9 (1.4)
49.2 (2.6)
-307.5 (3.4)
241.3 (8.0)
12.6 (8.0)
278.1 (4.0)
566.5 (4.0)
-227 (8.0)
-643 (8.0)
References 10
2,3,11
2,11
1,5,12
1
2,12
1,5,11
2,6,14
2,12
1,5,15
2,16
1,5,14
2,17
3,10,14
1,5,14
1,5,12
1,5,18
1,5,12
1,5,12
1,5,12
2,10,12
2,7,14
1,12
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
10
References – 1) Sion et al. 2014 2) Gianninas et al. 2011 3) Pancino et al. 2012 4) Skiff, 2014 5) Giammichele, et al. 2012, ApJS, 199, 2 6) Gudennvar et
al. 2012 7) Pickles et al. 2010 8) Bakos et al. 2002 9) Farihi et al. 2005 10) Bergeron et al. 2011 11) Smart 2013 12) 12) Zacharias et al. 2012 13) Zacharias et
al. 2004a 14) Roeser et al. 2010 15) Cutri et al. 2013 16) Stauffer et al. 2010 17) Ivanov 2008 18) Zacharias et al. 2004b
37!
!
!
Table 3.1 (continued)
WD
SIMBAD Name
Spectral Type
D (pc)
WD2149+021
WD2216-657
WD2246+223
WD2311-068
WD2316-173
WD2326+049
WD2359-434
G93-48
L 119-34
G67-23
G157-34
LP 822-50
G29-38
LHS 1005
DA2.8
DZ5
DA4.7
DQ6.8
DB3
DAV4.9
DA5.9
24.50
42.5
19.1 (1.5)
25.1
27.7
13.6 (0.8)
7.85 (0.4)
Proper Motion (mas/yr)
µαcosδ
µδ
16.4 (2.4)
-298.4 (2.4)
243.1
-688.3
522 (8.0)
59 (8.0)
-343.2
-166.7
241.4
8.5
-411
-273
718.7
-723.8
References 11
1,12
2,12
1,5,12
1,12
2,9,14
1,5,12
1,5,12
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
11
!!References – 1) Sion et al. 2014 2) Gianninas et al. 2011 3) Pancino et al. 2012 4) Skiff, 2014 5) Giammichele, et al. 2012, ApJS, 199, 2 6) Gudennvar et
al. 2012 7) Pickles et al. 2010 8) Bakos et al. 2002 9) Farihi et al. 2005 10) Bergeron et al. 2011 11) Smart 2013 12) 12) Zacharias et al. 2012 13) Zacharias
et al. 2004a 14) Roeser et al. 2010 15) Cutri et al. 2013 16) Stauffer et al. 2010 17) Ivanov 2008 18) Zacharias et al. 2004b!
38!
!
!
3.2$Results$
!
Figure 3.6 - The proper motion diagrams showing the motion of all objects in the field of WD0806-661 (left) and WD0101+048 (right)
between the first epoch and second epoch images. The dashed blue circles represent the 1! and 3! scatter of the distribution of the motions of
all objects, centred on the (filled in) white dwarf, to help determine possible common proper motion companions to the white dwarf. For
clarity, the error bars have not been plotted.
39!
!
!
!
!
!
!
Figure 3.7 - The proper motion diagrams showing the motion of all objects in the field of WD0552-041 (left) and WD1055-072 (right) between
the first epoch and second epoch images. The dashed blue circles represent the 1! and 3! scatter of the distribution of the motions of all objects,
centred on the (filled in) white dwarf, to help determine possible common proper motion companions to the white dwarf. For clarity, the error
bars have not been plotted.
40!
!
!
!
!
Figure 3.8 - The proper motion diagrams showing the motion of all objects in the field of WD1943+163 (left) and WD2311-068 (right) between
the first epoch and second epoch images. The dashed blue circles represent the 1! and 3! scatter of the distribution of the motions of all objects,
centred on the (filled in) white dwarf, to help determine possible common proper motion companions to the white dwarf. For clarity, the error
bars have not been plotted.
!
41
!
WD0806-661: is a DQ spectral type star with a helium rich atmosphere and is located at
a photometric distance of ~ 19.2 pc. The effective temperature (Teff) is ≤ 10250 K with
magnitudes VJ = 13.73 12, H = 13.74, J= 13.70 and K! = 13.78!(Subasavage et al. 2009)
13
. The Spitzer magnitude as estimated by this survey is ~ 14.15 14. Its assumed mass
(0.62 M⨀ 15) is equal to that of the mean of the DQ star masses found by Dufour et al.
(2005).
This ≤ 2 Gyr white dwarf serves as the test benchmark in this search for common proper
motion companions. The discovery of a very late type and particular faint companion at
4.5µm, WD0806-661B (Luhman et al. 2011), has a mass ranging 6 - 9 MJup (Rodriguez
et al. 2011) although it is unlikely to have been formed in the same manner as planets. It
is confirmed to be the coldest brown dwarf known (Teff in the range of 300 - 345 K,
Luhman et al. 2012) with an atmospheric temperature comparable with that of Earth.
The Wide-Field Infrared Survey Explorer (WISE, Wright et al. 2010) has been
instrumental in the detection of T spectral type and Y spectral type dwarfs and the
Spitzer Space Telescope with increased sensitivity compliments the search in smaller
fields (Werner et al. 2014). Such cool brown dwarfs prove invaluable for the studies of
atmospheres and interiors of substellar objects.
Proper motion of the selected white dwarf and objects are shown within the scatter
distribution plot (Figure 3.6). This study has recovered the known companion WD0806661B with a projected separation of 130.14′′ that corresponds to ~ 2500 AU at the
distance of the white dwarf. This value is in good agreement with that obtained by
Luhman et al. 2011. Our estimated survey magnitude I2 ~ 17.08 ± 0.06 16. This value
together with the calculated distance will be used in determining the companion’s mass
and age in Chapter 4. There is no evidence to support other objects in the field that
could be potential companions.
WD0101+048: is a DA spectral type, hydrogen rich atmospheric star located ~ 14.3 pc.
It has an effective temperature of ~ 8360 K (Kilic et al. 2007) and magnitudes V =
14.10 (Makarov et al. 2007), H = 13.39, J = 13.51 and K! = 13.38!(Giammichele et al.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
12
13
14
15
16
Subasavage et al. 2009. The central wavelength for optical magnitude VJ is 5475 Å.!
Near-infrared J H Ks photometry extracted from the 2MASS database.
The central wavelength for Spitzer I(RAC)2 band is 4.5 !m (Werner et al. 2014).
Subasavage et al. 2009.
For the second epoch observation.
42
2012) with I2 ~ 13.40. It is proposed that WD0101+048 is a distant common proper
motion companion (~ 27000 AU) to the K3 dwarf HIP 4849 binary star system
(Markarov et al. 2008). A closer inner K8 dwarf companion orbits HIP 4849 with a
period of 29 years. !
The system is further complicated in that the white dwarf is itself within a confirmed
close double degenerate (DD) binary system (Bergeron et al. 2001) having a
spectroscopically detected DC spectral type white dwarf companion, with a variable
velocity and an orbital period of 1.2 - 6.4 days (Maxted et al. 2000; Bergeron et al.
2001; Weston & Napiwotzski 2009). !
This search indicates the possible detection of a wide, faint companion on the proper
motion scatter distribution plot (Figure 3.6). Its angular separation to the selected white
dwarf as estimated by this survey is ~ 127′′ (corresponding to ~ 3300 AU) and its
estimated magnitude I2 ~ 16.48 ± 0.07 17. The companion’s mass will be computed in
Chapter 4 using this magnitude, its age and the calculated distance. Despite a relatively
crowded field, no other objects in the field can be considered as possible companions.
Future work should be done to confirm this detection.!
WD0552-041: is a cool helium-rich atmospheric white dwarf located at a distance of ~
6.9 pc. The effective temperature is ≤ 5180K and magnitudes V = 14.47 (Subasavage et
al. 2009) with H = 12.86, J = 13.05 and K! = 12.78! Subasavage!et!al. 2009 !and I2 ~
12.46. Its study is of particular interest as it is classified as a DZ spectral type star due to
the strong CaII (H and K doublet) lines exhibited in its optical spectrum (Bergeron et al.
2001). These heavier elements sink below the photosphere leaving a pure helium
surface, in shorter timescales than the white dwarf cooling age (Paquette et al. 1986).
They cannot originate from the white dwarf since these elements would otherwise sink
to the core. The standard explanation for the presence of metals in DZ stars is the result
of accretion from denser parts of the interstellar medium (as favored by the ISM
accretion model). This would account for the lack of dense interstellar clouds in the
solar neighbourhood and the extremely small abundances of hydrogen measured in DZ
white dwarfs.!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
17
For the second epoch observation.
43
Alternatively, it is argued that metal-rich material orbiting a white dwarf form a
circumstellar disk from the tidal disruption of a rocky planetary body within the star’s
Roche Radius and its accretion pollutes the atmosphere of the white dwarf (Farihi et al.
2010; B.Wolff et al. 2002 and Jura et al. 2003). The dusty disks together with the
detection of planetary material in the photosphere in multi-wavelength regimes, are
considered tracers to detect remnant exoplanetary systems. They offer the opportunity
to study the chemical composition and evolution of large rocky bodies near this type of
white dwarfs.!
Proper motion estimates of the white dwarf and objects are shown on the scatter
distribution plot (Figure 3.7). A possible companion has been found with a projected
angular separation of ~ 171.74′′ (corresponding to a distance of ~ 1200 AU). Its
estimated magnitude I2 ~ 15.42 ± 0.12 18 makes it the brightest of the companions
detected in this survey. The companion’s mass will be estimated in Chapter 4 using this
magnitude, its age and the computed distance. Additional study is warranted to ascertain
if this object is a brown dwarf, a planetesimal or even a circumstellar disk around the
white dwarf.!
WD1055-072: is a high proper motion, DA spectral type white dwarf with a hydrogen
rich atmosphere and is located within the solar neighbourhood. The effective
temperature is ≤ 7420K (Sion et al. 2014) and magnitudes V = 14.32 (Holberg et al.
2008), H = 13.71, J = 13.81 and K! = 13.69! Giammichele!et!al. 2012 and I2 ~ 13.52.
As can be seen in the proper motion scatter distribution plot (Figure 3.7), an object
exhibiting similar motion to the white dwarf has been detected. It has an angular
separation of ~ 145′′ (corresponding to a distance of ~ 2000 AU) and is approximately 3
magnitudes fainter (I2 ~ 16.91 ± 0.17 19) than that of the white dwarf. From these
values, the companion’s mass and age will be determined in Chapter 4. Despite the
object being discounted as a known nearby galactic object, the detection is inconclusive
due to the quality of the image caused by numerous star bleeds. However in an
extremely crowded field, no other objects lying within the scatter distribution plot can
be accounted as potential companions. Clearly, further investigation will be necessary
to determine the true nature of these objects.!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
18
19
For the second epoch observation.
For the second epoch observation.
44
WD1943+163: is a hot DA spectral type white dwarf located ~ 45 pc. This star has an
effective temperature of ~ 19400 K (Koester et al. 1998) and magnitudes V= 14.08
(Saffer et al. 1998), H = 14.63, J = 14.49 and K! = 14.63 (Cutri et al. 2003) and I2 ~
13.14. DA white dwarfs typically between 20000 K < Teff < 100000 K possess very
simple atmospheres in this temperature range with no convection zones, and have short
diffusion timescales.!
The discussion of disk accretion and planetary material detection extends to white
dwarfs in this regime (Koester et al. 2014). Hot DA white dwarfs like WD1943+163
show photospheric metals (Barstow et al. 2003; Dickinson et al. 2012) and the strong
surface gravity should lead to the settling of metals out of their atmosphere.
Furthermore, metals are expected at the hottest temperatures because of radiative
levitation (Michaud et al. 1979; Vennes et al. 1988; Chayer et al. 1995a,b) or at the cool
end of the cooling sequence through convective mixing with deeper layers (Koester et
al. 1982; Fontaine et al. 1984; Pelletier et al. 1986). Barstow et al. (2014) argue for
external pollution as the likely explanation of their origin.!
A very faint proper motion companion has been identified on the scatter distribution
plot (Figure 3.8). Its distance from the white dwarf is ~ 6300 AU (corresponding to an
angular separation of ~ 194′′) and it has directional proper motion within a few mas per
year to the documented motion of the star. Its estimated magnitude I2 ~ 15.95 ± 0.05 20
and the mass and age of the companion will be determined in Chapter 4 using this value
and the computed distance. However, additional objects that lie within the same scatter
distribution plot could not be discounted as known galactic objects or the result of star
saturation or bleeds in the mosaic image.!
WD2311-068: is a cool (Teff ≤ 7440K, Sion et al. 2014) DQ6 spectral type white dwarf
(Dufour et al. 2005) situated ~ 25.1 pc at the outer limit of the solar neighbourhood. The
associated magnitudes are V = 15.37 (Beers et al. 1992), H = 14.94, J = 14.95 and
K! = 14.73 (Hoard et al. 2007) and I2 ~ 14.83. The white dwarf’s characteristic
properties are the carbon (in molecular or atomic form) it has in the electromagnetic
spectrum caused by convention induced dredge-up together with the molecular
absorption bands of carbon and hydrocarbon. Hot DQ white dwarfs in comparison have
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
20
For the second epoch observation.
45
carbon atmospheres due to the earlier stages of stellar evolution and show atomic
absorption lines of CII.
No companions to this white dwarf were detected from infrared excess in previous work
done by Hoard et al. (2007) using 2MASS All Sky Data Release 21 and the groundbased wide-field proper motion imaging survey conducted by Farihi et al. (2005) 22.
However, a potential companion to the white dwarf has been detected in this search (see
Figure 3.8) and has the closest proximity to its star than any of the previous companions
discussed (~ 880 AU corresponding to an angular separation of ~ 37′′). Its estimated
magnitude I2 ~ 16.19 ± 0.13 23 which together with distance, will be used to calculate
its mass and age in Chapter 4. Given the time constraints of this search and that the
detected object has not been listed in the sky catalogs used, it is reasonable to conclude
that further photometric study is required. !
In summary, the methods employed in this search have resulted in the detection of 5
potential substellar or planetary companions to the white dwarfs in this sample. These
companions could help provide constraints on models for the evolution of planetary
systems during the final stages of stellar evolution. In Chapter 4, the age and mass of a
companion will be estimated using the white dwarf cooling age and the mass and the
lifetime of a main sequence progenitor. Once known, these parameters serve as a
model-free benchmark for the companion’s mass and luminosity and could then be used
to test evolutionary models (Pinfield et al. 2006).!
!
!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
21
22
23
Based on a binary separation ≤ 4′′.
For detecting companions at orbital separations in the range 50 - 5000 AU.!
For the second epoch observation.
46
Chapter(4(–(Completeness(Limits(And(IFMR(Of(
Observations(
!
4.1(–(Completeness(Limits(
In order to determine the completeness of the survey, it is necessary to measure the
faintest detectable sources. In this stage of the project, the completeness limits for
undetected substellar companions is estimated using a method analogous to the one
described in Burleigh et al. (2008) and Hogan, Burleigh & Clarke (2009).
The limiting magnitudes are determined at which 50% and 90% of the inserted artificial
stars were recovered from each final stacked image. It is only valid in the central region
of the image, where all the individual images contribute. The useable field of view
decreases further when the two epoch images are matched as the white dwarf is rarely
positioned in the centre of each epoch image.
The completeness of the survey is limited for example by the exposure time and
background and the extended nebulosity in the IRAC Channel 2 band that limits the
sensitivities when present.
The sensitivities of the mosaics were tested using a Monte-Carlo procedure: firstly, for
each target white dwarf, an IRAF STARLIST task was used to create a list of 100
artificial stars in randomly assigned positions and magnitudes (between the 10th and
22nd magnitudes) with a uniform luminosity distribution and constant spatial density.
The flux (!Jy) was determined using the following conversion for the IRAC 2 Channel:
Flux = 179.7!x!10! x 10!!.!∗!"#
Equation (4.1)
These stars were then inserted in both epoch mosaics in a similar approach described in
Chapter 3, using the Apex Single Frame pipeline in MOPEX. The result is point source
mosaics containing the artificial stars. Residual images were also created to test the
quality of the Point Response Function fitting by subtracting the fitted point source
from the input images. Due to the large number of images involved, a smaller tile size
(TILE_X/YSIZ) was adopted to avoid memory shortage. To ensure that the point source
mosaic edges were clean of outliers, dual spatial-temporal filtering algorithms were
47
automatically employed in MOPEX by setting the parameter
USE_DUAL_OUTLIER_FOR_RMASK = 1.The entire process was repeated 50 times
giving a total of 5000 inserted artificial stars. The next step was to recover the fake stars
from the point source mosaics by running an APEX User List Single Frame extraction
pipeline that gives the option to extract a specified list of sources, rather than extracting
all sources that were detected in the images. The default MOPEX selection criteria
included point sources having SNR > 5 and which were located inside the fitting area
and that no de-blending had been performed. In addition, each point source mosaic was
fitted with the Point Response Function (PRF) to estimate fluxes and refine positions of
the point-source candidates from the detection list. The output of APEX was a table of
extracted sources (pointsource_mosaic_extract.tbl), which gave the position and flux
for each object. These point sources were then compared to those stars in the original
inserted listing in order to obtain their magnitudes.
For each binned magnitude, the fraction of the recovered stars was computed as the
number of extracted stars divided by the number of inserted stars in the point source
mosaics. Finally, the completeness limits were determined as the magnitudes at which
50% and 90% of the injected artificial stars were recovered. These magnitudes are
summarized in Table 4.1.
Figures 4.1 through 4.7 show plots of the percentage of artificial stars recovered per 0.5
magnitude bin for selected target white dwarfs. As can be seen from these plots, the
recovery percentage never reaches 100% at the brighter magnitudes due to the
saturation of some stars and overlapping of other objects. The recovered fraction further
declines towards the sensitivity limits of the Spitzer Telescope and is also affected by
the relative crowding of objects in each field.
4.2(–(Calculating(Limits(On(Companion(Masses(
4.2.1(B(Summary(
The total age of the white dwarf since formation as a main sequence star and the
completeness limits are both required to infer the minimum mass and effective
temperature of any putative companion.
48
The white dwarf’s progenitor mass is determined from the initial mass-final mass
relation (IFMR; Dobbie et al. 2006) and the main sequence mass (MMS) and lifetime
(!MS) are found from models for main sequence stellar evolution.
The white dwarf’s mass, its effective temperature (Teff), surface gravity (log g) and
cooling age (!WD) were found from literature.
Note that the detection of a companion will only be possible if it is located outside the
extent of the point source function (PSF) of that white dwarf.
4.2.2(B(The(Initial(Final(Mass(Relation((
This relationship is a key aspect in stellar evolution research by which a white dwarf’s
mass is compared directly to the zero-age main sequence mass of its progenitor. It
provides a direct measurement of the integrated mass loss that occurs during a stellar
lifetime and its dependence on stellar mass; and the relation between the progenitor
mass and the white dwarf mass is needed to correctly evaluate the time spent before the
star joins the white dwarf cooling sequence.
Recent studies of white dwarfs within the Praesepe open cluster by Casewell at al.
(2009) have revised the IFMR parameters 24. These updated values have been adopted
since they are similar to the original estimates of Dobbie et al. (2006) 25. To determine
the mass of the progenitor, the linear IFMR is given as:
MMS =
!!"!!.!"#$)
!.!!"#
Equation (4.2)
The progenitor lifetime was found from using a main sequence lifetime model (Girardi
et al. 2000) that contained a range of main sequence masses and their lifespans. Hence,
the total age of the white dwarf system was subsequently calculated as the sum of the
progenitor lifetime and the white dwarf cooling age.
4.2.3(B(COND(Evolutionary(Models
The “COND” evolutionary models for cool brown dwarfs and extrasolar planets
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
24
25
Valid for masses between 1.15 - 7!M⨀ .
m=0.133 ± 0.015 and c=0.289 ± 0.051.
49
(
(
(
Figure 4.1 – Completeness limits for both epochs for WD0806-661 and WD0101+048.
50
(
(
Figure 4.2 – Completeness limits for both epochs for WD0552-041 and WD1055-072.(
!
!
51
Figure 4.3 – Completeness limits for both epochs for WD1943+163 and WD2311-068.!
52
!
!
Figure 4.4 – Completeness limits for both epochs for WD0009+501and WD2359-434.!
53
!
!
Figure 4.5 – Completeness limits for both epochs for WD0912+536 and WD1031-114.!
54
!
!
Figure 4.6 – Completeness limits for both epochs for WD1121+216 and WD1257+278.!
55
!
!
Figure 4.7 – Completeness limits for both epochs for WD1609+135 and WD1900+705.!
56
Table 4.1 – Stellar parameters derived for the sampled white dwarfs
WD
WD0009+501
WD0038-226
WD0101+048
WD0115+159
WD0126+101
WD0133-116
WD0141-675
WD0148+641
WD0208+396
WD0231-054
WD0552-041
WD0612+177
WD0732-427
WD0738-172
WD0752-676
WD0806-661
WD0839-327
WD0851-246
MWD
(!⨀ )
0.73
0.71
0.36
0.69
0.25
0.59
0.48
0.66
0.59
1.02
0.82
0.61
0.64
0.62
0.73
0.58
0.44
0.58
Log
g
8.23
7.93
7.54
8.17
7.20
7.97
7.81
8.00
8.11
8.45
8.37
7.94
8.08
8.06
8.23
8.00
7.71
8.00
MMS
(!⨀ )
3.12
1.45
0.03
2.78
0.89
1.96
1.03
2.53
1.95
5.54
3.87
2.11
2.32
2.20
3.12
1.86
0.69
1.86
!cool
(Gyr)
3.02
4.44
0.63
1.04
0.43
0.39
1.56
0.93
1.39
0.38
7.89
0.02
0.24
1.44
4.50
0.62
0.55
11.86
!MS
(Gyr)
0.78
0.96
3.74
0.80
1.09
0.89
1.05
0.83
0.89
0.70
0.73
0.87
0.85
0.86
0.78
0.90
1.17
0.90
90%
Mag
17.6
17.6
17.3
17.1
17.0
17.4
17.7
16.1
18.0
17.0
17.0
16.9
17.5
17.4
17.1
18.7
17.6
17.0
90% M
(MJup)
5.24
5.24
11.52
6.28
12.57
16.76
10.41
7.33
5.24
7.33
6.29
10.48
28.28
3.14
4.19
3.14
3.14
7.33
90% T
(K)
242
222
355
306
501
697
414
407
398
383
223
516
1250
228
179
246
219
341
50%
Mag
18.6
18.3
18.1
18.1
17.8
18.2
18.6
19.8
18.5
18.0
18.0
17.8
18.4
18.6
17.9
19.7
18.4
18.4
50% M
(MJup)
3.56
4.10
7.65
3.89
9.00
14.67
2.50
2.40
4.19
4.19
4.92
6.81
17.40
2.30
3.56
2.10
2.40
12.50
50% T
(K)
194
179
280
251
405
550
193
190
248
297
174
403
648
183
173
198
194
343
References 26
1
1,3
1
1
5
14
1
1
1
8
1
9,16
13
1
1
1
1
15
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
26
!References – 1) Giammichele, N. et al. 2012, ApJS, 199, 29 2) Bergeron P. et al. 2011, ApJ, 737, 28 3) Limoges M. M. & Bergeron P. 2010, ApJ, 714,
1037 4) Dufour P. et al. 2005, ApJ, 627, 404 5) Bergeron P. et al. 2001, ApJS, 133, 413 6) Farihi J. et al. 2009, ApJ, 694, 805 8) Koester D. et al. 2009, A&A,
505, 441 9) Lajoie C. P. & Bergeron P. 2007, ApJ, 667,1126 10) Farihi J. et al. 2008 ApJ, 681,1470 11) Holberg J.B. & Bergeron P. 2006, AJ, 132, 1221 12)
Gianninas A. et al. 2005, ApJ, 631, 1100 13) Renzini, A. & Bergeron, P. 1995, ApJ, 443, 735 14) Mullally F. et al. 2008, ApJ, 676, 573 15) Ruiz M. T. &
Bergeron P. 2001, ApJ, 558, 761 16) Landstreet J et al. 2012, A&A, 21,8 17) Koester D. et al. 2014, A&A, 566, A3
!
57
!
!
!
!
!
!
!
!
!
Table 4.1 (continued)
WD
WD0912+536
WD1031-114
WD1053-550
WD1055-072
WD1105-048
WD1121+216
WD1124-293
WD1204-136
WD1208+576
WD1257+278
WD1609+135
WD1615-154
WD1637+335
WD1655+215
WD1840-111
WD1943+163
MWD
(!⨀ )
0.75
0.58
0.51
0.85
0.53
0.71
0.63
0.60
0.56
0.82
1.07
0.66
0.72
0.52
0.75
0.57
Log
g
8.28
8.28
7.86
8.42
7.81
8.19
8.00
8.40
7.96
8.36
8.74
8.08
8.20
7.87
8.23
7.79
MMS
(!⨀ )
3.28
1.86
1.28
4.12
1.45
2.95
2.28
2.03
1.70
3.87
5.96
2.56
3.03
1.36
3.28
1.78
!cool
(Gyr)
2.45
0.02
0.15
2.93
0.14
1.77
0.60
0.40
2.22
1.40
2.71
0.01
0.74
0.63
0.75
0.06
!MS
(Gyr)
0.77
0.90
0.99
0.008
0.96
0.79
0.85
0.88
0.92
0.73
0.70
0.82
0.78
0.98
0.77
0.91
90%
Mag
17.6
17.7
17.6
17.8
17.8
17.7
17.7
17.7
17.7
18.8
17.7
17.7
17.7
17.6
16.1
17.1
90% M
(MJup)
4.19
8.40
4.19
4.19
5.24
5.24
8.38
16.76
7.33
8.38
7.33
42.95
7.33
6.29
10.50
11.52
90% T
(K)
235
431
308
242
338
257
405
585
308
362
294
1375
377
339
445
560
50%
Mag
18.4
18.5
18.7
18.5
18.5
18.4
18.6
18.5
18.5
19.8
18.5
18.4
18.5
18.6
17.6
19.3
50% M
(MJup)
3.47
5.14
2.82
3.56
3.77
3.67
5.65
10.58
5.66
5.34
5.66
26.19
5.34
2.41
4.92
4.40
50% T
(K)
200
350
251
209
280
222
323
463
264
283
257
923
306
273
288
314
References 27
1
9
8
1
11
1
6,10
6,10
1
3
1
11
3
1
12
17
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
27
References – 1) Giammichele, N. et al. 2012, ApJS, 199, 29 2) Bergeron P. et al. 2011, ApJ, 737, 28 3) Limoges M. M. & Bergeron P. 2010, ApJ, 714,
1037 4) Dufour P. et al. 2005, ApJ, 627, 404 5) Bergeron P. et al. 2001, ApJS, 133, 413 6) Farihi J. et al. 2009, ApJ, 694, 805 8) Koester D. et al. 2009, A&A,
505, 441 9) Lajoie C. P. & Bergeron P. 2007, ApJ, 667,1126 10) Farihi J. et al. 2008 ApJ, 681,1470 11) Holberg J.B. & Bergeron P. 2006, AJ, 132, 1221 12)
Gianninas A. et al. 2005, ApJ, 631, 1100 13) Renzini, A. & Bergeron, P. 1995, ApJ, 443, 735 14) Mullally F. et al. 2008, ApJ, 676, 573 15) Ruiz M. T. &
Bergeron P. 2001, ApJ, 558, 761 16) Landstreet J et al. 2012, A&A, 21,8 17) Koester D. et al. 2014, A&A, 566, A3
!
58
!
!
!
!
!
!
!
!
!
Table 4.1 (continued)
WD
WD2034-532
WD2039-682
WD2047+372
WD2105-820
WD2115-560
WD2117+539
WD2126+734
WD2130-047
WD2136+828
WD2140+207
WD2149+021
WD2216-657
WD2246+223
WD2311-068
WD2316-173
MWD
(!⨀ )
0.9
0.61
0.81
0.74
0.58
0.56
0.60
0.66
0.55
0.48
0.59
0.58
0.96
0.63
1.23
Log
g
8.48
8.59
8.31
8.23
7.96
7.91
7.97
8.11
7.86
7.83
7.99
7.50
8.57
8.09
9.11
MMS
(!⨀ )
4.54
5.21
3.79
3.20
1.86
1.70
2.03
2.53
1.61
1.03
1.95
1.86
5.04
2.28
7.29
!cool
(Gyr)
0.30
0.36
0.34
0.80
0.59
0.18
0.15
0.14
0.16
0.82
0.12
0.82
1.52
1.74
7.30
!MS
(Gyr)
0.71
0.70
0.74
0.77
0.90
0.92
0.88
0.83
0.93
1.05
0.89
0.90
0.70
0.85
0.76
90%
Mag
17.7
17.7
17.3
17.7
17.7
17.6
17.5
17.8
17.3
17.6
17.7
17.8
17.7
17.6
17.7
90% M
(MJup)
7.33
4.19
4.19
4.19
7.33
4.19
5.23
10.48
6.29
4.19
5.24
6.29
6.29
9.43
8.38
90% T
(K)
409
283
306
281
355
305
331
487
358
254
341
326
290
357
241
50%
Mag
18.6
18.5
18.8
18.6
18.5
18.7
18.5
18.5
18.1
18.5
18.6
18.6
18.6
18.4
18.5
50% M
(MJup)
4.82
2.93
2.30
3.14
4.60
2.72
3.04
7.23
3.67
2.73
3.35
4.40
4.19
6.29
5.87
50% T
(K)
329
259
230
238
286
249
265
405
278
213
275
274
252
291
200
References 28
2
1
1
1
1
1
1
2
9
1
6,11
6
1
4
2
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
28
References – 1) Giammichele, N. et al. 2012, ApJS, 199, 29 2) Bergeron P. et al. 2011, ApJ, 737, 28 3) Limoges M. M. & Bergeron P., 2010, ApJ, 714,
1037 4) Dufour P. et al. 2005, ApJ, 627, 404 5) Bergeron P. et al. 2001, ApJS, 133, 413 6) Farihi J. et al. 2009, ApJ, 694, 805 8) Koester D. et al. 2009, A&A,
505, 441 9) Lajoie C. P. & Bergeron P., 2007, ApJ, 667,1126 10) Farihi J. et al. 2008, ApJ, 681,1470 11) Holberg J.B. & Bergeron P. 2006, AJ, 132, 1221 12)
Gianninas A. et al. 2005, ApJ, 631, 1100 13) Renzini, A. & Bergeron, P., 1995, ApJ, 443, 735 14) Mullally F. et al. 2008, ApJ, 676, 573 15) Ruiz M. T. &
Bergeron P., 2001, ApJ, 558, 761 16) Landstreet J et al. 2012, A&A, 21,8 17) Koester D. et al. 2014, A&A, 566, A3
!
59
!
!
!
!
!
!
!
!
!
Table 4.2 – Results for the 23 equatorial and northern hemisphere white dwarfs in the DODO Survey 29
WD
WD0115+159
WD0148+467
WD0208+396
WD0341+182
WD0435−088
WD0644+375
WD0738−172
WD0912+536
WD1055−072
WD1121+216
WD1134+300
WD1344+106
WD1609+135
WD1626+368
WD1633+433
WD1647+591
WD1900+705
WD1953−011
WD2007−219
WD2047+372
WD2140+207
WD2246+223
MWD
(!⨀ )
0.69
0.53
0.60
0.57
0.53
0.54
0.63
0.75
0.85
0.72
0.96
0.65
1.07
0.60
0.68
0.80
0.95
0.74
0.69
0.69
0.49
0.97
Log
g
8.19
7.89
8.01
7.99
7.93
8.10
8.09
8.28
8.42
8.20
8.55
8.10
8.75
8.03
8.14
8.31
8.58
8.23
8.14
8.13
7.84
8.57
!cool
MMS
(!⨀ )
3.0
1.8
2.3
2.1
1.8
1.9
2.6
3.5
4.2
3.2
5.0
2.7
5.9
2.3
2.9
3.8
5.0
3.4
3.0
3.0
1.5
5.1
(Gyr)
1.02
0.21
1.38
1.79
1.79
0.07
1.45
2.54
3.01
1.76
0.20
1.67
2.71
1.02
2.28
0.56
0.94
1.63
0.76
0.26
0.82
1.56
!MS
(Gyr)
0.63
2.26
1.20
1.54
2.26
2.04
0.95
0.45
0.27
0.53
0.17
0.82
0.12
1.20
0.67
0.56
0.18
0.47
0.63
0.63
3.56
0.17
90%
Mag
21.0
20.4
20.5
22.0
21.2
20.5
–
20.9
21.0
21.2
20.8
20.8
21.7
22.1
21.1
19.6
21.2
19.2
21.2
–
20.0
22.0
90% M
(MJup)
10!!
!!
16!!
!!
16!!
!!
13!!
!!
13!!
!!
13!!
!!
–
13!!
!!
13!!
!!
10!!
!!
5!!
!!
16!!
!!
13!!
!!
9!!
!!
13!!
!!
9!!
!!
7!!
!!
16!!
!!
10!!
!!
–
21!!
!!
9!!
!!
90% T
(K)
430
480
480
400
380
460
–
410
400
390
440
480
420
380
410
400
400
510
450
–
490
490
50%
Mag
22.0
21.9
22.5
22.9
22.7
22.4
22.0
22.1
22.6
22.2
21.9
22.0
22.5
22.8
22.3
22.2
22.2
21.7
22.4
21.8
21.6
22.0
50% M
(MJup)
8!!
!!
10!!
!!
9!!
!!
10!!
!!
9!!
!!
8!!
!!
7!!
!!
9!!
!!
9!!
!!
8!!
!!
3!!
!!
13!!
!!
10!!
!!
8!!
!!
10!!
!!
5!!
!!
5!!
!!
8!!
!!
7!!
!!
6!!
!!
13!!
!!
9!!
!!
50% T
(K)
380
390
360
360
320
360
320
350
340
350
350
440
380
360
370
330
330
360
370
390
370
400
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
29
Reference – Hogan et al. 2009.
60
!
!
!
!
!
!
!
!
!
(Baraffe et al. 2003) along with the magnitudes at 50% and 90% completeness limits
are used to estimate the minimum mass of a detectable companion.
These models assume negligible irradiation effects and describe the spectral and
photometrical properties of substellar objects with effective temperatures Teff ≤ 1300 K.
They are composed of tables for the selected model system ages ranging between 0.2 8.2 Gyr that predict the absolute magnitudes of the objects depending upon their age.
Using an IDL program, the minimum companion mass and effective temperature as a
fraction of the total sample were interpolated from all of the tables at the completeness
limits (which were converted to absolute magnitudes) using the known distance to each
white dwarf and the system age of each white dwarf.
4.2.4$%$The$Projected$Separation$Of$Companion$To$A$White$Dwarf
White dwarfs are intrinsically faint stars and are significantly less luminous than their
main sequence progenitors. The contrast between any companion and the white dwarf is
greatly enhanced. Any companion that avoids direct contact with the red giant envelope
as the main sequence progenitor evolves into a white dwarf will migrate outwards as
!!
mass is lost from the central star by a maximum factor of !!!!!" (Jeans 1924). This
!"
increases the projected physical separation between the companion and the white dwarf.
4.3$%$Results$
The results from the use of the evolutionary models are summarized in Tables 4.1 and
4.3.
Cumulative completeness limits in terms of mass and effective temperature are plotted
in Figures 4.8 and 4.9 respectively. As can be seen ~ 95% of mass limits are placed
below the deuterium burning limit between the brown dwarfs and planets.
It is noted that these values are lower than those obtained by Hogan at al. (2009) in
Table 4.2. Furthermore, the effective temperatures are consistent with Hogan’s
temperatures and are indicative of the later spectral type brown dwarfs or giant planets.
61!
Table 4.3 – Completeness Limits for possible substellar companions to sampled
white dwarfs
WD
WD0806-661
WD0101+048
WD0552-041
WD1055-072
WD1943+163
WD2311-068
I2
Mag
17.08
16.48
15.42
17.80
15.15
16.19
90% M
(MJup)
6!!
!!
14!!
!!
6!!
!!
7!!
!!
22!!
!!
15!!
!!
90% T
(K)
347
445
190
287
1192
527
50% M
(MJup)
13!!
!!
5!!
!!
4!!
!!
6!!
!!
21!!"
!!"
13!!
!!
50% T
(K)
197
279
175
209
314
291
The following results are for the targets that have candidate companions. The quoted
mass uncertainties represent the error in the magnitudes of the companions and do not
include the unknown systematic errors within the model predictions.
WD0806-661: The results obtained for the companion WD0806-661B by Luhman et al.
(2011) indicate an apparent mean magnitude of 16.88 ± 0.05 which is 3 mag dimmer
than the white dwarf. Luhman estimated a mass in the range of 6 - 9 MJup and Teff = 330
K – 345 K, values which were based on a white dwarf total age of 2.0 ± 0.5 Gyr and
using the evolutionary models of Burrows et al. (2003) and Saumon & Marley (2008).
In this work, the companion was found to have an estimated magnitude I2 ~ 17.08 and
using the currently known mass of 0.58!M⨀ for WD0806-661 (Giammichele et al.
2012) with IFMR initial-final mass relations, I have computed a progenitor mass of ~
1.86!M⨀ and a white dwarf total age of ~ 0.9 Gyr. WD0806-661B should thus have an
inferred effective temperature of ~ 347 K and a mass in the range of 6.29 - 7.33 MJup.
The white dwarf progenitor mass is comparable to Luhman’s estimate of 2.1 ± 0.3 M⨀ ,
as well as the companion’s magnitude and temperature being in good agreement with
Luhman’s values.
WD0101+048: As noted in Chapter 3, the primary white dwarf resides in a close binary
system and shows velocity variations with an orbital period either 1.2 or 6.4 days
(Maxted et al. 2000). The cooling age for WD0101+048 is 0.63 ± 0.07 Gyr (Bergeron et
al. 2001). The primary’s mass, as determined from a combination of photometry and
known parallax, is ≤ 0.37 M⊙ (Bergeron et al. 2001). It is discrepant to the
spectroscopic mass of 0.77!M⊙ !that was derived from its trigonometric parallax
62!
measurement. The likely explanation for this difference is the over-luminosity of the
binary system (compared to a single star) resulting in a large-radius and less massive
secondary white dwarf (Makarov 2007).
This search has detected a possible resolved tertiary companion with I2 ~ 16.48 and a
projected physical separation of ~ 3300 AU. With a mass of between 16.76 - 17.80 MJup
and having an effective temperature of ~ 445 K, the companion is likely a transitional
T/Y spectral type brown dwarf.
Figure 4.8 –The cumulative completeness limits, in terms of companion mass, for the
52 white dwarfs taken from the original Burleigh survey. The red dotted–dashed line
indicates the frequency of the completeness limit (MJup) at which 90% of companions
with that mass could be detected, while the blue dashed line indicates the completeness
limit (MJup) at which 50% of companions with that mass could be detected.
WD0552-041: The progenitor has a calculated mass of ~ 3.87 M⊙ and an age of ~ 0.73
Gyr which infer a white dwarf total system age of ≤ 8.62 Gyr. The resolved companion
is 3 mag dimmer (I2 ~ 15.42) than the degenerate white dwarf and has a mass in the
range of 5.87 – 6.29 MJup. The original projected physical separation would have been ~
63!
!
254 AU around the main sequence progenitor, assuming an expansion factor !! !" =
!!
!!.!"!!⨀
!.!"!!⨀
~ 4.72. With Teff ~ 190 K, the object may be an ultra cool Y spectral type
brown dwarf (Whitney et al. 2014). The spectra of known objects in this class show
characteristic ammonia absorption ~ 1.55 µm (Leggett et al. 2009) and as such, this
feature could be searched for in future studies to determine the exact nature of this
companion.
Figure 4.9 - The cumulative completeness limits, in terms of companion temperature,
for the 52 white dwarfs taken from the Burleigh survey. The red dotted–dashed line
indicates the frequency of the completeness limit (K) at which 90% of companions with
that temperature could be detected, while the blue-dashed line indicates the
completeness limit (K) at which 50% of companions with that temperature could be
detected.
WD1055-072: As can be seen in Table 4.1, the companion is the dimmest of all of the
possible companions in relation it its host star with estimated magnitude I2 ~ 17.8. The
original projected physical separation would have been ≤ 412 AU around the main
64!
sequence progenitor, assuming an expansion factor
!!"
!!!
=
!!.!"!!⨀
!.!"!!⨀
~ 4.85. With a
possible mass in the range of 7.3 – 8.5 MJup and Teff ≤ 287 K, this object certainly
requires future investigation to determine if it is also an ultra cool Y spectral type brown
dwarf or a giant planet.
WD1943+163: With an estimated magnitude I2 ~ 15.15, the evolutionary models
indicate that the infrared excess is due to a possible T spectral type brown dwarf
companion having Teff ~ 1192 K and having a mass between 20.6 - 24.1 MJup. The
original projected physical separation would have been ~ 2017 AU around the main
!
sequence progenitor, assuming an expansion factor !!!" =
!!
!!.!"!!⨀
!.!"!!⨀
~ 3.12.
WD2311-068: The possible companion has an estimated magnitude I2 ~ 16.19. Its
associated mass is in the range of 13.61 – 16.76 MJup which is close to the deuterium
burning upper mass limit and it has an estimated Teff ~ 517 K. The corresponding
original projected physical separation was ~ 243 AU around the main sequence
!
!!.!"!!
progenitor, assuming an expansion factor !!!" =! !.!"!! ⨀ ~ 3.6. It is possible that the
!!
⨀
companion is a T spectral type brown dwarf and since no other properties are known,
further observation of this cool object would be required.
In summary, the results from the evolutionary models have reinforced the possible
detection of 5 previously unknown low mass companions to white dwarfs observed by
the Spitzer Telescope. Their predicted masses and effective temperatures are indicative
of possible brown dwarfs and gas giant planets.
!
!
!
65!
Chapter$5$–$Conclusion$And$Future$Work$
A comprehensive search has been conducted to detect faint, low mass and wide
common proper motion companions to target white dwarfs by combining multi-epoch
mosaic images obtained from the various Spitzer surveys.
Potential companions to their host stars were identified using the detection technique
described in Chapter 3. Subsequently, potential companions that were found to exhibit
high proper motion inconsistent with the white dwarf host or objects known already in
astronomical catalogues were ruled out as possible companions.
In Chapter 4, the 50% and 90% completeness limits were computed from the recovery
of artificial stars injected into the mosaic images for each epoch. The progenitor mass
and age along with the total age of each white dwarf were calculated using the known
white dwarf mass and the initial final mass relation. The masses for the detected
companions were determined using their apparent magnitudes and the COND
evolutionary models.
This search places limits on companions at wide separations around all target white
dwarfs with masses below the deuterium burning limit. Assuming only WD0806-661
has a confirmed planetary mass companion and using the 50% completeness limit, it is
inferred, for projected separations < 3000 AU, less than 8 % of white dwarfs and
progenitors have unresolved companions with masses < 5 MJup. In comparison, the
frequency is < 20% (3000 - 5000 AU), < 15% (5000 - 7000 AU) and ≤ 40% for
separations > 7000 AU. Furthermore, between separations of 3000 - 7000 AU, < 4%
of white dwarfs and progenitors were found to have unresolved companions with
masses ranging 5 - 13 MJup and < 2% for masses above the deuterium burning limit. It
is noted that these results are in accordance with those obtained by McCarthy &
Zuckerman (2004) who proposed that the frequency of companions orbiting at shorter
separations (i.e. between 75 - 300 AU) is ≤ 3%.
Furthermore, we suggest that the frequency of T and transitional T/Y spectral type
objects at these temperatures is < 8 % and using the 90% completeness limit. This
estimate is consistent with the recent MIR searches for unresolved substellar and
planetary mass companions on the frequency of these companions, for example ≤ 0.6 %
66!
(Farihi et al. 2008) and ≤ 0.5 % (Steele et al. 2011) down to masses near the deuterium
burning limit and at separations with a few hundred AU. In comparison, the Gemini
Deep Planet direct imaging survey conducted by Lafrenière et al. (2007) has found that
the frequency of stars with low-mass brown companions is 1.9% and at most 17% for
planets (with masses in the range of 0.5 - 13 MJup) located between 25 - 250 AU.
It was possible to detect companions that have effective temperatures ≥ 500 K and thus
probing well into the transition of the T dwarf sequence and the early Y spectral type
dwarf regime (e.g. Kirkpatrick et al. 2011). Using the 50% completeness limit, our
search could also detect ultra cool companions that have effective temperatures in the
range 300 - 450 K for < 45% of the white dwarf targets that would be later Y spectral
type (e.g Cushing et al. 2011; Luhman et al. 2011; Beichman et al. 2013).
We have detected resolved, 5 potential companions to the target white dwarfs, of which
4 companions are consistent with low mass brown dwarf or gas giant planetary
candidates. These objects exhibit masses between 6 - 24 MJup and with temperatures in
the range 200 - 1200 K, comparable to the coolest known brown dwarfs, e.g. later than
Y2 spectral type WISEPA J182831.08+265037.8 (Beichman et al. 2013). The
remaining companion has an effective temperature only ~ 20K warmer than Jupiter.
In conclusion, any future work of this search should be directed toward confirming the
candidate companions and their spectral types. The methods employed in this search
can also be extended to the remaining 30 white dwarfs from the original Burleigh
proper motion survey with Spitzer and to over 300 other white dwarfs from the Spitzer
Data Archive most of which have only one epoch of observations. It may be necessary
to obtain secondary epoch images for these intended targets, but by broadening the
search to significant larger sample, it will help our understanding of the brown dwarf
desert, planet formation and evolution and the fraction of white dwarfs and their
progenitors with planets or habitable planets.
67!
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