Download Document

Radial Velocity Detection of Planets:
II. Observations
1.
2.
3.
4.
5.
Period Analysis
Global Parameters
Classes of Planets
Dependence on Stellar Parameters
Sources of Noise
Lecture notes: www.tls-tautenburg.de
Click on Teaching -> lectures -> Extrasolar Planets
Binary star simulator:
http://instruct1.cit.cornell.edu/courses/astro101/java/binary/binary.htm#instructions
Also: www.exoplanet.eu
1. Period Analysis
How do you know if you have a periodic signal in your data?
What is the period?
Try 16.3 minutes:
Lomb-Scargle Periodogram of the data:
1. Period Analysis
1. Least squares sine fitting:
Fit a sine wave of the form:
V(t) = A·sin(wt + f) + Constant
Where w = 2p/P, f = phase shift
Best fit minimizes the c2:
c2 = S (di –gi)2/N
di = data, gi = fit
Note: Orbits are not always sine waves, a better approach would be
to use Keplerian Orbits, but these have too many parameters
1. Period Analysis
2. Discrete Fourier Transform:
Any function can be fit as a sum of sine and cosines
N0
FT(w) =  Xj (T) e–iwt
Recall eiwt = cos wt + i sinwt
j=1
X(t) is the time series
1
Power: Px(w) =
| FTX(w)|2
N0
2
1
Px(w) =
Xj cos wtj +
N0
[(S
N0 = number of points
2
) (S X sin wt ) ]
j
j
A DFT gives you as a function of frequency the amplitude
(power) of each sine wave that is in the data
FT
P
Ao
Ao
t
1/P
A pure sine wave is a delta function in Fourier space
w
1. Period Analysis
2. Lomb-Scargle Periodogram:
1
Px(w) =
2
[ S X cos w(t –t)]
j
j
S
2
j
1
+
2
2
Xj cos w(tj–t)
j
tan(2wt) =
[ S X sin w(t –t) ]
j
j
j
S X sin
j
2
w(tj–t)
(Ssin
2wtj)/(Scos 2wtj)
j
j
Power is a measure of the statistical significance of that
frequency (period):
False alarm probability ≈ 1 – (1–e–P)N = probability that noise
can create the signal
N = number of indepedent frequencies ≈ number of data points
2
Amplitude (m/s)
Least squares sine fitting: The best
fit period (frequency) has the
lowest c2
Discrete Fourier Transform: Gives
the power of each frequency that is
present in the data. Power is in
(m/s)2 or (m/s) for amplitude
Lomb-Scargle Periodogram: Gives
the power of each frequency that is
present in the data. Power is a
measure of statistical signficance
False alarm probability ≈ 10–14
Alias Peaks
Noise level
Alias periods:
Undersampled periods appearing as another period
Lomb-Scargle Periodogram of previous 6 data points:
Lots of alias periods and false alarm probability
(chance that it is due to noise) is 40%!
For small number of data points sine fitting is best.
Raw data
False alarm probability ≈ 0.24
After removal of
dominant period
Campbell & Walker: The Pioneers of RV Planet Searches
1988:
1980-1992 searched for planets around 26
solar-type stars. Even though they found
evidence for planets, they were not 100%
convinced. If they had looked at 100 stars
they certainly would have found
convincing evidence for exoplanets.
Global Properties of Exoplanets
2. Mass Distribution
The Brown Dwarf Desert
 e–0.3
Planet: M < 13 MJup → no nuclear burning
Brown Dwarf: 13 MJup < M < ~70 MJup → deuterium burning
Star: M > ~70 MJup → Hydrogen burning
There mass distribution falls off exponentially.
N(20 MJupiter) ≈ 0.002 N(1 MJupiter)
There should be a large population of low mass planets.
Brown Dwarf Desert: Although there are ~100-200
Brown dwarfs as isolated objects, and several in
long period orbits, there is a paucity of brown
dwarfs (M= 13–50 MJup) in short (P < few years) as
companion to stars
Number
Number
Semi-Major Axis Distribution
Semi-major Axis (AU)
Semi-major Axis (AU)
The lack of long period planets is a selection effect since
these take a long time to detect
2. Eccentricity distribution
e=0.4
e=0.6
e=0.8
w=0
w=90
w=180
e Eri
2 ´´
Mass versus
Orbital Distance
Eccentricities
3. Classes of planets: 51 Peg Planets
Discovered by Mayor & Queloz 1995
How are we sure this is really a planet?
Bisectors can measure the line shapes and tell you
about the nature of the RV variations:
Curvature
Span
What can change bisectors:
• Spots
• Pulsations
• Convection pattern on star
The David Gray Controversy
Gray & Hatzes 1997
If the bisector
variations were
real then 51 Peg
has no planet
Hatzes et al. : No bisector variations
The final proof that these are really planets:
The first transiting planet HD 209458
3. Classes of planets: 51 Peg Planets
• ~25% of known extrasolar planets
are 51 Peg planets (selection effect)
• 0.5–1% of solar type stars have
giant planets in short period orbits
• 5–10% of solar type stars have a
giant planet (longer periods)
3. Classes of planets: Hot Neptunes
McArthur et al. 2004
Santos et al. 2004
Butler et al. 2004
Msini = 14-20 MEarth
3. Classes: The Massive Eccentrics
• Masses between 7–20 MJupiter
• Eccentricities, e>0.3
• Prototype: HD 114762
m sini = 11 MJup
3. Classes: The Massive Eccentrics
There are no massive planets in circular orbits
3. Classes: Planets in Binary Systems
Why search for planets in binary stars?
• Most stars are found in binary systems
• Does binary star formation prevent planet formation?
• Do planets in binaries have different characteristics?
• For what range of binary periods are planets found?
• What conditions make it conducive to form planets?
(Nurture versus Nature?)
• Are there circumbinary planets?
Some Planets in known Binary Systems:
Star
16 Cyg B
55 CnC
HD 46375
t Boo
 And
HD 222582
HD 195019
a (AU)
800
540
300
155
1540
4740
3300
Nurture vs. Nature?
The first extra-solar Planet
may have been found by
Walker et al.
in 1992 in a
binary system:
g Cephei
Planet
Periode
Msini
2,47 Jahre
1,76 MJupiter
e
a
K
0,2
2,13 AE
26,2 m/s
Doppelstern
Periode
Msini
56.8 ± 5 Jahre
~ 0,4 ± 0,1 MSun
e
a
0,42 ± 0,04
18.5 AE
K
1,98 ± 0,08 km/s
g Cephei
Primärstern
Sekundärstern
Planet
The planet around g Cep is difficult to form and on the
borderline of being impossible.
Standard planet formation theory: Giant planets form beyond
the snowline where the solid core can form. Once the core is
formed the protoplanet accretes gas. It then migrates
inwards.
In binary systems the companion truncates the disk. In the
case of g Cep this disk is truncated just at the ice line. No ice
line, no solid core, no giant planet to migrate inward. g Cep
can just be formed, a giant planet in a shorter period orbit
would be problems for planet formation theory.
3. Planetary Systems
25 Extrasolar Planetary Systems (18 shown)
Star
P (d) MJsini a (AU) e
HD 82943 221 0.9
0.7
0.54
444 1.6
1.2
0.41
GL 876
47 UMa
30
61
1095
2594
0.6
2.0
2.4
0.8
HD 37124 153
0.9
550
1.0
55 CnC
2.8
0.04
14.6 0.8
44.3 0.2
260
0.14
5300
4.3
Ups And
4.6
0.7
241.2 2.1
1266
4.6
HD 108874 395.4 1.36
1605.8 1.02
HD 128311 448.6 2.18
919 3.21
HD 217107 7.1 1.37
3150 2.1
0.1
0.2
2.1
3.7
0.27
0.10
0.06
0.00
0.5
2.5
0.04
0.1
0.2
0.78
6.0
0.06
0.8
2.5
1.05
2.68
1.1
1.76
0.07
4.3
0.20
0.40
0.17
0.0
0.34
0.2
0.16
0.01
0.28
0.27
0.07
0.25
0.25
0.17
0.13
0.55
Star
P (d) MJsini
HD 74156 51.6
1.5
2300
7.5
HD 169830 229
2.9
2102
4.0
HD 160691 9.5
0.04
637
1.7
2986
3.1
HD 12661
263
1444
HD 168443 58
1770
HD 38529 14.31
2207
HD 190360 17.1
2891
HD 202206 255.9
1383.4
HD 11964
37.8
1940
m Ara: 4 planets
2.3
1.6
7.6
17.0
0.8
12.8
0.06
1.5
17.4
2.4
0.11
0.7
a (AU)
0.3
3.5
0.8
3.6
0.09
1.5
0.09
e
0.65
0.40
0.31
0.33
0
0.31
0.80
0.8
2.6
0.3
2.9
0.1
3.7
0.13
3.92
0.83
2.55
0.23
3.17
0.35
0.20
0.53
0.20
0.28
0.33
0.01
0.36
0.44
0.27
0.15
0.3
Resonant Systems Systems
Star
P (d) MJsini a (AU) e
HD 82943 221 0.9
0.7
0.54
444 1.6
1.2
0.41
→
GL 876
→ 2:1
55 CnC
30
61
0.6
2.0
0.1
0.2
14.6 0.8
44.3 0.2
0.1
0.2
0.27
0.10
0.0
0.34
2:1
→ 3:1
HD 108874 395.4 1.36
1605.8 1.02
1.05
2.68
0.07
0.25
→ 4:1
HD 128311 448.6 2.18
919 3.21
1.1
1.76
0.25
0.17
→ 2:1
2:1 → Inner planet makes two orbits for
every one of the outer planet
Eccentricities
•
Period (days)
Mass versus
Orbital Distance
Eccentricities
4. The Dependence of Planet Formation on Stellar Mass
Setiawan et al. 2005
Poor precision
Too faint (8m class tel.).
Ideal for 3m class tel.
RV Error (m/s)
Main Sequence Stars
A0
A5
F0
F5
G0
G5
Spectral Type
K0
K5
M0
Exoplanets around low mass stars
Ongoing programs:
• ESO UVES program (Kürster et al.): 40 stars
• HET Program (Endl & Cochran) : 100 stars
• Keck Program (Marcy et al.): 200 stars
• HARPS Program (Mayor et al.):~100 stars
Results:
• Giant planets (2) around GJ 876. Giant planets
around low mass M dwarfs seem rare
• Hot neptunes around several. Hot Neptunes
around M dwarfs seem common
Exoplanets around massive stars
Difficult on the main sequence, easier (in principle) for evolved stars
Hatzes & Cochran 1993
„…it seems improbable that all three would have companions
with similar masses and periods unless planet formation around
the progenitors to K giants was an ubiquitous phenomenon.“
P = 1.5 yrs
Frink et al. 2002
M = 9 MJ
The Planet around Pollux
McDonald 2.1m
CFHT
McDonald 2.7m
TLS
The RV variations of b Gem taken with 4 telescopes over a time span of 26 years. The
solid line represents an orbital solution with Period = 590 days, m sin i = 2.3 MJup.
HD 13189
P = 471 d
Msini = 14 MJ
M* = 3.5 Msun
HD 13189
Sp. Type
Mass
V sin i
K2 II–III
3.5 Msun
2.4 km/s
HD 13189 b
Period
471 ± 6 d
RV Amplitude
e
a
m sin i
173 ± 10 m/s
0.27 ± 0.06
1.5 – 2.2 AU
14 MJupiter
HD 13189 : Short Term Variations
Discovery of Stellar Oscillations in b Gem
Diploma work of Mathias Zechmeister
From Michaela Döllinger‘s thesis
P = 517 d
Msini = 10.6 MJ
e = 0.09
M* = 1.84 M‫סּ‬
P = 272 d
Msini = 6.6 MJ
e = 0.53
M* = 1.2 M‫סּ‬
P = 657 d
Msini = 10.6 MJ
e = 0.60
M* = 1.2 M‫סּ‬
P = 159 d
Msini = 3 MJ
e = 0.03
M* = 1.15 M‫סּ‬
P = 1011 d
Msini = 9 MJ
e = 0.08
M* = 1.3 M‫סּ‬
P = 477 d
Msini = 3.8 MJ
e = 0.37
M* = 1.0 M‫סּ‬
M sin i = 3.5 – 10 MJupiter
Stellar Mass Distribution: Döllinger Sample
10
N
9
8
7
6
5
4
3
2
1
0
1.05
1.25
Mean = 1.4 M‫סּ‬
Median = 1.3 M‫סּ‬
1.45
1.65
1.85
2.05
2.25
2.45
M (M‫)סּ‬
~10% of the intermediate mass stars
have giant planets
Eccentricity versus Period
50
Planet Mass Distribution
for Solar-type Dwarfs P>
100 d
40
30
20
10
0
1
3
5
7
9
11
13
15
7
Planet Mass Distribution
for Giant and Main
Sequence stars with M >
1.1 M‫סּ‬
6
5
N
4
3
2
1
0
1
3
5
7
9
11
13
M sin i (Mjupiter)
15
More massive stars
tend to have a more
massive planets and at
a higher frequency
4. The Planet-Metallicity Connection?
Astronomer‘s
Metals
More Metals !
Even more Metals !!
4. The Planet-Metallicity Connection?
These are stars with metallicity [Fe/H] ~ +0.3 – +0.5
Valenti & Fischer
There is believed to be a connection
between metallicity and planet formation.
Stars with higher metalicity tend to have a
higher frequency of planets.
Endl et al. 2007: HD 155358 two planets and..
Hyades stars have
[Fe/H] = 0.2 and
according to V&F
relationship 10% of
the stars should
have giant planets,
but none have been
found in a sample
of 100 stars
…[Fe/H] = –0.68. This certainly muddles the metallicity-planet connection
Percent
Planet-Metallicity Effect in Giant stars?
[Fe/H]
Giant stars show no metallicity effect
Maybe pollution can explain the metallicity-planet connection
Giant hosting planet stars do not show a metallicity enhancement such as
the planet hosting stars on the main sequence. Pasquini et al. (2007)
hypothesize that the high metal content is due to pollution by planets. When
the stars evolve to giants they have deeper convection zones which mixes
the chemicals.
Jovian Analogs
Definition: A Jupiter mass planet in a 11 year orbit (5.2 AU)
Period = 14.5 yrs
Mass = 4.3 MJupiter
e = 0.16
In other words we have yet to find one. Long term surveys (+15
years) have excluded Jupiter mass companions at 5AU in ~45 stars
e Eri
• Long period planet
• Very young star
• Has a dusty ring
• Nearby (3.2 pcs)
• Astrometry (1-2 mas)
• Imaging (Dm =20-22 mag)
• Other planets?
Clumps in Ring can be
modeled with a planet here
(Liou & Zook 2000)
Radial Velocity Measurements of e Eri
Hatzes et al. 2000
Large scatter is because this is an active star
Scargle Periodogram of e Eri Radial velocity measurements
False alarm probability ~ 10–8
Scargle Periodogram of Ca II measurements
Benedict et al: HST Astrometry on e Eri
• Mass = 1.55 MJupiter
• Orbital plane coincides
with dusty ring plane
One of our planets is missing:
HD 33636
P = 2173 d
Msini = 10.2 MJup
i = 4 deg → m = 142 MJup
Velocity (m/s)
5. Habitable Terrestrial Planets
Terrestrial planets in the habitable zone of low
mass stars
Kasting et
al. (1993)
The habitable zone is loosely defined as the distance where the
equilibrium temperature of the planet can support water in the liquid
state
Lovis et al. 2007
A Habitable Super Earth?
Some are in habitable zone of M
dwarf
P=5.4 d
P=12.9 d
P=83.6 d
Endl et al. can exclude 1 Mearth planet
in habitable zone of Barnard‘s star
5. Sources of „Noise“
Other phenomena can produce radial velocity variations and
thus „pretend“ to be a planet:
• Spots, plage, other surface structure
• Convection pattern on the star
• Pulsations
• Spots, plage, etc can cause RV
Variations in active stars
HD 166435
•Ca II H & K measurements are
important
• One can attempt to correct for the
activity RV variations by looking at
changes in the spectral line shapes
Correlation of bisector span with radial velocity for HD 166435
Ca II H & K core emission is a measure of magnetic activity:
Active star
Inactive star
HD 166435 shows variations in all quantities
Activity Effects: Convection
Hot rising cell
Cool sinking lane
•The integrated line profile is distorted.
•The ratio of dark lane to hot cell areas changes
with the solar cycle
This is a Jupiter!
RV changes can be as large as 10 m/s
with an 11 year period
One has to worry even about the nature
long period RV variations
Confirming Extrasolar Planet Discoveries made with
Radial Velocity Measurements
The commandments of planet confirmation:
• Must have long-lived coherent periodic variations
• RV amplitude must be constant with wavelength
• Must not have photometric variations with the same period
as the planet
• Must not have Ca II H&K emission variations with the
planet period
• Most not have line shape (bisector) variations with the same
period as the planet
The Planet around TW Hya
Setiawan et al. 2007
And my doubts…
The claim is no bisector variations in this star
Maximum RV
variations in the
velocity span is
~500 m/s
Doppler image of V 410 Tau: A Weak T Tauri Star
The spot distribution on V410 Tau has been present for 15
years!
• TW Hya is a T Tauri star (that will become a weak T
Tauri star) viewed pole-on
• It most likely has a decentered polar spot (Doppler
images of another TW Hya association star indeed
shows a polar spot)
• Polar spots on a star viewed pole on causes small
changes in the bisector span, but large changes in the
curvature
What is needed to confirm this:
1.
Contemporaneous photometry
2.
RV measurements in the infrared where the
spot contrast is smaller.
Summary
Radial Velocity Method
Pros:
• Most successful detection method
• Gives you a dynamical mass
• Distance independent
•
Will provide the bulk (~1000) discoveries in the
next 10+ years
Summary
Radial Velocity Method
Cons:
•
Only effective for late-type stars
•
Most effective for short (< 10 – 20 yrs) periods
•
Only high mass planets (no Earths!)
•
Projected mass (msin i)
•
Other phenomena (pulsations, spots) can mask as
an RV signal. Must be careful in the interpretation
Summary of Exoplanet Properties from RV Studies
• ~6% of normal solar-type stars have giant planets
• ~10% or more of stars with masses ~1.5 M‫ סּ‬have giant planets that tend to be
more massive
• < 1% of the M dwarfs stars (low mass) have giant planets, but may have a large
population of neptune-mass planets
→ low mass stars have low mass planets, high mass stars have more planets of
higher mass → planet formation may be a steep function of stellar mass
• 0.5–1% of solar type stars have short period giant plants
• Exoplanets have a wide range of orbital eccentricities (most are not in circular
orbits)
• Massive planets tend to be in eccentric orbits
• Massive planets tend to have large orbita radii
• Stars with higher metallicity tend to have a higher frequency of planets, but this
needs confirmation