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Radial Velocity Detection of Planets:
II. Results
1. Period Searching: How do you find
planets in your data?
2. Exoplanet discoveries with the radial
velocity method
Finding a Planet in your Radial Velocity Data
1. Determine if there is a periodic signal in your
data.
2.
Determine if this is a real signal and not due to
noise.
3. Determine the nature of the signal, it might not
be a planet!
4.
Derive all orbital elements
1. Period Analysis
How do you know if you have a periodic signal in your data?
Here are RV data from a pulsating star
What is the period?
Try 16.3 minutes:
Lomb-Scargle Periodogram of the data:
1. Period Analysis: How do you find a signal in your data
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 = amplitude2) 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
3. 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
The first Tautenburg Planet: HD 13189
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 Peak
Noise level
Alias periods:
Undersampled periods appearing as another period
Raw data
After removal of
dominant period
To summarize the period search techniques:
1.
Sine fitting gives you the c2 as a function of period. c2 is
minimized for the correct period.
2. Fourier transform gives you the amplitude (m/s in our
case) for a periodic signal in the data.
3.
Lomb-Scargle gives an amplitude related to the
statistical signal of the data.
Most algorithms (fortran and c language) can be found in
Numerical Recipes
Period04: multi-sine fitting with Fourier analysis. Tutorials
available plus versions in Mac OS, Windows, and Linux
http://www.univie.ac.at/tops/Period04/
2. Results from Doppler Surveys
Butler et al. 2006, Astrophysical Journal, Vol 646, pg 505
Telescope
1-m MJUO
1.2-m Euler Telescope
1.8-m BOAO
1.88-m Okayama Obs,
1.88-m OHP
2-m TLS
2.2m ESO/MPI La Silla
2.7m McDonald Obs.
3-m Lick Observatory
3.8-m TNG
3.9-m AAT
3.6-m ESO La Silla
8.2-m Subaru Telescope
8.2-m VLT
9-m Hobby-Eberly
10-m Keck
Instrument
Hercules
CORALIE
BOES
HIDES
SOPHIE
Coude Echelle
FEROS
2dcoude
Hamilton Echelle
SARG
UCLES
HARPS
HDS
UVES
HRS
HiRes
Wavelength Reference
Th-Ar
Th-Ar
Iodine Cell
Iodine Cell
Th-Ar
Iodine Cell
Th-Ar
Iodine cell
Iodine cell
Iodine Cell
Iodine cell
Th-Ar
Iodine Cell
Iodine cell
Iodine cell
Iodine cell
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.
Campbell, Walker, & Yang 1988
„Probable third body variation of 25 m s–1, 2.7 year
period, superposed on a large velocity gradient“
e Eri was a „probable variable“
The first extrasolar planet around a normal star: HD 114762
with Msini = 11 MJ discovered by Latham et al. (1989)
Filled circles are data taken at McDonald Observatory
using the telluric lines at 6300 Ang.
Global Properties of Exoplanets:
Mass Distribution
The Brown Dwarf Desert
Planet: M < 13 MJup → no nuclear burning
Brown Dwarf: 13 MJup < M < ~80 MJup → deuterium burning
Star: M > ~80 MJup → Hydrogen burning
Up-to-date Histograms with all planets:
One argument: Because of unknown vsini these are
just low mass stars seen with i near 0
i decreasing
probability decreasing
Argument against stars #1
P(i < q) = 1– cos q
Probability an orbit has an
inclination less than q
e.g. for m sin i = 0.5 MJup for this to have a true mass of
0.5 Msun sin i would have to be 0.01. This implies q = 0.6
deg or P =0.00005: highly unlikely!
Argument against stars #2
Some planetary systems have multiple planets, for
example m1 x sini = 5 MJup, and m2 x sini = 0.03 MJup. To
make the first planet a star requires sini =0.01. Other
planet would still be mtrue=3 MJup
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
An Oasis in the Brown Dwarf Desert: HD 137510 = HR 5740
A note on the naming convention:
Name of the star: 16 Cyg
If it is a binary star add capital letter B, C, D
If it is a planet add small letter: b, c, d
55 CnC b : first planet to 55 CnC
55 CnC c: second planet to 55 CnC
16 Cyg B: fainter component to 16 Cyg binary system
16 Cyg Bb: Planet to 16 Cyg B
The IAU has yet to agree on a rule for the naming of
extrasolar planets
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
The short period planets are also a selection effect: they are the easiest to find
and now transiting surveys are geared to finding these.
Updated:
Eccentricity distribution
Fall off at high eccentricity may be partially due to an observing
bias…
e=0.4
e=0.6
e=0.8
w=0
w=90
w=180
…high eccentricity orbits are hard to detect!
For very eccentric
orbits the value of the
eccentricity is is often
defined by one data
point. If you miss the
peak you can get the
wrong mass!
At opposition with Earth would
be 1/5 diameter of full moon,
12x brighter than Venus
e Eri
2 ´´
Comparison of some eccentric orbit planets to our solar system
Mass versus
Orbital Distance
Eccentricities
There is a relative lack of massive close-in planets
Classes of planets: 51 Peg Planets: Jupiter mass
planets in short period orbits
Discovered by Mayor & Queloz 1995
Classes of planets: 51 Peg Planets
• ~35% 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)
Another short period giant planet
Classes of planets: Hot Neptunes
Santos et al. 2004
McArthur et al. 2004
Butler et al. 2004
Msini = 14-20 MEarth
If there are „hot Jupiters“ and „hot Neptunes“ it makes sense that
there are „hot Superearths“
CoRoT-7b
Mass = 7.4 ME
P = 0.85 d
Classes: The Massive Eccentrics
• Masses between 7–20 MJupiter
• Eccentricities, e > 0.3
• Prototype: HD 114762 discovered in 1989!
m sini = 11 MJup
Classes: The Massive Eccentrics
There are no massive planets in circular orbits
Planet-Planet Interactions
Initially you have two giant
planets in circular orbits
These interact gravitationally.
One is ejected and the
remaining planet is in an
eccentric orbit
Lin & Ida, 1997, Astrophysical Journal, 477, 781L
Red: Planets with masses < 4 MJup
Blue: Planets with masses > 4 MJup
Planets in Binary Systems
Why should we care about 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
For more examples see Mugrauer & Neuhäuser 2009, Astronomy &
Astrophysics, vol 494, 373 and references therein
There are very few planets in close binaries. The
exception is g Cep.
The first extra-solar Planet
may have been found by
Walker et al.
in 1992 in a
binary system:
Ca II is a measure of stellar activity (spots)
g Cephei
Planet
Period
Msini
2,47 Years
1,76 MJupiter
e
a
K
0,2
2,13 AU
26,2 m/s
Binary
Period
Msini
56.8 ± 5 Years
~ 0,4 ± 0,1 MSun
e
a
0,42 ± 0,04
18.5 AU
K
1,98 ± 0,08 km/s
Walker et al. Excluded the planet hypothesis largely because the Ca II line
strength showed variations with the same period as the velocity data. However, if
you divide the Ca II in half (two time series) a signal is seen in the first half but
not the last half. The signal in the last half is not the same period as the planet
signal.
g Cephei
Primary star (A)
Secondary Star (B)
Planet (b)
Neuhäuser et al. Derive an orbital inclination of AB of 119 degrees. If the binary
and planet orbit are in the same plane then the true mass of the planet is 1.8 MJup.
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.
The interesting Case of 16 Cyg B
Effective Temperature: A=5760 K, B=5760 K
Surface gravity (log g): 4.28, 4.35
Log [Fe/H]: A= 0.06 ± 0.05, B=0.02 ± 0.04
16 Cyg B has 6 times less Lithium
These stars are identical and are „solar twins“. 16 Cyg B
has a giant planet with 1.7 MJup in a 800 d period
Kozai Mechanism: One Explanation for the high
eccentricty of 16 Cyg B
Two stars are in long period orbits around each other.
A planet is in a shorter period orbit around one star.
If the orbit of the planet is inclined, the outer planet can „pump up“ the
eccentricity of the planet. Planets can go from circular to eccentric orbits.
This was first investigated by Kozai who showed that satellites in orbit
around the Earth can have their orbital eccentricity changed by the
gravitational influence of the Moon
Kozai Mechanism: changes the inclination and
eccentricity
Planetary Systems: 49 Multiple Systems
49 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
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
The 5-planet System around 55 CnC
0.17MJ
5.77 MJ
•0.11 M
J
Red lines: solar system plane orbits
0.82MJ
•
•0.03M
J
The Planetary System around GJ 581
16 ME
7.2 ME
5.5 ME
Inner planet 1.9 ME
Can we find 4 planets in
the RV data for GL 581?
Note: for Fourier analysis
we deal with frequencies
(1/P) and not periods
n1 = 0.317 cycles/d
n2 = 0.186
n3 = 0.077
n4 = 0.015
Almost:
The Period04 solution:
P1 = 5.38 d, K = 12.7 m/s
Published solution:
P1 = 5.37 d, K = 12.5 m/s
P2 = 12.99 d, K = 3.2 m/s
P2 = 12.93 d, K = 2.63 m/s
P3 = 83.3 d, K = 2.7 m/s
P3 = 66.8 d, K = 2.7 m/s
P4 = 3.15, K = 1.05 m/s
P4 = 3.15, K = 1.85 m/s
s=1.17 m/s
s=1.53 m/s
Conclusions: 5.4 d and 12.9 d probably real, 66.8 d period is
suspect, 3.15 d may be due to noise and needs confirmation.
A better solution is obtained with 1.4 d instead of 3.15 d, but
this is above the Nyquist sampling frequency
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
30
61
55 CnC
14.6
44.3
2:1
0.6
2.0
0.1
0.2
0.27
0.10
→ 2:1
0.8
0.2
0.1
0.2
0.0
0.34
→ 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)
Red points: Systems
Blue points: single planets
Mass versus Orbital Distance
Eccentricities
Red points: Systems
Blue points: single planets
On average, giant planets in planetary sytems tend to be lighter than single planets. Either 1)
Forming several planets in a protoplanetary disks „divides“ the mass so you have smaller
planets, or 2) if you form several massive planets they are more likely to interact and most get
ejected.
The Dependence of Planet Formation on Stellar Mass
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.):~200 stars
Results:
• Giant planets (2) around GJ 876. Giant planets
around low mass M dwarfs seem rare
• Hot neptunes around several.
Currently too few planets around M dwarfs to make any real
conclusions
12
11
10
9
8
7
6
5
4
3
2
1
0
0.025
0.225
0.425
0.625
0.825
1.025
2 planets with masses 2.1, 2.3 MJup
1 Planet with mass 4.9 MJup
1.225
1.425
GL 876 System
1.9 MJ
0.6 MJ
Inner planet 0.02 MJ
Exoplanets around massive stars
Difficult with the Doppler method because more massive
stars have higher effective temperatures and thus few
spectral lines. Plus they have high rotation rates. A way
around this is to look for planets around giant stars. This
will be covered in „Planets off the Main Sequence“
Result: Only a few planets around early-type, more massive
stars, and these are mostly around F-type stars (~ 1.4 solar
masses)
Galland et al. 2005
HD 33564
M* = 1.25
msini = 9.1 MJupiter
P = 388 days
e = 0.34
F6 V star
A Planet around an F star from the Tautenburg Program
HD 8673
An F4 V star from the
Tautenburg Program
P = 328 days
Msini = 8.5 Mjupiter
e = 0.24
Scargle Power
M* = 1.4 M‫סּ‬
Frequency (c/d)
Mstar ~ 1.4 Msun
Mstar ~ 0.2 Msun
Mstar ~ 1 Msun
Preliminary conclusions: more massive stars have more massive
planets with higher frequency. Less massive stars have less
massive planets → planet formation is a sensitive function of the
planet mass.
Planets and the Properties of the Host Stars: The StarMetallicity Connection
Astronomer‘s
Metals
More Metals !
Even more Metals !!
The „Bracket“ [Fe/H]
Take the abundance of heavy elements (Fe for instance)
Ratio it to the solar value
Take the logarithm
e.g. [Fe/H] = –1 → 1/10 the iron abundance of the sun
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. This is
often used as evidence in favor of the core accretion theory
There are several problems with this hypothesis
Endl et al. 2007: HD 155358 two planets and..
…[Fe/H] = –0.68. This certainly muddles the metallicity-planet connection
The Hyades
The Hyades
• Hyades stars have [Fe/H] = 0.2
• According to V&F relationship 10% of the stars should have giant planets,
• Paulson, Cochran &
Hatzes surveyed 100
stars in the Hyades
• According to V&H
relationship we should
have found 10 planets
•We found zero
planets!
Something is funny about
the Hyades.
False Planets
or
How can you be sure that you have actually
discovered a planet?
HD 166435
In 1996 Michel Mayor announced at a conference in
Victoria, Canada, the discovery of a new „51 Peg“
planet in a 3.97 d. One problem…
HD 166435 shows the same period in in
photometry, color, and activity indicators.
This is not a planet!
What can mimic a planet in Radial Velocity Variations?
1. Spots or stellar surface structure
2.
Stellar Oscillations
3.
Convection pattern on the surface of the star
Starspots can produce Radial Velocity Variations
Spectral Line distortions
in an active star that is
rotating rapidly
Tools for confirming planets: Photometry
Starspots are much cooler than
the photosphere
Light Variations
Color Variations
Relatively easy to measure
Tools for confirming planets: Ca II H&K
Active star
Inactive star
Ca II H & K core emission is a measure of magnetic activity:
HD 166435
Ca II emission
measurements
Tools for confirming planets: Bisectors
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
Spots produce an „anti-correlation“ of Bisector
Span versus RV variations:
Correlation of bisector span with radial velocity for HD 166435
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
The Great 51 Peg Controversy, or
My personal piece of professional rubbish
Variations of Bisectors with Pulsations
The 51 Peg Controversy
Gray & Hatzes
Gray reported bisector
variations of 51 Peg
with the same period
as the planet. Gray &
Hatzes modeled these
with nonradial
pulsations
A beautiful paper that
was completely wrong.
Hatzes et al.
More and better bisector data for 51 Peg showed that the Gray measurements
were probably wrong. 51 Peg has a planet!
How do you know you have a planet?
1. Is the period of the radial velocity reasonable? Is it the
expected rotation period? Can it arise from pulsations?
•
E.g. 51 Peg had an expected rotation period of ~30
days. Stellar pulsations at 4 d for a solar type star
was never found
2. Do you have Ca II data? Look for correlations with RV
period.
3. Get photometry of your object
4. Measure line bisectors
5. And to be double sure, measure the RV in the infrared!
Radial Velocity Planets
Period in years → 30 90
Red line: Current detection limits
Green line detection limit for a precision of 1 m/s
1000
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
• ~5% 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 (more on this later in the course)
• < 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 orbital radii
• Stars with higher metallicity tend to have a higher frequency of planets, but this
needs confirmation