Radial Velocity Detection of Planets:
II. Results
1. Period Analysis
2. Global Parameters
3. Classes of Planets
Binary star simulator:
http://instruct1.cit.cornell.edu/courses/astro101/java/binary/binary.htm#instructions
The Nebraska Astronomy Applet Project (NAAP)
http://astro.unl.edu/naap/
This is the coolest astronomical website for learning basic
astronomy that you will find. In it you can find:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Solar System Models
Basic Coordinates and Seasons
The Rotating Sky
Motions of the Sun
Planetary Orbit Simulator
Lunar Phase Simulator
Blackbody Curves & UBV Filters
Hydrogen Energy Levels
Hertzsprung-Russel Diagram
Eclipsing Binary Stars
Atmospheric Retention
Extrasolar Planets
Variable Star Photometry
The Nebraska Astronomy Applet Project (NAAP)
On the Exoplanet page you can find:
1.
2.
3.
Descriptions of the Doppler effect
Center of mass
Detection
And two nice simulators where you can interactively change
parameters:
1. Radial Velocity simulator (can even
add data with noise)
2. Transit simulator (even includes
some real transiting planet data)
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 = 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
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
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
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
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/
Results from Doppler Surveys
Butler et al. 2006, Astrophysical Journal, Vol 646, pg 505
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“
Probably the first extrasolar planet: 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.
A short time-line of Radial Velocity (RV) Planet Discoveries
1979: Campbell und Walker use HF cell to survey 26 solar-type stars. They
find evidence for possible companions around e Eri and g Cep.
1989: Latham et al (1989) report 11 MJupiter companion round the star HD 114762.
1992: Wolszczan discovers planets around pulsars
1992: Walker et al. Publish the discovery of RV variations with 2,47 years in g Cep
can be due to a 1.5 MJupiter companion. They think it is due to stellar
rotation.
1993: Hatzes & Cochran report long period RV variations in 3 K giant stars.
Suggest planets may be one explanation
1995: Mayor & Queloz announce discovery of planet around 51 Peg
Today: over 300 known extrasolar planets
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
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
Argument against stars #2
Some planetary systems have multiple planets, for
example msini = 5 MJup, and msini = 0.03 MJup. To make
the first planet a star requires sini =0.01. Other planet
would still be mtrue=3 MJup
There mass distribution falls off exponentially.
N(20 MJupiter) ≈ 0.002 N(1 MJupiter)
There should be a large population of very 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
An Oasis in the Brown Dwarf Desert: HD 137510 = HR 5740
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
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
3. Classes of planets: 51 Peg Planets
Discovered by Mayor & Queloz 1995
How are we sure this is really a planet?
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)
So how do you form a Giant planet at 0.05 AU?
Prior to 1995 the standard model was:
• Giant planets form beyond the „ice line“ at 3-5 AU
• Enough ices to form a 10-13 MEarth core
• Once core forms it can accrete gaseous envelope
• Voila! A giant planet at > 5 AU
Solution:
• Form planet in ``normal´´
manner
• When planet has 1 MJ mass
tidal torques open a gap in the
disk
• Disk torques on the planet
cause it to migrate inwards
Timescales ~ 500.000 years
Trilling et al 1998
Problem for giant planet formation at 0.05 AU:
• At a < 0.1 AU disk is too hot for grains to form
• Too little solid material to form 10-15 Mearth core
• Too little gas to build envelope
Migration Theory is not without problems:
• What stops the migration?
• Jupiter should not exist!!
You will learn more from the planet formation part of
the course
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 discovered in 1989!
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:
Ca II is a measure of stellar activity (spots)
g Cephei
Planet
Periode
Msini
2,47 Years
1,76 MJupiter
e
a
K
0,2
2,13 AU
26,2 m/s
Binary
Periode
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
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.
Konacki (2005)
HD 188753
Binary Orbit
Planet Orbit
M1
= 1.06 s.m.
M2
= 0.96 s.m.
P
= 25.7 yrs
a
= 12.3 AU
m sin i
P
a
e
e
= 0.5
Disk truncated at 1.3 – 1.5 AU!
=
=
=
=
1.14 MJ
3.35 days
0.05 AU
0.0
Eggenberger et al. 2007
Eggenberger et al. 2007 could not confirm presence of planet
3. Planetary Systems
33 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: solar system planets
0.82MJ
•
•0.03M
J
The Planetary System around GJ 581
16 ME
7.2 ME
5.5 ME
Inner planet 1.9 ME
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)
Red points: Systems
Blue points: single planets
Mass versus
Orbital Distance
Eccentricities
Red points: Systems
Blue points: single planets
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
~10000 K
2 Msun
A5
F0
F5
G0
G5
Spectral Type
K0
K5
M0
~3500 K
0.2 Msun
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. Hot Neptunes around
M dwarfs seem common
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.
Result: few planets around early-type, more massive stars,
and these 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
HD 8673
An F4 V star from the
Tautenburg Program
P = 328 days
Msini = 8.5 Mjupiter
e = 0.24
Scargle Power
M* = 1.2 M‫סּ‬
Frequency (c/d)
The Tautenburg F-star Planets
Parameter
30 Ari B
HD 8673
Period (days)
e
K (m/s)
a (AU)
M sin i (MJup)
Sp. T
Stellar Mass (M‫)סּ‬
338
0.21
278
1.06
10.1
F4 V
1.4
1628
0.711
290
2.91
12.7
F7 V
1.2
Exoplanets around evolved massive stars
Difficult on the main sequence, easier (in principle) for evolved stars
A 1.9 M‫ סּ‬main sequence star
A 1.9 M‫ סּ‬K
giant star
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.
Mass of star = 1.9 x that of sun
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 is also a pulsating star
This explains the large scatter in the
RV measurements
From Michaela Döllinger‘s Ph.D 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
Blue points are results from Giant stars
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
Preliminary results from Surveys of Intermediate Mass Stars
• More massive stars have a higher frequency of planets
compared to solar type stars (~factor of two)
• More massive stars tend to have more massive planets
Jovian Analogs: Giant Planets at ≈ 5 AU
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
Expectations
Reality
1. Planets should be common
1. 5-10% of solar type stars have
Giant planetary companions
2. Giant planets at 5 AU
2. Giant planets have a wide range
of a down to a = 0.02
3. Planets are in circular orbits
3. Many planets with very
eccentric orbits.
4. One Jovian -mass planet
4. ESP systems can have several
Jovian-mass planets
Expectations based on one example are often wrong!