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Radial Velocity Detection of Planets:
II. Results
1. Mutiple Planets
2. The Planet-Metallicity connection
3. Fake Planets
Planetary Systems: 41 Multiple Systems
41 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
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 frequency
Measurements from two telescopes: AAT (red) and Keck (blue)
s = 2.17 m/s
The Planetary System around 61 Vir?
Note: a 0.895 m/s offset was applied to the AAT data
The Period04 solution:
P1 55.5 d, K = 1.2 m/s
Published solution:
P1 = 4.214 d, K = 2.09 m/s
P2 = 3.8 d, K = 1.2 m/s
P2 = 38.01 d, K = 3.58 m/s
P3 = 39 d, K = 1.14 m/s
P3 = 124 d, K = 3.18 m/s
s = 2.02 m/s
s = 2.17 m/s
With different periods and amplitudes (and the same number
of sine functions) we have come up with a better solution.
Problem #1
Largest peak is at 55 d,
second peak is at 3.8 d, not
4.2 d. The False Alarm
Probability of the 3.8 d
peak is 0.004. I only believe
planets with FAP << 0.001
Problem #2
Removing first two signals
gives a peak at 39 d, but I
do not believe it!
AAT Data only
Peak at 55 d (0.018
c/d), but nothing
signficant at 4.2 d
(0.24 c/d)
Remove the strongest
peak and get two signals
at 0.033 c/d (30 d, moon
contamination?) and
another at 0.26 c/d (3.8
d), but smaller peak at
4.44 d
Keck Data only
Peak at 10.3 d
(0.097c/d)
Remove the
dominant peak and
residuals show a peak
at 4.26 d (0.24 c/d)
AAT
Keck
?
AAT
Keck
Conclusions about the „Planetary
System“ around 61 Vir
1.
Combined data shows a 3.8 d period, not 4.26 d
2. AAT data shows 3.8 d peak
3. Individual data sets do not show either 39 d, or 124 d
signal
There might be a signal at ~4 d, but the fact that different
data sets give different answers makes me doubt this
The other two „planets“ are noise
→ This is not a robust or confirmed planetary system because
a different approach gives an entirely different answer!
„The first principle is that you must not fool
yourself – and you are the easiest person to fool.“
- Richard Feynman
RV (m/s)
The CoRoT-7 Planetary System
JD
Radial Velocity Measurements of CoRoT-7b with HARPS. CoRoT-7b is a
transiting planet discovered by CoRoT. The additional planets were
found from the radial velocity follow up.
44
The RV variations are dominated by the stellar activity. This must
be removed in order to find the planet(s) signal(s).
CoRoT-7b
CoRoT-7c
P = 3.7 Days
Mass = 12.4 ME
P = 0.85 Days
Mass = 6.9 ME
CoRoT-7d
P = 9 Days
Mass = 16.7 ME
0.045 AU
0.017 AU
CoRoT-7d
CoRoT-7b
CoRoT-7c
0.082 AU
47
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
Crazy idea: If you divide the disk mass among
several planets, they each have a smaller mass
The Dependence of Planet Formation on Stellar Mass
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.
Currently too few planets around M dwarfs to make any real
conclusions
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: 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)
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
As we will see later, more massive stars tend to have
more massive planets.
M ~ 1.4 Msun
M ~ 0.2 Msun
M ~ 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.
Jovian Analogs: Giant Planets at ≈ 5 AU
Definition: A Jupiter mass planet in a 11 year orbit (5.2 AU)
One of the better candidates:
Period = 14.5 yrs
Mass = 4.3 MJupiter
e = 0.16
Why care about Jupiter analogs?
There is a lot of junk in the solar
system and in the past there was
more.
b Pic: A young star with
planets
e Eri: A young stars
with a planet(s)
And sometimes this junk
hits something.
On Jupiter you get big
holes.
On the Earth it can destroy
most of life.
What would the Solar System Look Like
without Jupiter?
G. Wetherill asked this question and through numerical
simulations establised:
• The gravitational influence of Jupiter quickly
removes most of the junk from the solar system.
• Without Jupiter the frequency of a cataclysmic
collision like the one that killed off the dynosaurs
would occur every 100.000 years instead of every
150.000.000 Years
Conclusion: Jupiters at 5 AU may be important for the
development of intelligent life!
A good Jovian analog but with a lot
of junk, and in an eccentric orbit
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. It has been argued
that this is not a planet at all, but rather the signal due to activity.
Scargle Periodogram of e Eri Radial velocity measurements
False alarm probability ~ 10–8
Scargle Periodogram of Ca II measurements
Period
Msini
6.85 Years
1.55 MJupiter
e
a
K
0.7
3.39 AU
19 m/s
The Best Candidates
Planet
Mass
(MJup)
Period
(years)
a
(AU)
e
HD 187123c
1.99
10.4
4.89
0.25
HD 13931b
1.88
11.3
5.15
0.02
HD 160691e
1.81
11.5
5.2
0.1
HD 217107c
2.49
11.5
5.27
0.51
55 Cnc c
3.83
14.3
5.77
0.02
HD 134987 c
0.82
13.7
5.8
0.12
Jupiter
1
11.9
5.2
0.05
Note: These are the best candidates for direct imaging
Wittenmyer et al. Combined data from 2 programs (McDonald
and CFHT) to get a time base of over 23 years (probes to 8
AU). Could exclude M sin i > 2.0 ± 1.1 MJup for 17 objects
(frequency < 6%)
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.
Something else is funny about the Hyades:
Spitzer observations of the Hyades suggest that the
fraction of stars in the Hyades with debris disks is
comparable to old field stars and significantly less than
for stars with planets.
→ In the cluster environment of the Hyades,
whatever something removed the disks so planets
could not form.
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
Oscillations can produce Radial Velocity Variations
P = 4.8 days
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
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:
Where does this emission core come from?
Keep in mind:
1. Strong spectral lines are formed higher up in the atmosphere
2. The core of a line is formed higher up than the wings.
The core of the line is formed
in the chromosphere where
the temperature is higher
Dl
(Å)
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
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!
In a Galaxy (The Milky Way) a long time ago (1990) I
did some simulations. I new that active stars had polar
spots and I asked the question: „What would the RV
and bisector variations look like for a star with a polar
spot viewed nearly pole on. My results (from memory):
1. The RV curve is nearly sinusoidal
2. There are virtually no bisector span variations
detectable at resolving power R =100,000
3. The largest effect is in the bisector curvature, but
high resolution is needed to detect this. R ´= 50,000
(resolving power of TW Hya measurements) is too
low.
• 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)
From my lecture of 2009: What is needed to
confirm this:
1. Contemporaneous photometry (but this
star has a disk and complicated light
variations)
2. RV measurements in the infrared where
the spot contrast is smaller.
Il =
2hc2
1
l5 (exp(hc/lkT) – 1)
(exp(hc/lkTp) – 1)
Ispot/Iphotosphere =
(exp(hc/lkTs) – 1)
Tspot ≈ 3000 K
Tspot ≈ 5000 K
At 5500 Å contrast ratio = 0.03
At 1.5 mm contrast ratio = 0.25 → weaker distortions in
line profile
Figueira et al. 2010, Astronomy and Astrophysics, 511, 55
A constant star
Points: IR measurements, Solid line is the
orbital solution using optical radial velocity
measurements, but with one-third the
optical amplitude → No planet!
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
Why I think CoRoT-7b is a 3 planet System
Another source of „Fake Planets“
Secular changes in proper motion:
Small proper
motion
Perspective effect
Large proper
motion
The Secular Acceleration of
Barnard‘s Star (Kürster et
al. 2003).
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!
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 (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