Radial Velocity Detection of Planets:II. Observations

1. Period Analysis

2. Global Parameters3. Classes of Planets4. Dependence on Stellar Parameters5. Sources of Noise

Lecture notes: www.tls-tautenburg.de

Click on Teaching -> lectures -> Extrasolar Planets

http://instruct1.cit.cornell.edu/courses/astro101/java/binary/binary.htm#instructions

Binary star simulator:

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(t + ) + Constant

Where = 2/P, = phase shift

Best fit minimizes the 2:

2 = 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

FT() = Xj (T) e–itN0

j=1

A DFT gives you as a function of frequency the amplitude (power) of each sine wave that is in the data

Power: Px() = | FTX()|2

1

N0

Px() =

1

N0

N0 = number of points

[( Xj cos tj + Xj sin tj ) ( ) ]2 2

Recall eit = cos t + i sint

X(t) is the time series

A pure sine wave is a delta function in Fourier space

t

P

Ao

FT

Ao

1/P

1. Period Analysis

2. Lomb-Scargle Periodogram:

Power is a measure of the statistical significance of that frequency (period):

1

2Px() =

[ Xj sin tj–]2

j

Xj sin2 tj–

[ Xj cos tj–]2

j

Xj cos2 tj–j

+1

2

False alarm probability ≈ 1 – (1–e–P)N = probability that noise can create the signal

N = number of indepedent frequencies ≈ number of data points

tan(2) = sin 2tj)/cos 2tj)j j

Least squares sine fitting: The best fit period (frequency) has the lowest 2

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

Am

plit

ude

(m/s

)

Noise level

Alias Peaks

False alarm probability ≈ 10–14

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.

False alarm probability ≈ 0.24

Raw data

After removal of dominant period

Campbell & Walker: The Pioneers of RV Planet Searches

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.

1988:

The Brown Dwarf Desert

e–0.3

2. Mass Distribution

Global Properties of Exoplanets

Planet: M < 13 MJup → no nuclear burning

Brown Dwarf: 13 MJup < M < ~70 MJup → deuterium burning

Star: M > ~70 MJup → Hydrogen burning

N(20 MJupiter) ≈ 0.002 N(1 MJupiter)

There mass distribution falls off exponentially.

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

Semi-Major Axis Distribution

Semi-major Axis (AU) Semi-major Axis (AU)N

umbe

r

Num

ber

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

=0

=90

=180

2 ´´

Eri

EccentricitiesMass versus Orbital Distance

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:

What can change bisectors:• Spots• Pulsations • Convection pattern on star

Span

Curvature

The David Gray Controversy

If the bisector variations were real then 51 Peg has no planet

Gray & Hatzes 1997

Hatzes et al. : No bisector variations

The final proof that these are really planets:

The first transiting planet HD 209458

• ~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: 51 Peg Planets

Butler et al. 2004

McArthur et al. 2004 Santos et al. 2004

Msini = 14-20 MEarth

3. Classes of planets: Hot Neptunes

3. Classes: The Massive Eccentrics

• Masses between 7–20 MJupiter

• Eccentricities, e>0.3

• Prototype: HD 114762

m sini = 11 MJup

There are no massive planets in circular orbits

3. Classes: The Massive Eccentrics

• 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?

Why search for planets in binary stars?

3. Classes: Planets in Binary Systems

Star a (AU)16 Cyg B 80055 CnC 540

HD 46375 300Boo 155 And 1540

HD 222582 4740HD 195019 3300

Some Planets in known Binary Systems:

Nurture vs. Nature?

The first extra-solar Planet may have been found by

Walker et al. in 1992 in a

binary system:

2,13 AEa

0,2e

26,2 m/sK

1,76 MJupiterMsini

2,47 JahrePeriode

Planet

18.5 AEa

0,42 ± 0,04e

1,98 ± 0,08 km/sK

~ 0,4 ± 0,1 MSunMsini

56.8 ± 5 JahrePeriode

Doppelstern Cephei

Cephei

Primärstern

SekundärsternPlanet

The planet around 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 Cep this disk is truncated just at the ice line. No ice line, no solid core, no giant planet to migrate inward. 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 30 0.6 0.1 0.27 61 2.0 0.2 0.10

47 UMa 1095 2.4 2.1 0.06 2594 0.8 3.7 0.00

HD 37124 153 0.9 0.5 0.20 550 1.0 2.5 0.4055 CnC 2.8 0.04 0.04 0.17 14.6 0.8 0.1 0.0 44.3 0.2 0.2 0.34 260 0.14 0.78 0.2 5300 4.3 6.0 0.16Ups And 4.6 0.7 0.06 0.01 241.2 2.1 0.8 0.28 1266 4.6 2.5 0.27HD 108874 395.4 1.36 1.05 0.07

1605.8 1.02 2.68 0.25HD 128311 448.6 2.18 1.1 0.25 919 3.21 1.76 0.17HD 217107 7.1 1.37 0.07 0.13 3150 2.1 4.3 0.55

Star P (d) MJsini a (AU) eHD 74156 51.6 1.5 0.3 0.65 2300 7.5 3.5 0.40

HD 169830 229 2.9 0.8 0.31 2102 4.0 3.6 0.33

HD 160691 9.5 0.04 0.09 0 637 1.7 1.5 0.31

2986 3.1 0.09 0.80

HD 12661 263 2.3 0.8 0.35

1444 1.6 2.6 0.20

HD 168443 58 7.6 0.3 0.53 1770 17.0 2.9 0.20HD 38529 14.31 0.8 0.1 0.28 2207 12.8 3.7 0.33HD 190360 17.1 0.06 0.13 0.01 2891 1.5 3.92 0.36HD 202206 255.9 17.4 0.83 0.44 1383.4 2.4 2.55 0.27HD 11964 37.8 0.11 0.23 0.15

1940 0.7 3.17 0.3

Ara: 4 planets

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 0.6 0.1 0.27 61 2.0 0.2 0.10

55 CnC 14.6 0.8 0.1 0.0 44.3 0.2 0.2 0.34

HD 108874 395.4 1.36 1.05 0.07 1605.8 1.02 2.68 0.25

HD 128311 448.6 2.18 1.1 0.25 919 3.21 1.76 0.17

2:1 → Inner planet makes two orbits for every one of the outer planet

→

→

2:1

2:1

→ 3:1

→ 4:1

→ 2:1

•

Eccentricities

Period (days)

EccentricitiesMass versus Orbital Distance

4. The Dependence of Planet Formation on Stellar Mass

Setiawan et al. 2005

A0 A5 F0 F5

RV

Err

or (

m/s

)

G0 G5 K0 K5 M0

Spectral Type

Main Sequence Stars

Ideal for 3m class tel. Too faint (8m class tel.). Poor precision

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

„…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.“

Hatzes & Cochran 1993

Frink et al. 2002

P = 1.5 yrs

M = 9 MJ

CFHT

McDonald 2.1m

McDonald 2.7m TLS

The Planet around Pollux

The RV variations of 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

Period 471 ± 6 d

RV Amplitude 173 ± 10 m/s

e 0.27 ± 0.06

a 1.5 – 2.2 AU

m sin i 14 MJupiter

Sp. Type K2 II–III Mass 3.5 Msun

V sin i 2.4 km/s

HD 13189 HD 13189 b

HD 13189 : Short Term Variations

Diploma work of Mathias Zechmeister

Discovery of Stellar Oscillations in Gem

From Michaela Döllinger‘s thesis

M sin i = 3.5 – 10 MJupiter

P = 272 d

Msini = 6.6 MJ

e = 0.53

M* = 1.2 Mּס

P = 159 d

Msini = 3 MJ

e = 0.03

M* = 1.15 Mּס

P = 477 d

Msini = 3.8 MJ

e = 0.37

M* = 1.0 Mּס

P = 517 d

Msini = 10.6 MJ

e = 0.09

M* = 1.84 Mּס

P = 657 d

Msini = 10.6 MJ

e = 0.60

M* = 1.2 Mּס

P = 1011 d

Msini = 9 MJ

e = 0.08

M* = 1.3 Mּס

0

1

2

3

4

5

6

7

8

9

10

1.05 1.25 1.45 1.65 1.85 2.05 2.25 2.45

M (Mּס)

NStellar Mass Distribution: Döllinger Sample

Mean = 1.4 Mּס

Median = 1.3 Mּס~10% of the intermediate mass stars have giant planets

Eccentricity versus Period

0

1

2

3

4

5

6

7

1 3 5 7 9 11 13 15

M sin i (Mjupiter)

N

Planet Mass Distribution for Solar-type Dwarfs P> 100 d

0

10

20

30

40

50

1 3 5 7 9 11 13 15

Planet Mass Distribution for Giant and Main Sequence stars with M > 1.1 Mּס

More massive stars tend to have a more massive planets and at a higher frequency

Astronomer‘s

Metals

More Metals !

Even more Metals !!

4. The Planet-Metallicity Connection?

These are stars with metallicity [Fe/H] ~ +0.3 – +0.5

There is believed to be a connection between metallicity and planet formation. Stars with higher metalicity tend to have a higher frequency of planets.

Valenti & Fischer

4. The Planet-Metallicity Connection?

Endl et al. 2007: HD 155358 two planets and..

…[Fe/H] = –0.68. This certainly muddles the metallicity-planet connection

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

Planet-Metallicity Effect in Giant stars?

[Fe/H]

Per

cent

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)

In other words we have yet to find one. Long term surveys (+15 years) have excluded Jupiter mass companions at 5AU in ~45 stars

Period = 14.5 yrs

Mass = 4.3 MJupiter

e = 0.16

• Long period planet

• Very young star

• Has a dusty ring

• Nearby (3.2 pcs)

• Astrometry (1-2 mas)

• Imaging (m =20-22 mag)

• Other planets?

Eri

Clumps in Ring can be modeled with a planet here

(Liou & Zook 2000)

Radial Velocity Measurements of Eri

Large scatter is because this is an active star

Hatzes et al. 2000

Scargle Periodogram of Eri Radial velocity measurements

False alarm probability ~ 10–8

Scargle Periodogram of Ca II measurements

• Mass = 1.55 MJupiter

• Orbital plane coincides with dusty ring plane

Benedict et al: HST Astrometry on Eri

One of our planets is missing:

HD 33636

P = 2173 d

Msini = 10.2 MJup

i = 4 deg → m = 142 MJup

Vel

ocit

y (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

A Habitable Super Earth?

P=5.4 d

P=12.9 d

P=83.6 d

Some are in habitable zone of M dwarf

Lovis et al. 2007

Endl et al. can exclude 1 Mearth planet in habitable zone of Barnard‘s star

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

5. Sources of „Noise“

• Spots, plage, etc can cause RV Variations in active stars

•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

HD 166435

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

RV changes can be as large as 10 m/s with an 11 year period

This is a Jupiter!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

Setiawan et al. 2007

The Planet around TW Hya

And my doubts…

Maximum RV variations in the velocity span is ~500 m/s

The claim is no bisector variations in this star

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 Mּס have 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