Radial Velocity Detection of Planets:II. Results

1. Period Analysis

2. Global Parameters3. Classes of Planets

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

Binary star simulator:

The Nebraska Astronomy Applet Project (NAAP)

This is the coolest astronomical website for learning basic astronomy that you will find. In it you can find:

1. Solar System Models 2. Basic Coordinates and Seasons 3. The Rotating Sky 4. Motions of the Sun 5. Planetary Orbit Simulator 6. Lunar Phase Simulator 7. Blackbody Curves & UBV Filters 8. Hydrogen Energy Levels 9. Hertzsprung-Russel Diagram 10. Eclipsing Binary Stars 11. Atmospheric Retention 12. Extrasolar Planets

13. Variable Star Photometry

http://astro.unl.edu/naap/

The Nebraska Astronomy Applet Project (NAAP)

On the Exoplanet page you can find:

1. Descriptions of the Doppler effect2. Center of mass3. 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(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 = amplitude2) 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

The first Tautenburg Planet: HD 13189

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 Peak

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

To summarize the period search techniques:

1. Sine fitting gives you the 2 as a function of period. 2 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

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:

„Probable third body variation of 25 m s–1, 2.7 year period, superposed on a large velocity gradient“

Campbell, Walker, & Yang 1988

Eri was a „probable variable“

Filled circles are data taken at McDonald Observatory using the telluric lines at 6300 Ang.

Probably the first extrasolar planet: HD 114762 with Msini = 11 MJ discovered by Latham et al. (1989)

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 Cep can be due to a 1.5 MJupiter companion. They think it is due to stellar rotation.

1995: Mayor & Queloz announce discovery of planet around 51 Peg

Today: over 300 known extrasolar planets

1993: Hatzes & Cochran report long period RV variations in 3 K giant stars.Suggest planets may be one explanation

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

One argument: Because of unknown vsini these are just low mass stars seen with i near 0

i decreasing

probability decreasing

P(i < ) = 1-cos Probability an orbit has an inclination less than

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 #1

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

N(20 MJupiter) ≈ 0.002 N(1 MJupiter)

There mass distribution falls off exponentially.

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

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

Fall off at high eccentricity may be partially due to an observing bias…

e=0.4 e=0.6 e=0.8

=0

=90

=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!

2 ´´

Eri

Comparison of some eccentric orbit planets to our solar system

At opposition with Earth would be 1/5 diameter of full moon, 12x brighter than Venus

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?

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

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

Trilling et al 1998Timescales ~ 500.000 years

• 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

Problem for giant planet formation at 0.05 AU:

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

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 discovered in 1989!

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:

Ca II is a measure of stellar activity (spots)

2,13 AUa

0,2e

26,2 m/sK

1,76 MJupiterMsini

2,47 YearsPeriode

Planet

18.5 AUa

0,42 ± 0,04e

1,98 ± 0,08 km/sK

~ 0,4 ± 0,1 MSunMsini

56.8 ± 5 YearsPeriode

Binary 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.

M1 = 1.06 s.m.

M2 = 0.96 s.m.

P = 25.7 yrs

a = 12.3 AU

e = 0.5

m sin i = 1.14 MJ

P = 3.35 days

a = 0.05 AU

e = 0.0

Konacki (2005)

Disk truncated at 1.3 – 1.5 AU!

Binary Orbit Planet Orbit

HD 188753

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 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

The 5-planet System around 55 CnC

5.77 MJ

Red: solar system planets

•0.11 MJ ••

0.17MJ

0.03MJ

0.82MJ

The Planetary System around GJ 581

7.2 ME

5.5 ME

16 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 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)Red points: SystemsBlue points: single planets

EccentricitiesMass versus Orbital Distance

Red points: SystemsBlue points: single planets

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

~10000 K ~3500 K

2 Msun 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

Frequency (c/d)

Sca

rgle

Pow

erP = 328 days

Msini = 8.5 Mjupiter

e = 0.24

An F4 V star from the Tautenburg Program

M* = 1.2 Mּס

Parameter 30 Ari B HD 8673

Period (days) 338 1628

e 0.21 0.711

K (m/s) 278 290

a (AU) 1.06 2.91

M sin i (MJup) 10.1 12.7

Sp. T F4 V F7 V

Stellar Mass (Mּס) 1.4 1.2

The Tautenburg F-star Planets

Exoplanets around evolved massive stars

Difficult on the main sequence, easier (in principle) for evolved stars

A 1.9 Mּס main sequence star

A 1.9 Mּס K giant star

„…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.

Mass of star = 1.9 x that of sun

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 is also a pulsating star

This explains the large scatter in the RV measurements

From Michaela Döllinger‘s Ph.D 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

Blue points are results from Giant stars

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

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)

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

Expectations based on one example are often wrong!

Expectations

1. Planets should be common

2. Giant planets at 5 AU 3. Planets are in circular orbits 4. One Jovian -mass planet

Reality

1. 5-10% of solar type stars have Giant planetary companions 2. Giant planets have a wide range of a down to a = 0.02 3. Many planets with very eccentric orbits. 4. ESP systems can have several Jovian-mass planets