Radial Velocity Detection of Planets: II. Observations 1. Period Analysis 2. Global Parameters 3. Classes of Planets 4. Dependence on Stellar Parameters 5. Sources of Noise Lecture notes: Click on Teaching -> lectures -> Extrasolar Planets Binary star simulator: Also:

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 =  d i –g i ) 2 /N d i = data, g i = 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(  ) =  X j (T) e –i  t N0N0 j=1 A DFT gives you as a function of frequency the amplitude (power) of each sine wave that is in the data Power: P x (  ) = | FT X (  )| 2 1 N0N0 P x (  ) = 1 N0N0 N 0 = number of points [(  X j cos  t j +  X j sin  t j ) ( ) ] 2 2 Recall e i  t = cos  t + i sin  t X(t) is the time series

A pure sine wave is a delta function in Fourier space t P AoAo FT  AoAo 1/P

1. Period Analysis 2. Lomb-Scargle Periodogram: Power is a measure of the statistical significance of that frequency (period): 1 2 P x (  ) = [  X j sin  t j –  ] 2 j  X j sin 2  t j –  [  X j cos  t j –  ] 2 j  X j cos 2  t j –  j 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 2  t j )/  cos 2  t j ) 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 Amplitude (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 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 – Mass Distribution Global Properties of Exoplanets Planet: M < 13 M Jup → no nuclear burning Brown Dwarf: 13 M Jup < M < ~70 M Jup → deuterium burning Star: M > ~70 M Jup → Hydrogen burning

N(20 M Jupiter ) ≈ N(1 M Jupiter ) There mass distribution falls off exponentially. There should be a large population of low mass planets. Brown Dwarf Desert: Although there are ~ Brown dwarfs as isolated objects, and several in long period orbits, there is a paucity of brown dwarfs (M= 13 – 50 M Jup ) in short (P < few years) as companion to stars

Semi-Major Axis Distribution Semi-major Axis (AU) Number The lack of long period planets is a selection effect since these take a long time to detect

2. Eccentricity distribution

e=0.4e=0.6e=0.8  =0  =90  =180

2 ´´  Eri

Eccentricities Mass 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

~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 McArthur et al. 2004Santos et al Msini = M Earth 3. Classes of planets: Hot Neptunes

3. Classes: The Massive Eccentrics Masses between 7–20 M Jupiter Eccentricities, e>0.3 Prototype: HD m sini = 11 M Jup

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

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 M Jupiter Msini 2,47 JahrePeriode Planet 18.5 AEa 0,42 ± 0,04e 1,98 ± 0,08 km/sK ~ 0,4 ± 0,1 M Sun Msini 56.8 ± 5 JahrePeriode Doppelstern  Cephei

Primärstern Sekundärstern Planet

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) M J sini a (AU) e HD GL UMa HD CnC Ups And HD HD HD Star P (d) M J sini a (AU) e HD HD HD HD HD HD HD HD HD  Ara: 4 planets

Resonant Systems Systems Star P (d) M J sini a (AU) e HD GL CnC HD HD :1 → Inner planet makes two orbits for every one of the outer planet → → 2:1 →3:1 →4:1 →2:1

Eccentricities Period (days)

Eccentricities Mass versus Orbital Distance

4. The Dependence of Planet Formation on Stellar Mass Setiawan et al. 2005

A0 A5 F0 F5 RV Error (m/s) G0G5 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 P = 1.5 yrs M = 9 M J

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 M Jup.

HD P = 471 d Msini = 14 M J M * = 3.5 M sun

Period471 ± 6 d RV Amplitude173 ± 10 m/s e0.27 ± 0.06 a1.5 – 2.2 AU m sin i14 M Jupiter Sp. Type K2 II – III Mass3.5 M sun V sin i2.4 km/s HD HD b

HD : 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 M Jupiter P = 272 d Msini = 6.6 M J e = 0.53 M * = 1.2 M סּ P = 159 d Msini = 3 M J e = 0.03 M * = 1.15 M סּ P = 477 d Msini = 3.8 M J e = 0.37 M * = 1.0 M סּ P = 517 d Msini = 10.6 M J e = 0.09 M * = 1.84 M סּ P = 657 d Msini = 10.6 M J e = 0.60 M * = 1.2 M סּ P = 1011 d Msini = 9 M J e = 0.08 M * = 1.3 M סּ

M (M סּ ) N Stellar Mass Distribution: Döllinger Sample Mean = 1.4 M סּ Median = 1.3 M סּ ~10% of the intermediate mass stars have giant planets

Eccentricity versus Period

M sin i (M jupiter ) N Planet Mass Distribution for Solar-type Dwarfs P> 100 d Planet Mass Distribution for Giant and Main Sequence stars with M > 1.1 M סּ 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 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] Percent 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 M Jupiter 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 M Jupiter Orbital plane coincides with dusty ring plane Benedict et al: HST Astrometry on  Eri

One of our planets is missing: HD P = 2173 d Msini = 10.2 M Jup i = 4 deg → m = 142 M Jup

Velocity (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 Endl et al. can exclude 1 M earth 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

Correlation of bisector span with radial velocity for HD

Ca II H & K core emission is a measure of magnetic activity: Active star Inactive star

HD 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 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 M סּ 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