Radial Velocity Detection of Planets: II. Results 1.Period Searching: How do you find planets in your data? 2.Exoplanet discoveries with the radial velocity method

Finding a Planet in your Radial Velocity Data 1. Determine if there is a periodic signal in your data. 2. Determine if this is a real signal and not due to noise. 3.Determine the nature of the signal, it might not be a planet! 4. Derive all orbital elements

1. Period Analysis How do you know if you have a periodic signal in your data? Here are RV data from a pulsating star What is the period?

Try 16.3 minutes:

Lomb-Scargle Periodogram of the data:

1. Period Analysis: How do you find a signal in your data 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 = amplitude 2 ) 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 3. 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

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 Amplitude (m/s)

Noise level Alias Peak False alarm probability ≈ 10 –14

Alias periods: Undersampled periods appearing as another period

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

2. Results from Doppler Surveys Butler et al. 2006, Astrophysical Journal, Vol 646, pg 505

TelescopeInstrumentWavelength Reference 1-m MJUOHerculesTh-Ar 1.2-m Euler TelescopeCORALIETh-Ar 1.8-m BOAOBOESIodine Cell 1.88-m Okayama Obs,HIDESIodine Cell 1.88-m OHPSOPHIETh-Ar 2-m TLSCoude EchelleIodine Cell 2.2m ESO/MPI La SillaFEROSTh-Ar 2.7m McDonald Obs.2dcoudeIodine cell 3-m Lick ObservatoryHamilton EchelleIodine cell 3.8-m TNGSARGIodine Cell 3.9-m AATUCLESIodine cell 3.6-m ESO La SillaHARPSTh-Ar 8.2-m Subaru TelescopeHDSIodine Cell 8.2-m VLTUVESIodine cell 9-m Hobby-EberlyHRSIodine cell 10-m KeckHiResIodine cell

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:

„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. The first extrasolar planet around a normal star: HD with Msini = 11 M J discovered by Latham et al. (1989)

The Brown Dwarf Desert Mass Distribution Global Properties of Exoplanets: Planet: M < 13 M Jup → no nuclear burning Brown Dwarf: 13 M Jup < M < ~80 M Jup → deuterium burning Star: M > ~80 M Jup → Hydrogen burning

Up-to-date Histograms with all planets:

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 M Jup for this to have a true mass of 0.5 M sun sin i would have to be This implies  = 0.6 deg or P = : highly unlikely! Argument against stars #1 Argument against stars #2 Some planetary systems have multiple planets, for example m 1 x sini = 5 M Jup, and m 2 x sini = 0.03 M Jup. To make the first planet a star requires sini =0.01. Other planet would still be m true =3 M Jup

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

An Oasis in the Brown Dwarf Desert: HD = HR 5740

A note on the naming convention: Name of the star: 16 Cyg If it is a binary star add capital letter B, C, D If it is a planet add small letter: b, c, d 55 CnC b : first planet to 55 CnC 55 CnC c: second planet to 55 CnC 16 Cyg B: fainter component to 16 Cyg binary system 16 Cyg Bb: Planet to 16 Cyg B The IAU has yet to agree on a rule for the naming of extrasolar planets

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 The short period planets are also a selection effect: they are the easiest to find and now transiting surveys are geared to finding these.

Updated:

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

e=0.4e=0.6e=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

Eccentricities Mass versus Orbital Distance There is a relative lack of massive close-in planets

Classes of planets: 51 Peg Planets: Jupiter mass planets in short period orbits Discovered by Mayor & Queloz 1995

~35% 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) Classes of planets: 51 Peg Planets

Another short period giant planet

Butler et al McArthur et al Santos et al Msini = M Earth Classes of planets: Hot Neptunes

If there are „hot Jupiters“ and „hot Neptunes“ it makes sense that there are „hot Superearths“ Mass = 7.4 M E P = 0.85 d CoRoT-7b

Classes: The Massive Eccentrics Masses between 7–20 M Jupiter Eccentricities, e > 0.3 Prototype: HD discovered in 1989! m sini = 11 M Jup

There are no massive planets in circular orbits Classes: The Massive Eccentrics

Planet-Planet Interactions Initially you have two giant planets in circular orbits These interact gravitationally. One is ejected and the remaining planet is in an eccentric orbit Lin & Ida, 1997, Astrophysical Journal, 477, 781L

Red: Planets with masses 4 M Jup

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 should we care about binary stars? Planets in Binary Systems

Some Planets in known Binary Systems: There are very few planets in close binaries. The exception is  Cep. For more examples see Mugrauer & Neuhäuser 2009, Astronomy & Astrophysics, vol 494, 373 and references therein

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

Walker et al. Excluded the planet hypothesis largely because the Ca II line strength showed variations with the same period as the velocity data. However, if you divide the Ca II in half (two time series) a signal is seen in the first half but not the last half. The signal in the last half is not the same period as the planet signal.

 Cephei Primary star (A) Secondary Star (B) Planet (b)

Neuhäuser et al. Derive an orbital inclination of AB of 119 degrees. If the binary and planet orbit are in the same plane then the true mass of the planet is 1.8 M Jup.

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.

The interesting Case of 16 Cyg B Effective Temperature: A=5760 K, B=5760 K Surface gravity (log g): 4.28, 4.35 Log [Fe/H]: A= 0.06 ± 0.05, B=0.02 ± Cyg B has 6 times less Lithium These stars are identical and are „solar twins“. 16 Cyg B has a giant planet with 1.7 M Jup in a 800 d period

Kozai Mechanism: One Explanation for the high eccentricty of 16 Cyg B Two stars are in long period orbits around each other. A planet is in a shorter period orbit around one star. If the orbit of the planet is inclined, the outer planet can „pump up“ the eccentricity of the planet. Planets can go from circular to eccentric orbits. This was first investigated by Kozai who showed that satellites in orbit around the Earth can have their orbital eccentricity changed by the gravitational influence of the Moon

Kozai Mechanism: changes the inclination and eccentricity

Planetary Systems: 49 Multiple Systems

49 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

The 5-planet System around 55 CnC 5.77 M J Red lines: solar system plane orbits 0.11 M J 0.17M J 0.03M J 0.82M J

The Planetary System around GJ M E 5.5 M E 16 M E Inner planet 1.9 M E

Can we find 4 planets in the RV data for GL 581? 1 = cycles/d 2 = = = Note: for Fourier analysis we deal with frequencies (1/P) and not periods

The Period04 solution: P1 = 5.38 d, K = 12.7 m/s P2 = d, K = 3.2 m/s P3 = 83.3 d, K = 2.7 m/s P4 = 3.15, K = 1.05 m/s P1 = 5.37 d, K = 12.5 m/s P2 = d, K = 2.63 m/s P3 = 66.8 d, K = 2.7 m/s P4 = 3.15, K = 1.85 m/s  =1.53 m/s  =1.17 m/s Almost: 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 sampling frequency Published solution:

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) Red points: Systems Blue points: single planets

Eccentricities Mass versus Orbital Distance Red points: Systems Blue points: single planets On average, giant planets in planetary sytems tend to be lighter than single planets. Either 1) Forming several planets in a protoplanetary disks „divides“ the mass so you have smaller planets, or 2) if you form several massive planets they are more likely to interact and most get ejected.

The Dependence of Planet Formation on Stellar Mass

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

2 planets with masses 2.1, 2.3 MJup 1 Planet with mass 4.9 MJup

GL 876 System 1.9 M J 0.6 M J Inner planet 0.02 M J

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: Only a few planets around early-type, more massive stars, and these are mostly around F-type stars (~ 1.4 solar masses)

Galland et al HD M * = 1.25 msini = 9.1 M Jupiter P = 388 days e = 0.34 F6 V star

HD 8673 A Planet around an F star from the Tautenburg Program

Frequency (c/d) Scargle Power P = 328 days Msini = 8.5 M jupiter e = 0.24 An F4 V star from the Tautenburg Program M * = 1.4 M סּ

M star ~ 1.4 M sun M star ~ 1 M sun M star ~ 0.2 M sun

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.

Astronomer‘s Metals More Metals ! Even more Metals !! Planets and the Properties of the Host Stars: The Star- Metallicity Connection

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

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. This is often used as evidence in favor of the core accretion theory Valenti & Fischer The Planet-Metallicity Connection? There are several problems with this hypothesis

Endl et al. 2007: HD two planets and.. …[Fe/H] = –0.68. This certainly muddles the metallicity-planet connection

The Hyades

Hyades stars have [Fe/H] = 0.2 According to V&F relationship 10% of the stars should have giant planets, The Hyades 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.

False Planets or How can you be sure that you have actually discovered a planet?

HD 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 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

Tools for confirming planets: Photometry Starspots are much cooler than the photosphere Light Variations Color Variations Relatively easy to measure

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

HD Ca II emission measurements

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 Tools for confirming planets: Bisectors

Correlation of bisector span with radial velocity for HD Spots produce an „anti-correlation“ of Bisector Span versus RV variations:

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

The Great 51 Peg Controversy, or My personal piece of professional rubbish

Variations of Bisectors with Pulsations

Gray & Hatzes Gray reported bisector variations of 51 Peg with the same period as the planet. Gray & Hatzes modeled these with nonradial pulsations A beautiful paper that was completely wrong. The 51 Peg Controversy

Hatzes et al. More and better bisector data for 51 Peg showed that the Gray measurements were probably wrong. 51 Peg has a planet!

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!

Radial Velocity Planets Period in years → Red line: Current detection limits Green line detection limit for a precision of 1 m/s

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 ~5% 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 (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