Extrasolar Planets and Stellar Oscillations in K Giant Stars Notes can be downloaded from

OBAFG KM Absolute Magnitude Luminosity (Solar Lum.) Effective Temparature Spectral Class White Dwarfs Main Sequence Giants Supergiants

Why the interest in K giants for exoplanets and asteroseismology? K giants occupy a „messy“ region of the H-R diagram Progenitors are higher mass stars Evolved A-F stars

The story begins: Smith et al found a 1.89 d period in Arcturus

1989 Walker et al. Found that RV variations are common among K giant stars These are all IAU radial velocity standard stars !!!

First, planets around K giants stars…

Hatzes & Cochran surveyed 12 K giants with precise radial velocity measurements

Footnote: Period Analysis 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

If a signal is present, for less noise (or more data) the power of the Scargle periodogram increases. This is not true with Fourier transform -> power is the related to the amplitude of the signal.

Many showed RV variations with periods of days

 Her has a 613 day period in the RV variations But what are the variations due to?

The nature of the long period variations in K giants Three possible hypothesis: 1.Pulsations (radial or non-radial) 2. Spots (rotational modulation) 3. Sub-stellar companions

What about radial pulsations? Pulsation Constant for radial pulsations: Q = P M MסּMסּ () 0.5 R RסּRסּ () –1.5 For the sun: Period of Fundamental (F) = 63 minutes = days (using extrapolated formula for Cepheids) Q = P  סּסּ () 0.5 =

Footnote: The fundamental radial mode is related to the dynamical timescale: d2Rd2R The dynamical timescale is the time it takes a star to collapse if you turn off gravity dt 2 = GM R2R2 Approximate: R  ≈ G  R  is the mean density For the sun  = 54 minutes  = (G  ) –0.5

What about radial pulsations? K Giant: M ~ 2 M סּ, R ~ 20 R סּ Period of Fundamental (F) = 2.5 days Q = Period of first harmonic (1H) = 1.8 day → Observed periods too long

What about radial pulsations? Alternatively, let‘s calculate the change in radius V = V o sin (2  t/P),  R =2 V o sin (2  t/P) = ∫ 0  /2 VoPVoP   Gem: P = 590 days, V o = 40 m/s, R = 9 R סּ  R ≈ 0.9 R סּ Brightness ~ R 2  m = 0.2 mag, not supported by Hipparcos photometry

What about non-radial pulsations? p-mode oscillations, Period < Fundamental mode Periods should be a few days → not p-modes g-mode oscillations, Period > Fundamental mode So why can‘ t these be g-modes? Hint: Giant stars have a very large, and deep convection zone

Recall gravity modes and the Brunt–Väisälä Frequency The buoyancy frequency of an oscillating blob: N 2 = g ( 1   P dPdP drdr – dd drdr ) g is local acceleration of gravity  is density P is pressure Where does this come from?     P dPdP dd () ad First adiabatic exponent

Brunt Väisälä Frequency ** 00 00  T  rr  Change in density of surroundings:  =  0 + ( dd drdr ) rr  * =  0 + ( dd dPdP ) rr Change in density due to adiabatic expansion of blob: dPdP drdr  * =  0 + ( 1 11 ) rr dPdP drdr  P

Brunt Väisälä Frequency ** 00 00  T  rr  Difference in density between blob and surroundings :  =  –  * = rr ( 1 11 ) dPdP drdr  P dd drdr – Buoyancy force f b = – g   r = –  ( 1  ) dd drdr 1 11 dPdP drdr P – F = –kx →  2 = k/m Recall This is just a harmonic oscillator with  2 = N 2 rr

Brunt Väisälä Frequency Criterion for onset of convection: However if  * < , the blob is less dense than its surroundings, buoyancy force will cause it to continue to rise ( 1 11 )  dPdP drdr  P dd drdr In convection zone buoyancy is a destabilizing force, gravity is unable to act as a restoring force → long period RV variations in K giants cannot be g modes

What about rotation? Spots can cause RV variations Radius of K giant ≈ 10 R סּ Rotation of K giant ≈ 1-2 km/s P rot ≈ 2  R/v rot P rot ≈ 250–500 days Its possible!

Rotation (and pulsations) should be accompanied by other forms of variability 1.Have long lived and coherent RV variations 2. No chromospheric activity variations with RV period 4. No spectral line shape variations with the RV period 3. No photometric variations with the RV period Planets on the other hand:

 Case Study  Gem CFHTMcDonald 2.1m McDonald 2.7mTLS

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

Ca II emission variations

Hipparcos Photometry

Test 2: Bisector velocity From Gray (homepage)

Spectral line shape variations

Period590.5 ± 0.9 d RV Amplitude40.1 ± 1.8 m/s e0.01 ± a1.9 AU Msin i2.9 M Jupiter The Planet around  Gem M = 1.7 M sun [Fe/H] = –0.07 The Star

Frink et al P = 1.5 yrs M = 9 M J

P = 711 d Msini = 8 M J Setiawan et al. 2005

Setiawan et al. 2002: P = 345 d e = 0.68 M sini = 3.7 M J

 Tau

 Tau has line profile variations, but with the wrong period Hatzes & Cochran 1998

Period653.8 ± 1.1 d RV Amplitude133 ± 11 m/s e0.02 ± 0.08 a2.0 Msin i10.6 M Jupiter The Planet around  Tau M = 2.5 M sun [Fe/H] = –0.34 The Star

 Dra

Period712 ± 2.3 d RV Amplitude134 ± 9.9 m/s e0.27 ± 0.05 a2.4 Msin i13 M Jupiter The Planet around  Dra? M = 2.9 M sun [Fe/H] = –0.14 The Star

Setiawan et al The evidence supports that the long period RV variations in many K giants are due to planets…so what?

B1I V F0 V G2 V

Planets around massive K giant stars  Dra –0.14  Tau –0.34

Period

Characteristics: 1. Supermassive planets: 3-11 M Jupiter Theory: More massive stars have more massive disks 2. Many are metal poor Theory: Massive disks can form planets in spite of low metallicity 3. Orbital radii ≈ 2 AU Theory: Planets in metal poor disks do not migrate because they take so long to form.

And now for the stellar oscillations…

Hatzes & Cochran 1994 Short period variations in Arcturus n = 1 (1H) n = 0 (F)

n 0 F 1 1H 2 2H

 Ari Alias n≈3 overtone radial mode

 Dra

 Dra : June 1992

 Dra : June 2005

 Dra

Photometry of a UMa with WIRE guide camera (Buzasi et al. 2000) Radial modes n =

Conclusion: most (all?) K giant stars pulsate in the radial and low-overtone modes. So what?

HD P = 471 d Msini = 14 M J M * = 3.5 s.m.

P = 4.8 days P = 2.4 days HD short period variations For M = 3.5 M סּ R = 38 R F = 4.8 d 2H = 2.7 d → oscillations can be used to get the stellar mass

Current work on K giants 1. TLS survey of 62 K giants (Döllinger Ph.D.) 2. Multi-site campaigns planned (GLONET) 3. MOST campaign on  Oph and  Gem 4. CoRoT additional science program (150 days of photometry) 5. Lots of theoretical work to model pulsations needs to be done

Döllinger Ph.D. work: 62 K giants surveyed from TLS ≈ 10% show long period variations that may be due to planetary companions

Time (days) Intensity 5.7 days Aldebaran with MOST

Summary K giant (IAU radial velocity standards) are RV variable stars! Multi-periodic on two time scales: days and 0.25 – 8 days Long period variations are most likely due to giant planets around stars with M star > 1 M סּ Short period variations are due to radial pulsations in the fundamental and overtone modes Pulsations can be used to get funamental parameters of star