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Extrasolar Planets and Stellar Oscillations in K Giant Stars Notes can be downloaded from www.tls-tautenburg.de→Teaching Spectral Class O B A F G K M -10 Supergiants -5 1.000.000 10.000 0 Giants 100 +5 1 +10 0.01 White Dwarfs 0.0001 +15 +20 20000 14000 10000 7000 5000 Effective Temparature 3500 2500 Why the interest in K giants for exoplanets and asteroseismology? Evolved A-F stars K giants occupy a „messy“ region of the H-R diagram Progenitors are higher mass stars The story begins: Smith et al. 1989 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… 1990-1993 Hatzes & Cochran surveyed 12 K giants with precise radial velocity measurements Footnote: Period Analysis Lomb-Scargle Periodogram: Px(w) = 1 2 [ S X cos w(t –t)] j j S 2 j 1 + 2 2 Xj cos w(tj–t) j tan(2wt) = [ S X sin w(t –t) ] j j j S Xj sin2 w(tj–t) (Ssin 2wtj)/ (Scos 2wtj) j j Power is a measure of the statistical significance of that frequency (period): False alarm probability ≈ 1 – (1–e–P)N = probability that noise can create the signal N = number of indepedent frequencies ≈ number of data points 2 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 200-600 days p 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= M 0.5 P( ) Mסּ R –1.5 (R ) = סּ P ( r 0.5 ) rסּ For the sun: Period of Fundamental (F) = 63 minutes = 0.033 days (using extrapolated formula for Cepheids) Q = 0.033 Footnote: The fundamental radial mode is related to the dynamical timescale: d2R dt2 GM = R2 The dynamical timescale is the time it takes a star to collapse if you turn off gravity Approximate: R t2 ≈GrR t = (Gr)–0.5 For the sun t = 54 minutes r is the mean density What about radial pulsations? K Giant: M ~ 2 M סּ, R ~ 20 Rסּ Period of Fundamental (F) = 2.5 days Q = 0.039 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 = Vo sin (2pt/P), p/2 DR =2 ∫ Vo sin (2pt/P) = VoP p 0 b Gem: P = 590 days, Vo = 40 m/s, R = 9 Rסּ DR ≈ 0.9 Rסּ Brightness ~ R2 Dm = 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: N2 =g G1 = ( ( 1 r dP G1 P dr r dP P dr )ad – dr dr ) First adiabatic exponent g is local acceleration of gravity r is density P is pressure Where does this come from? Brunt Väisälä Frequency r DT Dr r* Change in density of surroundings: r = r0 + Dr ( ) Dr Change in density due to adiabatic expansion of blob: r* = r0 + r0 dr dr ( dr dP dP dr ( 1 G1 r0 r* = r0 + r P ) Dr dP dr ) Dr Brunt Väisälä Frequency r Difference in density between blob and surroundings : DT Dr r* Dr = r – r* Dr = ( 1 G1 r P dP dr – dr dr 1 1 dr dP – = –r r dr G1 P dr ( r0 r0 Recall F = –kx ) Dr ) Dr Buoyancy force fb = – gDr dr → w2 = k/m This is just a harmonic oscillator with w2 = N2 Brunt Väisälä Frequency However if r* < r, the blob is less dense than its surroundings, buoyancy force will cause it to continue to rise Criterion for onset of convection: ( 1 G1 r P dP dr ) dr < dr 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? Radius of K giant ≈ 10 Rסּ Rotation of K giant ≈ 1-2 km/s Prot ≈ 2pR/vrot Prot ≈ 250–500 days Its possible! Spots can cause RV variations Rotation (and pulsations) should be accompanied by other forms of variability Planets on the other hand: 1. Have long lived and coherent RV variations 2. No chromospheric activity variations with RV period 3. No photometric variations with the RV period 4. No spectral line shape variations with the RV period Case Study: b Gem CFHT McDonald 2.1m McDonald 2.7m TLS 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 The Planet around b Gem Period RV Amplitude e a Msin i 590.5 ± 0.9 d 40.1 ± 1.8 m/s 0.01 ± 0.064 1.9 AU 2.9 MJupiter The Star M = 1.7 Msun [Fe/H] = –0.07 P = 1.5 yrs Frink et al. 2002 M = 9 MJ Setiawan et al. 2005 P = 711 d Msini = 8 MJ Setiawan et al. 2002: P = 345 d e = 0.68 M sini = 3.7 MJ a Tau Hatzes & Cochran 1998 a Tau has line profile variations, but with the wrong period The Planet around a Tau Period RV Amplitude e a Msin i 653.8 ± 1.1 d 133 ± 11 m/s 0.02 ± 0.08 2.0 10.6 MJupiter The Star M = 2.5 Msun [Fe/H] = –0.34 g Dra The Planet around g Dra? Period RV Amplitude e a Msin i 712 ± 2.3 d 134 ± 9.9 m/s 0.27 ± 0.05 2.4 13 MJupiter The Star M = 2.9 Msun [Fe/H] = –0.14 The evidence supports that the long period RV variations in many K giants are due to planets…so what? Setiawan et al. 2005 B1I V F0 V G2 V Planets around massive K giant stars g Dra 2.9 13 2.4 712 0.27 –0.14 a Tau 2.5 10.6 2.0 654 0.02 –0.34 Period Characteristics: 1. Supermassive planets: 3-11 MJupiter 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 1 2 F 1H 2H a Ari Alias n≈3 overtone radial mode g Dra g Dra : June 1992 g Dra : June 2005 g Dra Photometry of a UMa with WIRE guide camera (Buzasi et al. 2000) Radial modes n = 0 1 2 3 Conclusion: most (all?) K giant stars pulsate in the radial and low-overtone modes. So what? HD 13189 P = 471 d Msini = 14 MJ M* = 3.5 s.m. P = 4.8 days For M = 3.5 Mסּ R = 38 R F = 4.8 d 2H = 2.7 d → oscillations can be used to get the stellar mass HD 13189 short period variations P = 2.4 days 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 b Oph and b 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 Aldebaran with MOST Intensity 5.7 days Time (days) Summary • K giant (IAU radial velocity standards) are RV variable stars! • Multi-periodic on two time scales: 200-600 days and 0.25 – 8 days • Long period variations are most likely due to giant planets around stars with Mstar > 1 Mסּ • Short period variations are due to radial pulsations in the fundamental and overtone modes • Pulsations can be used to get funamental parameters of star