Seismic measurements of stellar rotation with Corot: theoretical expectations and HH results

1. Seismic measurements of stellar rotation with Corot: theoretical expectations and HH results Goupil, Samadi, Barban, Dupret, (Obs. Paris) Appourchaux (IAS) and Corot sismo HH3 group 1. What can we expect upon detection , precision of splitting measurements ? 2. Illustration : results from one HH exercise: HD 49933 3. What amount of information upon rotation can we expect?

2. An oscillating star: time variability L(t) --> power spectrum • nnlm = frequency for a given oscillation mode: n, l , m (l,m from a description with spherical harmonics Ylm) • No rotation : nnl a2l+1 degenerate mode (m=-l, l) • Rotation (W) breaks the azimuthal symetry , lifts the degeneracy: 2l+1 modes (given n,l): • Rotational splitting: Dnnlm = nnlm - nnl to be measured n0 W n-mn0 nm

3. splitting rotation rate Dnnlm =m W(r,q) Knl(r,q) dq dr (Knlrotational kernel ) = m Ws Cnl if uniform rotation measureddeduced

4. Two cases: • Opacity driven oscillations: d Scuti, b Cep, gDor .., masses > ~ 1.5 Msol • Large amplitudes, fast rotators, infinite lifetime: 'zero' width • Detection, precision : easy but who is who ? Mode identification pb • Stochastically excited, damped oscillations: solar like : • Sun, a Cen, Procyon, n Boo, HD49933 • Small amplitude, 'slow' rotators, finite lifetime: width • Detection? precision ? Resolved triplet Non resolved triplet A damped triplet l=1 modes:

5. How many splittings, what precision for what star? Signal to noise ratio SNR Splitting : Dn G: width T :observing time interval Detection criterion: SNR > 9 and Dn/2p > G1+G0/2 ~ G0 Precision : s ( T/G0) f(SNR) (Libbrecht 92)

6. How many splittings, what precision for what star? Detection criterion: SNR > 9 andDn/2p > G1+G0/2 ~ G0 Precision: s ( T/G0) f(SNR) (Libbrecht 92) SNR = funct(A1, noise level (app. mag(distance)) ) (SNR = SNR0 10(m-5.7) ; SNR0 = funct(A1,G0) (Corot specification) ) A1/A0 = funct(visibility (inclination angle)) A0, G0, W = funct(mass, age) T = 150 days or 20 days observing time interval Dn = funct(W) Input: mass(luminosity), age (Teff), distance, W,i, T Output: splitting detected, precision of measurement

7. Selected models in HR diagram: 4 TAMS models and one ZAMS model, p3Ori Signal to Noise Ratio 1.2 Mo 1.3Mo 1.4 Mo 9 Number of detected splittings increases with mass and age

8. Be B2III B9V B9ApV B8IV G5II B0.5V F0V solar-like F1V G0 solar-like F2V LRa1 sismo 5.5<mv<9.5

9. p3Ori width G (mHz) Dn (for v=10,20,30 km/s) s Uncertainty of splitting measurement s (mHz) v=10 km/s s v=20km/s s v=30 km/s Colours correspond to detected splittings for different inclination angle Number of detected splittings increase withi, W

10. Illustrative case: HH3 HD49933 (1.4 Msol, 6700 K) Target for Corot --> HH exercise --> Observed from ground with Harps(Mosser et al 2005): detection of solar like oscillation Differences between input splitting values from simulation (Roxburgh, Barban) and output splitting values from blind analysis (Appourchaux) Many splittings detected. Only a few correct within 0.5 mHz and with error bars < 0.5 mHz

12. 3. What amount of information upon rotation ? • 3 levels: • level 1: Only a few modes Prot as an average: • Prot-1 = (1/N) Sj=1,N (Dnj + ej) • level 2: Enough splittings with enough precision for a forward indication of r-variation rotation profile W(r) • level 3: Enough accurate splittings with appropriate nature for successful inversion process

13. Splitting with uniform rotation with W(r) : Wc/Ws ~2 Level 2: s (mHz) Uncertainty for detected splittings Vrot =13 km/s s(mHz) Vrot = 30 km/s Colors = different inclination angle i

14. Blue: 1.5 Msol TAMS model i > 60° v =30 km/s Red: 1.3 Msol TAMS model Prot,split - Protsurfture ~ a few hours For nonuniform rotation Protsurfture ~ days Wcore/Wsurf ~ 2 level 1 level 2 level 3 uncertainties DProt/Prot ~10-4

15. Summary Most favorable cases: relatively massive (1.4-1.6 Msol), cool, brightest, relatively high v sin i (high v and/or high i) ~ 5 Corot stars for inversion (W(r) ) (Lochard, 2005) ~ perhaps a few 10 for forward technique (hint for W(r) ) ~ a few more for Prot (but independent of activity, spots) Pessimist view : Testing rotation analogous to the solar case is going to be difficult Instrumental noise, stellar activity 'noise' not included Optimist view: Assumed Wcore/Wsurf ~ 2 seems to be conservative, underestimation

16. FIN

21. Summary

24. How seismology can help infer information on rotation (and related processes) Goupil, MJ, Observatoire de Paris Lochard J., Samadi R., Moya A., Baudin F., Barban C.,Baglin A. French-spanish connection: Suarez JC., Dupret M., Garrido R. Ultimate goal: determine W (r,q,t) from PMS to compact object for small to large mass stars COROT: significant advances in the field expected

25. One info (Prot surf) -- many stars Statistical studies: relations rotation - others quantities 1. Rotation- light elements abundance- convection ---------->> José Dias do Nascimento 2. Age - rotation (v sin i) in young clusters 3 . Rotation (Rossby number) – activity relation (periodic variability)

26. 3.Rotation (Rossby number) – activity relation (periodic variability) From A. Baglin to day COROT Activity level photometric variability 10 -2 -3 10 -4 -5 versus Stellar parameters convection, rotation, Ro Prot Ground observations Precision 10-2 Sun Extension of the knowledge of magentic activity to stars earlier than G8

27. How ? Histograms: 1. Measurements of v sin i (Royer et al 2002; Custiposto et al 2002) F A, B stars G K 100 v sin i (km/s) 30 10 v sin i (km/s)

28. 2. Determination of surface rotation period: Prot Detection of spots , activity level Latitude differential rotation (Petit et al 2004 , Donati et al 2003, Reiners et al 2003, Strassmeier 2004) MS massive stars (9 -20 Msol): Meynet, Maeder (04) evolution of surface rotation affected by mass loss and internal transport mechanisms v/vcrit ~ 0.9 (Townsend et al. 04) --> vesc ~cs nonradial puls. driven wind (Owocki 04) --> AM Hubert Mass loss or transport mechanism is dominant in influencing Prot depending on the mass of the star (M >12 <12Msol) Determination ofProt versus distance from the ZAMS

29. One star -- many periods Seismology: rotation Diagnostic of transport processes inside stars Depth dependence W(r): 2 extreme cases: * uniform rotation * conservation of local angular momentum Reality is somewhere in-between depending on the mass and age of the star

30. W(t) = J(t) / I(t) Rotation profile inside a star is representative of redistribution of angular momentum J from one stellar region to another : • caused by evolution: contractions and dilatations of stellar regions: I(t) • caused by dynamical and thermal instabilities: meridional circulation, differential rotation and turbulence: J(t) • caused by surface losses by stellar winds (B, thermal) or surface gain by interaction with surrounding : J(t) These processes cause chemical transport which in turn affects the structure and evolution of the star

31. We want to identify region of uniform rotation and region of differential rotation (depth, latitude dependence) inside the star (Wcore/Wsurf) This depends on the type of star

32. Small and intermediate mass main sequence stars • Schematically : • PMS stars: I varies a lot • Small mass (FGK) stars – • : external convective zone • --> stellar wind - magnetic breaking • --> loss of angular momentum • --> slow rotators • Intermediate and large mass (OBA) stars: • no or thin external convective zone --> • no loss of angular momentum --> • intermediate and fast rotators COROT will tell: a bit too simplified view !!!

33. How ? --> seismology Determination of rotation profile: seismic diagnostics with forward and inversion techniques Forward: compute n from a model, given W and compare with nobs Inversion: compute <W>(r) from appropriate combinations of {nobs}

34. SolarCase • Latitudinal in convective region: B, tachocline • Uniform in radiative region: transport of J : meridional • circulation + turbulent shear : not sufficient add B ? • (Zahn and Co) • Tachocline: new abundances  • sound speed inversion : needs • rotational mixing ? Give hints what to search for other stars Result from inversion

35. OTHER STARS b Cephei d Scuti g Doradus Solar-like Oscillations (F-G-K ) A~cm/s to ~m/s P~min-h WD from C. Barban & MA Dupret

36. Other stars •  other problems ! • Unknown : mass, age, X, Z, , W, i , physics, (n,l,m) •  new philosophy • Efforts developed from ground: we must use multisite • observations, multitechniques, • i.e. use seismic and non seismic information • To built a seismic model (non unique solution) • (determine all unknown quasi at the same time) • serves at improving -determination of stellar parameters ie ages • -test different physical prescriptions • gives a model closer to reality for iteration and inversion techniques

37. Axisymetric --> W(r,q) --> W(r) = < W(r,q) >horiz We must distinguish fast, moderate and slow rotators : e = W2 / (GM/ R3) centrifugal over gravitational m = W/w coriolis / oscillation period - Slow (e, m <<1 ) : first order perturbation is enough - Intermediate (e, m ~ < 0.5) : higher order contributions necessary - Fast (e, m> 0.5) : 2D eq. models + nonperturbative osc. app.

38. e-m diagram • Rapid rotation: structure: oblatness, meridional circulation , chemical mixing : large e • Slow rotation but W/w large fast moderate small

39. Frequency of the component m of a multiplet of modes (n,l) nm= n0+ mWsurf C Coriolis 1st order contr. no rot Surface rotation rate Generalized splitting: Then the linear splitting is: dm = nm-n(-m) m m If Wuniform, then dm/C = W is constant, V m

40. Variable white dwarfs PG1159-035 oscillate with asymptotic g modes Mode identification rather easily Many l=1 triplets and l=2 multiplets Weakly sensitive to depth variation of W DBV GD358: Non uniform (depth) rotation: Winget et al 1991 Winget et al 1994 --> Kepler

41. A, B type stars • a slow rotator b Cepheid • a g Dor star : W small but w also ! • Rapid rotators : d Scuti type (PMS , MS, post MS) • v sin i= 70-250 km/s e =up to 0.3 • Not discussed here : • Ro Ap stars slow rotators but indirect effect of rotation Rapid rotators B, Be ---> A.M. Hubert Extension of mixed inner region for rotating convective core ? overshoot + rotation will depend on the type of stars , on each star ?

42. Rotating convective core of A stars3 D simulations (Browning et al 2004) 2 Msol ; rotation 1/10 to 4 times Wsol Differential rotation (q)for convective core rc = 0.1 R* r0= 0.15 R* W increases --> larger mixed region Rotating convective core is prolate Heat (enthalpy) flux

43. * a b Cepheid HD 129929 : (Dupret et al 04; Aerts et al 04) Lot of effort ! : multisite observations + multitechniques then frequencies + location in HR diagram + mode identification (l degree) + nonadiabatic (n order) then Seismic models can be built • A triplet l=1 and some l=2 components yield : • dov = 0.1 +_ 0.05 • Wcore/ Wsurf = 3.6 • --> Core rotates faster than envelope (Ps = 140 d; surface 2 km/s) * n Eri (Ausseloos et al 2004) 4 frequencies : no standard model fits, asymetric multiplets Wcore = 3 Wsurf (Pamyatnykh et al 2004) but 2 different studies: different conclusions ---->> Nonstandard physics in stellar models: diffusion, rotational distorsion e

44. * HD 12901 a g Dor(Moya et al. 2004) • Long oscillation periods: g modes: asymptotics yields radial order •  Seismic models can be built (non unique) • (v sin i 53-66 km/s; Prot =1,15 d) • use mode excitation (nonadiabatic) information • but must take into account effects of large W/w (Dintrans, Rieutord,2000) • P < 3 days second order pert. tech no longer valid

45. *GX Peg a d Scuti(Goupil at al 1993) spectroscopic binary  slow rotator Prot known 3 frequencies  nonuniform rotation (Wcore >> Wsurf)  overshoot versus synchronisation of inner layers  Asymetric multiplet (2nd order) weak point: mode identification * FG Vir (Breger et al …, many works over the last 10 y) many frequencies , no standard model fit slow rotator ? some l known but m ? Same for other cases

46. d Scuti stars • Short periods, mixed modes (turn off of isochrones) • Rapid rotators: location in HR diagram visibility of modes, mode identification mode excitation, selection • Time dependent convection • hence d Scuti stars require theoretical developements • in order to be ready for • Corot and d stars in clusters ! • in progress : • multisite, multi-techniques • mode identification: more secure time dependent convection • (Dupret et al 04, Dazynska et al 04) • include rotation: moderate (Meudon group) , fast (Rieutord, Lignieres)

47. Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot

48. COROT COROT Inversion for rotationfor d Scuti like oscillations (e Cep) with mixed modes: access to Wc • Needs a model as close as possible • to reality: a seismic model • W from • model = input model: squares • model is not input model: crosses Assume Corot performances but done only with linear splittings No distorsion effects included input : 1.8 Msol 7588K 120 km/s used : 1.9 Msol 7906K 0 km/s

49. 2nd order : O(W2): Coriolis + centrifugal force: on waves AND distorsion of the star nonspherical distorsion on waves geff pseudo rotating model 1D / 1,5 D / 2D models

50. Effects of rotationally induced mixing on structure(1,5 D) From Zahn92; Talon, Zahn 97 and many other work since then Tracks in a HR diagram (FG Vir) Vaissala frequency log L/Lsol log Teff convective core implemented in some ev. codes , soon in Cesam (Morel, Moya ..)