How seismology can help infer information on rotation (and related processes)

1. 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

2. 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)

3. 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

4. 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)

5. 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

6. 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

7. 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

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

9. 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 !!!

10. 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}

11. n0nlm = frequency for a given oscillation mode: n, l , m • No rotation : n0nl a2l+1 degenerate mode (m=-l, l) • Rotation breaks the azimuthal symetry , lifts the degeneracy: 2l+1 modes (given n,l): • n0nlm = n0nl + m W(r,q) Knl(r,q) d(solid angle) n0 W n-mn0 nm Rotational kernel

12. 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

13. 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

14. 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

15. 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.

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

17. 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

18. 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

19. 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 ?

20. 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

21. * 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

22. * 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

23. *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

24. 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)

25. Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot Corot

26. 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

27. 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

28. 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 ..)

29. Second order perturbation : Add near degeneracy (Endemic desease of pert.tech.: small denominator) Two modes with d = na (Yla) -nb (Ylb) ~ 0 then mode a contaminated by mode b naobs (Yla,Ylb) mode b contaminated by mode a nbobs (Ylb,Yla) --> naobs = n- (1/2) sqrt( d2+ H2) nbobs =n + (1/2) sqrt( d2+ H2) with n = (1/2) (na+nb) mean frequency d small separation ; H coupling coef. naobs nbobs na nb repelling effect 2-10 mHz 0.5% -2%

30. Moderate rotation (DG92, Soufi et al, Goupil et al, Suarez et al) l=2 l=0 cubic deg distorsion pseudo rot + Coriolis 1st 1.8 Msol 93 km/s no rot

31. Moderate rotator: recovering the rotation profile Generalized splittings dm = nm-n(-m)/m eliminate 2nd order poll. Combining splittings with different m eliminate cubic order poll. and allows to recover the rotation profile Here : red curve d1+d2/2 (input) uniform rotation 15.3 mHz Inversion : by iteration

32. Non uniform rotation detectable with Corot ? Uniform versus differential (depth) moderate rotation ndiffnlm-nunifnlm ndiffnlm-nunifnlm l = 1 modes m = 0, +1 (mHz) Surface v ~ 100 km/s Wcore/Wsurf ~ 2 differences > 1 mHz from JC Suarez 04 radial order n

33. FGK stars (solar like oscillators) v sin i measurements External convective zone and rotation : dynamo and J loss : spin down from the surface ie redistribution of ang. mom and chemicals Ex. HD 171488 (G0, 30 Myr) W~ 20 Wsol (Strassmeier et al 2003) --> slow rotators but … black dots v in i > 12 km/s open dots v sin i < 12 km/s

34. Solar like oscillators : slow rotators Seismic data from ground: First seismic models: a Cen, hBoo, Procyon Slow rotators then classical techniques with linear splittings: • not yet the splittings ! Splitting large enough to be detected • High frequency p-modes probe external layer rotation

35. Rotation forward and inversionpossiblefor high enough, evolved enough solar like oscillator stars 1.55 Msol • Mixed modes : a few indeed excited and detectable (h Boo type) access central rotation values but requires knowledge of a model close to the reality : seismic model forward with Corot estimated performances from Lochard et al 04

36. l=2 l=0 l=3 l=1 20km/s FGK stars : slow rotators but excited modes = high frequency modes ie small inertia, more sensitive to surface properties and rotation more efficient in surface • small separationna-nb affected by Wdegeneracy then echelle diagram affected is used for mode (l) identification then not affected (m=0 only) But with m components : a mess !!! FGK 30km/s 50 km/s Black dots W=0 Open dots W = 20, 30, 50 km/s From Lochard et al 2004

37. To built a seimic model, fit the small separation Small separation nla,n-nlb,n-1 la=3, lb=1 modes no rot no rot ~1.2 mHz 1mHz ~> 1Gy rot rot n (mHz) from Lochard et al 04

39. 1.54 Msol l=1,l=3 small separation polluted by rotation (65 km/s) Small separation free of rotation pollution recovered Small separation with no rotation

40. Get for free!: Vn = W(r) (Prot-Pnorot) yn dr eigenmode pressure Vn is a measurable seismic quantity and can be inverted for the distorted structure With a little extra work: Another quantity can be measurable with mixed modes: Sn= W(r) (rrot-rnorot) yn dr density --> Strength of baroclinicity grad P ^ grad r ?

41. Summary : with seismology what we really want is to detect and localize grad W Fast rotation = oblateness, baroclinic, shellular assumption ? Much better if we also have: * surface Prot or a relation between Prot and stellar parameters * Seismic model : (is wanted by itself and wanted for rotation determination) better use slow rotators if possible otherwise must remove pollution by rotation AND COROT data! Must use all what we have : seismic and nonseismic info complementary forward and inverse info

42. Further work before june 2006: • visibility, mode identification versus rotation • validity of perturbation techniques, 2D calculations • initial conditions: • rotation profile of slow rotators depends on its history • latitudinal dependence (observations from ground already) • warning!: probably not possible to consider W only by itself: • relation with B, activity, convection ….

43. FIN

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45. Rotating convective core of A stars3 D simulations (Browning et al 2004) 2 Msol ; rotation 1/10 to 4 times Wsol Rotating convective core is prolate Rotating convective is nonhomogeneous

46. Overshoot from a rotating convective core 3D simulations: Extension of overshoot modified by rotation Rotation increases --> larger mixed region Heat (enthalpy) flux

47. HD 12901 g Dor(Moya et al. 2004) • Long oscillation periods: g modes • Asymptotics yields radial order • Slow rotators •  Seismic models are built • (non unique) • Next : • use mode excitation (nonadiabatic) information • but must take into account effects of small W/w • (Dintrans, Rieutord, 2000)

48. The b Cepheid HD 129929 : (Dupret et al 04; Aerts et al 04) • Advantages: no external convective zone, • mode identification more fiable; • slow rotator: rotation as an advantage and not a problem; • mixed p-g modes ; splitting << large sep/2 • Inconvenients: long periods : 3h-8h 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

49. A triplet l=1 and some l=2 components yield : • dov = 0.1 +_ 0.05 • W = Wcore + (x-1) W1 = .0071334 - 0.0185619 (x-1) c/d ; x=r/R • --> Core rotates faster than envelope (surface 2 km/s) Vaissala frequency Rotation kernels p modes g modes Core Surface x=r/R Vaissala pulsation : buoyancy restoring force/unit mass From MA Dupret

50. ie linked to distorted structure quantities