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?

An oscillating star: time variability L(t) --> power spectrumnlm = frequency for a given oscillation mode: n, l , m (l,m from a description with spherical harmonics Ylm)

• No rotation : nl a 2l+1 degenerate mode (m=-l, l)

• Rotation () breaks the azimuthal symetry , lifts the degeneracy: 2l+1 modes (given n,l):

Rotational splitting:nlmnlm - nl to be

measured

-

mm

splitting rotation rate

nlm = m r Knl(r,) d dr (Knl rotational kernel )

= m s Cnl if uniform rotation measured deduced

Two cases:•Opacity driven oscillations: Scuti, Cep, Dor .., masses > ~ 1.5 MsolLarge 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 ?

A damped triplet l=1 modes:

Resolved triplet Non resolved triplet

Signal to noise ratio SNRSplitting : widthT :observing time interval

How many splittings, what precision for what star?

Detection criterion: SNR > 9 and > 1+0/2 ~ 0

Precision : ( T/) f(SNR) (Libbrecht 92)

SNR = funct(A1, noise level (app. mag(distance)) )

(SNR = SNR0 10(m-5.7) ; SNR0 = funct(A1,) (Corot specification) ) A1/A0 = funct(visibility (inclination angle)) A0, 0 = funct(mass, age) T = 150 days or 20 days observing time interval = funct()

Input: mass(luminosity), age (Teff), distance, ,i, T

Output: splitting detected, precision of measurement

How many splittings, what precision for what star?

Detection criterion: SNR > 9 and > 1+0/2 ~ 0

Precision: ( T/) f(SNR) (Libbrecht 92)

Selected models in HR diagram: 4 TAMS models and one ZAMS model, p3Ori

1.2 Mo 1.3Mo 1.4 Mo

Signal to Noise Ratio

Number of detected splittings increases with mass and age

LRa1 sismoB2IIIBe

F0V solar-like

G0 solar-like

B0.5V

F1V

B9V

B9ApV

G5II

F2V

B8IV

5.5<mv<9.5

width Hz

(for v=10,20,30 km/s)

3Ori

v=10 km/s

v=20km/s

v=30 km/s

Uncertainty of splitting measurement (Hz)

Colours correspond to detected splittings for different inclination angle

Number of detected splittings increase withi

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

Many splittings detected.Only a few correct within 0.5 Hz and with error bars < 0.5 Hz

Differences between input splitting values from simulation (Roxburgh, Barban) and output splitting values from blind analysis (Appourchaux)

3 levels:

level 1: Only a few modes Prot as an average: Prot

-1 = (1/N) j=1,N (j + j)

level 2: Enough splittings with enough precision for a forward indication of r-variation rotation profile (r)

level 3: Enough accurate splittings with appropriate nature for successful inversion process

3. What amount of information upon rotation ?

Vrot =13 km/s

Vrot = 30 km/s

Level 2:

(Hz)

Uncertaintyfor detected splittings

Hz

Splitting with uniform rotation

withrcs

Colors = different inclination angle i

Blue: 1.5 Msol TAMS model

i > 60° v =30 km/s

Red: 1.3 Msol TAMS model

level 1level 2level 3

Prot,split - Protsurfture ~ a few hours

For nonuniform rotationProtsurfture ~ days core/surf ~ 2

uncertainties Prot/Prot ~10-4

Summary

Pessimist view :Testing rotation analogous to the solar case is going to be difficultInstrumental noise, stellar activity 'noise' not included

Optimist view: Assumed core/surf ~ 2 seems to be conservative, underestimation

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 ((r) ) (Lochard, 2005)~ perhaps a few 10 for forward technique (hint for (r) )~ a few more for Prot (but independent of activity, spots)

Summary

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

Ultimate goal: determine (r,,t)

from PMS to compact object

for small to large mass stars

COROT: significant advances in the field expected

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.

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)

to day COROT

Activity level photometric variability 10 -2 -3 10 -4 -5

versusStellar parameters convection, rotation, Ro Prot

Extension of the knowledge of magentic activity to stars earlier than G8

Sun

Ground observationsPrecision 10-2

From A. BaglinFrom A. Baglin

3. Rotation (Rossby number) – activity relation (periodic variability)

1. Measurements of v sin i (Royer et al 2002; Custiposto et al 2002)

A, B stars

v sin i (km/s)

100

F

G

K

3010

v sin i (km/s)

Histograms:

2. Determination of surface rotation period: Prot

Detection of spots , activity levelLatitude 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 mechanismsv/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 of Prot versus distance from the ZAMS

One star -- many periods

Seismology : rotation

Depth dependence(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

Diagnostic of transport processes inside stars

(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

We want to identify

region of uniform rotation and region of differential rotation (depth, latitude dependence)

inside the star (core/surf)

This depends on the type of star

Small and intermediate mass main sequence stars

•Intermediate and large mass (OBA) stars: •no or thin external convective zone --> no loss of angular momentum --> intermediate and fast rotators

Schematically :• PMS stars: I varies a lot

•Small mass (FGK) stars – : external convective zone --> stellar wind - magnetic breaking--> loss of angular momentum --> slow rotators

COROT will tell: a bit too simplified view !!!

Determination of rotation profile: seismic diagnostics with forward and inversion techniques

Forward:

compute from a model, given and compare with obs

Inversion:

compute <rfrom appropriate combinations of {obs}

Solar Case

•Latitudinal in convective region: B, tachocline

•Uniform in radiative region: transport of J : meridional

circulation + turbulent shear : not sufficient add B ?

(Zahn and Co)

Result from inversion

•Tachocline: new abundances

sound speed inversion : needs

rotational mixing ?

Give hints what to search for other stars

Solar-like Oscillations

(F-G-K )

A ~ cm/s to ~ m/s

P ~ min-hfrom C. Barban & MA Dupret

Cephei

Scuti

Doradus

WD

OTHER STARS

Other stars

other problems ! Unknown : mass, age, X, Z, , iphysics, (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

Axisymetric --> (r,) --> (r) = < (r,) >horiz

We must distinguish fast, moderate and slow rotators :

= G R3) centrifugal over gravitational = / coriolis / oscillation period

- Slow ( <<1 ) : first order perturbation is enough

- Intermediate ( ~ < 0.5) : higher order contributions necessary

- Fast ( > 0.5) : 2D eq. models + nonperturbative osc. app.

- diagram• Rapid rotation: structure: oblatness, meridional circulation , chemical mixing : large

•Slow rotation but / large

moderate

small

fast

Then the linear splitting is:

Frequency of the component m of a multiplet of modes (n,l)

no rotCoriolis 1st order contr.

Surface rotation rate

If uniform, then m/C = is constant, V m

Generalized splitting:

mm = m-(-m)

m

m= 0+ m surf C

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

DBV GD358: Non uniform (depth) rotation:

Winget et al 1991

Winget et al 1994 --> Kepler

A, B type stars

Extension of mixed inner region for rotating convective core ? overshoot + rotation will depend on the type of stars , on each star ?

• a slow rotator Cepheid

• a Dor star : small but also !

• Rapid rotators : Scuti type (PMS , MS, post MS)

v sin i= 70-250 km/s =up to 0.3

Not discussed here :

Ro Ap stars slow rotators but indirect effect of rotation Rapid rotators B, Be ---> A.M. Hubert

Rotating convective core is prolate

Rotating convective core of A stars3 D simulations (Browning et al 2004)

2 Msol ; rotation 1/10 to 4 times sol

Differential rotation ()for convective core

Heat (enthalpy) flux

increases --> larger mixed region

rc = 0.1 R*r0 = 0.15 R*

* a 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• core/ surf = 3.6--> Core rotates faster than envelope (Ps = 140 d; surface 2 km/s)

4 frequencies : no standard model fits, asymetric multiplets core = 3 surf (Pamyatnykh et al 2004)

but 2 different studies: different conclusions ---->>

Nonstandard physics in stellar models: diffusion, rotational distorsion

Eri (Ausseloos 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 (Dintrans, Rieutord,2000)

P < 3 days second order pert. tech no longer valid

DaDor (Moya et al. 2004)

spectroscopic binary slow rotator Prot known

3 frequencies nonuniform rotation (core >> surf)

overshoot versus synchronisation of inner layers

Asymetric multiplet (2nd order)

weak point: mode identification

* GX Peg a Scuti (Goupil at al 1993)

many frequencies , no standard model fit

slow rotator ? some l known but m ? Same for other cases

* FG Vir (Breger et al …, many works over the last 10 y)

hence Scuti stars require theoretical developements in order to be ready for

Corot and 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)

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

Inversion for rotationfor Scuti like oscillations

with mixed modes: access to c

Needs a model as close as possible to reality: a seismic model from •model = input model: squares•model is not input model: crosses

Assume Corot performances but done only with linear splittingsNo distorsion effects included

Cep)

input : 1.8 Msol 7588K 120 km/sused : 1.9 Msol 7906K 0 km/s

2nd order : O(2): Coriolis + centrifugal force: on wavesAND distorsion of the star

geff pseudo rotating model 1D / 1,5 D / 2D models

nonspherical distorsion on waves

Effects of rotationally induced mixing on structure (1,5 D)

Vaissala frequency Tracks in a HR diagram (FG Vir)

From Zahn92; Talon, Zahn 97 and many other work since then

convective corelog Teff

log L/Lsol

implemented in some ev. codes , soon in Cesam (Morel, Moya ..)

Second order perturbation :

a b

aobs b

obs

Add near degeneracy

Two modes with = a (Yla) -b (Ylb) ~ 0 thenmode a contaminated by mode b a

obs (Yla,Ylb)mode b contaminated by mode a b

obs (Ylb,Yla)--> a

obs = - (1/2) sqrt( 2+ H2)b

obs = + (1/2) sqrt( 2+ H2)

with = (1/2) (a+b) mean frequencysmall separation ; H coupling coef.

(Endemic desease of pert.tech.: small denominator)

repelling effect

2-10 Hz

0.5% -2%

Moderate rotation (DG92, Soufi et al, Goupil et al, Suarez et al)

l=2 l=0

no rot

pseudo rot +Coriolis 1st

deg

distorsion

cubic

1.8 Msol 93 km/s

Moderate rotator: recovering the rotation profile

(input) uniform rotation 15.3 mHz

Combining splittings with different m eliminate cubic order poll. and allows to recover the rotation profile

Here : red curve 1+2/2

Inversion : by iteration

Generalized splittings m = m-(-m)/meliminate 2nd order poll.

Non uniform rotation detectable with Corot ?Uniform versus differential (depth) moderate rotation

Hz) diff nlm-unif nlm

l = 1 modes m = 0, +1

from JC Suarez 04

Surface v ~ 100 km/score/surf ~ 2

diff nlm-unif nlm

radial order n

differences > 1 Hz

FGK stars (solar like oscillators)

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) ~ 20 sol

(Strassmeier et al 2003)

--> slow rotators but … black dots v in i > 12 km/s

open dots v sin i < 12 km/s

v sin i measurements

Solar like oscillators : slow rotators

Splitting large enough to be detected • not yet the splittings !

Seismic data from ground:

First seismic models: Cen, Boo, Procyon Slow rotators then classical techniques with linear splittings:

•High frequency p-modes probe external layer rotation

Rotation forward and inversion possible

for high enough, evolved enough solar like oscillator stars

• Mixed modes : a few indeed excited and detectable

Boo type)

access central rotation values

but requires knowledge of a model close to the reality : seismic model

1.55 Msol

with Corot estimated performances from Lochard et al 04

forward

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 separation a-b affected by degeneracy

then echelle diagram affected

is used for mode (l) identification then not affected (m=0 only)But with m components : a mess !!!FGK

From Lochard et al 2004

l=2 l=0 l=3 l=1

Black dots =0Open dots = 20, 30, 50 km/s

20km/s

30km/s

50 km/s

To built a seimic model, fit the small separation

la=3, lb=1 modes

z

no rot

rot

Small separationla,n-lb,n-1

~1.2 Hz

rot

no rot

from Lochard et al 04

1Hz ~> 1Gy

l=1,l=3 small separation polluted by rotation (65 km/s)

Small separation free of rotation pollution recovered

Small separation with no rotation

1.54 Msol

Vn = (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:

S = (r) (rot-norot) yn dr

density

--> Strength of baroclinicity grad P ^ grad

Get for free!:

Summary : with seismology what we really want is to detect and localize grad 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

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 only by itself:

relation with B, activity, convection ….

FIN

Rotating convective core of A stars3 D simulations (Browning et al 2004)

2 Msol ; rotation 1/10 to 4 times sol

Rotating convective core is prolate Rotating convective is nonhomogeneous

Overshoot from a rotating convective core

3D simulations:

Extension of overshoot modified by rotation

Rotation increases --> larger mixed region

Heat (enthalpy) flux

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 (Dintrans, Rieutord, 2000)

DDor (Moya et al. 2004)

• 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

The 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

From MA Dupret

A triplet l=1 and some l=2 components yield : • dov = 0.1 +_ 0.05• = core + (x-1) 1 = .0071334 - 0.0185619 (x-1) c/d ; x=r/R --> Core rotates faster than envelope (surface 2 km/s)

Rotation kernelsVaissala frequency

x=r/RCore Surface

Vaissala pulsation : buoyancy restoring force/unit mass

p modes

g modes

ie linked to distorted structure quantities

Second order perturbation :

a b

aobs b

obs

Add near degenerary

• PMS: protostars rotate fast. Interaction with disk ?

Spin down, spin up phases ?• End of life: - mass loss mechanisms ?

- rotation of remnants WD ?

- asymmetric nebulae ?

- role of rotation of pre-supernova central stars ?

What ? Rotation and related processes

PMS to compact objects

• Massive stars : WR stages, yields • Small and intermediate and mass stars

Small to massive stars

from M. Rieutord Aussois 04

from M. Rieutord Aussois 04