Transcript Asteroseismology and stellar rotation - IAG-Usp

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 spectrum
nnlm = frequency for a given oscillation mode: n, l , m
(l,m from a description with spherical harmonics Ylm)
• No rotation : nnl a 2l+1 degenerate mode (m=-l, l)
n0
• Rotation (W) breaks the azimuthal symetry , lifts the
degeneracy: 2l+1 modes (given n,l):
W
n-m
Rotational splitting:
Dnnlm = nnlm - nnl
n0
nm
to be measured
splitting
Dnnlm
rotation rate
= m  W(r,q) Knl(r,q) dq dr
= m
measured
Ws
Cnl
deduced
(Knl rotational kernel )
if uniform rotation
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:
How many splittings, what precision for what star?
Signal to noise ratio SNR
Splitting : Dn
G: width
T :observing time interval
Detection criterion:
Precision :
SNR > 9 and Dn/2p > G1+G0/2 ~ G0
s  ( T/G0) f(SNR) (Libbrecht 92)
How many splittings, what precision for what star?
Detection criterion:
Precision:
SNR > 9 and Dn/2p > G1+G0/2 ~ G0
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
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
LRa1 sismo
Be
B2III
B9V
B9ApV
B8IV
G5II
B0.5V
F1V
F2V
5.5<mv<9.5
F0V
solar-like
G0
solar-like
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 with i, W
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
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
Splitting with
uniform rotation
Level 2:
with
W(r) : Wc/Ws ~2
s (mHz)
Uncertainty
for detected
splittings
Vrot =13 km/s
s(mHz)
Vrot = 30 km/s
Colors = different inclination angle i
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 3
level 2
level 1
uncertainties DProt/Prot ~10-4
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
Summary
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
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. Rotation (Rossby number) – activity relation (periodic variability)
From A. Baglin
to day COROT
Activity level
versus
Stellar parameters
Ground
observations
Precision
10-2
photometric variability
convection, rotation, Ro
10 -2 -3
10 -4 -5
Prot
Sun
Extension of the knowledge of magentic activity to stars earlier than G8
1. Measurements of v sin i
(Royer et al 2002; Custiposto et al 2002)
Histograms:
F
A, B stars
G
K
100
v sin i (km/s)
10
30
v sin i (km/s)
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 of Prot versus distance from the ZAMS
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
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
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
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 !!!
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}
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)
•Tachocline: new abundances 
sound speed inversion : needs
rotational mixing ?
Give hints what to search for other stars
Result from inversion
OTHER STARS
b Cephei
d Scuti
g Doradus
WD
Solar-like
Oscillations
(F-G-K )
A ~ cm/s to ~ m/s
P ~ min-h
from C. Barban & MA Dupret
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
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.
e-m diagram
• Rapid rotation: structure: oblatness, meridional
circulation , chemical mixing : large e
•Slow rotation but W/w large
fast
moderate
small
Frequency of the component m of a multiplet of modes (n,l)
nm= n0+ m Wsurf C
no rot
Coriolis 1st order contr.
Surface rotation rate
Then the linear splitting is:
Generalized splitting:
dm =
nm-n(-m)
m
m
If
W uniform,
then dm/C = W is constant,
V m
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
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 ?
Rotating convective core of A stars
3 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
* 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
* 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
* 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
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)
Inversion for rotation
for d Scuti like oscillations
with mixed modes: access to Wc
(e Cep)
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
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
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 ..)
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
na nb
nbobs
repelling effect
2-10 mHz
0.5% -2%
Moderate rotation (DG92, Soufi et al, Goupil et al, Suarez et al)
l=2
cubic
deg
distorsion
pseudo rot +
Coriolis 1st
1.8 Msol 93 km/s
no rot
l=0
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
Non uniform rotation detectable with Corot ?
Uniform versus differential (depth) moderate rotation
ndiff
unif
-n
nlm
nlm
(mHz)
ndiff nlm-nunif nlm
l = 1 modes
m = 0, +1
Surface v ~ 100 km/s
Wcore/Wsurf ~ 2
differences > 1 mHz
from JC Suarez 04
radial order n
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
Solar like oscillators : slow rotators
Seismic data
from ground:
First seismic models:  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
Rotation forward and inversion possible
for 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
with Corot estimated performances
forward
from Lochard et al 04
FGK stars : slow rotators
but excited modes = high
frequency modes
ie small inertia,
more sensitive to surface properties
and rotation more efficient in
surface
l=2 l=0
l=3 l=1
20km/s
30km/s
• small separation na-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
50 km/s
Black dots W=0
Open dots W = 20, 30, 50 km/s
From Lochard et al 2004
To built a seimic model, fit the small separation
Small separation
nla,n-nlb,n-1
la=3, lb=1 modes
no
norotrot
~1.2 mHz
1mHz ~> 1Gy
rot
from Lochard et al 04
n (mHz)
rot
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
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 ?
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
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 ….
FIN
Rotating convective core of A stars
3 D simulations (Browning et al 2004)
2 Msol ; rotation 1/10 to 4 times Wsol
Rotating convective is nonhomogeneous
Rotating convective core is prolate
Overshoot from a rotating convective core
3D simulations:
Extension of overshoot modified by rotation
Rotation increases --> larger mixed region
Heat (enthalpy) flux
HD 12901 g Dor
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)
(Moya et al. 2004)
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
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)
--> Core rotates faster than envelope (surface 2 km/s)
Vaissala frequency
c/d
; x=r/R
Rotation kernels
p modes
g modes
Core
x=r/R
Surface
Vaissala pulsation : buoyancy restoring force/unit mass
From MA Dupret
ie linked to distorted structure quantities
Second order perturbation :
Add near degenerary
naobs
na nb
nbobs
What ? Rotation and related processes
PMS to compact objects
• 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 ?
Small to massive stars
• Massive stars : WR stages, yields
• Small and intermediate and mass stars
from M. Rieutord Aussois 04
from M. Rieutord Aussois 04