A tool to simulate COROT light-curves
R. Samadi1 & F. Baudin2
1: LESIA, Observatory of Paris/Meudon2: IAS, Orsay
Purpose :
to provide a tool to simulate CoRoT light-curves of the seismology channel.
Interests : ● To help the preparation of the scientific analyses● To test some analysis techniques (e.g. Hare and Hound exercices) with a validated tool available for all the CoRoT SWG.
Public tool: the package can be downloaded at :http://www.lesia.obspm.fr/~corotswg/simulightcurve.html
Main features:
➔ Theoretical mode excitation rates are calculated according to Samadi et al (2003, A&A, 404, 1129) ➔ Theoretical mode damping rates are obtained from the tables calculated by Houdek et al (1999, A&A 351, 582)➔ The mode light-curves are simulated according to Anderson et al (1990, Apj, 364, 699) ➔ Stellar granulation simulation is based on : Harvey (1985, ESA-SP235, p.199).➔ Activity signal modelled from Aigrain et al (2004, A&A, 414, 1139) ➔ Instrumental photon noise is computed in the case of COROT but can been changed.
Simulated signal = modes + photon noise + granulation signal + activity signal
Instrumental noise (orbital periodicities) not yet included (next version)
Simulation inputs:• Duration of the time series and sampling• Characteristics (magnitude, age, etc…) of the star• Option : characteristics of the instrument performances (photon noise level for the given star magnitude)
Simulation outputs: time series and spectra for :• mode signal (solar-like oscillations)• photon noise, granulation signal, activity signal
Modeling the solar-like oscillations spectrum (1/4)
Each solar-like oscillation is a superposition of a large number of excited and damped
proper modes:
Aj : amplitude at which the mode « j » is excited by turbulent convection
tj : instant at which its is excited
: mode frequency
: mode (linear) damping rate
H : Heaviside function
j
ccj
ttHj
ttij
A ..][)](exp[]0
2exp[
Modeling the solar-like oscillations spectrum (2/4)
Fourier spectrum :
Power spectrum :
Line-width :
The stochastic fluctuations from the mean Lorentzian profil are simulated by generating the imaginary and real parts of U according to a normal distribution (Anderson et al , 1990).
j
ccj
ttHj
ttij
A ..][)](exp[]0
2exp[
/)(21
)(
/)(21)(
00
i
U
i
A
F jj /
j
jAU )(
20
22
]/)(2[1
)()()(
U
FP
Line-width
• and L/L predicted on the base of theoretical models• Excitations rates according to Samadi & Goupil(2001) model• Damping rates computed by G. Houdek on the base of Gough’s formulation of convection
constraints on:
We have necesseraly:
Modeling the solar-like oscillations spectrum (3/4)
where <(L)²> is the rms value of the mode amplitude
20
22
]/)(2[1
)()()(
U
FP
)()()( 2kk
kk PdPL
2)(U
²L
Modeling the solar-like oscillations spectrum (4/4)
Simulated spectrum of solar-like oscillations for a stellar model with M=1.20 MO
located at the end of MS.
Photon noise
Flat (white) noise
COROT specification: For a star of magnitude m0=5.7, the photon noise in an amplitude spectrum of a time series of 5 days isB0 = 0.6 ppm
For a given magnitude m, B = B010(m – m0)/5
Granulation and activity signals
Non white noise, characterised by its auto-correlation function: AC = A2 exp(-|t|/)
A: “amplitude”: characteristic time scale
Fourier transform of the auto-correlation function=> Fourier spectrum of the initial signal:P() = 2A2/(1 + (2)2)
(or « rms variation ») from 2 = P() d
and P() = 42/(1 + (2)2)
Modelling the granulation characteristics (continue)
Granulation spectrum = function of:• Eddies contrast (border/center of the granule) : (dL/L)
granul
• Eddie size at the surface : dgranul
• Overturn time of the eddies at the surface : granul
• Number of eddies at the surface : Ngranul
Modelling the granulation characteristics ● Eddie size : dgranul = dgranul,Sun (H*
/HSun
)● Number of eddies : N
granul = 2(R
*/dgranul)²
● Overturn time : granul
= dgranul / V ● Convective velocity : V, from Mixing-length Theory (MLT)
Modelling the granulation characteristics (continue)
● Eddies contrast : (dL/L)granul
= function (T)● T : temperature difference between the granule and the
medium ; function of the convective efficiency, .● and T from MLT● The relation is finally calibrated to match the Solar
constraints.
Granulation signal
Inputs:● characteristic time scale ()● dL/L for a granule |● size of a granule | ()● radius of the star |
Inputs from models
Modelled on the base of the Mixing-length theory
All calculations based on 1D stellar models computed with
CESAM, assuming standard physics and solar metallicity
fi are empirical (as )
Activity signal
Inputs:● characteristic time scale of variability
[Aigrain et al 2004, A&A] = intrinsic spot lifetime (solar case) or Prot
How to do better?
● standard deviation of variability [Aigrain et al 2004, A&A, Noyes et al 1984, ApJ] = f1 (CaII H & K flux)CaII H & K flux = f2 (Rossby number: Prot /bcz) Prot = f3 (age, B-V) and B-V= f4 (Teff)
bcz , age, Teff from models
The solar case
Not too bad, but has to be improved
Example: a Sun at m=8
Example: a Sun at m=8
Example: a young 1.2MO star (m=9)
Example: a young 1.2MO star (m=9)
Next steps: - improvement of granulation andactivity modelling
- rotation (José Dias & José Renan)- orbital instrumental perturbations
Simulation are not always close to reality,but they prepare you to face reality
Prospectives