A tool to simulate COROT light-curves R. Samadi 1 & F. Baudin 2 1 : LESIA, Observatory of Paris/Meudon 2 : 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 :

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 t j : instant at which its is excited  : mode frequency  : mode (linear) damping rate H : Heaviside function

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).

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 is the rms value of the mode amplitude

Modeling the solar-like oscillations spectrum (4/4) Simulated spectrum of solar-like oscillations for a stellar model with M=1.20 M O located at the end of MS.

Photon noise Flat (white) noise COROT specification: For a star of magnitude m 0 =5.7, the photon noise in an amplitude spectrum of a time series of 5 days is B 0 = 0.6 ppm For a given magnitude m, B = B 0 10 (m – m0)/5

Granulation and activity signals Non white noise, characterised by its auto-correlation function: AC = A 2 exp(-|t|/  ) A: “amplitude”  : characteristic time scale Fourier transform of the auto-correlation function => Fourier spectrum of the initial signal: P( ) = 2A 2  /(1 + (2  ) 2 )  (or « rms variation ») from  2 =  P( ) d  and P( ) = 4  2  /(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 : d granul Overturn time of the eddies at the surface :  granul Number of eddies at the surface : N granul Modelling the granulation characteristics ● Eddie size : d granul = d granul,Sun (H * /H Sun ) ● Number of eddies : N granul = 2  (R * /d granul )² ● Overturn time :   granul = d granul / 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

f i are empirical (as  ) Activity signal Inputs: ● characteristic time scale of variability  [Aigrain et al 2004, A&A]  = intrinsic spot lifetime (solar case) or P rot How to do better? ● standard deviation of variability  [Aigrain et al 2004, A&A, Noyes et al 1984, ApJ]  = f 1 (CaII H & K flux) CaII H & K flux = f 2 (Rossby number: P rot /  bcz ) P rot = f 3 (age, B-V) and B-V  = f 4 (T eff )  bcz, age, T eff from models

The solar case Not too bad, but has to be improved

Example: a Sun at m=8

Example: a young 1.2M O star (m=9)

Next steps: - improvement of granulation and activity modelling - rotation (José Dias & José Renan) - orbital instrumental perturbations Simulation are not always close to reality, but they prepare you to face reality Prospectives