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