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A tool to simulate COROT light-curves

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

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A tool to simulate COROT light-curves

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  1. A tool to simulate COROT light-curves R. Samadi1 & F. Baudin2 1: LESIA, Observatory of Paris/Meudon 2: IAS, Orsay

  2. 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

  3. 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.

  4. 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

  5. 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 0 : mode frequency  : mode (linear) damping rate H : Heaviside function

  6. Modeling the solar-like oscillations spectrum (2/4) Line-width : Fourier spectrum : Power spectrum : 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).

  7. Modeling the solar-like oscillations spectrum (3/4) We have necesseraly: Line-width where <(L)²> is the rms value of the mode amplitude  constraints on: • and L/Lpredicted 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

  8. 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.

  9. 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 is B0 = 0.6 ppm For a given magnitude m, B = B010(m – m0)/5

  10. Granulation and activity signals Non white noise, characterised by its auto-correlation function: AC = A2 exp(-|t|/t) A: “amplitude” t: characteristic time scale Fourier transform of the auto-correlation function => Fourier spectrum of the initial signal: P(n) = 2A2t/(1 + (2ptn)2) s (or « rms variation ») from s2 =  P(n) dn => s = A/2and P(n) = 4s2t/(1 + (2ptn)2)

  11. 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 : tgranul • Number of eddies at the surface : Ngranul Modelling the granulation characteristics • Eddie size : dgranul = dgranul,Sun (H*/HSun) • Number of eddies : Ngranul = 2p(R*/dgranul)² • Overturn time : tgranul= dgranul / V • Convective velocity : V, from Mixing-length Theory (MLT)

  12. 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.

  13. Granulation signal Inputs: • characteristic time scale (t) • dL/L for a granule | • size of a granule | (s) • radius of the star | 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 Inputs from models

  14. Activity signal Inputs: • characteristic time scale of variability t [Aigrain et al 2004, A&A] t = intrinsic spot lifetime (solar case) or Prot How to do better? • standard deviation of variability s [Aigrain et al 2004, A&A, Noyes et al 1984, ApJ] s = f1 (CaII H & K flux) CaII H & K flux = f2 (Rossby number: Prot /tbcz) Prot = f3 (age, B-V) and B-V= f4 (Teff) tbcz , age,Teff from models fi are empirical (as t)

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

  16. Example: a Sun at m=8

  17. Example: a Sun at m=8

  18. Example: a young 1.2MO star (m=9)

  19. Example: a young 1.2MO star (m=9)

  20. Prospectives 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

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