Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Transcript

A tool to simulate COROT light-curves R. Samadi1 & F. Baudin2 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 : 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: A j exp[ 2i 0 ] exp[ (t t j )]H [t t j ] c.c. j 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 Modeling the solar-like oscillations spectrum (2/4) A j exp[ 2i 0 ] exp[ (t t j )]H [t t j ] c.c. j Fourier spectrum : A Line-width : U ( ) F ( ) 1 2i ( 0 ) / 1 2i ( 0 ) / j j U ( ) A j j Power spectrum : P( ) F ( ) / 2 U ( ) 2 1 [2( 0 ) / ]2 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). Modeling the solar-like oscillations spectrum (3/4) P( ) F ( ) 2 U ( ) 2 1 [2( 0 ) / ]2 We have necesseraly: L² Line-width (L) 2 P( )d k Pk ( k ) k where <(L)²> is the rms value of the mode amplitude constraints on: U ( ) 2 • 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 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 is B0 = 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|/t) A: “amplitude” t: characteristic time scale Fourier transform of the auto-correlation function => Fourier spectrum of the initial signal: P() = 2A2t/(1 + (2t)2) s (or « rms variation ») from s2 = P() d > s A/2 and P() = 4s2t/(1 + (2t)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 : tgranul • 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 : tgranul = 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 (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 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) 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) 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