Prsentation PowerPoint

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

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• Main features
• Theoretical mode excitation rates are calculated
  according to Samadi et al (2003, AA, 404, 1129)
• Theoretical mode damping rates are obtained from
  the tables calculated by Houdek et al (1999, AA
  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, AA, 414, 1139)
• Instrumental photon noise is computed in the
  case of COROT but can been changed.

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• 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

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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
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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).
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Modeling the solar-like oscillations spectrum
(3/4)
We have necesseraly
Line-width
where lt(?L)²gt is the rms value of the mode
amplitude
? constraints on

• ? 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 Goughs formulation of convection

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Modeling the solar-like oscillations spectrum
(4/4)
Simulated spectrum of solar-like oscillations for
a stellar model with M1.20 MO located at the end
of MS.
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• Photon noise
• Flat (white) noise
• COROT specification
• For a star of magnitude m05.7, 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

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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 gt Fourier
spectrum of the initial signal P(n) 2A2t/(1
(2ptn)2) s (or  rms variation ) from s2 ?
P(n) dn gt s A/?2 and P(n) 4s2t/(1
(2ptn)2)
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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)

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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.

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• 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
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Activity signal

• Inputs
• characteristic time scale of variability t
• Aigrain et al 2004, AA
• t intrinsic spot lifetime (solar case) or Prot
• How to do better?
• standard deviation of variability s
• Aigrain et al 2004, AA, 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)
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The solar case
Not too bad, but has to be improved
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Example a Sun at m8
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Example a Sun at m8
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Example a young 1.2MO star (m9)
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Example a young 1.2MO star (m9)
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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