Prsentation PowerPoint

1
Curvelet analysis of asteroseismic data The
Procyon noise-reduced MOST power spectrum R.
A. García (1,2) , P. Lambert (1,2), J. Ballot
(2,3) , S. Pires (4,1) , P.A.P. Nghiem (1,2), S.
Turck-Chièze (1,2) J.M. Matthews (5)
(1)  DSM/DAPNIA/Service dAstrophysique,
CEA/Saclay, 91191 Gif sur Yvette, France (2)  AIM
- Unité Mixte de Recherche CEA - CNRS -
Université Paris 7 - UMR n7158, CEA/Saclay,
91191 Gif sur Yvette, France (3)  Max-Planck-Insti
tut für Astrophysick, Karl-Schwarzschild-Str.1,
Postfach 1317, 85741 Garching,
Germany (4)  DSM/DAPNIA/EDI, CEA/Saclay, 91191
Gif sur Yvette, France (5)  Department of Physics
and Astronomy, University of British Columbia,
6224 Agricultural Road, Vancouver V6T IZI, Canada
COROT Week 9, 5-9 December 2005, ESTEC,
Netherlands
2
INTRODUCTION

• Recent photometric observations of Procyon A by
  MOST have shown no clear p-mode signal while
  power spectra of ground-based velocity
  measurements show power excess and peaks
  interpreted as evidence for the presence of
  p-modes.
• The statistical distribution of the highest
  peaks in MOST is not consistent with simple noise
  and has been interpreted by some as possible
  p-mode signal at roughly the expected level.
• We aim to enhance the S/N ratio of the MOST
  observations to a level high enough to see if
  those peaks are part of a bum in power caused by
  the presence of acoustic mode power.
• A curvelet filtering is applied to the echelle
  diagram in order to enhance curved structures.
• After filtering a clear bump appears in the
  power spectrum around 1 mHz as already observed
  from ground.

3
CONTEXT

• Many independent reports of p-mode properties
  have been published based on very high-resolution
  spectrometric techniques from ground-based
  observations Martic et al. 1999, 2004
  Egenberger et al. 2004.
• The first spaced-based asteroseismic photometric
  mission MOST could not uncover the presence of
  p-mode signal in the amplitude spectrum (Matthews
  et al. 2004).
• Bedding et al. (2005) argued that the
  non-detection of oscillations in Procyon A by
  MOST could be explained considering that p-modes
  could be severely diluted by intrinsec convective
  noise which was expected to be stronger in light
  than in velocity. They conclude that the
  distribution of the highest peaks was not
  consistent with simple noise and could be the
  signature of p-mode power.
• Robinson et al. (2005) performed hydrodynamic
  simulations of convection in a Procyon model.
  They suggest that the convection characteristics
  in Procyon are different from those of the Sun.
  Their theoretical results are consistent with
  both the light and velocity measurements.

4
RAW POWER SPECTRUM

• MOST data January 8 to February 9 2004
• 32 days with 99 duty cycle
• First 20 days with a mean sampling of 15s the
  last 12 days with a mean sampling of 7.5s ? rebin
  the latter to obtain a mean interval of 15s.
• Low-frequency trend removed
• Computing the power spectrum iterative
  least-squares fitting of sine waves (SWF)
• Normalisation of the spectrum by the standard
  deviation of the noise at high frequency (4-5
  mHz)
• The Earthshine scattering modulated by the
  orbital period (101.413min) power is removed
  from the spectrum in bands of 2 ?Hz wide centred
  on the orbital frequency and its harmonics

5
RAW POWER SPECTRUM
Smoothed spectrum with a boxcar filter 270 ?Hz
2-order polynomial fit (in log-log parameter
space) to the background noise
6
METHOD THE CURVELET ANALYSIS

• We apply a new multiscale image processing
  technique, the curvelet transform, to the MOST
  data. This transform was developed to deal with
  images containing highly anisotropic patterns
  (Candès Donoho 1999).
• The curvelet transform can be used to reduce the
  noise in the asteroseismic echelle diagrams
  (Lambert et al. 2005) and consequently allows us
  to obtain a power spectrum with an enhanced S/N.
• To proceed a noise reduction using this
  transform, we follow the implementation of
  Starck, Candès Donoho 2002.

7
FILTERED POWER SPECTRUM

• How do we proceed ?
• Estimation of the large spacing ??0 (FFT or
  autocorrelation of the raw spectrum) to have a
  folding frequency
• Building of the raw echelle diagram
• Filtering with the curvelet transform
• Unfolding the filtered echelle diagram
• Repeating this operation with different values of
  ??0 slightly different (1 bin) and averaging to
  reduce the dependence to the exact folding
  frequency

8
FILTERED POWER SPECTRUM
Smoothed spectrum with a boxcar filter 270 ?Hz
2-order polynomial fit (in log-log parameter
space) to the background noise
Removed Orbital harmonics
9
FILTERED POWER SPECTRUM

• Power-based rank test taking the 15 highest
  peaks ranked by their power.
• Comparison between the frequencies of the 15
  ranked peaks and the p-modes reported by
• Martic et al. 2004 6, 9, 12 peaks at 1-, 2- and
  3-? of the central frequencies given in table 2.
• Eggenberger et al. 2004 4 peaks compatible
  inside 3-?
• Probability of having these results caused by
  pure noise
• Monte Carlo simulation
• Probabilities having, at least, 6, 9, 12 peaks
  compatible with 1-, 2- and 3-? error are 7.6,
  12.4 and 13.3

10
FILTERED POWER SPECTRUM
Vertical lines the 15 ranked peaks
1? 2? 3? from
frequencies reported by Martic et al. 2004
The bar width represents the observational error
? 2?Hz
11
?Uncovering the presence of a clear bump in the
MOST power spectrum for the same position of the
one already measured from ground-based
observations.?A power rank based test of the 15
highest peaks in this region gives coincidences
with previous identified p-mode frequencies from
Martic et al. 2004
CONCLUSION