Gap interpolation by inpainting methods : Application to Ground and Space-based Asteroseismic data

 

Authors: S. Pires, S. Mathur, R. A. Garcia, J. Ballot, D. Stello, K. Sato
Journal: Astronomy & Astrophysics
Year: 2014
Download: ADS | arXiv


Abstract

In asteroseismology, the observed time series often suffers from incomplete time coverage due to gaps. The presence of periodic gaps may generate spurious peaks in the power spectrum that limit the analysis of the data. Various methods have been developed to deal with gaps in time series data. However, it is still important to improve these methods to be able to extract all the possible information contained in the data. In this paper, we propose a new approach to handle the problem, the so-called inpainting method. This technique, based on a sparsity prior, enables to judiciously fill-in the gaps in the data, preserving the asteroseismic signal, as far as possible. The impact of the observational window function is reduced and the interpretation of the power spectrum is simplified. This method is applied both on ground and space-based data. It appears that the inpainting technique improves the oscillation modes detection and estimation. Additionally, it can be used to study very long time series of many stars because its computation is very fast. For a time series of 50 days of CoRoT-like data, it allows a speed-up factor of 1000, if compared to methods of the same accuracy.


Summary

The paper "Gap interpolation by inpainting methods : Application to Ground and Space-based Asteroseismic data" has been accepted for publication in A&A. This paper is describing the software K-inpainting.

The software K-inpainting has been developed to handle the problem of missing data in the asteroseismic signal of Kepler. This technique, based on a sparsity prior, enables to judiciously fill-in the gaps in the data, preserving the asteroseismic signal, as far as possible.

More recently, it has been implemented in the CoRoT pipeline to process the data from missing data.

The K-inapinting software is available here

3346_3

Power Density Spectrum for a duty cycle of 83% computed using an FFT on the inpainted time series.

Impact on asteroseismic analyses of regular gaps in Kepler data

 

Authors: R.A. Garcıa, S. Mathur, S. Pires, et al.
Journal: Astronomy & Astrophysics
Year: 2014
Download: ADS | arXiv


Abstract

The NASA Kepler mission has observed more than 190,000 stars in the constellations of Cygnus and Lyra. Around 4 years of almost continuous ultra high-precision photometry have been obtained reaching a duty cycle higher than 90% for many of these stars. However, almost regular gaps due to nominal operations are present in the light curves at different time scales. In this paper we want to highlight the impact of those regular gaps in asteroseismic analyses and we try to find a method that minimizes their effect in the frequency domain. To do so, we isolate the two main time scales of quasi regular gaps in the data. We then interpolate the gaps and we compare the power density spectra of four different stars: two red giants at different stages of their evolution, a young F-type star, and a classical pulsator in the instability strip. The spectra obtained after filling the gaps in the selected solar-like stars show a net reduction in the overall background level, as well as a change in the background parameters. The inferred convective properties could change as much as 200% in the selected example, introducing a bias in the p-mode frequency of maximum power. When global asteroseismic scaling relations are used, this bias can lead up to a variation in the surface gravity of 0.05 dex. Finally, the oscillation spectrum in the classical pulsator is cleaner compared to the original one.

Curvelet analysis of asteroseismic data

 

Authors: P. Lambert, S. Pires, J. Ballot, R.A. Garcia, J.-L. Starck, S. Turck-Chièze
Journal: A&A
Year: 2006
Download: ADS | arXiv

 

Abstract

Context. The detection and identification of oscillation modes (in terms of their l, m, and successive n) is a great challenge for present and future asteroseismic space missions. “Peak tagging" is an important step in the analysis of these data to provide estimations of stellar oscillation mode parameters, i.e., frequencies, rotation rates, and further studies on the stellar structure.
Aims. Our goal is to increase the signal-to-noise ratio of the asteroseismic spectra computed from the time series that are representative of MOST and CoRoT observations (30- and 150-day observations).

Methods. We apply the curvelet transform – a recent image processing technique that looks for curved patterns – to echelle diagrams built using asteroseismic power spectra. In the resulting diagram, the eigenfrequencies appear as smooth continuous ridges. To test the method, we use Monte-Carlo simulations of several sun-like stars with different combinations of rotation rates, rotation-axis inclination, and signal-to-noise ratios.

Results. The filtered diagrams enhance the contrast between the ridges of the modes and the background, allowing a better tagging of the modes and a better extraction of some stellar parameters. Monte-Carlo simulations have also shown that the region where modes can be detected is enlarged at lower and higher frequencies compared to the raw spectra. In addition, the extraction of the mean rotational splitting from modes at low frequency can be done more easily using the filtered spectra rather than the raw spectra.