UNBIASED ESTIMATION OF A MULTIFREQUENCY SOLUTION IN DELTA SCUTI - - PowerPoint PPT Presentation

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UNBIASED ESTIMATION OF A MULTIFREQUENCY SOLUTION IN DELTA SCUTI - - PowerPoint PPT Presentation

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UNDERSTANDING THE ROLES OF ROTATION, PULSATION AND CHEMICAL PECULIARITIES IN THE UPPER MAIN SEQUENCE 11th - 16th September 2016, Lake District, UK UNBIASED ESTIMATION OF A MULTIFREQUENCY SOLUTION IN DELTA SCUTI STARS Javier Pascual Granado, Juan

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Javier Pascual Granado, Juan Carlos Suárez Yanes, Rafael Garrido Haba, and José Ramón Rodón

UNBIASED ESTIMATION OF A MULTIFREQUENCY SOLUTION IN DELTA SCUTI STARS

UNDERSTANDING THE ROLES OF ROTATION, PULSATION AND CHEMICAL PECULIARITIES IN THE UPPER MAIN SEQUENCE

11th - 16th September 2016, Lake District, UK

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STANDARD ANALYSIS PROCEDURE IN ASTEROSEISMOLOGY

  • Pre-processing: removal of systematics, outliers, de-trending,

etc.

  • Pre-whitening cascade – CLEAN method, SigSpec, etc.
  • Filtering harmonics, combinations and/or spurious frequencies.
  • Characterization of the spectrum: Dn, nmax, s
  • Model fitting

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PRE-WHITENING

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PRE-WHITENING

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Breger, M., Handler, G., Garrido, R., et al. 1996, DSN, 10, p.24

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HD 50844: an interpretation challenge

  • More than a

thousands of frequencies detected.

  • The residuals of

the prewhitening sequence are not white noise (plateau)

Poretti et al. 2009, A&A, 506, 85-93

Also HD 50870, HD49434, …

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AIMS

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Impact of pre-whitening on frequency detection

  • Gapped data
  • ARMA interpolation: preserving the original frequency

content

  • Linear interpolation: non-preserving the original

frequency content

Pascual-Granado, J., Garrido, R., and Suárez, J. C. 2015, A&A, 575, A78

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THE SAMPLE

Advantages of higher cadence data:

  • increased sampling rate
  • higher Nyquist frequency
  • fewer low-frequency artefacts
  • reduced errors on frequency, amplitude and phase

determinations in the Fourier spectrum

Murphy, Simon J., 2012, MNRAS, 422 (1), 665-671

CoRoT seismofield data. Why CoRoT?

CoRoT seismofield observations have ~twice the cadence of Kepler SC

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THE SAMPLE

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THE SAMPLE

Gdor

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THE SAMPLE

Binarity

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THE SAMPLE

HADS

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THE SAMPLE

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AIMS

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Study of the impact of pre-whitening techniques used for frequency detection on asteroseismology Three datasets are used:

  • Gapped data
  • ARMA interpolation: preserving the original frequency

content

  • Linear interpolation: non-preserving the original

frequency content

Pascual-Granado, J., Garrido, R., and Suárez, J. C. 2015, A&A, 575, A78

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Wrong data produced by the South Atlantic Anomaly

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IN INTERPOLATION: HD170699

Li Line nearly ly interpola lated ARM ARMA interpol

  • lated

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Spurious peaks produced by the spectral window

Pascual-Granado et al., CUP 2012, IAUS285, pp.392-393

CoRoT pass assing th through th the SAA in intr troduce sp spurious peaks

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FREQUENCY DETECTION: : SIGSPEC

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Reegen, P. 2007, A&A, 467, pp.1353-1371

Iterative process consisting of four steps:

1.

Computation of the significance spectrum.

2.

Exact determination of the peak with maximum significance.

3.

MultiSine least-squares fit of the frequencies, amplitudes and phases of all significant signal components detected so far.

4.

Pre-whitening of the sinusoidal components. The residuals are used as input for the next iteration.

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COMBINATIONS FILTERING

  • The procedure followed is similar to
  • Independent freqs. used to find combinations with Combine from

Reegen, P.

  • Harmonics and combinations up to 3rd order within a 1/Tobs interval.
  • A set of 12 independent freqs. Is used, harmonics until the 5th order,

and combinations AFa + BFb being A, B = [1,3].

  • Interactions with the satellite orbital freq. (fs = 13.972 d-1) for F1 to F4

and the 4 first harmonics of fs.

  • Sidelobes of the 1 d-1 alias around fs and its harmonics.

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García Hernández, A., Moya, A., Michel, E. et al. 2013, A&A, A63, 14 Reegen, P., 2011, CoAst, 163, p.119

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RESULTS: : HISTOGRAM OF F FREQUENCIES

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RESULTS: : HISTOGRAM OF F FREQUENCIES

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RESULTS: : HISTOGRAM OF F FREQUENCIES

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RESULTS: : HISTOGRAM OF F FREQUENCIES

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RESULTS: : HISTOGRAM OF F FREQUENCIES

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RESULTS: : HISTOGRAM OF F FREQUENCIES

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RESULTS: : HISTOGRAM OF F FREQUENCIES

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RESULTS: : HISTOGRAM OF F FREQUENCIES

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IN SUMMARY

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Expectations from prewhitening This is what actually happens

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CONCLUSIONS

  • Prewhitening techniques (CLEAN) are not always reliable.
  • An unbiased estimator of the frequency spectrum is not

guaranteed when classical prewhitening techniques are used. More info on this:

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Limits in the application of harmonic analysis to pulsating stars Pascual-Granado, J., Garrido, R., Suárez, J. C., 2015, A&A, 581, A89