On detecting the large separation in the autocorrelation of stellar oscillation times series

By B. Mosser, T. Appourchaux. 2009

175 citations recorded by the source corpus.

Context. The observations carried out by the space missions CoRoT and Kepler provide a large set of asteroseismic data. Their analysis requires an efficient procedure first to determine if a star reliably shows solar-like oscillations, second to measure the so-called large separation, third to estimate the asteroseismic information that can be retrieved from the Fourier spectrum. Aims. In this paper we develop a procedure based on the autocorrelation of the seismic Fourier spectrum that is capable of providing measurements of the large and small frequency separations. The performance of the autocorrelation method needs to be assessed and quantified. We therefore searched for criteria able to predict the output that one can expect from the analysis by autocorrelation of a seismic time series. Methods. First, the autocorrelation is properly scaled to take into account the contribution of white noise. Then we use the null hypothesis H0 test to assess the reliability of the autocorrelation analysis. Calculations based on solar and CoRoT time series are performed to quantify the performance as a function of the amplitude of the autocorrelation signal. Results. We obtain an empirical relation for the performance of the autocorrelation method. We show that the precision of the method increases with the observation length, and with the mean seismic amplitude-to-background ratio of the pressure modes to the power 1.5 ± 0.05. We propose an automated determination of the large separation, whose reliability is quantified by the H0 test. We apply this method to analyze red giants observed by CoRoT. We estimate the expected performance for photometric time series of the Kepler mission. We demonstrate that the method makes it possible to distinguish � = 0 from � = 1 modes. Conclusions. The envelope autocorrelation function (EACF) has proven to be very powerful for the determination of the large separation in noisy asteroseismic data, since it enables us to quantify the precision of the performance of different measurements: mean large separation, variation of the large separation with frequency, small separation and degree identification.

Subfields: Astronomy and Astrophysics, Computational Mechanics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/fab51079379354005e6165041dd8cbf178ed9519

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. D. Huber
2. W. Chaplin
3. D. Stello
4. E. Gaidos
5. A. Miglio
6. T. Bedding
7. B. Mosser
8. D. Charbonneau

In Computational Mechanics

1. D. Huber
2. D. Stello
3. Y. Elsworth
4. T. Bedding
5. S. Hekker
6. J. Ridder
7. T. Kallinger
8. K. Belkacem

In Instrumentation

1. D. Huber
2. D. Stello
3. W. Chaplin
4. B. Mosser
5. T. Bedding
6. A. Miglio
7. E. Gaidos
8. Y. Elsworth

Citations in the corpus

• REVISED STELLAR PROPERTIES OF KEPLER TARGETS FOR THE QUARTER 1–16 TRANSIT DETECTION RUN (2013, methodology): “We have analyzed Q0–14 long-cadence data of 13420 unclassified stars using the asteroseismic detection pipelines described by Huber et al. (2009), Hekker et al. (2010), Mosser & Appourchaux (2009) and Mathur et al. (2010).”
• ASTEROSEISMOLOGY OF RED GIANTS FROM THE FIRST FOUR MONTHS OF KEPLER DATA: GLOBAL OSCILLATION PARAMETERS FOR 800 STARS (2010, methodology): “We have investigated the slope of the power law using amplitudes from four different methods (A2Z, COR, OCT and SYD, see Table 1 for references) and find on average: A650nm ∝ ν −0.8 max .”
• TESTING SCALING RELATIONS FOR SOLAR-LIKE OSCILLATIONS FROM THE MAIN SEQUENCE TO RED GIANTS USING KEPLER DATA (2011, methodology): “…Garćıa et al. (2011) and analyzed using several automated analysis methods (Bonanno et al. 2008; Campante et al. 2010; Hekker et al. 2010b; Huber et al. 2009; Kallinger et al. 2010a; Karoff et al. 2010; Mathur et al. 2010a; Mosser & Appourchaux 2009; Mosser et al. 2011b; Verner & Roxburgh 2011).”
• Asteroseismology and Gaia: Testing Scaling Relations Using 2200 Kepler Stars with TGAS Parallaxes (2017, methodology): “Specifically, we used a flat distance prior, reddening measured from the grid-modeling method described in Section 3.2, as well as nmax and nD values from the COR pipeline (Mosser & Appourchaux 2009).”
• Probing the core structure and evolution of red giants using gravity-dominated mixed modes observed with Kepler (2012, methodology): “The signal-to-noise ratio is defined from the envelope autocorre- lation function (Mosser & Appourchaux 2009).”
• Red-giant seismic properties analyzed with CoRoT (2010, methodology): “Contrary to the linear dependence with δνenv, which has been theoretically justified by Mosser & Appourchaux (2009), the variation of F with H/B was empirically derived from a fit based on main-sequence stars.”
• ASTEROSEISMIC CLASSIFICATION OF STELLAR POPULATIONS AMONG 13,000 RED GIANTS OBSERVED BY KEPLER (2013, methodology): “We found a similar number (13 182) when using the method described in Mosser & Appourchaux (2009).”
• Mixed modes in red-giant stars observed with CoRoT (2011, methodology): “Simulations have shown that the threshold level provided by the method (Mosser & Appourchaux 2009) combined with the detection in multiple frequency ranges excludes spurious signature.”
• CALCULATING ASTEROSEISMIC DIAGRAMS FOR SOLAR-LIKE OSCILLATIONS (2011, background): “In HD49933, Scenario B is now accepted as the correct identification (Benomar et al. 2009), and Scenario 1 in HD181420 seems most likely (Barban et al. 2009; Mosser & Appourchaux 2009; Bedding & Kjeldsen 2010).”
• Spin down of the core rotation in red giants (2012, methodology): “At small ∆ν, the non-detection is explained by the limited frequency resolution, but also by the poorer quality of the spectra, as expressed by the EACF coefficient (Mosser & Appourchaux 2009).”
• Asteroseismology of red giants from the first four months of Kepler data: Fundamental stellar parameters (2010, methodology): “There is, however, the so-called autocorrelation method described by Mosser & Appourchaux (2009), which Fig.”
• The universal red-giant oscillation pattern; an automated determination with CoRoT data (2010, methodology): “…to variability in the amplitudes, resulting in an apparently irregular comb structure; second, the finite mode lifetime blurs the estimates of the eigenfrequencies; third, estimates are affected by the stellar noise and granulation signal superimposed onthe oscillations (Mosser & Appourchaux 2009).”
• SOLAR-LIKE OSCILLATIONS IN LOW-LUMINOSITY RED GIANTS: FIRST RESULTS FROM KEPLER (2010, result): “Similar results were found using pipelines developed by four other groups (Hekker et al. 2010b; Mosser & Appourchaux 2009; Kallinger et al. 2010; Mathur et al. 2010), and the dotted lines in Figure 1 show the region inside which ∼80% of those measurements lay.”
• PLATO as it is: a legacy mission for Galactic archaeology (2017, unknown): “We follow the approach described in Mosser (2017) based on the work by Mosser & Appourchaux (2009), and explore the effect of varying the duration of the observations ( 𝜏 ) and the apparent magnitude range ( m V ) on the asteroseismic yields expected from the underlying stellar population (see…”
• The Second APOKASC Catalog: The Empirical Approach (2018, methodology): “The CAN pipeline is described in Kallinger et al. (2010); the COR pipeline is described in Mosser & Appourchaux (2009); the OCT pipeline is described in Hekker et al. (2010); and the SYD pipeline is described in Huber et al. (2009).”