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DIAMONDS: A new Bayesian nested sampling tool-Application to peak bagging of solar-like oscillations
Context. Thanks to the advent of the space-based missions CoRoT and NASA's Kepler, the asteroseismology of solar-like oscillations is nowadays at the base of our understanding about stellar physics. The Kepler spacecraft especially, is releasing excellent photometric observations of more than three years length in very high duty cycle, which contain a large amount of information that has not yet been investigated. Aims. In order to exploit the full potential of Kepler light curves, sophisticated and robust analysis tools are now required more than ever. Characterizing single stars with an unprecedented level of accuracy and subsequently analyze stellar populations in detail will be fundamental to further constrain stellar structure and evolutionary models. Methods. We developed a new code, termed Diamonds, for Bayesian parameter estimation and model comparison by means of the Nested Sampling Monte Carlo (NSMC) algorithm, an efficient and powerful method very suitable for high-dimensional and multimodal problems. A detailed description of the features implemented in the code is given, with a focus on the novelties and differences with respect to other existing methods based on NSMC. Diamonds is then tested on the bright F8 V star KIC 9139163, a challenging target for peak bagging analysis due to its large number of oscillation peaks observed, coupled to the blending occurring between = 2, 0 peaks, and the strong stellar background signal. We further strain the performance of the approach by adopting a 1147.5 days-long Kepler light curve, accounting for more than 840,000 data bins in the power spectrum of the star. Results. The Diamonds code is able to provide robust results for the peak bagging analysis of KIC 9139163, while at the same time preserving a considerable computational efficiency for identifying the solution. We test the detection of different astrophysical backgrounds in the star and provide a criterion based on the Bayesian evidence for assessing in detail the peak significance of the detected oscillations. We present results for 59 individual oscillation frequencies, amplitudes and linewidths and provide a detailed comparison to the existing values in the literature, from which significant deviations are found when a different background is used. Lastly, we successfully demonstrate an innovative approach to peak bagging that exploits the capability of Diamonds to sample multimodal distributions, of great potential for possible future automatization of the analysis technique.
EPJ Web of Conferences, 2015
The peak bagging analysis, namely the fitting and identification of single oscillation modes in stars' power spectra, coupled to the very high-quality light curves of red giant stars observed by Kepler, can play a crucial role for studying stellar oscillations of different flavor with an unprecedented level of detail. A thorough study of stellar oscillations would thus allow for deeper testing of stellar structure models and new insights in stellar evolution theory. However, peak bagging inferences are in general very challenging problems due to the large number of observed oscillation modes, hence of free parameters that can be involved in the fitting models. Efficiency and robustness in performing the analysis is what may be needed to proceed further. For this purpose, we developed a new code implementing the Nested Sampling Monte Carlo (NSMC) algorithm, a powerful statistical method well suited for Bayesian analyses of complex problems. In this talk we show the peak bagging of a sample of high signal-to-noise red giant stars by exploiting recent Kepler datasets and a new criterion for the detection of an oscillation mode based on the computation of the Bayesian evidence. Preliminary results for frequencies and lifetimes for single oscillation modes, together with acoustic glitches, are therefore presented.
Bayesian peak bagging analysis of 19 low-mass low-luminosity red giants observed with Kepler
Astronomy and Astrophysics
The currently available Kepler light curves contain an outstanding amount of information but a detailed analysis of the individual oscillation modes in the observed power spectra, also known as peak bagging, is computationally demanding and challenging to perform on a large number of targets. Our intent is to perform for the first time a peak bagging analysis on a sample of 19 low-mass low-luminosity red giants observed by Kepler for more than four years. This allows us to provide high-quality asteroseismic measurements that can be exploited for an intensive testing of the physics used in stellar structure models, stellar evolution and pulsation codes, as well as for refining existing asteroseismic scaling relations in the red giant branch regime. For this purpose, powerful and sophisticated analysis tools are needed. We exploit the Bayesian code Diamonds, using an efficient nested sampling Monte Carlo algorithm, to perform both a fast fitting of the individual oscillation modes and...
Monthly Notices of the Royal Astronomical Society, 2015
Kepler has revolutionized our understanding of both exoplanets and their host stars. Asteroseismology is a valuable tool in the characterization of stars and Kepler is an excellent observing facility to perform asteroseismology. Here we select a sample of 35 Kepler solar-type stars which host transiting exoplanets (or planet candidates) with detected solar-like oscillations. Using available Kepler short cadence data up to Quarter 16 we create power spectra optimized for asteroseismology of solar-type stars. We identify modes of oscillation and estimate mode frequencies by 'peak bagging' using a Bayesian Markov Chain Monte Carlo framework. In addition, we expand the methodology of quality assurance using a Bayesian unsupervised machine learning approach. We report the measured frequencies of the modes of oscillation for all 35 stars and frequency ratios commonly used in detailed asteroseismic modelling. Due to the high correlations associated with frequency ratios we report the covariance matrix of all frequencies measured and frequency ratios calculated. These frequencies, frequency ratios, and covariance matrices can be used to obtain tight constraint on the fundamental parameters of these planet-hosting stars.
Automated asteroseismic peak detections
Monthly Notices of the Royal Astronomical Society, 2018
Space observatories such as Kepler have provided data that can potentially revolutionize our understanding of stars. Through detailed asteroseismic analyses we are capable of determining fundamental stellar parameters and reveal the stellar internal structure with unprecedented accuracy. However, such detailed analyses, known as peak bagging, have so far been obtained for only a small percentage of the observed stars while most of the scientific potential of the available data remains unexplored. One of the major challenges in peak bagging is identifying how many solar-like oscillation modes are visible in a power density spectrum. Identification of oscillation modes is usually done by visual inspection that is time-consuming and has a degree of subjectivity. Here, we present a peak-detection algorithm especially suited for the detection of solar-like oscillations. It reliably characterizes the solar-like oscillations in a power density spectrum and estimates their parameters without human intervention. Furthermore, we provide a metric to characterize the false positive and false negative rates to provide further information about the reliability of a detected oscillation mode or the significance of a lack of detected oscillation modes. The algorithm presented here opens the possibility for detailed and automated peak bagging of the thousands of solar-like oscillators observed by Kepler.
Estimating stellar parameters from spectra using a hierarchical Bayesian approach
Monthly Notices of the Royal Astronomical Society, 2007
A method is developed for fitting theoretically predicted astronomical spectra to an observed spectrum. Using a hierarchical Bayesian principle, the method takes both systematic and statistical measurement errors into account, which has not been done before in the astronomical literature. The goal is to estimate fundamental stellar parameters and their associated uncertainties. The non-availability of a convenient deterministic relation between stellar parameters and the observed spectrum, combined with the computational complexities this entails, necessitates the curtailment of the continuous Bayesian model to a reduced model based on a grid of synthetic spectra. A criterion for model selection based on the so-called predictive squared error loss function is proposed, together with a measure for the goodness-of-fit between observed and synthetic spectra. The proposed method is applied to the infrared 2.38-2.60 μm Infrared Space Observatory (ISO)-Short Wavelength Spectrometer (SWS) data of the star α Bootis, yielding estimates for the stellar parameters: effective temperature T eff = 4230 ± 83 K, gravity log g = 1.50 ± 0.15 dex and metallicity [Fe/H] = − 0.30 ± 0.21 dex.
A Bayesian approach to scaling relations for amplitudes of solar-like oscillations in Kepler stars
Monthly Notices of the Royal Astronomical Society, 2013
We investigate different amplitude scaling relations adopted for the asteroseismology of stars that show solar-like oscillations. Amplitudes are among the most challenging asteroseismic quantities to handle because of the large uncertainties that arise in measuring the background level in the star's power spectrum. We present results computed by means of a Bayesian inference on a sample of 1640 stars observed with Kepler, spanning from main sequence to red giant stars, for 12 models used for amplitude predictions and exploiting recently wellcalibrated effective temperatures from Sloan Digital Sky Survey photometry. We test the candidate amplitude scaling relations by means of a Bayesian model comparison. We find the model having a separate dependence upon the mass of the stars to be largely the most favoured one. The differences among models and the differences seen in their free parameters from early to late phases of stellar evolution are also highlighted.
arXiv (Cornell University), 2022
Asteroseismic time-series data have imprints of stellar oscillation modes, whose detection and characterization through time-series analysis allows us to probe stellar interiors physics. Such analyses usually occur in the Fourier domain by computing the Lomb-Scargle (LS) periodogram, an estimator of the power spectrum underlying unevenly-sampled time-series data. However, the LS periodogram suffers from the statistical problems of (1) inconsistency (or noise) and (2) bias due to high spectral leakage. In addition, it is designed to detect strictly periodic signals but is unsuitable for non-sinusoidal periodic or quasi-periodic signals. Here, we develop a multitaper spectral estimation method that tackles the inconsistency and bias problems of the LS periodogram. We combine this multitaper method with the Non-Uniform Fast Fourier Transform (mtNUFFT) to more precisely estimate the frequencies of asteroseismic signals that are non-sinusoidal periodic (e.g., exoplanet transits) or quasi-periodic (e.g., pressure modes). We illustrate this using a simulated and the Kepler-91 red giant light curve. Particularly, we detect the Kepler-91b exoplanet and precisely estimate its period, 6.246 ± 0.002 days, in the frequency domain using the multitaper F-test alone. We also integrate mtNUFFT into the PBjam package to obtain a Kepler-91 age estimate of 3.96 ± 0.48 Gyr. This 36% improvement in age precision relative to the 4.27 ± 0.75 Gyr APOKASC-2 (uncorrected) estimate illustrates that mtNUFFT has promising implications for Galactic archaeology, in addition to stellar interiors and exoplanet studies. Our frequency analysis method generally applies to time-domain astronomy and is implemented in the public Python package tapify, available at https://github.com/aaryapatil/tapify.
Tutorial: Asteroseismic Stellar Modelling with AIMS
2018
The goal of aims (Asteroseismic Inference on a Massive Scale) is to estimate stellar parameters and credible intervals/error bars in a Bayesian manner from a set of asteroseismic frequency data and so-called classical constraints. To achieve reliable parameter estimates and computational efficiency, it searches through a grid of pre-computed models using an MCMC algorithm—interpolation within the grid of models is performed by first tessellating the grid using a Delaunay triangulation and then doing a linear barycentric interpolation on matching simplexes. Inputs for the modelling consist of individual frequencies from peak-bagging, which can be complemented with classical spectroscopic constraints. aims is mostly written in Python with a modular structure to facilitate contributions from the community. Only a few computationally intensive parts have been rewritten in Fortran in order to speed up calculations.
Asteroseismic Stellar Modelling with AIMS
2017
The goal of AIMS (Asteroseismic Inference on a Massive Scale) is to estimate stellar parameters and credible intervals/error bars in a Bayesian manner from a set of asteroseismic frequency data and so-called classical constraints. To achieve reliable parameter estimates and computational efficiency, it searches through a grid of pre-computed models using an MCMC algorithm -- interpolation within the grid of models is performed by first tessellating the grid using a Delaunay triangulation and then doing a linear barycentric interpolation on matching simplexes. Inputs for the modelling consist of individual frequencies from peak-bagging, which can be complemented with classical spectroscopic constraints. AIMS is mostly written in Python with a modular structure to facilitate contributions from the community. Only a few computationally intensive parts have been rewritten in Fortran in order to speed up calculations.