arXiv subjects

Vinay L. Kashyap

Publications and source records attributed to Vinay L. Kashyap.

58 records · Page 4Linked to original sources

arXiv2002

Are Coronae of Magnetically Active Stars Heated by Flares? II. EUV and X-Ray Flare Statistics and the Differential Emission Measure Distribution

(Abridged) We investigate the EUV and X-ray flare rate distribution in radiated energy of the late-type active star AD Leo using long EUVE and BeppoSAX observations. We compare the observed light curves with light curves synthesized from model flares that are distributed in energy according to a power law with selectable index alpha (dN/dE ~ E^{-alpha}). Two methods are applied, the first comparing flux distributions of the binned data, and the second using the distributions of photon arrival time differences in the unbinned data. We find acceptable alpha values between 2.0-2.5 for the EUVE DS and the BeppoSAX LECS data. The BeppoSAX MECS data indicate a somewhat shallower energy distribution than the LECS data, which is attributed to the harder range of sensitivity of the MECS detector and the increasing peak temperatures of flares with increasing total (radiative) energy. The results suggest that flares can play an important role in the energy release of this active corona. We discuss caveats related to time variability, total energy, and multiple power-law distributions. Studying the limiting case of a corona that is entirely heated by a population of flares, we derive an expression for the time-averaged coronal differential emission measure distribution (DEM) that can be used as a diagnostic for the flare energy distribution. The shape of the analytical DEM agrees with previously published DEMs from observations of active stars.

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arXiv2002

Statistics: Handle with Care, Detecting Multiple Model Components with the Likelihood Ratio Test

The likelihood ratio test (LRT) and the related $F$ test, do not (even asymptotically) adhere to their nominal $χ^2$ and $F$ distributions in many statistical tests common in astrophysics, thereby casting many marginal line or source detections and non-detections into doubt. Although there are many legitimate uses of these statistics, in some important cases it can be impossible to compute the correct false positive rate. For example, it has become common practice to use the LRT or the $F$ test for detecting a line in a spectral model or a source above background despite the lack of certain required regularity conditions. In these and other settings that involve testing a hypothesis that is on the boundary of the parameter space, {\it contrary to common practice, the nominal $χ^2$ distribution for the LRT or the $F$ distribution for the $F$ test should not be used}. In this paper, we characterize an important class of problems where the LRT and the $F$ test fail and illustrate this non-standard behavior. We briefly sketch several possible acceptable alternatives, focusing on Bayesian posterior predictive probability-values. We present this method in some detail, as it is a simple, robust, and intuitive approach. This alternative method is illustrated using the gamma-ray burst of May 8, 1997 (GRB 970508) to investigate the presence of an Fe K emission line during the initial phase of the observation.

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arXiv2000

Analysis of Energy Spectra with Low Photon Counts via Bayesian Posterior Simulation

Over the past 10 years Bayesian methods have rapidly grown more popular as several computationally intensive statistical algorithms have become feasible with increased computer power. In this paper, we begin with a general description of the Bayesian paradigm for statistical inference and the various state-of-the-art model fitting techniques that we employ (e.g., Gibbs sampler and Metropolis- Hastings). These algorithms are very flexible and can be used to fit models that account for the highly hierarchical structure inherent in the collection of high-quality spectra and thus can keep pace with the accelerating progress of new space telescope designs. The methods we develop, which will soon be available in the CIAO software package, explicitly model photon arrivals as a Poisson process and, thus, have no difficulty with high resolution low count X-ray and gamma-ray data. We expect these methods to be useful not only for the recently launched Chandra X-ray observatory and XMM but also new generation telescopes such as Constellation X, GLAST, etc. In the context of two examples (Quasar S5 0014+813 and Hybrid-Chromosphere Supergiant Star alpha TrA) we illustrate a new highly structured model and how Bayesian posterior sampling can be used to compute estimates, error bars, and credible intervals for the various model parameters.

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arXiv2000

EUV Flare Activity in Late-Type Stars

\textit{Extreme Ultraviolet Explorer} Deep Survey observations of cool stars (spectral type F to M) have been used to investigate the distribution of coronal flare rates in energy and its relation to activity indicators and rotation parameters. Cumulative and differential flare rate distributions were constructed and fitted with different methods. Power laws are found to approximately describe the distributions. A trend toward flatter distributions for later-type stars is suggested in our sample. Assuming that the power laws continue below the detection limit, we have estimated that the superposition of flares with radiated energies of about $10^{29}-10^{31}$ergs could explain the observed radiative power loss of these coronae, while the detected flares are contributing only $\approx 10$%. While the power-law index is not correlated with rotation parameters (rotation period, projected rotational velocity, Rossby number) and only marginally with the X-ray luminosity, the flare occurrence rate is correlated with all of them. The occurrence rate of flares with energies larger than $10^{32}$ergs is found to be proportional to the average total stellar X-ray luminosity. Thus, energetic flares occur more often in X-ray bright stars than in X-ray faint stars. The normalized occurrence rate of flares with energies larger than $10^{32}$ergs increases with increasing \lxlbol and stays constant for saturated stars. A similar saturation is found below a critical Rossby number. The findings are discussed in terms of simple statistical flare models in an attempt to explain the previously observed trend for higher average coronal temperatures in more active stars. It is concluded that flares can contribute a significant amount of energy to coronal heating in active stars.

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