Vinay L. Kashyap

The Statistical Challenges of Wavelet-Based Source Detection

Wavelet functions are proving extremely useful for detecting sources in binned, two-dimensional photon counts images. In this chapter, we describe the mission-independent source detection algorithm WAAVDETEET, part of the Chandra Interactive Analysis of Observations (CIAO) software package, and discuss the statistical challenges we have faced in its development, such as: what is the best way to estimate the local background in each pixel, if it is a priori unknown? What is the best way to eliminate false detections caused by instrumental variations? And what is the significance of a detected source?

AXAF Data Analysis Challenges

The high quality of the AXAF X-ray data provides new challenges for the X-ray data analysis. It is clear that an “old” approach is not enough to fully exploit the capabilities of the AXAF instruments. We describe a few of the statistical and computational problems that we have so far identified. Some of them appear to be theoretically solvable but computationally challenging, while others state problems for theoretical statistics which, so far as we know, are unsolved.The problems divide, from an astronomical point of view, into: Modeling the Data (e.g. nonlinear parameter estimation, uncertainties in the model, weighting the data, correlated residuals), Source Detection (events in N-space, use of wavelets, significance of detected structures) and Instrument Related Issues (pile-up in AXAF ACIS, overlapping orders in grating spectra).

Evaluation of source counts and upper limits in crowded ROSAT PSPC fields

We present a method for determining source counts, S/N, and upper limits at specified positions in a crowded ROSAT PSPC field using a combination of publicly available software packages. The algorithm is based on the so‐called ‘Local DETECT’ method of source detection, and improves upon currently available software, to permit a meaningful comparison of non‐detections with detected sources. We also present a recipe to obtain source counts and S/N in the case of point sources which overlap significantly.

An Analysis of X-Ray Flares in Pleiades Stars

In the assumption that stellar flares, in analogy to many solar flares, occur in coronal magnetic loops (see Serio 1995), Reale et al. (1995) have devised a method, calibrated with extensive hydrodynamics modeling, to derive quantitative constraints on loop length (L) and the characteristic time scale of heating (T ht ) from quantities observed during the decay phase. We have applied this method to flares observed in the Pleiades. This work is based on those on solar flares by Serio et al. (1991) and Jackimiec et al. (1992) which showed that the Slope of the curve traced by flares in the density-temperature (n-T) plane during the decay depends only on the presence of significant heating during the decay (i. e. with e-folding time, T ht , at least, comparable to the loop thermodynamic decay time, T tdh ). The resulting diagnostics has been succesfully applied to flares observed with SMM (Sylwester et al. 1993). Reale et al. (1993) have extended this modeling to stellar cases analyzing the dependence from gravity, g, and shown that the Slope in the (n-T) diagram depends also on the ratio of loop length, L, and pressure scale height H = 2kT/gμ,. The time evolution of soft X-ray flare spectra is non-parametrically described in terms of Spectral Shape Indexes (SSI) computed projecting the time resolved spectra observed during flare decay along a set of principal component axes derived from the analysis of a sample of spectra of hydrostatic loop models.