Determining X-Ray Source Intensity and Confidence Bounds in Crowded Fields

F. A. Primini and V. L. Kashyap

Welcome to our XAP web page. We're interested in the general problem of aperture photometry in high energy astrophysics photon-count images, in which the statistical noise model is Poisson, not Gaussian. We're particularly interested in regions of high source density, where multiple source apertures partially overlap and source and background apertures contain contributions from one or more sources. We discuss this problem in detail in Primini & Kashyap, 2014, hereafter PK2014 ( 2014ApJ...796...24P or astro-ph 1410.2564v2 ) . We describe a procedure for addressing the problem, based on Bayesian Statistics. We present here sample Python code and example data used in that article.

Obtaining Sample Code and Data

The package may be obtained by downloading XAP.tar.gz. To install it, simply uncompress the tar file and extract all files from it into a local directory. The package requires approximately 22MB of disk space. The package requires a CIAO environment to be set up and running, but there are no other external dependencies. A README file describing the contents of the distribution (also included in the distribution) may be found here.

A Simple Example

Consider the case shown here (from Fig. 2 of PK2014).

Primini & Kashyap, 2014, Fig. 2

The image data are a sub-section of the broad band image for Chandra OBSID 1575, obtained from the Chandra Source Catalog (CSC) (Evans et al. 2010ApJS..189...37E). The source regions shown are also obtained from the CSC and a background region was defined to include all four sources. We wish to determine intensities and confidence bounds for all four sources and background. As described in PK2014, we proceed by constructing the joint posterior probability distribution on a 5-dimensional mesh, using Maximum Likelihood estimates for intensities and sigmas to define the mesh. We assume here uninformative flat priors for all intensities. We compute the marginalized posterior distribution for each intensity in turn by seqeuential one-dimensional integrations over all other dimensions in the mesh.

In addition to the event list, the inputs to the program are stacks containing filenames of the source regions, psf images, and expmaps, all also obtained from the CSC. A background region file is also required. A log of the analysis run is included in the XAP/Example directory and may also be obtained here.

The program output is a binary FITS table, with one extension for each source and background, appearing in the order in which the sources appeared in the input stacks. A CHIPS session demonstrating how to read and display the file contents is provided here. The session produces the following plot:

Primini & Kashyap, 2014, Fig. 2


Francis A. Primini Vinay L. Kashyap

Section Photo