Detection of Variable Sources

Vinay Kashyap, Robert Rosner

Dept. Astron. & Astrop., 5640 S. Ellis, Chicago, IL 60637

Abstract:

1. Introduction

Most existing X-ray source detection algorithms search for sources in a 2-dimensional spatial field, and ignore the temporal dimension (an exception is the algorithm used to generate the WGA catalog of ROSAT Point Sources; White, Giommi, & Angelini 1994). Here we present a preview of a conceptually simple and computationally fast algorithm to detect X-ray sources which takes into account temporal variability. In addition to automatic identification of variable sources, our emphasis is on identifying sources that may be too weak to be detected over the entire time-span of the observation, but could be detected in a shorter segment.

In Section 2 , we describe the algorithm and its features. We describe simulations carried out to test its effectiveness in Section 3, and give some examples of its application in Section 4.

2. Algorithm

This algorithm is designed as a quick-look tool for identification of ``interesting'' sources in the data and to work on workstations with limited memory even with the large data sets that may become available with AXAF. Below we describe the algorithm in detail:

1. Remove gaps in the data. It is assumed that gaps exist only because of interruptions in the temporal observation sequence, and hence only the time-axis is affected.

2. Obtain bin-indices for each photon in the data.

3. Create spatial subsets of the data such that when a 3D image of this spatial region is constructed, the array size is smaller than the memory capacity of the workstation.

4. Determine the background-counts/pixel (B) over the sub-image by `fitting' a Poisson distribution to the observed frequency histogram of the counts. It is possible to account for variations in B over time. (B is strongly dependent on the number of pixels with 0, 1, and 2 counts.)

5. For each time bin anchored at a given , we compute the probability of obtaining the observed number of counts in each bin , given the background, B: . Work on generalizing this expression to the case where the value of B is uncertain is in progress.

6. If a pre-set threshold (say, an expectation of 1 false warning per sub-image), this time series is analyzed in greater detail:

   (a) First, a `quiescent' emission level Q, is determined (again by fitting to the observed frequency distribution of counts, but now only for the time bins being considered).

   (b) Next, the probabilities of obtaining given Q are computed, and these probabilities are compared to a pre-set threshold (say, expecting 1 false warning in 100 tests).

   (c) If threshold at some time bin, is marked and stored as a `source' pixel.

7. Steps (3)--(6) are repeated after shifting bin boundaries by a fraction of the bin widths.

8. All adjoining source pixels are then grouped together and labeled.

This conceptually simple algorithm identifies ``interesting'' sources in 3-dimensional data (2 spatial, and 1 temporal); many of which are likely to be variable sources. It is significantly fast compared to other algorithms for source detection, with a computational cost (where is the product of the bin sizes in the 3 dimensions), compared with for FFT-based techniques and for convolution-based techniques (also see Kashyap 1996). Despite this, it is highly sensitive (see Figure 1), and has the added advantage of being able to detect both excesses and deficiencies of counts.

3. Simulations

  
Figure 1: Detection efficiencies of (a) variable and (b) constant sources for various source strengths. The curves are labeled by the values of the background counts in each pixel. The difference in adopting a threshold of 1 (solid line) and 0.1 (dotted line) false sources per sub-image are also illustrated.
Figure 1: PS 135 Kb

In order to determine the effectiveness of this algorithm, we applied it to simulations of fields with artificial sources of various intensities (as multiples of background rates). Typical background values for ROSAT PSPC and HRI were used to set the range of background count rates used in the simulations. The resulting detection efficiencies of variable and constant sources are shown in Figure 1. An average peak count rate of ct pix results in an efficiency of regardless of the background rate for reasonable values of B.

The thresholds adopted in generating the above figures signify upper limits to the average number of expected false sources. For larger values of the background B, this limit approaches the true rate of false detections.

4. Application

For illustrative purposes, we have applied our algorithm to ROSAT PSPC and HRI observations of the Pleiades cluster. The Pleiades, with its large number of X-ray sources, constitutes a very useful test case. It has also been analyzed in detail using traditional methods (Micela et al. 1996; Stauffer et al. 1994). Below we show selected results from the application of our algorithm to the Pleiades (cf. Figure 2):

  
Figure 2:
Figure 2: PS 57 Kb

1. Figure 2a shows the PSPC count-rate light-curve of Hz892 (HHJ435) showing a strong flare (cf. Sciortino et al. 1994).

2. Figure 2b shows the other extreme of very weak variability, in the case of Hz738. This star is known to be optically variable, and was suspected to be X-ray variable as well, based on its non-detection in the ROSAT All-Sky Survey.

3. Figure 2c shows the ROSAT HRI light-curve of HCG 315, a faint Pleaides cluster member. This was previously detected with ROSAT PSPC data, but was not known to be variable.

4. Figure 2d shows an uncatalogued, previously undetected X-ray source from ROSAT HRI data of the Pleiades region. This is an example of a source that would remain undetected if the temporal dimension were ignored.

Acknowledgments:

This work was supported by the AXAF Science Center.

References:

Micela, G., Sciortino, S., Kashyap, V., Harnden, F. R., Jr., & Rosner, R. 1996, ApJS, 102, 75

Sciortino, S., Micela, G., Kashyap, V., Harnden, F. R., Jr., & Rosner, R. 1994, presented at 8th Cool Star Workshop, in press

Stauffer, J. R., Caillault, J.-P., Gagne, M., Prosser, C. F., & Hartmann, L. W. 1994, ApJS, 91, 625

White, N. E., Giommi, P., & Angelini, L. 1994, BAAS, 185, #41.11