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Astronomical Data Analysis Software and Systems IV
ASP Conference Series, Vol. 77, 1995
R. A. Shaw, H. E. Payne, and J. J. E. Hayes, eds.
QPSIM: An IRAF/PROS Tool for Source Simulation
K. R. Manning, J. DePonte, and F. Primini
Smithsonian Astrophysical Observatory, 60 Garden St., Cambridge, MA
02138
Abstract. The generation of simulated sources whose physical proper­
ties are well understood is useful in assessing the functionality of point
source analysis software. Qpsim is an IRAF/PROS task which will gen­
erate events from sources of given intensity, shape, and position and ei­
ther overlay them on a flat background in a new QPOE file or inject them
into an existing QPOE file. We present an overview of the capabilities of
qpsim and some examples of its use.
1. Introduction
Qpsim is a task which will simulate X­ray events for a ROSAT High Resolution
Imager (HRI) observation in QPOE format. The task may be used to generate
a random flat background as well as sources of a specific intensity, shape and
position. The simulated data can be a useful tool in calibrating point source
analysis software.
2. Describing the Data
An STSDAS table file is used to describe the source and background data to be
generated. Each row in the table represents information for a single source with
the background treated as a special case. An example is shown in Table 1.
(row) x y itype intensity prf type prf param
pixels pixels count s \Gamma1 jcounts oaajsigma
1 2000 4000 rate 0.50 gauss oaa 18.00
2 5000 2500 counts 200.00 roshri 20.00
3 3000 3000 counts 150.00 gauss sig 15.00
4 0 0 rate 5.00 bkgd INDEF
Table 1. Example of a qpsim source table
The desired intensity may be specified as either ``counts'' or ``rate.'' In the
latter case, the user must provide a value for the livetime in order to calculate
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the source counts. The livetime value may be entered via a task parameter or
extracted from a reference QPOE file.
The background data is designated by ``bkgd'' in the ``prf type'' column.
Two point­response functions (PRFs) are available for source data, either the
ROSAT HRI PRF (described by David et al. 1993) or a Gaussian function. The
ROSAT HRI PRF, designated ``roshri'', is described by an off­axis angle value.
The Gaussian may be described by either a sigma value (``gauss sig'') or by an
off­axis angle (``gauss oaa'') where the off­axis dependency of sigma is deduced
from a 50% power radius assuming a Gaussian distribution (David et al. 1993,
p. 17). Off­axis angle values are given in units of arc minutes, and sigma values
in units of pixels.
Off­axis angle values are treated independently from source position, giving
the user control over source shape. This allows the generation of identical sources
at many positions in the field. Such fields can increase the efficiency of methods
used to study simulated data and to calibrate source detection software. If an
off­axis angle value of ``INDEF'' is given, the value will then be calculated from
the source position.
All source positions are constrained to lie within the field size limits of an
unrolled image. For the ROSAT HRI, this is taken to be the central region
defined by the pixel range [2048:6144]. The exception to this is the background
specification for which the table values of X; Y and ``prf param'' are ignored.
3. Algorithm for Generating Events
Qpsim loops over the rows in the source table, generating the data for each
source independently. The background ``source'' is treated as a special case, but
the source data is generated with a general routine which invokes the appropriate
PRF function. In this way, other PRF functions can be easily added to the
program.
The IRAF system function ``urand'' is used to to select random, real num­
bers between 0.0 and 1.0. The X; Y coordinates of the background events are
generated independently through a simple translation and scaling of random
numbers:
ran num = urand(seed) (1)
X = ran num \Lambda X max (2)
If the resulting number is not within the field limits, a new random number is
generated and the process repeats until a valid coordinate value is found.
Azimuthally averaged versions of the PRFs are used to generate source
events. The distance of each event from the source center is determined by the
solution of the integral equation:
Z R
0
PRF (r) 2úr dr = ran num (3)
for R. An angle is then randomly selected, and the projected X; Y coordinates
are calculated, so that we have:
\Theta = 2ú \Lambda urand(seed) (4)

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Figure 1. Radial Profiles of Simulated HRI sources (Radius (pixels)
vs. counts/pixel). On the left is a source generated with the on­axis
PRF, on the right, a source generated at 11: 0 7 off­axis.
X = SRCX +R \Lambda cos(\Theta) (5)
Y = SRC Y +R \Lambda sin(\Theta) (6)
where SRCX ; SRC Y in equations (5) and (6) are the coordinates of the source
center. This method ensures that the events are uniformly distributed over
azimuth. The coordinates of the source events are then screened to fall within
the field limits, and the process is repeated until a valid X; Y pair is determined.
The simulated data are output as an ASCII list representing events from all
of the sources specified in the source table. The list is then converted to QPOE
format with the IRAF/PROS tasks qpcreate and qpappend; at this point the
user may select a real observation to which the events are appended.
4. Radial Profiles of Simulated Sources
Radial profiles of simulated sources were generated to verify that the data ex­
hibits the expected spatial properties. Profiles of Gaussian and HRI sources at
different off­axis angles were created. Figure 1 shows the radial profiles of two
HRI sources of equal intensity. The source on the left was generated on­axis and
the source on the right at 11: 0 7 off­axis.
The ROSAT HRI PRF is described as the combination of two Gaussian
functions and an exponential function (David et al. 1993). In the on­axis figure,
the two Gaussian functions are not easily distinguishable, and quickly decrease
to the exponential tail. In the off­axis figure, the two Gaussian functions are
discernible and they decrease more gradually to the exponential factor.

4
Figure 2. A ROSAT HRI observation of the Kepler supernova rem­
nant with a point source injected into the center of the shell (shown in
the box region).
5. Projected Uses of the QPSIM
The ability to generate random background and sources of known position, shape
and intensity can useful in calibrating source detection software. Some exam­
ples of what may be accomplished with data generated by qpsim are: assess
the ability of the software to calculate source properties, such as position, source
counts and signal to noise ratio; assess the significance of assuming a particular
source model when identifying a detection (for example, the use of a Gaussian
model when applied to HRI data); determine the software's ability to discrimi­
nate sources of equal intensity in close proximity.
In addition, simulated data can be injected into a real observation in order
to determine physical properties in a region of interest. For example, a point
source can be added to a supernova remnant to determine the capability of
analysis software to detect a pulsar in the midst of the remnant. An example of
such a simulation is shown in Figure 2.
6. Extendibility of QPSIM
Currently, QSIM will only simulate data for the ROSAT HRI. However, the
program has been designed to be easily extended to other instruments provided
an azimuthally averaged version of the instrument Point Response Function is
available. The simulation of source data in event rather than image format
allows the extension of qpsim to simulate other events attributes, such as event
time or pulse height.
Acknowledgments. This work is partially supported by NASA contracts
to the ROSAT Science Data Center (NAS5--30934) and Einstein (NAS8--30751).

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References
David, L. P., Harnden, F. R., Jr., Kearns, K. E., & Zombeck, M. V. 1993, The
ROSAT High Resolution Imager (HRI) (Boston, U.S. ROSAT Science
Data Center/SAO)