A new method is presented of analyzing skymap-type gamma ray data. Each photon event is replaced by a probability distribution on the sky corresponding to the observing instrument's point spread function. The skymap produced by this process may be used for source detection or identification. Most important, the use of these photon weights for pulsar analysis promises significant improvement over traditional techniques

Brown, Lawrence E.

Clayton, Donald D.

Hartmann, Dieter H.

English

NASA Technical Reports Server

N92-21908
Gamma Ray Pulsar Analysis from Photon
Probability Maps
Lawrence E. Brown, Donald D. Clayton, and Dieter H. Hartmann
Department of Physics and Astronomy
Clemson University
Clemson, SC 29634-1911, U.S.A.
Abstract
We present a new method of analyzing skymap-type 7-ray data. Each photon
event is replaced by a probability distribution on the sky corresponding to the
observing instrument's point spread function. The skymap produced by this process
may be useful for source detection or identification. Most important, the use of
these photon weights for pulsar analysis promises significant improvement over
traditional techniques.
1 The Method
We have used the derived point spread function for the COS-B experiment to develop
data analysis tools with improved ratios of signal to background with applications to
source identification and searches for faint "/-ray pulsars. We generate a weighted photon
probability map to enhance any significant 7-ray signal present in the data and suppress
undesirable background fluctuations. The basis for this method can be formulated in two
equivalent ways:
a) By definition, the point spread function (PSF) of an imaging instrument describes
the redistribution of photons from a particular direction on the sky into the observed
distribution. Thus, each event may be represented as a continuous distribution of event
weights on the sky (for COS-B, the PSF vanishes for 0 > 20°).
b) Correspondingly, any location on the sky receives some weight from each 7-ray seen
during the experiment. In other words, each observed photon has a certain probability,
given by the PSF, to have originated at that location.
Based on this concept, we smooth each photon arrival direction into an extended
probability map. When investigating a particular source location, our analysis includes
all 7-ray events through their weights at that position. To demonstrate the usefulness
of this approach we apply it to the light curve of the Crab pulsar. The extraction of a
source list from our COS-B probability map is in progress.
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https://ntrs.nasa.gov/search.jsp?R=19920012665 2020-03-17T13:15:36+00:00Z
2 COS-B Probability Maps
The observed direction of each photon event does not correspond directly to its point of
origin on the sky. Information on the detector angular resolution is contained in the PSF
of the detector. To identify ")'-ray sources, the intrinsic fuzziness of -)'-ray detectors
can be included in the analysis by creating a skymap of "probability flux" rather than
"photon count flux".
The weight of a -)'-ray event with observed direction a for a small solid angle A0
centered on a point p is defined as
w(p;a) = PSFSR(O(o_,p))AO,
where PSFSR is the point spread function per steradian. We use the PSFSR derived by
the COS-B team using the Vela pulsar (Mayer-Hasselwander 1985).
The celestial -),-ray intensity, Ic, at a point on the sky (in terms of weight) is
I¢(p) = - _ Ib,
df'lw(H(p)
where the summations are taken over all events seen by the experiment, the w(p)'s are
the weights of the individual events, w(ANb(p)) is the weight, at p, of the instrumental
background correction for all other points on the sky, and w(H(p)) is the weight, at p, of
the exposure (in cm 2 s) for all other points on the sky. h is the "standard" background
correction as given by the COS-B team. The units of Ic are photons/cm 2 s st.
This defines our weighted sky intensity probability distribution. We have sampled
this continuous map at .5 ° intervals for the whole sky. The resultant maps in the energy
ranges 50-150 MeV, 150-300 MeV, and 300-5,000 MeV are shown in figure 1.
This technique may not be ideal for some aspects of source identification. It results
in a skymap which may be "too fuzzy" since the photons are effectively convolved twice
through the PSF. That is, they are spread once in passing through the detector and again
by our technique. However, it does not make any arbitrary smoothing assumptions. A
comparison of our source list (in progress) with those resulting from other techniques
(e.g.Simpson & Mayer-Hasselwander 1987; Bloemen 1989) will be useful. For instance,
our technique finds a possible source of high intensity but low statistical weight at l =
309.5, b = -30.5 in the middle energy range (see figure) it should be instructive to see if
the maximum likelihood methods of Grenier et al. confirm this source candidate.
3 Lightcurve of the Crab Pulsar
For analysis of periodic sources, we analyze weights vs. phase instead of counts vs. phase.
Superimposed on a background that is ,,, uniform in space and time, the 7-ray pulsar
adds a signal that is localized both in space and time. Standard analysis of 7-ray phases
considers all photons within a given acceptance cone equally. Photon arrival directions
268
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t.%<.<!_._)_..__.:_;i,. , "!"' _::.:_;: i.._i,.;_; • . . " :..':;..7 " ..... ,..z:" ::;'- ._,_i_._ :._:_
_ii .........ii:.:i!i::<
Figure 1: Skymaps of photon weight of the COS-B observations for the energy ranges
50-150 MeV_ 150-300 MET/, and 300-5,000 MeV. The photon weight distribution on the
whole sky is sampled on a grid of.5 degree spacing. Since COS-B did not observe all areas
of the sky, some regions of the map at high galactic latitudes are blank. The graymaps
used here represent intensity of photons/cm 2 s sr, with intensity increasing from black
to white. This graymap is wrapped around 10 times between the faintest and brightest
spots for better monochrome resolution. It is, essentially a grayscale "contour map". The
graymaps are assigned individually for each map (i. e. equal gray intensities on different
maps do not represent equal photon fluxes).
269
TABLE 1: Signal to backsround
Observation Peak Signal Integrated Signal
( Std. Dev.) ( Std. Dev.)
weights counts weights counts
Crab Pulsar 43 18 176 101
1/2 Crab Pulsar 33 12 107 59
closer to the pulsar position have a higher probability of containing the sought after
pulsed signal. Thus, by considering both space and time, we gain an added degree of
freedom for extracting the signal from the background.
The standard binning technique folds solar barycentric arrival times with the mea-
sured period characteristics obtained from radio observations (Buccheri et al. 1983).
Traditionally, one defines an acceptance cone around the source direction with opening
angle
Om_ = 12.5E(MeV) -a6.
Inside this cone, all photons contribute equally to the light curve. In our approach,
PSF weighting implicitly performs this task; thus, we can utilize the maximum aperture
consistent with a non-zero PSF (Om_ = 20 ° for COS-B).
Then, instead of binning counts by phase to create a light curve histogram, we bin
weights by phase. Results for the two methods for the Crab Pulsar are shown in our
figure 2.
Figure 3 highlights the differences between the two approaches. Essentially, the tra-
ditional method uses a uniform probability function inside an acceptance cone that has
an energy dependent width. We have used, instead, a probability function which extends
over the full range of non-zero PSF, but binned into 3 energy ranges. This binning follows
COS-B tradition, could easily be made finer.
To allow direct comparison of the two methods, we plot the standard deviation for
each bin. To calculate the average background level, we have used the "flat" portion of
the Crab pulsar's ")'-ray light curve between the second peak and the end of the period.
The resulting plot shows counts (weights) minus average background divided by stan-
dard deviation from background. We show results for all, and half of the Crab pulsar
observations of COS-B to demonstrate the performance of this technique for reduced
sampling times. The results in terms of maximum signal above background and total
integrated signal are given in table 1. While the exact numbers are dependent on bin
size, the improvement is dramatic in all cases.
This obvious increase in significance of detected pulses should also benefit the cluster
analysis algorithm of Buccheri, et al. (1988). We are currently investigating this and
other extensions to the general weighting technique.
270
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Weighted Photons --
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Crab Pulsar (COS-B,
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WeLghted Photons
Raw Counts ....
't
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Phase
0 l
Figure 2: Shown are the weighted photon method (solid) and the standard count method
(dashed) of phase binnin 9 for the full COS-B data set for the Crab pulsar. Note the
dramaticall_t improved signal for the weighted photon method. (Number of bins = 50.)
271
Effective 'Weight' Distribution
I.........IOur Weighting FunctionTraditional Analysis
I
• I i i i
0 2 4 6 8 i0 12 14 16 18 20
angle
Figure 3: Schematic drawing comparing the effective probability "weight" distribution for
traditional pulsar analysis (dashed) and our weighting function (solid) for a given energy
(_ IOOMeV).
Acknowledgements
This research was supported in part by NASA Grant NAG 5-1578. We thank Mark
Leising and Lih-Sin The for many valuable discussions.
References
Bloemen, H. 1989, Ann. Rev. Astron. Astrophys., 27, 469
Buccheri, R., et al. 1983, Astron. Astrophys., 128,245
Buccheri, R., Di Gesu', V., Maccarone, M.C., and Sacco, B. 1988, Astron. Astrophys.,
201,194
Grenier, I.A., Hermsen, W., and Pollock, A.M.T. 1991, in AlP Conference Proceedings,
(New York), p. 3.
Mayer-Hasselwander, H. A. , ed. 1985, Explanatory Supplement to the COS-B Final
Database.
Simpson, G., and Mayer-Hasselwander, H.A. 1987, Proceedings of the 20th ICRC,
(Moscow), 1:89
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