The results of a study (Carter et. al.) of gamma ray bursts using long duration balloon exposure are analyzed. Arguments are presented against the conclusion that the size spectrum extrapolates to a power law with index from -1.0 to -0.5, and that therefore the gamma ray bursts are of galactic origin. It is claimed that the data are consistent with an upper limit over 100 times that proposed, and that therefore no conclusion can be drawn from the measurements regarding the nature or origin of gamma ray bursts. The resulting upper limit to the rate of occurrence of small bursts lies above the -1.5 index power law extrapolation of the size spectrum of known events, i.e., greater than the rate expected from an infinitely extended source region

Cline, T. L.

Schmidt, W. K. H.

English

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https://ntrs.nasa.gov/search.jsp?R=19760027022 2020-03-22T13:25:56+00:00Z
X-661-76-222
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NO NEW LIMIT ON THE SIZE
DISTRIBUTION OF GAMMA-RAY BURSTS
(?NASA-T VI-X- 7120 5 ) X10 NEW 11MIT ON THE SIZE 	 N76-34110
DISTIRIBUTI011 OF GAMNA • Rll y BURS1S ( -:NASA) 9 P
H(". $3.50	 CSC? 03C	
uncla.9
G3/93 06451
T. L. CLINE
W. K. H. SCHMIDT
OCTOBER 1976
GiOl [PIOARD SPACE FLIGHT CENTER
GREENBELT, MARYLAND
	 920'A
171,OCT 1976
RECEIVED
NASA STI FACILITY
INPUT BRANCH
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No NewLimit on The	 i
Size Distribution of
j Gamma-Ray Bursts
1
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1
T. L. Cline and W. K. H. Schmidt	 I
NASA/Goddard Space flight Center
Greenbelt, Maryland 20771, USA
E
i'f,
*NAS/NRC Senior Post-Doctoral Fellow
No New Limit on the Size Dl ,:tributio ti of Gamma-Ray Bursts
Carter at al. 1 have recently published the results of their search
for small gamma-ray bursts with a long-duration balloon exposure, from
which they have concluded that the size spuctrum el^=apolates to a power
law with index from -1. to -0.5. They draw the firm conclusion that
gamma-ray bursts are therefore of galactic origin. When assessing their
data we did not find a sound basis for their arguments-; In fact, we
claim in what follows that their data are consistent with an upper limit
that is over 100 times above their results, There is therefore no
conclusion regarding the nature or origin of gaiina-ray bur sts that can
be drawn from their measurements. The resulting upper limit to the rate
of occurrence of small bursts lies above the -1.5 index power-law extra-
polation of the size spectrum of known events, 1.t-., greater than the
rate expected from an infinitely extended source region.
A number of basic considerations in the treatment of the data
apparently were either ignored or inappropriately minimized by the authors,
each of which independently pushes their upper limit upwards. Our treat-
ment of these issues is indicated in Figure 1, in which the claimed
results of Carter et al. 1 are shown, adjusted by the following six
individual considerations.
(1) Their .selection criterion for finding statisticall y significant
bursts in the gamma-ray count rate was that of seekin3 three successive
increases in 0.6-second accumulations. This requirement will ignore
most known gamma-ray bursts due to their varying temporal nature	 some
are only 0.1 second or less in duration and most consist of 0.1-sec to
ORIGINAL PAU 19
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41
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0,3-sec increases occurring randomly throughout durations up to 30
seconds in extent2 ' 3 ' 4 . Tt is fair to estimate that, at most, 20%
of 25% of the known events could be found using this single criterion.
If, instead, one searches typical, scintillation counter data for 0.1-sec
increases, the number found is always too great to be of value,
result which necessarily dictates an undesirably high upper limit to
the gamma-ray burst occurrence rate. A thorough treatment of the
f
	 data must either evaluate the upper limits for all known types of
r
	
	 burst time histories, or normalize to the subset of selected types ---
either method would certainly increase their upper limit by a factor
F
of at least 4. (The data selection interpretation of Carter et al. may
not be the only one in print suffering from this problem since, in
the absence of a comprehensive, published study of gamma-ray burst
time histories, a full appreciation of their variability may not be
widespread.. However, it has been known since the beginning that bursts
are not usually one or two seconds in duration.)
(2) The total photon energy measured in the given three successive
0,6-sec intervals, or in whatever selection requirement used, does.not
represent the entire energy emitted in that burst, again, because of the
varying temporal nature of gamma-ray bursts. To take into account
missing energy due to fluctuations requires reassigning the.magnitude
of the event size under consideration by an undetermined factor, which
can be estimated to be usually over a factor of two.
(3) A related consideration is that satellite gamma-ray burst size
spectra are customarily plotted after the measured flux of each event
t
1
-3
is multiplied by .another factor of twt1, ' ,4 in order to include the
missing energy below the usual threshold of .100 to 1,50 keV. This has
been done with knowledge of only a fe=w low-energy spectra 5,6 as an
admittedly arbitrary treatment which wpposes that all events have thei a	
same spectrum below 100 keV, on the basis of the fact that all known	 j
spectra are similar. above 100 keV 7 . Thus, for purposes of comparison,
f
I	 balloon data with similar enort,v threshold's must includes the same or
equivalent normalization.
(4) The author,. knowingly plotted :1 one-standard deviation upper
limit. We plead that small-number statis.- .c. demand the more commonly
employed and firmer confidence limit of 95;. This is recognized by
Carter et al. 1 in their text but ignored, and raises the upper limit
by another factor of three.
i
I
(5) The fraction of the sky observed front their balloon -borne
detector was apparently taken to be one half, which we ;infer from
I
estimating their results, given the raw data and using their stated
i
methods of analysis. However, since the atmosphere presents a great
absorption to photons of these energies at large zenith angles, the
equivalent fraction of the sky viewed in an unobscured manner is about
0.25 to 0.3, a consideration which raises their limit by another factor
of 1.7 to 2.
(6) The response of a flat, horizontally-positioned detector to
a distribution of gamma-ray bursts distorts the measurement of the
size spectrum of the bursts, even from an isotropic distribution. A
consideration of this point can be condensed as follows: Given an
^
yAGF
OF
-4-
intrinsic burst size spectrum N(S) dS = kS -Y dS with isotropic arrival
directions, an ideal, flat, totally absorbing detector above the
.atmosphere would observe events of :apparent size Z - S cos 0 such that
the size spectrum would be
N(Z)d!. = 1 1'" S° N(S)dS sin0d0ds = k7. -YdZ ('go 2 in©cosY-1Odo0 0	 0
=kZ -'YdZ SOo g (0)d0 •
0
Aie smallest detectable event of size Z is not equal to the expected
smallest detectable burst size S. A more meaningful estimate of the
smallest detectable S would be the average burst size S that would
ontribute to the smallest Z. Thus,
S -
	 S	 o
(Y-2)
7-
	
100 
7 g (0) d0 /SOo g (0)d0 = 
y-I	 1-cos	 0
0	 0	 Y-2	 1-cos(Y-1)© 0
which is the average of the relative size S/Z that contributes to Z.
Testing the hypothesis of a -2.5 index power law differential spectrum
with an ideal detector and with 0 0 = 90% results in a shift on the
vertical, N(S), axis of 1/0.4 = 2.5 upwards,from the first equation,
and a horizontal shift of 1.67 towards larger size, from the second,
i.e., when converting from Z to S coordinates. Using a real detector,
with the photon energy spectrum of E -2 considered by Carter et al.,I
folded with the response of their 1-cm thick NaI(Ti,) detector, an
approximate fit to a totally absorbing disk for 70 percent of counts
above 100 keV and to a zenith-independent detector for 30 percent is
found. We approximate the atmospheric effect using a simple cutoff
at 0 = 70°. The result gives a vertical shift of 1/0.45 = 2.2 and a
..IF
1
-5-
horizontal shift of 1.3,not as severe as for the ideal, disk-shaped
detector, because the real one has a finite volume and some of the
radiation is penetrating. This incorporates the zenith angle effect
In our fifth point above and is independent of the other four consider-
ations.
The combined effect of points (1) to (6) is that the upper limit
derived from the data of Carter et al. l is actually above the -1.5
index power law extrapolation of the size spectrum of known events.
Even if we assume, somewhat arbitrarily, a comoined error for all
considerations (1) to (6) of 50%, the conclusion of this letter remains
that no inference regarding either the small-event size spectrum or
the origin of cosmi c gamma-ray bursts can be drawn from all the balloon
data published up to the present time.
As a post script, we add the following remark: Even if, on the
basis of the 1.^_k of observation of a single event, an upper limit
well below -1.5 index power law extrapolation were found, it would be
misleading to assume that this result alone would necessarily prove
either the burst size spectrum model or the origin hypothesis
suggested by Carter et al. 1 A metagalactic origin with a cosmological
cutoff or one of a variety of otiier models could also fit. The ultimate
choice between these would require an independent measurement, such
as an anisotropy or a spectral dependence on size. If such a size
cutoff is ever found, it would be by itself imply only that the source
PAGE-13QUA
Ii	 1	 ^
-6-
distribution is not infinite in extent, assuming that the average
absolute magnitude of emitters is independent of distance.
T. L. Cline
W. K. I1. Schmidt*
NASA
Goddard Space Flight Center
Greenbelt, MD 20771 USA
*NAS-NRC Senior Post-doctoral Fellow
I Carter, J., Dean, A. J., Manchada, R. K., and Ramsden, D., Nature,
262, 369 (1976).
2Klebesadel, R. W., and Strong, T. B., Paper A.1.1, Proceedings of
the 1975 COSPAR Symposium, Varna, Bulgaria, May, 1975; to be published.
3Strong, I. B., Klebesadel, R. W., and Evans, D., Ann. N.Y. Acad, Sci.,
262, 145 (1975).
4Strong, I. B., Klebesadel, R. W., and Olson, R. A., Astrophys. J. Lett.
188, L1 (1974).
5Wheaton, W. A., Ulmer, M. P., Bal%y, W. A., Datlowe, D. W., Elcan, M. J.,
Peterson, L. E., Klebesadel, R. W., Strong, 1. B., Cline, T. L., and
Desai, U. D., Astrophys._1. Lett., 185, L57 (1973).
6Metzger, A. F.., Parker, R. H., Gilman, D., Peterson, L. E., and
Trombka, J. I., Astrophys. J. Lett., 94, 1,19 (1974).
7Cline, T. L., and Desai, U. D., Astrophys. J. Lett., 196, L43 (1975).
Figure Caption
Fig. 1. The results of Carter et al. l , adjusted by the six factors
considered in this letter, numbered accordingly. The observed burst size
spectrum of Vela events and comparison models, as incorporated in
Figure 1 of Carter et al., 1 are included.
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No new limit on the size distribution of gamma-ray bursts

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