The log N-log S data acquired by the Pioneer Venus Orbiter Gamma Burst Detector (PVO) are presented and compared to similar data from the Soviet KONUS experiment. Although the PVO data are consistent with and suggestive of a -3/2 power law distribution, the results are not adequate at this state of observations to differentiate between a -3/2 and a -1 power law slope

Fenimore, E. E.

Klebesadel, R. W.

Laros, J.

English

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Los Alamos National Laboratory Is operated by the University of California for the United States Department of Energy under contraei W-7405-ENG-36
TITLE: LOG N-LOG S IS INCONCLUSIVE
AUTHOR(S):	 R. W. Klebesadel, E. E. Fenimore, and J. Laros
SUi'MIT'EDTO: Steer Worshol -n Astronomy and Astrophysics at Lick Observatory
Santa Cruz, California
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Old
1= is
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	0 enomas Los Alamos National Laboratory
 Los Alamos New Mexico 87545,
FGRM NO 836 R4
ST NO 2629 5141
LOG N-LOG S IS INCONCLUSIVE
(Expurgated Version of Title)
R. W. Klebesadel, E. E. Fenimore, and J. G. Laros
University of California, Los Alamos National Laboratory,
Los Alamos, NM 87545
ABSTRACT
The log N-log S data acquired by the Pioneer Venus Orbiter Gamma
Burst Detector ( PVO) are presented and compared to similar data from
the Soviet KONUS experiment. Although the PVO data are consistent
with and suggestive of a -3 / 2 power law distribution, the results are
not adequate at this state of observations to differentiate between a
-3/2 and a -1 power law slope.
INTRODUCTION
In an attempt to resolve the apparent inconsistencies between
the PVO (and earlier IMP/Vela 1 ^ cosmic gamma-ray burst log N-log S
data and the Soviet KONUS data we have more critically evalua'.ed the
response of both the PVO and Vela instruments. Initiajly (as
reported at the 157th meeting of the AAS, January 1981 ) there
appeared to be general agreement between PVO and KONUS data.
Further, a careful reanalysis of in-flight calibration data from both
PVO and ISEE-3, more extensive Monte Carlo analyses of instrument
response functions, and additional intercomparisons of iata
(particularly for solar-flare X-ray bursts whose softer spectra
enhance the ability to discern the thresholds of the measurements)
verified that the PVO instrument is operating at almost exactly the
intended sensitivity. We have also considered the methods of
presentation of these data, and their effects on the comparisons of
results from different experiments.
DISCUSSION
The latest analysis of the PVO data resulted in only minor
variations from the original analysis. The PVO log N-log S data are
shown graphically in Figure 1. The convention we employ is to plot a
histogram of the integral event frequency with steps at the level of
fluence observed for each event. A -3/2 power-law f nction is shown
fit to the data at a level of fluence 5 10-4 erg cm . Below this
level of fluence it is clear that the data diverge from a -3/2 power-
law function, but it is also clear that instrumental threshold
effecte contribute heavily to this deviation. Also shown is the -3/2
Cd
i
S-'	 s%
DVO1	 (KOIJUS1
a0
-1
3	 -4 -S
e
1
J
O
-4
LOG CLUEi10E- EMS PLQ OMU E CaM Ena
Figure 1. Log N-Log S for PVO
data acquired through 1979.
Power law functions with a
slope of -3/2 as fit to these
data and as have been fit to
KONUS data2 are included.
(Note the impression that the
KONUS data show a higher level
of fluence than do the PVO
data.)
LOG 8
Figure 2. Two presentations of
the KONUS data2 for events with
quoted levels of fluence >10-5
erg cm-2. Data taken from the
tables 2
 are plottttd as the
lighter, irregular curve using
the same convention as in
Figure 1. Also shown as the
bold histogram are a portion of
the binned data with the -3/2
power-law slope transcribed
from Figure 1683.
power law which has been presented with the KON'JS data 2 . It is
apparent that the KONUS -3/2 power-law approximation is not
consistent with the PVO data. Note, however, that Mazets et al. do
not present this function as a good fit to the data but, rather,
claim that the slope is leas than unity3.
We have taken the liberty of presenting the portion of the KONUS
data at fluences > 10 5 erg cm-2 , as derived from the tabular listings
-)f Mazets et al. 2 , and using the convention employed in presenting
the PVO data. This is shown as Figure 2. Note that a dead-time
correction is required in order to properly determine the effective
event frequency. We have used the observin; time as quoted by Mazets
et al. 2. The shape of the curve will be independent of this
correction, and will be only a function of the fluences listed in the
tables. This assumes that the fluences listei in the table are fully
corrected for geometric and spectral effects, and that no further
manipulation of the data is necessary before presentation in a
graphical form.
Figure 2 also includes the curve transcribed from Mazets et al.3
in which the same data are binned into quarter-decade intervals and
fit with the -3/2 power law that was shown in figure 1. The binned
presentation tends to suggest a higher average level because the data
are actually represented by the lower left-hand corner of each step
rather than the aid -point. We are not able to explain why the binned
histogram does not conform to the curve which we have plotted from
the tabulated data. We ha ,^,e previocsly ( from the preliminary version
of the KONUS catalog) been successful in reproducing the binned form
of the KONUS Log N-Log S curve from the tabular data, supporting our
assumption that no further corrections are required. Note that we
performed no editing in presenting the KONUS data, but have included
every event with fluence quoted at a level >10
-5 erg cm-2. It is
also particularly interesting that there is no event listed in th
KONUS catalog with a fluence in the range 5.6-10 x 10
-4 erg cm-1
although preliminary versions of the catalog did include one event in
this range.
In fact, KONUS and PVO results are in reasonable agreement when
compared in a consistent manner. The data shown in Figures 1 and 2
have been combined and are shown in Figure 3. It was found that the
effect of two events (GBi91115 and GB791ll6, which were not recorded
by the KONUS experiment) created a rajor impact in the comparison of
the two curves. Therefore, anotler comparison was performed,
including PVO data only for those events also observed by the KONUS
experiment. This comparison is shown in Figure 4, and the agreement
betw en KONUS and PVO is seen to be remarkably good. This is true in
spite of the fact that the KONUS catalog contains a number of weak
but long duration events ( such as GB791101 and G9791230), for which
2
c ^uug^
i
90
1L
s
0
MODUS)
( VVO)
LOG S
Figure 3. PVO (bold line) and
KONUS (light line) data (from
Figures 1 and 2, respectively)
compared directly. Note the
impression that the KONUS data
define a smaller slope.
LOGS S
Figure 4. The subset of PVO
data representing only those
events alsn observed by the
KONUS experiment compared
directly to the KONUS data from
Figure 7.
are quoted rather high levels of fluence but which were not recorded
or recorded at only a very low level by the PVO instrument. It is
also noteworthy that there is not general agreement in the levels of
fluence quoted from the two data sets for individual events but,
rather, variations over a range of a facto r of -40 are observed.
Thus, the impression created by the log N-log S is very
sensitive to the effects of only a few large events if one is allowed
to be misled by the upper end of the curve, which is poorly defined,
statistically. Since these events are expected to occur in a
stochastic fashion, we have attempted to model such observations and
characterize the statistical significance of the data through Monte
Carlo simulations. The results of a family of such simulations, for
an input distribution conforming to a -3 /2 power law, is shown in
Figure 5. This was intended to represent the present ( 145 events)
state of observations. The uncertainty of ±0.15 in fitting the slope
implies that there can be expected to be observed only a marginally
significant ( 3a) difference between a -1 and a -3/2 power-law slope,
even if the observations are unperturbed by thresholding effects.
Further, the threshold effects are likely to create an impact over a
large range of the data, since a number of instantaneously weak but
long duration events (particularly in the BONUS data) contribute
tiward the distribution at high fluences. Similar events only
slightly weaker may be below the threshold of detecticn, creating a
deficiev.::y et moderate and lower fluences4.
Several miscellaneous points should be mentioned. First,
presenting the log N-log a data in differential form would be less
likely to be misleading; however, the number of events available for
analysis is yet so small that a problem exists in subdividing the
data into more than a few intervals. Actually, this problem is only
I
Figure 5. A family of Monte
Carlo simulations representing
145 event per year drawn from
an N a S-372 distribution. The
average slope of the simulated
observatons was found to be
-1.48 ±0.15.
-'b	 -4	 -5	 -2
LOG 9
2
^i
J
0
masked by using the integral form. In any case, the low frequency of
events observed at the sensitivity of present long-duration
(satellite borne) gamma burst monitors precludes resolution of the
shape of the Log N-Log S curve in the near future. Second, the
frequency of events as a functior of maximum intensity (log N-log P)
is much less sensitive to distortions caused by the instrument
threshold effects. Both PVO and KONUS Log N-Iog P curves much more
nearly conform to a -3/2 power law. Third, measurements made by
balloon-borne instruments, ostensibly having much greater sensitivity
than present satellite-borne experiments, imply an upper limit for
event frequency at very low fluences which is well below an
extrapolation downward at a slope of -3/2. Although thefe is some
uncertainty in relating the balloon and satellite data, the balloon
data seem internally to deny a -3/2 power-law distribution at very
low levels of fluences.
CONCLUSIONS
In summary, we feel that PVO and KONUS log N-log S data are in
reasonable agreement. The impression of disagreement has been
created in part by the differing methods of data presentation and in
part by the statistics of the observations (instrumental duty cycle
and statistics of occurrence). The data appear to be consistent with
a -3/2 power-law distribution, however, the present state of the
observations has not produced sufficient data to allow the slope or
shape of the curve to be clearly defined.
ACKNOWLEDGMENT
This work was performed under the auspices of the
U.S. Department of Energy and was partially supported by the National
Aeronautics and Space Administration under contract 98331A.
REFERENCES
1. T. L. Cline, U. D. Desai, W. K. H. Schmidt, and B. J. Teegarden,
Nature, 266, 692 (1977).
2. E. P. Mazets, S. V. Golenetskii, V. N. Il'inskii, V. N. Panov,
R. L. Aptekar, Yu. A. Gur'yan, M. P. Proskura, I. A., Sokolov, Z.
A. Sokolova, T. V. Kharitanova, A. V. Dyatchkov, and N. G.
Khavenson, Astrophysics and Space Science, 80, (1981).
3. R. W. Klebesadel, W. D. Evans, E. E. Fenimore, J. G. Laros, and
N. J. Terrell, Bull. of AAS, 12, 810 (1981).
4. J. C. Higdon, proceedings of this conference.
5. A. J. Fishman, proceedings of this conference.


Log N-log S in inconclusive

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