Discussions are presented of the associations between cosmic gamma ray bursts and transient X-ray sources, and the release of gravitational binding energy during the formation of neutron stars. The model for studying the associations is described along with the release of neutrinos during the collapse of white dwarfs

Cohen, J. M.

Desai, U. D.

Holt, S. S.

English

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USA [i I.
GAMMA-RAY BURSTS DURING NEUTRON
STAR FORMATION
JEFFREY M. COHEN
REUVEN RAMATY
GAMMA RAY BURSTS AND TRANSIENT
X-RAY SOURCES
R. RAMATY, U. D. DESAI, S. S. HOLT
(N'SA — TM — X-7C510)	 GA,'il'A — :'AY EUSSTS L'UHIhG	 h74-10777
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OCTOBER 1973 0^N 732 
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GAMMA-RAY BURSTS DURING NEUTRON STAR FORMATION
r	 '
Jeffrey M. Cohen* and Reuven Ramaty
Laboratory for High Energy Astrophysics
Goddard Space Flight Center, Greenbelt, Maryland
^r
*Permanent address: Physics Department
University of Pennsylvania
Philadelphia, Pennsylvania
'	 October 1973
nGAMMA-RAY BURNS AND TRANSIENT X-RAY SOURCES
R. Ramaty, U. D. Desai and S. S. Holt
Goddard Space Flight Center,
Greenbelt, Md. 20771
We wish to point out a possible association between cosmic gamma-ray
bursts (1) and transient X-ray sources. We find that the gamma-ray burst
IF	 of April 21, 1971 could have signalled the birth of the transient X-ray
source 2U 1543-47.
Five transient X-ray sources have been reported with a frequency of
-1 year -1 : Cen X-2 (Ref. 2), Cen X-4 (Ref. 3), 2U 1735-28 (Ref. 4),
2U 1543-47 (Ref. 5) and Cep X-4 (Ref. 6). As sky coverage is not complete
for transient X-ray sources, it is conceivable that the actual frequency
of these objects is comparable to Lhat of 'y-ray bursts. We have compared
both the starting times and positions of these sources with the dates and
available positional information of gamma-ray bursts (7) For a correla-
tion we demand that the position of the gamma-ray burst and X-ray source
should coincide, and that the date of the gamma-ray burst should precede
the starting time of the transient X-ray source. However, because the
lifetime of the X-ray sources is about a few months, an acceptable candi-
date gamma-ray burst should not precede the start of the X-ray source by
more than such a time interval.
We have found a possible association between the April 21, 1971
gamma-ray burst and the transient X-ray source 2U 1543-47 (Ref. 5).
'this X-ray source appeared s •:., ` ; -.ie between March 25, 1971 and August
17, 1971, and its intensity decreased by about an order of magnitude
1
V
-I- -
- 2 -
by December, 1971. The position of 2U 1543-47 was a l = 235°96 and
A l = - 47°56 with an error of about 0°5. The gamma-ray burst of
April 21, 1971 was observed by 2 satellites of the Vela system, and
thus only a circle of positions could be determined. The center of this
circle was at a, = 247°4 ind 6„ = 34°, and its radius was between 80°8
and 85 °2 (Ref. 7 and I. B. Strong, private communication, 1973). The
error in the position of the center of the circle is small in compari-
son with the error in angular size of the radius. The angular separation
between the X-ray source and the center of the position-circle of the
gamma-ray burst is 82°2, i.e. well within the range of radii of the
position circle. Thus, both the temporal and positional data are
consistent with an association between the burst of April 21, 1971 and
2U 1543-47.
The y-burst error circle has a total solid angle which is less
than 0.04 of 4n, so that 0.04 is a fair estimate of the probability
of a random association between the burst and 2U 1543-47 with regard
to the positional coincidence alone. There is, however, one other g-
ray burst (that of June 30, 1971) in the temporal window for which there
is no positional information. If we allow some delay between the y-ray
burst and Lhe appearance of the X-ray source, there are bursts on
January 2, March 15 and March 18, 1971 which might also be candidates,
but there is no positional information for the January 2 burst, and the
other two have positions which cannot be reconciled with 2U 1543-47.
We have searched for associations of the other transient X-ray
sources with y-ray bursts, with inconclusive results. No y-ray bursts
r
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1x the August 22,	 1970 burst as seen by detectors on 3 different satellites.
This burst consists of 2 peaks separated by about 6 seconds, with con-
s
siderable fine structure within the first peak.	 Because the time reso-
lution of the experiment decreases with time after the	 initial trigger,
it cannot determine whether similar fine structure exists in the second
peak as well. This double peaked structure seems to he a property of
a fraction of the gamma-ray bursts; some bursts are single, but others
show three or more peaks on a time scale of 10 to 20 seconds.
The exact rise times of the bursts is not known but rapid fluctua-
tions on time scales less than 1/64 seconds have been observed on several
occasions. The decay time of the first peak is about 1 to 2 seconds,
and that of the second peak appears to be of the same magnitude. Among
the single peaked bursts, however, there are events with shorter decay
times as well.
We propose the following sequence of events to account for the gamma-
ray bursts. A white dwarf accreting matter (possibly from a binary com-
panion) collapses when its mass exceeds the Chandreshekhar limit. Since
this limit is less than the maximum stable mass of a neutron star, the
+I
collapse should proceed to a neutron star. This process releases about
(1)
10 53 ergs of gravitational energy. Most of this energy is carried away
by neutrinos (d) , but a significant part of it can be in heat and in
pulsations.
A collapsed hot object is expected to emit blackbody radiation () with
luminosity L given by
L = 4-Tr2JT4
	
(1)
ti
-4-
t#
-5 4cm-2 sec -1 ,where, a = 5.7x10erg (°K) - r is	 the radius,	 and T is
the surface '.emperature.	 The observed photon flux density of the
2 l keV -1 )bursts	 (meas.,red in photons cm- sec -	is proportional to exp
4
( 5)(-E/E0 ), where E is photon energy and E 	 is a parameter which
varies from event to event but is generally in the range from about
100 to 200 keV.	 A blackbody spectrum with constant temperature is
not consistent with such a spectrum. 	 However, a cooling blackbody
(4)
does provide a very good fit to the observations.	 The point is
that the spectral measurements are made over time intervals of the same
order as the duration of the bursts, and the	 temperature is expected
to vary over this interval.	 The deduced initial temperature of the
°K.(4)bursts is about 2x10 9
Cocke and Cohen 
(10) 
have studied the large amplitude pulsations
106of a degenerate star oscillating between radii of about 	 to 3x10 8 cm.
The period of these oscillations is about a few seconds. These pulsa-
tions can	 account for the 6 seconds separation between peaks in the
(8,10)
burst.	 The large neutrino luminosity,	 however, will rapidly damp the
oscillations.	 This can explain	 the	 transient nature of the bursts, 	 as
well as the observation that some bursts do not show multiple peaked
structures.
The descent of the unstable white dwarf into the neutron star
configuration takes place	 in a time comparable to the	 free-fall time.
Since the gravitational energy is expected to be released close to 	 the
neutron star radius, 	 the rise time,	 t r ,	 of the bursts should be of the
If
1
r	{
I.
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order of the free-fall time from a radius comparable to the radius of the
neutron star,
-1/2t 	 (n/2)r3/2(2GM)(2)
r
Here G is	 the gravitational constant and M is 	 the mass of the star.
For M = 1 solar mass and r ° 3 neutron-star radii,	
t 
	 is about
5x10
-4
 seconds.
	
This time is much shorter than the presently available
observational upper limit on the rise time; 	 future observation of rise
times of the order of 	 milliseconds will provide observational
support	 to the present model.
The decay times of the bursts are probably determined by the cooling
of the -tar.	 The time-integrated gamma-ray flux of the bursts is in
: the range 10
-5	
to 2x10
-4
 erg cm-2 (Ref.	 2).	 With a duration of 2 seconds
r and T
	
10 9	Equation	 (1) yields:-y	 °K,
r 0.8x1018r < d 4 3x10 18 r,	 (3)
where d is	 the distance	 to the source and r its radius, both	 in centi-
meters.
	
With r in the range 10 6 to 3xJ0 8cm, d	 is between 0.2 to 300 Mpc.
. Thus,	 for our model to be valid,	 the bursts should be extragalactic,
be.ause	 the lower limit on d is greater than any galactic dimension.
The upper limit on d is much greater than the distance to the Virgo
cluster	 (— 10 Mpc, Ref.	 11).	 Most of the galaxies within a distance
of about 10 Mpc	 from our own are in the Virgo cluster 	 (--'	 = 284°, b0 = 74'),
but among the seven bursts for which arrival directions are known,(12)
none come from this cluster.	 This means that the sources of the majority
of the bursts are probably farther than about 10 Mpc. 	 If the minimum
distance is about 25 Mpc, say,	 then the minimum size is about 108cm
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and the minimum gamma-ray luminosity is —7x10 48
 erg sec -1 . In our
model, the maximum size is about 3x10 8cm: hence the maximum
luminosity is 7x1049 erg sec -1 . Because the total energy released
during the collapse is ­ 10 S3 ergs, the ganuna-ray efficiency is about
10
-4 
to 10 -3 . Also, for r in the range 10 8 to 3xlO8cm, eq.(3) yields
25 Mpc 5 d 4 300 Mpc. with a density of 0.03 galaxies per Mpc-3
(ref. 11), the observed rate of —6 gamma-ray bursts per year implies
that the rate per galaxy is greater than about 1 event per 5x10 5 years.
on the other hand, because no bursts were seen from the ­2500 galaxies
in the Virgo cluster (11) , the rate of gamma-ray bursts per galaxy is
less than about 1 event per 400 years.
The observed temporal structure of the gamma-ray bursts could be
due to oscillations. As iiscussed above, the second peak at about 6
seconds could be due to a rebound of the neutron star. The fine
structure within the first peak could be caused by oscillations of the
rebounding star. Because the radius of the star during rebound is
intermediate between the radii of a neutron star and a white dwarf, its
oscillation period could also be intermediate between the oscillation
periods of such objects. The period of a white dwarf is of the order
of a few seconds (13) , and the period of a neutron star is about 10-3
seconds (14) . Iliese periods bracket the time constants of the fine
structure which are of the order of a few tenths of seconds.
The principal observational tests of our model are:
1.	 Spectral measurements over narrow time intervals (--0.1 seconds)
which would confirm the blackbody nature of the emission.
i
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2. Observation of the rapid rise time of the bursts (--10 -4 seconds).
However, because the radius of the object is expected to increase as
a result of the rebound of the star, there could be an additional
slower increase of the intensity after the initial rapid rise.
3. Detection of a neutrino burst in coincidence with the gamma-ray
burst.
1
d
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REFERENCES
1. Borner, G. and Cohen, J. M., Astrophys. J. (in press) (1973).
2. Klebesadel, R. W., Strong, I. B., and Olson, R. A., Astrophys.
J. Letters, 182, L85 (1973).
3. V eeler, J. A., Ann. Rev. Astron. Astrophys., 4, 393 (1966).
4. Ramaty, R., and Cohen, Jeffrey IM., Cooling Blackbody: A Mechanism
for Cosmic Gamma-Ray Bursts, Proceedings of the Los Ale.js
Conference on Transient Cosmic Gaixna- and X-Ray Sources, September
1973 (in press).
5. Cline, T. L., Desai, U. D., Klebesadel, R. W., and Strong, I. B.,
Astrophys. J. Letters, 185, L1 (1973).
6. Wheaton, W. A., Ulmer, M. P., Baity, W. A., Datlowe, D. W.,
Elcan, M. E., Peterson, L. E., Klebesadel, R. W., Strong, I. B.,
Cline, T. L., and Desai, U. D., Astrophys. J. Letters, 185, L57
(1973).
7. Hoyle, F., and Narlikar, J., Nature, 218, 123 (1968).
8. Bahcall, J. N. and Wolf, R. A., Phys. Rev. Letters, 14, 343, (1965)
9. Orszag, S. A., Astrophys. J., 142, 473 (1965)
10. Cocke, W. J. and Cohen, Jeffrey M., Nature, 219, 1009 (1968).
11. Allen, C. W., Astrophysical Quantities (Athlowe Press, London)
(1963).
12. Strong, I. B., Klebesadel, R. W., and Olson, R. A., A Preliminary
Catalog of Transient Cosmic Gamma-Ray Sources Observed by the Vela
Satellites, Proceedings of the Los Alamos Conference on Transient
Cosmic Gh mna- and X-Ray Sources, September 1973 (in press).
r\'
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13. Cohen, J. M., and Cameron, A.G.W., Astrophysics and Space Science,
10, 227 (1971).
14. Cohen, J. M., Lapidus, A. and Cameron, A.G.W., Astrophysics and
Space Science, S, 113 (1969).
i
GAMAIA-RAY BURSTS DURING NEUTRON STAR FORMATION
.Jeffrey M. Crhen'r and Reuven Ramaty
Laboratory for High Energy Astrophysics
Goddard Space Flight Center, Greenbelt, Maryland, USA
During the formation of neutron stars, large amounts of gravita-
tional binding energy (­ 10	 ergs) are released (1) , and	 small fraction
%f this energy could go into prompt high-energy photon emissions. We
propose that such cmissioni could account for the recently observed
gam,na-ray bursts of cosmic origin(2).
Brcause the prompt nature of the bursts indicates little absorp-
tion o : ammia rays, we expect that these neutron stars are not
surrounded by large amounts of matter. This might explain why no
I	 optical supernovae were observed in coincidence with the gaimna-ray
bursts. The neutron stars could be formed from collapsing white
dwarfs (3) , the collapse being caused by accretion which raises the
mass above the Chriedrashekhar limit. The rise time of the bursts should
be of the order of the free-fall time of the star L om a radius compar-
able to the radius of the neutron star (— 10 -4 seconds). The gravitational
energy released during the collapse heats the star and causes the
emission of neutrinos. The surface of the star radiates as a blackbody;
we have shown (4) that blackbody radiation of variable temperature can
explain the observed spectra of the bursts (5) . The temperature variation
is due to cooling: an initial temperature of about 2x10 9 °K decreases
by a factor of 2 to 3 during the observed decay of the bursts of about
* Permanent address: Physics Department, University of Pennsylvania,
Philadelphia, Pennsylvania, USA.
0
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1 to 2 seconds. Time-integrated blackbody emission (4) can then
account for the observed spectrum in the gamma-ray region. When tire
temperature is further decreased, blackbody emission can also account
for tire x-ray observations(6).
Tire decay of the bursts is due to cooling or other processes
which dissipate the initial thermal energy. The double or multiple-
peaKed structures of some of the bursts could be caused by rebounds (7)
of the neutron star. Other observed temporal fine structure could be due
to oscillations of the rebounding star.
Considerations of blackbcdy emission and the possiole size of the
emitting region imply that the sources of the gamma-ray bursts should
be extragalactic at distances from several tenths of megaparsecs to
about 300 Mpc. The comparison of arrival directie • is with the distri-
bution of nearby galaxies limits this range to distances greaten than
a few tens of megaparsecs, The total gamma-ray energy of the bursts
is then 1049 to 10 50 ergs and the frequency of the bursts is greater
than about 1 event per 500 years per galaxy.
About twentv short bursts of photons in the energy range from about
100 keV to 1 MeV have been observed over n 3-year period by the Vela
satellite system
(2)
. Some of these bursts have also been observed in
coincidence by a garama-ray detector on IMP-6 (5) and an X-ray telescope
on OSO-7 (6) . Various time-of-flight techniq^.es and direct directional
observations by the OSO-7 detector seem to establish the reality of tire
bursts and their extra solar-system origin.
Klebesadel et al. (2) have shown as an example the tem poral variations of
a3 -
are reported prior to April, 1967, when Cen X-2 was first detected.
No y-ray bursts were dQ !cted between July 2, 1967 and July 3, 1969, the
latter occurring clos( _o the appearance of Cen X-4 between July 6, 1969
and July 9, 1969, but the positions do not agree. Barring any sys-
tematic problem associated with the computation of the Y-ray burst
position ring, Cen X-4 is not positionally compatible with the July 3,
1969 burst. No bursts for which there are positional data agree with
the appearance of 2U 1735-28 in March, 1971, although there exists a
burst on January 2, 1971 which lacks positional information. Similarly,
no bursts preceding the discovery of Cep X-4 on June 20, 1972 have posi-
tions in agreement with that source, although there are bursts which
lack positional data on June 30. 1971, January 17, 1972 and March 12,
1972.
There are at least two explanations for these negative results,
assuming that the association with 2U 1543-47 is real. Firstly, not
all transient X-ray sources necessarily represent the same phenomenon,
and hence not all of them should be preceded by gamma-ray bursts.
Secondly, both the X-ray and the burst data are incomplete: positional
information is not available for all gamma-ray sources, and, moreover,
some bursts may not have been detected by the Vela detectors. How-
ever, if the April 21, 1971 gamma-ray burst, being one of the weakest
events, was indeed followed by a transient X-ray source, similar as-
sociations should exist for other gamma-ray bursts. This could be
tested by future X-ray surveys of regions around gamma-ray bursts
shortly after their occurrence, but not later than a few months after
the date of the burst.
I\
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Finally, we mention the time-integrated fluxes. These were about
3x10-e erg cm	 for the burst of April 21, 1971 (I. B. Strong, private
communication, 1973), and —0.1 erg cm- 2 for 2U 1543-47. Thus, if the
proposed association is real, the source of these events emits about
3x104 more energy in quasi long-term X-rays than in prompt gamma rays.
Acknowledgment: We wish to acknowledge I. B. Strong for the communi-
cation of data prior to its publication.
arm-
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REFERENCES
1. Klebesadel, R. W., Strong, I. B., and Olson, R. A., Astrophys. J.
•	 Letters, 182, L85 (1973).
2. Chodil, G., Mark, H., Rodrigues, R., and Swift, C. D., 1968, Astrophys.
J. Letters, 152, L45 (1968).
3. Evans, W. D., Belian, R. D. and Conner, J. P., Astropys. J. Letters,
159, L57 (1970).
4. Giacconi, R., Murray, S., Gursky, H., Kellogg, E., Astrophys. J., 178,
281 (1972).
5. Matilsky, T. A., Giacconi, R., Gursky, H., Kellogg, E. M. and Tananbaum,
H. D., 1972, Astrophys. J. Letters, 174, L53 (1972).
6. Ulmer, M. P., Baity, W. A., Wheaton, W. A. and Peterson, L. E.,
Astrophys. J. Letters, 184, L117 (1973).
7. Strong, I. B., Klebesadel, R. W. and Olson, R. A., A Preliminary Cata-
log of Transient Cosmic Gamma Ray Sources Observed by the Vela
Satellites, Proceedings of the Los Alamos Conference on Transient
Cosmic Gamma- and X-Ray Sources, in press (1973).
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Gamma-ray bursts during neutron star formation. Gamma-ray bursts and transient X-ray sources

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