The spectra of the broadening 0.511 MeV annihilation line produced by high temperatures was calculated in the case of unthermalized plasma; i.e., T sub e(+) is not = T sub e(-). The flattening in the spectrum of the annihilation lines for large differences of electron and positron temperatures is a strong indication that the observed features of the hard tailed spectrum of the gamma bursts can be well described by annihilation of unthermalized positrons. It is proposed that the charge separation occurring in Eddington limited accretion onto a neutron star or the one photon pair production in strong magnetic fields as a mechanism for the production of unthermalized positrons in the sources of gamma bursts. From the best fit of experimental spectra by the model, the parameters of sources for which the regions with different plasma temperatures can exist is evaluated

Karakula, S.

Tkaczyk, W.

English

NASA Technical Reports Server

N92-21914
UNTHERMALIZED POSITRONS IN GAMMA-RAY BURST SOURCES
W. Tkaczyk, S. Karakula
Institute of Physics, University of L6d_.
ul. Pomorska 149/153, 90-236 Ldd_, Poland
Abstract. The spectra of the broadening 0.511-MeV annihilation line produced by high
temperatures was calculated in the case of unthermalized plasma; i.e., To+ * To-. The
flattening in the spectrum of the annihilation lines for large differences of electron and
positron temperatures is a strong indication that the observed features of the hard-tailed
spectrum of the gamma bursts can be well described by annihilation of unthermalized
positrons.
We propose the charge separation occurring in Eddington limited accretion onto a
neutron star or the one-photon pair production in strong magnetic fields as a mechanism for
the production of unthermalized positrons in the sources of gamma bursts.
From the best fit of experimental spectra by our model, the parameters of sources for
which the regions with different plasma temperatures can exist is evaluated.
1. Intrggtuction. The gamma-ray bursts are short flashes of hard photons with an energy of
1 keV a to few tens of MeV. The gamma-ray bursts are bright, energetic, short-lived
phenomena that are characterized by extremely hard spectra. The spectroscopic study of
gamma-ray burst spectra on the Solar Maximum Mission (SMM) satellite [1,2] have provided
a rich materials avenue towards the understanding the origin of these events. For detailed
discussions of the experimental data of gamma-ray bursts, see review articles [2,3,4,s].
The major characteristic of gamma-ray bursts are as follows [3]:
1. The bursts are divided by their duration into two classes: short (< 1 s) and long (1 s to
a few minutes).
2. The continuum spectra of bursts evolve rapidly with time.
3. The absorption features in the energy range of 30-100 keV are, in most cases, the strongest
in the initial phase of the burst.
4. The broad annihilation lines of 350-450 keV are also the strongest at the beginning of the
burst or at intense peaks of the time profile.
5. The total energy release in a gamma-ray burst is not constant; it increases approximately
in proportion to the time duration of the event.
6. Gamma-ray bursts may be accompanied by intense X-ray emission and optical flashes.
The localization of gamma burst sources are not clear yet, but the log n (number of
events) versus log Nm_x (maximum count rate in the time profile) plots are in full agreement
with an isotropic distribution of the sources over the celestial sphere. The above argument
prefers a Galactic origin of gamma bursts. Neutron stars are proposed as a candidate for that
source distribution. The lines in the 30-100 keV region have been interpreted as broad
cyclotron scattering in a strong magnetic field. Emission features in the 350-450 keV range
have been interpreted as gravitationally redshifted annihilation e+e - lines produced near the
surface of neutron stars. Hard power-law tails observed in the spectra of gamma bursts
309
https://ntrs.nasa.gov/search.jsp?R=19920012671 2020-03-17T13:15:49+00:00Z
continuein some cases to at least -'10 MeV. The existence of such high-energy photons and
cyclotron absorption-line spectra have caused difficulty in the construction of self-consistent
models of gamma burst sources. The high-energy emission region should be nearer to the
neutron surface than the cyclotron absorption region in the case of interpreting observations
of annihilation lines as gravitational redshifts. Moreover, the detailed analysis of relations
between redshifted annihilation lines and their widths in observed gamma burst spectra shows
significant disagreements when thermal pair dominant plasma annihilation has been assumed
In this paper, we propose annihilation of unthermalized plasma (T.+ _ T,-) as the
mechanism of producing gamma-ray burst spectra with line e+e - and hard-tail features. In
that case, the redshifts of line e+e - are mainly due to kinematics of the annihilation process,
so the relativistic emission region can be located on larger distances than absorption from the
surface of a neutron star. The spectra with hard tails measured by KONUS, SMM and HEAO
A-4 experiments have been fitted by thermal bremsstrahlung in soft-energy regions, and in
annihilation lines of unthermalized plasma in hard-energy regions. From the best fit, we have
evaluated the temperature of electrons T,-, positrons T,+ and the clumpiness parameter of
gamma-ray burst sources.
2. The spectra from _nnihil_tiQn. The broadening of the annihilation line 0.511 MeV can
be produced by high temperatures, a strong magnetic field and Doppler shift due to bulk
-10
-11
-12
i ,
-_ -14
-16
-17
-18
-5 -4 -3 -2 -1 0 1
log E[ISeV ]
Fig. I. Fig. 2.
-1 0 1
log E [GeV]
motion and the gravitational field. Recently we have calculated the spectra of annihilation
lines for two cases: thermalized To- = T,+ [7] and unthermalized T,+ , T,- [7]. Figure
1 shows spectra for a thermalized plasma. Figure 2 shows spectra for an unthermalized
310
plasmawith electrontemperaturesof 105K andselectedtemperaturesof positrons. Thepeak
energiesandwidthsof annihilationspectraaredifferent in the caseof unthermalizedplasma
in comparisonwith annihilationspectrafor equaltemperaturesof electronsandpositrons[8,9].
We should note that the peak energy in the spectrais not blueshifted when the
temperaturepositron increases,but in fact, it evendecreasesbelow 0.511 MeV. For large
differencesbetweencomponenttemperatures,thepeakenergyapproachesthevalue mJ2.
Moreover, the spectra from unthermalized plasma at that point are harder and approach
the power-law type with a power index -1. The spectra indicate similar features as observed
in gamma-ray burst spectra with hard tails.
3. Models of gamma burst source. Recently the states of plasma in gamma burst sources
have been investigated in many papers. The main question is, when can the line be seen?
As was shown by Svensson [_0] and Zdziarski [_i], the annihilation line is not expected from
plasma in the pair equilibrium; i.e., the pair annihilation rate balances the pair production
rate. Moreover, the gamma-ray burst spectra cannot be explained by an optically thick
thermal model with plasma in a weak magnetic field; i.e., B < < Bcr (magnetic field B is much
lower than critical Bcr=4.413 × 10 _2 Gs). For plasma in a magnetic field B>_BCr, one-photon
pair e+e - production and annihilation rates should be included. Harding [12] shows that a
thermal model of gamma bursts with pair production and annihilation in a strong magnetic
field requires a maximum source size which is much smaller than a neutron star radius.
Moreover, the time scale of synchrotron emission in the gamma-ray burst sources in a
magnetic field above 10 a2 Gs is on the order of less than 10 -_6 s. In that case, the
synchrotron emission dominates the annihilation line. The above results show that in both
cases, a low and strong magnetic-field thermal, optically thick model with plasma in
equilibrium is not convenient for explaining all features in gamma-ray burst spectra. We
propose a thermal bremsstrahlung, optically thin model of gamma bursts with unthermalized
plasma To+ * Te-. The continuum component of the spectrum is due to bremsstrahlung of
a hotter source region but the relativistic component is due to annihilation of a hotter plasma
of positrons with a cooler plasma of electrons. The region of continuum emission and the
relativistic component are separated. The annihilation region can be placed far from the
neutron star surface. This supports the fact that the burst spectra do not cut-off above a few
MeV and indicates that few high-energy gamma rays are eliminated by photon-photon or one-
photon pair production in the magnetic field. The photon beaming along magnetic field lines
avoids these difficulties. In our proposition, the annihilation line is redshifted due to
kinematics. The unthermalized plasma can exist in the case of turbulent motion or additional
heating of positrons or electrons. Figure 3 shows the annihilation time of unthermalized
plasma (full lines) and relaxation time (broken line) for plasma with a concentration of
n_+=n_-=102° as a function of temperature. From comparison of those times, we can
conclude that annihilation time is shorter than the relaxation time if the temperature of the
electrons is less than 108K and the temperature of the positrons is greater than 101°K. For
both types of models of gamma bursts: i) accretion matter on neutron star [131, and ii)
thermonuclear explosion [14], a hot plasma with a temperature > 109K is predicted.
In the accretion model recently proposed by Colgate and Petschek [13], details of
producing unthermalized plasma were discussed in our paper [7,_5]. We have proposed that
the charge separation in the matter of Eddington limited accretion onto a neutron star can
311
_ I _ , I I /I//
/ Ne-=Ne+:lo20 i/I"
/.<"11/,;<o.._
. l/? ./" / -
-6 _ i/
-71 I//
--8 l_ ,It I I 1 I
7 8 9 10 11 12 13
IogTe-
 'ig. 3
14
produce unthermalized positrons.
The scenario can be briefly
described as follows: a layer of
the thickness r-1 falls onto the
neutron star. The electrons will
be pushed away from the star by
the photon flux outgoing from
the surface. This produces a
charge separation and
consequently, an electric field.
The electrons are heated by
interaction with the photons.
Photons are produced by
annihilation of positrons and by
the compression caused by the
matter falling onto the star
surface. The pair production
processes caused by photons or
other particles are the source of
the positrons which are
accelerated not only by photon
interactions, as are the electrons,
but also by the electric field.
In a thermonuclear
explosion model, the strong
electric field generated by the motion of matter in a magnetic field, accelerated electrons up
to relativistic energies.
In a strong magnetic field, the electron energy is converted to the hot pair dominated
plasma. The plasma is considered to occupy a region of size R[cm], which is in a constant
homogeneous magnetic field of strength B' =B/Bcr , (Bcr=m2-c3/e_ =4.414 x 1013Gs). The pair
plasma's equilibrium state is determined by its temperature, T_" = kT/mc 2 (mc 2 is the electron
rest energy) and the values of B' and R. In order to calculate the positron concentration n,
we made the following assumptions: i) the plasma is confined, so that positrons do not escape
before annihilation; ii) the pair annihilation occurs by the two-photon process in
unthermalized plasma; iii) one-photon pair production by synchrotron photons dominates over
photon-photon and photon-particle processes (for some parameters of plasma it is a good
approximation [_6]; and iv) the electrons with temperature T_* have an isotropic Maxwellian
energy distribution.
a) Photons. The source of photons is the synchrotron emission of thermal electrons (T_*< 1).
The photon production spectrum was obtained from the emissivity of the synchrotron radiation
[17], and is done by formula:
s
n (E,O)= n 3.c _" .A(T*).T*.exp - T *z B'
- - sin0 _ J
312
where: O is the angle between the emitted photon momentum and magnetic field line, c -
velocity of light, n- concentration of electrons, A(T_ - normalization constant, E=Ev/mc _
is the photon energy in me 2 units, and r,=_/mc 2 is the classical electron radius.
We have evaluated the photon density by solving simple diffusion equations, taking
into account photon escaping time and one-photon pair creating rate.
b) Positrons. The synchrotron photon spectrum was taken to determine the rate of pair
production by the one-photon process:
E
rain
where: n (E,Q) - the photon spectrum, rI_(B',E,Q) - the rate of pair
production per photon of energy E.
The spectra of positrons was calculated using the formula:
dR_ dQ. n (E,Q).-- dEdE d6 dE '
÷ E +
rain
where: e=E /E is the fractional energy of one particle in the pair,
÷
=E +l/sin(O), r B(6) iS the pairs production rate for an individualEmin +
photon.
:5 lo_(ra')=-:.z _ -
lO
u_ : -I .6
e. -2/-f t
o -5 / I
-i0_ .// ]
-15 i
/
-: o -o,8 .4
log(T_')
Fig. 4. The rate of one-photon pair
production by electrons synchrotron
emission as function of temperature T_*
for the different values of magnetic
field strength and R=Icm.
°8['.4o,g(T')---o8
,o. | _- "---.b.
I "<. - "-. ,
×
,E
÷
0.4. _" .... .,
o o.3 r _. _ _,,
O.2 _ "-... "-.. '\
o _L \\
00 _-_-- _---+--_+__
--_ -1.8 --2.6 -1.4 --1.2
:og(B')
06
0.5
0.4
3.3
!o.2 .2°
Fig. 5. The peak eneEgy of
positrons in units E*=E /mc L (left
+ ÷
hand scale) and temperature of
positrons (right hand scale) as a
function of magnetic field.
313
101
10-3
o,1
10o
10"
102
Z
0
!--
0
-r 103
25 January
1982
1,0 1(20E(/WeV)
Fig. 6
\ I •
\ 191178
4",_
-4,-.
"t- \.
-,¥ \\.
-,- \ \
÷'t \
Te-: 106 K
Te+ : 3"10 m K
I
102
?t 4.
t
-4-
I
103 104
E (keY)
Fig. 8
101
E
LJ
E
0
102
r"
103
I I
200382 _
'l_'k_ =1010
01 102 103 104
I<eV
Fig. 7
Because of the threshold of the one-photon
pair production process, the positron spectra
has a peak at some energy. From this peak
energy, we have evaluated the temperatures
in units T_=kT+/mc 2. The positron
temperature is greater than (30-60) times the
temperature of parental electrons. The
generated pairs rapidly lose their transfer
energy by synchrotron emission. Before
annihilation they move along magnetic field
lines at a large distance from a neutron star
surface where the magnetic field is weaker
and the plasma is cooler. Hot positrons
annihilate with cold electrons. The photons
can escape from the magnetosphere without
appreciable attenuation.
314
4. The results. Figures 6, 7 and 8 show the spectra of two gamma-ray bursts described by
our model. The temperatures of the hot and cold components are indicated on the graphs.
The efficiency of bremsstrahlung emission is dependent on the concentration squared (n 2 hot
component), but annihilation is proportional to the product of (no-n,+). Thus from the best
fit of experimental data, it is possible to evaluate the clumpiness parameter defined as:
where n = n + + n -
e e
f_--
4. <n + •n ->
e o
<n> 2
In Table 1 we have collected parameters of 9 gamma-ray burst sources evaluated from
the best fit of experimental data by our model.
Table i.
GRB
2
3
4
5
6
7
8
9
19.04.80
19.11.80
06.04.79
31.12.81
25.03.78
20.03.82
13.01.79
08.09.82
19,11.78
T +
e
1010-3.1010
1010-3.1010
<108
T _
e
3.109
3.109
i0 I0
<108
<108
<108
<108
<108
3.1010
3.109
i0 I0
i0 I0
109
3.109-1010
<108
f
-3
6,3.10
0,i0
0.41
0.02
0.41
0,37
-3
1.3.10
0.33
0.88
5. Conclusions. The detailed analysis shows that in short time scales, the unthermalized-pair-
dominant plasma can exist. The annihilation time scale is shorter than the bremsstrahlung
time scale, when temperatures of components are as follows:
To-< 10gK and T_+ > 101°K or Te+ < 108K and Te-> 101°K.
The spectra of gamma bursts with a hard tail are very well described by a thermal
bremsstrahlung (continuum component) and the annihilation line of an unthermalized plasma.
From a best fit of our spectra to experimental data, it is possible to evaluate the temperatures
of electrons and positrons and the ratio of concentration (Table 1). The temperatures of
electrons and positrons evaluated from the best fit satisfy the condition of unthermalized
plasma.
The Gamma Ray Burst spectra from BATSE on the GRO can support or reject our
model.
6. Acknowledgements. This work was sponsored by Polish Ministry of Education.
315
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316


Unthermalized positrons in gamma ray burst sources

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