The pair e(+)-e(-) annihilation phenomena in hot plasma was studied in order to evaluate the photon energy spectrum. The spectra of the broadening 0.511 MeV annihilation line was calculated in the case of unthermalized plasma, i.e., T sub e(-) does not equal T sub e(+). The energy spectra from annihilation process for unthermalized positrons are characterized by the presence of flat part for energies greater than 0.511 MeV. The flattening in the spectrum of annihilation unthermalized plasma is a strong indication that the observed features of the hard tailed spectrum of the gamma bursts can be well described by annihilation of hot positrons and cold electrons. It is proposed that the mechanism for the production of unthermalized positrons is associated with the charge separation in Eddington limited accretion onto a neutron star

Karakula, S.

Tkaczyk, W.

English

NASA Technical Reports Server

1 § OG 1.1-5
UNTHERMALIZED PLASMA IN BURSTS SOURCES
W. Tkaczyk and S. Karakuta
Institute of Physics, University of L6d£. Poland
ABSTRACT
We have studied the pair e+-e - annihilation phenomena in hot
plasma in order to evaluate the photon energy spectrum. The spect-
ra of the broadening 0.511 MeV annihilation line was calculated in
the case of unthermalized plasma i.e. Te-_= Te + The energy spectra
from annihilation process for unthermalized positrons are characte-
rized by the presence of flat part for energies greater than 0.511
MeV. The flatening in the spectrum of annihilation unthermalized
plasma is a strong indication that the observed features of the hard
tailed spectrum of the gamma bursts can be well described by an-
nihilation of hot positrons and cold electrons. We propose that the
mechanism for the production of unthermalized positrons is associa-
ted with the charge separation in Eddington limited accretion onto
a neutron star.
i. INTRODUCTION
The spectra of many bursts contain absorption (fop energy
E <i00 keV) and emission (E = 350-450 keV) features which have
been interpreted, respectively as broad cyclotron scattering and
redshiffed annihilation lines (Mazeis e% el., 1981 ). One of the most
important result of the gamma bursts spectral studies given by both
Konus (Mazeis e% el., 1983) and SMM (Solar Maximum Mission,
Nolan et el., 1983) experiments is fact that gamma bursts spectra
can have in some phase hard tails extending to a few MeV or even
higher. For example the spectrum of this type has the burst
OB81iZ31a from Ix%onus experiment. The spectrum of another burst
GB820320 has even a harder tail. This last burst was also recor-
ded by SMM (Rieger et el., 1982), where a hard tail could be fol-
lowed up to 40MeV.We can shortly summarize the experimental facts:
i) there are some classes of burst with hard fail in the energy
spectrum extended up to few MeV, it) the registrated hard tail be-
gins near the energy range of 400-500 k eV i.e. in the region where
the annihilation features are seen, iii) the spectral index of the pho
ton spectrum can even aproach 1 (CRB820320) in the energy range
of E> 513_ keV (one must notice that data errors are lar_e). These
may indicate that at sufficently high temperatures the plasma becomes
5 OG 1.~-5 
NTHERMALIZED LASMA IN URSTS OURCES 
. kaczyk nd . rakula 
Institute of hysics,· niversity of 6dz, oland 
BSTRACT 
e have studied the pair e + -e annihilation phenomena in hot 
plasma in order to evaluate the photon energy spectrum. The spect-
ra of the broadening 0.5~~ eV annihilation line as calculated in 
t e ase f nthermalized lasma i.e. e - :/= e"': he nergy s ectra 
fro  annihilation rocess for unthermalized positrons are characte-
rized by the presence. of flat part for energies greater than 0.5~~ 
eV. he fl t ing in t e s ectrum f nihilation nthermalized 
plasma is a strong indication that the observed features of the hard 
tailed spectrum of the ga ma bursts can be ell described by an-
nihilation of hot positrons and cold electrons. e propose that the 
echanism for the production of unthermalized ositrons is associa-
ted ith the charge separation in ddington li ited accretion onto 
 eutron t r. 
1. TRODUCTION 
he spectra of any bursts contain absorption (for energy 
E  ~OO ke ) and e ission (  = 350-450 keV) features hich have 
been interpreted, respectively s broad cyclotron scattering and 
redshifted annihilation lines ( azets et al., ~981 ). ne of the ost 
i portant result of the ga ma ursts s ectral st dies given y both 
onus ( azets et al., ~ 983) and S M (Solar axi um ission, 
Nolan et a1., ~ 983) experim~nts is fact that gamma bursts spectra 
can hav~ in so e phase hard tails extending to a fe  eV or even 
higher. or example the spectrum of this type as the burst 
GB8~1.23~a fro  Ko s experiment. he spectrum of another burst 
B82 320 as en  arder . his t urst as l o cor-
ded by S M ( ieger et a1., ~982)t here a hard tail could be fol-
lo ed up to 40 eV.We can shortly su marize the experimental facts: 
i) there are so e dasses of burst ith hard tail in the energy 
spectrum extended up to fe  eV, ii) the registrated hard tail be-
gins near the energy range of 400-500 ke  i.e. in the region here 
the annihilation features are seen, iii) the spectral index of the ph£. 
ton spectrum can even aproach ~ (G 820320) in the energy range 
of E > 5~~ ke  ( e ust notice that data errors are large). hese 
ay indicate that at sufficently high te peratures the plasma becomes 
• 
https://ntrs.nasa.gov/search.jsp?R=19850025594 2020-03-20T17:55:23+00:00Z
/ 1 6 OO 1.1-5
pairs dominand, [he emission processes in such a plasma acts as
an additional source of hard gamma rays.
In this paper we have calculated the photons spec[ra from
annihilation process for unthermalized positrons i. e. T + _= T -.
e e
The spectra indicated similar features as observed in the spectrum
of bursts. So _ve have proposed the model for the gamma bursts
source with annihilation of positrons additionally heated by the char-
ge separation in the time of matter accretion onto neutron star.
2. ANNIHILATION LINE FROM UNTHERMALIZED POSITRONS
The broadening of annihilation line 0.511 MeV can be produced
by high temperatures, intense magnetic field and Doppler shifts due
to bulk motion and gravitational field. We have considered only tem-
perature effect in unthermalized pair dominant plasma i.e. ,-_ _ T e- ,
In order" to calculate the energy spectra from unthermalized plasma
followin_ assumption was made: i) the electrons have the tempera-
lure T - and Maxwellian momentum
e
distribution, it) the positrons have -9 , , ,
temperature Te+ and Maxwellian A
momentum distribution, iii) the angu- -10 / I'---Te--=IOgK
lar distributions of momentum is iso- T -11
....
rb-,o ,..-12I-//.. I\-- T£--lO1°
T _ 9 4-- m6 -13 ,
E / 7 - 14 f'_ 101<
c_-lO -15
o"
_o
-11 I ......
.-17
500 520 540 560 - 4 -3 -2 -1 0
E [keV] Ioq E [GeV]
Fig. i. The photon spectra for
Te- = 105 I< and Te + = Fig. 2. The photon spectra for.
105 , i06, 107, 108 K, T e- = 109K and TO+ =
respectively. 109, i010, i011, 1012 K,
re spe ctive ly.
/  G 1.  
pairs do inand, the e ission processes in such a plas a acts as 
an additional source of hard ga ma rays. 
In this paper we have calculated the photons spectra from 
annihilation process for unthermalized positrons i. e. T + =1= T -. 
e e 
The spectra indicated similar feature s as observed in the spectrum 
of bursts. So we have proposed the odel for the ga ma bursts 
source with annihilation of positrons additionally heated by the char-
ge se aration in the time of atter accretion onto neutron star. 
. NN H1LATION INE OM THERMALIZED SITRONS 
The broadening of annihilation line 0.511 eV can be produced 
by high temperatures, intense agnetic field and oppler shifts due 
to bulk motion and gravitational field. e have considered only tem-
perature effect in unthermalized pair dominant. plasma i.e. '·l+ -!= T - , 
e e 
In order to calculate the energy spectra fro  unthermalized plasma 
following assumption was made: i) the electrons have the tempera-
t re '1' nd axwellian omentum 
 
i tri tion, ii) t  ositrons ave 
temperature T + and Maxwellian 
e 
omentum distribution, iii) the angu-
lar distri butions of omentum is iso-
-8 
..-
'III - 9 
M 
E 
8 
-UJ 
0 10 
C' 
 
- 1 
500 520 540 560 
E [keV] 
photon spectra f r 
5 
-10 
,-, 
'T  
> CI) 
<:) 
1~12 (/) 
M 
E 8 -13 
UJ 
0-1  
C' 
.9 
15 
-16 
- 17 '---I..-_.a...-.---'I--.....L-J 
 -3 -2 -1  
Joq E [GeV] 
Fig. 1. he 
'1' -
e 
= 10 K and '1' + 
e Fig. 2. The photon spectra for. 
10 5 , 10 6 , 1.0 7 , 10 8 K, 
re s p e ctive ly. 
g 
'1' - == 10 K and e 
10 g 1010 1011 , , , 
respectively. 
'1'+ = 
e 
10 12 K, 
• 
1 7 OG 1.1-5
tropic for both electrons and positrons. The kinematics of annihilation
and numerical calculation of spectra for above conditions should be
analyzed in most general case, as it was shown for thermallzed
plasma (Svensson, 1982: Karaku_a and _i_kaczyk, 1984). As examp-
le we present on the Fig. i the photon spectra (in detail scale)
from annihilation of electrons with temperature T e- =105 K and po-
sitrons with temperature: 105, 106 . 107 , 108 K. Figure 2 shows the
spectra for higher temperatures ( see also Fig. I in paper OG 2.7-
ii). rghe curves on this Figures are labeled by %emperalures of po-
sitrons. We can notice that the spectra have a flalening tendency for
energy E >0.511 Ik4eV. For the large difference of electrons and po-
sitrons temperatures the spectra are of the invers power low type
with power index = i. We have analyzed relations between annihila-
tion time and aitenuation energy time for bremsstrahlung and we can
3_1
conclude that for temperature of plasma T e- = Te+ = 3.10 Ix[ the
annihilation process is more efficient than bremsstrahlung. So taking
in the consideration the shape of spectrum and efficiency of the
process, the observed features in the spectrum of the gamma bursts
with hard tail can be well described by annihilation of unthermalized
positrons. We have proposed that the charge separation in %he matter
Of Eddington limited accrefion onto a neutron star can produce un-
thermalized positrons (Colgate and Petschek, 1983). q_he scenario
can be shortly described as: the layer of the thickness (_7=I) falls
onto %he neutron star. The electrons will be pushed away from %he
star by the photons flux outgoing from the surface. This produces
a charge separation and consequently and electric field. The elect-
rons are heated by interaction with the photons. Photons are pro -
duced by annihilation of positrons and by the compression caused
by %he mai_er fallin_ onio %he star surface. The pair producfion pro-
cesses caused by photons or other particles are the source of the
positrons which are accelerated not only by phoions interactions,
as electrons, but also by the electric field.
3. DISCUSSION AND CONCLUSIONS
The calculated spectra from annihilation process of the un -
thermalized positrons (T e- _= Te+ ) are characterized by the presen-
ce of flat part for energies greater than 0.511 MeV. q_he annihilation
• 
17 G .1-5 
tropic for oth lectrons nd ositrons. he inematics f a nihilation 
d umerical lculation f ectra f r bove nditions ould e 
alyzed i  ost eneral ase, s it as own f r t ermalized 
plasma (Svensson, 1982: arakula and Tkaczyk, 1984). s examp-
le e present on the ig. 1 the photon spectra (in detail scale) 
from annihilation of electrons with temperature T - :=10 5 K and po-
567 8 e 
ns ith t perature:  , 0 , 0 ,  . igure  ows t  
s ectra f r i her t peratures ( s e lso ig. 1 i  aper G . -
11). T e urves n t is igures are' l eled y t peratures f o-
sitrons. e can notice that the spectra have a flatening tendency for 
energy E  0.511 MeV. or the large difference of electrons and po-
sitrons te peratures the spectra are of the invers power lo  type 
ith ower i ex := 1. e ave analyzed relations etween a nihila-
ti  ti e nd tt nuation ergy ti e f r remsstrahlung d e n 
11 
conclude that for temperature of plasma T e - = T e + = 3· 10 K the 
annihilation rocess is ore efficient than bremsstrahlung. o taking 
i  t e nsideration t e s ape f s ectrum d ffi i ncy f t e 
rocess, t  bserved f atures i  t  ectrum f t e a ma ursts 
ith ard t il n e ell escribed y nihilation f nthermalized 
ositrons. e ave roposed t at t e charge separation in t e atter 
of dington li ite  cretion nto a eutron st r n roduce n-
,thermalized positrons ( olgate and Petschek, 1983). The scenario 
n e s ortly escribed s: t e l er f t  t Ickness (t'=1) f lls 
nto t e eutron st r. he l ctrons ill e ushed ay fr  t e 
star by the photons flux outgoing fro  the surface. his produces 
a charge separation a d c nsequently and electric field. he elect-
r ns re eated y i teraction ith t e hotons. hotons re ro -
uced y a nihilation of ositrons a d y t e c mpression aused 
by the atter falling onto the star surface. 'The pair production ro-
e ses aused y hotons r t er articles re t e s urce of t e 
ositrons hich re ccelerated t ly y hotons i t ractions, 
s electrons, but also y t e electric field. 
. ISCUSSION ND ONCLUSIONS 
he lculated ectra fr  nihilation rocess f t  n -
thermalized po sitrons (T - :/= T +) are characterized by the pre sen-
 e 
e f fl t art f r ergies reater t an . 1 eV. T e nihilation 
I 8 OG i.i-5
process is sufficiently effective for generalbr acceptable parameters
of the gamma bursts sources and can describe the obseved spect-
rum with hard tail. "I'he temperatures of electrons _i_ - = 10 8 K and
10 e
positrons rf, + =i0 }< and concentration of order magnitude n - =
8e -3 e
n + = [L01 cm secures the observing high energy (E > 0.511h/_oV)e
flux in burs% OB81123ia located a% typical galactic distance. Validi-
b/ of our result is guaran%eed by using the same procedures of cal-
culations as we have used in %he %hermalized case, results of which
are in compliance with Svensson (1982). Our model has a common
part with the model recently proposed by Colgate arld Petschek
(1983), it is the charge separation as the source of additional hea-
ting of positrons. We show [hat the positrons can effectively annihi-
late. Colgate and Peischek proposed [hat the positrons can additio-
naly heat photons producing hard tail in the spectrum.
REFERENCES
Colgate, S., Petschek, A., 1983, AIP Conf. Proc. No 101 ( ed.
Burns e[ al.) 94-97 (ALP, New York).
Karakuta, S., and "I'kaczyk, W., 1984, Frascati Workshop "Multifre-
quenc W behaviours of Galactic accreting sources", in press.
Mazets, E.P., Oolene_skii, S.V., Apiekar, R.L., Outran, Yu.A., and
llyinskii, V.N., 1981, Nature, 29____O0,378.
Maze ks, E.P., Oolene[skii, S.V., Outran, Yu.A., Aptekar, R.L.,
llyinskii, V.N., Panov, V.N., 1093, AIP Conf. Proc. No I01 ( ed.
o
Burns et al.) 36-53 (ALP, New York).
Nolan, P.L., Share, G.H., Forrest, D.J., Chupp, E.L., ]k4atz, S., Rieger,
E., 1983, AlP Conf. Proc. No 101 (ed. Burns et al.,), 59-63,
(ALP, New York ).
Svensson, R., 1982, As_rophys. J., 25____8_8, 321-334.
Rieger , E., Reppin, C., !<anbach, G., Forrest, D.3., Chupp, E.L.,
Share, G.H., Accreting Neu%ron Star, MPE Report i77, po 229,
(C%arching, 1982).
18 OG 1.1-5 
process is suff ciently effective for g neraly acceptable p rameters 
of the gamma bursts sources and can describe the obseved spect-
rum with hard tail. The tempe atures of lectrons T - = 10 8 K and 
e 
positrons T + =1010 K and concentration of order magnitude 
e 1'1 - = 
1018 -3 th b ° h O 1'1 + = cm secures e 0 servIng Igh nergy 
e 
e 
(E> 0.511 MeV) 
flux in burst GB811231a located at typical g la tic distance. Validi-
ty of our result is guaranteed by using the same procedures of cal-
culations as we have used in the thermalized case, results of w ich 
are in compliance with Svensson (1982). Our model has a common 
part with the model r cently pr posed by Colgate and Petschek 
(1983), it is the charge separation as the source of additional hea-
ting of positrons. We show that the positrons can effectively annihi-
late. Colgate and Petschek proposed that the positrons can additio-
naly heat photons producing hard tail in the spectrum. 
REFERENCES 
Colgate, S., Petschek, A., 1983, AlP Conf. Proc. No 01 ( ed. 
Burns et al.) 94-97 (AlP, New York). 
Karakuia, S., and Tkaczyk, W-., 1984, Fr scati WorkshOp "Multifre-
quency behaviours of Galactic accreting sources", in press. 
Mazets, E.P., Golenetskii, S.V., Aptekar, R.L., Guryan, Yu.A., and 
Ilyinskii, V.N., 1981, Nature, 290, 378. 
Mazets, E.P., Golenetskii, S.V., Guryan, Yu.A., Aptekar, R.L., 
Ilyinskii, V.N., Panov, V.N., 1093, AlP Conf. Proc. No 01 ( ed. 
Burns et al.) 36-53 (AlP, New York). 
Nolan, P.L., Share, G .H., Forrest, D.J., Chupp, E.L., Matz, S., Rieger, 
E., 1983, AlP Conf. Proc. No 01 (ed. BUrns et al. ), 59-63, 
(AlP, New York). 
Sve sson, R., 1982, Astrophys. J., 258, 321-334. 
Rieger, E., Reppin, C., Kanbach, G., Forrest, D.J., Chupp, E.L., 
Share, G.B., Accreting Neutron Star, MPE Report 177, po 229, 
(Garching, 1982). 
• 


Unthermalized plasma in bursts sources

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