The results of computations of the Comptomization of low frequency radiation in weakly relativistic plasma are presented. The influence of photoabsorption by iron ions on a hard X-ray spectrum is considered

Pozdnyakov, L. A.

Sobol, I. M.

Sonyayev, R. A.

English

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tNASA TECHNICAL, MEMORANDUM
	 NASA TM-76181
COMPTOMIZATION AND RADIATION SPECTRA OF X-RAY SOURCES.
CALCULATION OF THE I f"NTE CARLO METHOD
L. A. Pozdnyakov, I. M. Sobol',
R. A. Sonyayev
(NASA-TM-76181) COMP20MIZATION AND	 NEO-28193
RADIATION SPECTRA OF I-RAY SOURCES.
CALCULATION OF THE MONTE CARLO METHOD
(National Aeronautics and Space 	 Unclas
Administration) 10 p HC A02/MF A01 CSCL 201 G3/75 28025
Translation of "Komptonizatsiya i Spektra Izlucheniya
Rentgenogskikh Istochnikov. Raschety Metoda Monte Kar1a,V"
Academy of Sciences USSR, Institute of Space Research,
Moscow, Report Pr-447, 1978, pp. 1-12.
i
1.
yn^. 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
WASHINGTON, D. C. 20546
	 JUNE 1980
STANDARD TITLE PAGE
a
NASA-110
b
i
t
•
1.	 Report No. 1. Government Accession No, Recipients Catalog No.
NASA TM-76181
A.	 Title end Subtitle S.	 Report Date
CCMPTOMT7AW TON ANI1 RAPTA`P"rON OPE;C trRA nm	 lo8o
6.	 Performing Organisation CodeOF X— RAY SOPR("M1 .	 CALCULATION BY rI'I fiE
MONTF? CARLO METHOD
7.	 Author(s) S. Performing Orgoas•tien Report N•.
L.	 A.	 Po.,., dnyakov , 	 T. 'M.	 Sokol. t >
R. A. Fonyayov 10.	 Work Untt No.
9.	 Performing Organisation Name anti Aririnps 11.	 Contrast at Grant No.
.SC!Tr%AN NAS14-3198
17. Type of Report end Period CoveredBox 5456
Santa Barbara, CA 93108 Translation
12.	 Sponsoring Agency Name and Address'
National Aeronautics and Space Administration 14. Sponsoring Agency Code
Washington, D.C.	 20546
15.	 Supplementary Notes
'"ron,slat ion • 'of'11 omp'tonizat s iy,a A Spektra 7zluchonlya
Rentgonop-ckikh Tstochnikov. Raschet y MYtoda Monte-Karlo.,'"
.Academy of Sciences USSR, Tn; t t.tute of `'pace Reseavch,
:4ok cow, Repoa,t Pr-U47, 1 97 8 , pp: 1-12,
16.	 Abstract
Tho reoults of computations of tho c'omptomizati.on or law
frecluonCy radiation in weakly' relativistic. plasma kbr
presented.
	 The inf—luenco of phot6absorption by iron ;ions
on a herd X-ray spectrum is considered.
17. Key Words (Selected by Author(s)) 18.	 Distribution St•t•m•nt
Unclassified — Unlimited
19.	 Security Clossii. (of this report) 20.	 Security Clossil. (a( this page) 21. No. •1 Pages 22.
Unclassified Unclassified 10
t
COMPTOMIZATION AND RADIATION SPECTRA
OF X-RAY SOURCES
CALCULATION BY THE MONTE CARLO METHOD
L. A. Pozdnyakov, I. M. Sobol', R. A. Sonyayev
I. COMPTOMIZ!"TION OF LOW FREQUENCY RADIATION
	
/3*
The change in the frequency of photons in the case of
scattering by hot electrons is one of the basic mechanisms 'or
the formation of radiation from X-ray sources [1]. Let u, con-
sider a spherical cloud of plasma with the radius R with the
optical thickness according to the Thompson scattering T-dk R
and the temperature K T^t Q%^ . In the center of the cloud,
there is a source of low frequency photons with a Planck spec-
trum and the temperature	 In  the case of scattering
by hot electrons, the low frequency photons increase their energy
and fall into the hard region of the spectrum.. The energy of the
photons leaving the cloud depends on the number of tested scatter-
ings and on the electron temperature.	 .
Using the diffusion approximation in [2], it was shown numeric-
ally and analytically in [ 3] and [ 41 that in this problem for
k.'^, <M4Cit and I +% % the spectrum of outgoing radiation must be a
power spectrum 1.0 — T`c , in a wide region of energyT2 ,, thv ,*zk ^,
where the spectral index
r
Simultaneously, the studies [5] and [6] used the Monte Carlo method
and shDwed analytically the same thing for an optically thin,
and relativistic and semi-relativistic plasma. In this
*
The ". numbers in the margin indicate pagination of original foreign
text.
1
Case
where a = 12 at m>r, I .. The case of a slightly relativistic
plasma kT, 4w !)U+;,bO keV has not been studied. This case may be de-
scribed by a simple Companeyts equation (since relativistic cor-
rizctions are important). Among the sources of X-ray radiation
there are many bright ones in the 50 - 300 keV range (particular-
ly, the sources Cyg X-1, Cys X-3 and NGc 4151). This article
has investigated the process of comptomizatlon In a slightly
relativistic plasma. The computational method is discussed in
[61,
We confined ourselves to three values of the electron tem-
perature: kT. = 50, 100 and 256 keV and two values for the tem-
perature of the low frequency photons: kT% = 0.5 keV and 1.5
keV. The case kTt = 0.5 eV, apparently corresponds to the situ-
ation in the nuclei of the galaxy and quasars ,  where the source
of low frequency photons is infrared ., optical or ultraviolet
radiation.
Figure 1 gives the results of calculations. The radiation
intensity decreases in the low frequency region 1tV'* 1<T'. , retain-
ing the Rayleigh-Jeans inclination nature of the spectrum. This
effect was observed previously in 171•
In every case, the spectrum of X-ray radiation was a power
spectrum up to hv rv 3kT., , and in the variation T = 5 at kT. = 100
keV (Fig. lc) there was a tendency toward the formation of a Wien
spectrum with the average temperature kT* .
	At T = 3 and energies of kT*	50, 100, 256 keV, the spectral
	
indices equaled, respectively: a 	 0.65, 0.35, 0.1 (the latter
variation was calculated by the authors previously, see 151).
(2)
This clearly Cojjfjrmz J*.ho results of tho diffusion theory:
formula (1) gives the valuos a = O.6R 3 0.37, 0.16. 4t the
same time It may be readily established that at. I S;fZ
It greatly exceeds the value of cc-
Under these conditions, we may assum , tho semi-empLical
formula
- tq T Z/OL
which at n >', 1 cling 	 Into (2).u 	 Formula (3) describes all ofL	 , 
the variations with T e; 1, , which we have calculated (here and
previously), as well as the variations With T = 3 and n > O.F).
In the case of accretion of matter on a neutron star with-
out a strong magnetic field, part of the gravitational energy
liberated is changed Into black-body radiation, and part goes
toward the formation of a hot rarified upper atmosphere -- the
analogue of t;bo solar oorona. A similar Situation arises in
the boundary layer in the case of disk accretion on a neutron
,tar.
We shall model this situation in Fig. 2, selecting kT,
1. 5 keV and 10'	 100 and 2 116 lceV. It may be seen that for
small T the tail of hard X-ray radiation Is formed in the spec-
trum. It is possible that this mechanism is responsible for a
burst of hard X-ray radiation observed on Sco X-1 (see the summary
of the experimental, data In [81).
II. PHOTOABSORPTIOM AND COMPTOMATION
Lot us consider a cloud of a comparatively cold plasma (kT e
0 or kT.' = 0.1 keV) with an optical scattering thickness T. In
the centor of the cloud we assign the source of hard X-ray photons
with a power spectrum r. — 9-1 • We are interested in a change of
I a
the radiation spectrum due to the interaction of photons with
electrons.
Since the change in the photon energy due to the recoil
effect is greater than the ionization potential of a hydrogen
atom, it does not matter whether scattering occurs for free
electrons or for electrons connected in the hydrogen atoms. 	 16
We also consider photoabsorption by atoms and ions of slightly
ionized iron. The problem is a model. problem: We do not con-
sider the degree of ionization (close to the X-ray source it may
be very large). We assume that elements with Z < 26 are strongly
ionized by X-ray radiation, and therefore there is insignificant
photoabsorption of photons with kV < 7 keV. At 10> 7 keV,
photoabsorption of the photons by an iron ion is accompanied
by radiation with the probability of 0.34 of a photon K a (with
Kv# = 6.41 keV). The cross section at photoabsorption threshold
is assumed to equal 6s . This corresponds to a decrease of the
of iron by a factor of 2-3 as compared with the solar
value or its photoionization.
Figures 3 and 4 give the results of the calculation. It
may Oe seen in Fig. 3 that the difference in the plasma tempera-
Lure is only observed on the profile of the K a line. The role
of the photoabsorption is so great that at T > 1 absorption bound-
ary may be assumed to be a sharp drop in the spectrum (Fig. 4)•
If the photoabsorption cross section exceeds the Thompson cross
section at the absorption boundary, then the effect will be more
pronounced (this fact was noted in [9]).
The spectral resolution of the calculation in bhe vicinity
of the Ka line equals 0.05 keV, The line produced has a colossal
equivalent width W. For example, at T = 1 and kT.	 0, we have
6,SS
w^ S { Iy — "y (0)] 41AV . Iye (0)] ^0^,4 keV
5,75
*) Illegible in foreign text.
4
This is not surprising, because a third of the absorbed photons
with 4V> 7
 
keV overlaps the Ka lane. Tine line intensity may de-
crease only when there is strong photoabsorption by the lighter
elements.
REFERENCES
1. A. F.	 lllarorov, R. A. Slonyayev. Astron.	 Zh. 1972,	 49,
58.
2. J. I. Katz.	 As —orb.y q , J.,	 1976, 206,	 810.
3.. S. L.	 Shapiro, A.	 P. Lightman, D. W. Eardley.	 Astrophys. J.,
1976,
	
204,	 187.
4. R. A.	 Slonyayev, L. G. Titarchuk. 1978 Preprint IKI AN SSSR.
5. L. A. Pozdnyakov, I. M. Sobol',	 R. A. Slonyayev. Letters to
AZh,	 1976,	 2,	 140.
6. L. A.	 Pozdnyakov, I. M. Sobol',	 R. A.	 Slonyayev. Astron. Zh.
1977, 6, 1?4u".
7. R. A.	 Slonyayev. Astrophys. Space Sci.,Ya.B.Zel'2s8o5vich,
8. S. Miyamoto, Matsucka, 1977, Space Sci.	 Rev.,	 20, 687.
9. R. Rose, R. Waaver, R. McCray.	 Astrophys. J.,	 1978, 219, 292.
/7
5
FIGURE CAPTIONS
	
/8
Fig. 1. ;'nectrum of a central source with a temperature of
h'J'% = 0.5 eV and the radiation spectrum emanating;
from a cloud for different km e and T.
Fig. 2. Srectrum of the central source with a temperature of
ltTe= 1.5 eV and the radiation spectrum emanating
from a cloud for different kT e
 and T.
Fig. 3. Evolution of continuous spectrum (d,,rect) as the re-
sult of Compton scattering and photoabsorption at
different temperatures kT e
 of the cloud.
Fig. 4. Evolution of the continuous spectrum (direct) as the
result of Compton scattering and photoabsorption for
different thicknesses T of the cloud.
6
Y F
^^ N
low
I j
4% &if
•t t
	 h 
L,.
r
T • 1
t
i	 ^•^L
i
111	 i..^
r
. 
kT,OckeV,
(a)
r
^^
LU
 t
L	
r
T kT,. iookeV
	 Q:^
. ^	 ♦ 	 •!	 J	 •D	 •t	 N	 r
(6)
	 4(ho/„dJ
Fig, 1
0.1	 t	 70^	 t0^	 1	 J	 IA	 if9;	 10 keV
rr
i
ar^^	 ^,i a :i 31 .t
-a.fi .,
	 4=0.5	 i 3 S
	i	 ri S	 ^: ^^ 2=1
1	 16 '	 4
	
L	 L
_	
k Te= !00 keV
	
•5 ! kT, = 256 keV
.^	 .a.	 -s	 n	 ^	
-.^	 -z	
-1	 c	 1
( '	 2Jb 	 F^ ,.fiv ltmc
Fig. 2
/10
7
1{
f
i
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t
i
i
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FOaAL	
^
.y
.,
s	 ;	 a	 t:eV
t
l^	 r
It	
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.v	 kT're 0
. 2s
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rr
	
lA	
•l7
Fig	 /moil;
	
Hj•	 1	 i	 f ,}
	
p	 1	 µ	 K	 4	 EtkeV
r,
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112
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Fig. 4	
Cy (hJ /m^•1
II


Comptomization and radiation spectra of X-ray sources. Calculation of the Monte Carlo method

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