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OCR for page 144
Generation of Ultrahigh-Energy Gamma Rays
in Accreting X-Ray Pulsars
YU.N. GNEDIN AND N.R. IKHSANOV
Central Astronomical Observatory
ABSTRACT
Relativistic protons producing ultrahigh-energy gamma rays as a result
of nuclear collisions are expected to generate close to the neutron star
surface as a result of accretion. The high efficiency of He accreting
matter's gravitational energy conversion into the acceleration energy and
high efficiency of the acceleration itself are the mam peculiarities of the
considered mechanism. It Is shown that a distribution of the "loss cone"
type accreting protons takes place during accretion onto a neutron star with
a strong magnetic field. This distribution effec~vetr generates small-scale
Alfven, proton cyclotron waves, and non-linear waves (magneto-acoustic
and Alfven solitons) due to instabilities. The electric field of the moving
solitons may accelerate the protons to energies > 10~5 eV. The region
of acceleration covers the Amen surface to distances of 2-3 radii of the
neutron star from its surface. New possible sources of ultrahigh~nergy
gamma-rays are predicted. They may be binary X-ray systems with neutron
stars permeated by magnetic fields of ~ 109 Gauss.
INTRODUCllON
One of the recent and most interesting astronomical discoveries was
the detection of very high-energy (10~2 to 1014 eV) and ultrahigh-energy
(lOl4 to 1016 eV) Gamma rays from X-ray binaries. Radiation of ultrahigh-
energy quanta of four binary systems (Her X-1, 4U0115+63, Vela X-1, and
Cog X-3) have been observed by at least two independent groups (Lamb
and Weekes 1987~. The radiation detected pulsates with He star's rotation
144
OCR for page 145
HIGH-ENERGY ASTROPHYSICS
145
period. bible 1 gives the basic characteristics of these sources. As it follows
from this table, the main physical properb luminosity in the gamma-ray
range: x-ray range ratio-is within
L,/Lr > 10-3
(1)
and perhaps ~ 1.
It is evident that such a traditional model as radiation of relativistic
particles generating in the electric and magnetic fields of a fast-rotating
neutron star, will not do for this physical situation. The rotation rate
of neutron stars ~ Her X-1 and 4U0115163 is too small to provide the
necessary energy. Thus, relativistic protons and electrons originating very
high-energy gamma rays should generate close to the neutron star's surface
as a result of accretion.
At present there is no general theoretical conception of the mechanism
of relativistic proton generation near the surface of the Secreting neutron
star, although there are quite a few ideas (see Brecher 1987; Hillas 1987~.
The main peculiarities of such a mechanism should be as follows:
1. High efficiency of gravitational energy conversion of accretion mat-
ter into fiche acceleration source energy, since the ratio of the ultrarelativistic
particle energy power to the X-ray emission energy power can be rather
large:
Ln/Lm 1
r,
(2)
Tomb and Weekes 1987; Hillas 1987~.
2. High efficiency of the mechanism of acceleration, since the char-
acteristic time of energy losses due to synchrotron radiation of protons is
very short
tSyn ~-4.4 x 10-l2E~siB-2
where E15 is the proton energy given in 1015 eV and B12 is the magnetic
field measured in 10~2 Gauss.
3. Another essential difficult for acceleration is the high density of
the accelerated plasma which prevents accumulation of the energy of the
accelerating particle because of frequent coulomb collisions. There must be
a mechanism in the Faceting plasma, which causes a strong inhomogeneity
of the plasma such as dense and small plasma drops.
The goal of the present paper is to End such a mechanism of conversion
of fiche accreting plasma gravitational energy in the neutron starts magneto-
sphere into the relativistic proton energy. This conversion should provide
for the necessary energy and high efficiency of acceleration. Such a mech-
anism is generation of non-linear waves (Al~en and fast magneto-acoustic
OCR for page 146
146
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OCR for page 147
HIGH-ENERGY ASTROPHYSICS
147
solitons) in the accreting plasma. The accreting plasma automatically be-
comes essentially mhomogeneous.
MEClIANISM OF lam CONVERSION OF GRAVITATIONAL ENERGY
TO ULTRA-REIATIVISTIC PROTON ENERGY
lithe idea of the proposed mechanism lies in the assertion that a dis-
tribution of accreting protons of "the loss cone" type takes place during
accretion onto the neutron star with a strong magnetic field (Leroy and
Mangeney 1984; Benz and Thejappa 1989~. This distribution is character-
istic for generation of Stabilities and given by
F(P1,P~) = Cexp [_(P~ P2~) _ (Pl P2l0) ~ /\Pl ~ /\pl~2 (4)
where
C= [7r3/27\pl~p~i Tempo_ Pol )+~ Pol t! + erf ~ Pol )] )]
_ (5)
In the case of sperical accretion P = me x Vff, where mp is the proton
mass and Vff is the free-fall velocity of the accreting plasma.
What is the physical justification of the above assertion? First of all
this distn~ution (4) can take place at the entrance of the accreting plasma
onto the cusp level of the magnetized neutron star due to the conservation
of the adiabatic invariant AP' /B = Const. Another possible reason for
this distribution may be plasma reflection from a strong shock wave formed
doling the accretion. One can note three possible locations of the shock
wave: Alfv~n surface where the shock wave is formed as a result of the
interaction of the accreting matter with the neutron star's magnetospheric
plasma, in the region of the so-called magnetopause. The protons may
resect from the magnetopause forming distribution (4) or a bit different
distribution (Leroy and Mangeney 1984~. This reflection may take place
deep in the magnetosphere closer to the neutron star's surface as a result
of the formation of a shock wave or a strong narrowing of the magnetic
cusp in the region of the accretion energy release. In the latter case, we
have tO deal with the reflection from a magnetic mirror (Vlahos 1987~.
As to the shock wave, it can be formed due to the radiation pressure
if its strength is close to the Eddington limit (Basko and Sunyaev 1976~.
The cross section of the photon scattering by the electron is resonant at
the Cyclotron frequency Gibe in the magnetic field of the neutron star. This
OCR for page 148
148
AMERICAN AND SOVIET PERSPECTIVES
increases the pressure in comparison with the case without the magnetic
field (Mitrophanov and Pavlov 1982; Gnedin and Nagel 1984; Zheleznyakov
and Litvinchuk 1986).
A distribution of the (4) type is unstable and generates small-scale
Alfven, proton Cyclotron and hybrid waves (Meerson and Rogachevsldi
1983; Machabeli et ale 1987) as well as nonlinear waves: solitons which are
magneto-acoustic and Alfven vortices in plasma (Petviashvili and Pohotelov
1973~. Solitons are effectively generated at the moment of the resection
e.g., from the magnetic wall or in the region of the shock wave formation
(Alsop and Arons 1988; Arons 1988) of the moving plasma.
The frequency of the excited linear waves is given by LO) ~ ~ giVA/v
where win Is the ion cyclotron frequency, VA is the Alf~en velocity, and V
is the plasma beam velocity equal to Vf I.
The instability increment is equal to (Zaitsev and Stepanov 1985)
~ ~ 0.4(8~Wp/B2)Wff
(6)
where Wp is the energy density of the proton beam causing instability.
In our case we may assume this value to be close to the densitr of the
accreting plasma gravitational energy, i.e.,
Wp < Wff = 1/2pVff
(~7~)
where p is the accreting plasma, with density depending on accretion rate
M.
The generated waves become more intensive in direction close to that
of the magnetic field lines: Kit < (~/wB~/2. On the Aliven surface
VA ~ Vff and w ~ Alibi, be., ion cyclotron waves are effectively generated.
Within the magnetosphere: ~ > win.
A soliton as a magneto-acoustic vortex may be considered as a nonlin
ear packet of fast magneto-acoustic waves. This packet is an axial-symmetric
formation, propagating along the magnetic field B. Its dimensions in the
direction of ache propagation ~: and in the direction of the radius ~ are
given by
id ~ `, A2 ;tr ~ `~, A3
where A is the dimensionless amplitude of the vortex Since A < 1, as a
rule, the vortex is hastened along the magnetic field lines. The magnetic
field of the magneto-acoustic vortex is mainly radial, ABr = AB, and its
propagates with the velocity, V5 = VA (1 A2)
The Alf˘6n vortex on the contrary, is elongated along B. (˘: ~ tr)
and its magnetic field Is predominancy azimuthal 1\B`' = AB. It can be
OCR for page 149
HIGH-ENERGY ASTROPHYSICS
149
considered as a waveguide along the direction of the B radius p = 1/AK' 3 .
There are other types of Alfv~n solitons (see Mihailovsky et al. 1976;
Ovenden et al. 1983~.
In order to provide for effective development of the instabilities of
the (4~-~6) type one should have: byte > 1, where tD is the characteristic
dissipation time of the process in question. This dissipation leads to
damping of linear and nonlinear waves and, in particular, to breaking of
solitons. One of the effective channels of dissipation is coulomb collisions:
tD ~ 1/ue ~ Ff3f/Ne
(9)
where me is the effective frequency of collisions of the accreting proton
beam with the background plasma. AD ~ 104 for the Alf~en surface, i.e.,
mechanism (43 operates electively. This condition AD > 1 is also satisfied
near the neutron star's surface. The mechanism of soliton dissipation is
widetr discussed in scientific literature, although the problem has not yet
been finally solved.
We can put down the final conclusion as follows: the conversion of the
accreting flux gravitational energy into the ultrarelativistic particle energy
as a result of the development of the "loss cone" type instability (43 takes
place at a characteristic distance to the neutron star. This generation radius
1S:
R3, ~ Rgen < RA
(10)
PROTON ACCELERATION TO ULTRARELAIIVISTIC ENERGIES IN
THE REGION OF THE "LOSS CONE" lYPE INSTABILITY
GENERATION
The electric field of a fast solution can be the most effective mechanism
of the proton acceleration to ultrarelativistic energies:
E = 1/Ct~A^B]; AB = AB
(11)
On the Alfven surface VA ~ Vff; that is, it is equal to the plasma free-fall
velocity. Inside the accretion column VA ~ C. Since the magnetic field
of the magnet~acoustic soliton is radial IBM ~ 0, and that of the Alfven
soliton is azimuthal FIB<,, ~ O relative to the magnetic field lines of the
_ _
neutron star B. the electric field acts transverse to the magnetic field B
lines in accordance with (11~. It is the azimuthal E<' ~ O in the case of the
generation of magneto-acoustic solitons and the radial En ~ O in the case
of the Alf~en solitons. Therefore, the main source of energy losses of the
accelerating protons is synchrotron radiation
OCR for page 150
150
AMERICAN AND SOVIET PERSPECTIVES
The equation for the accelerating proton energy acquired due to the
electric field E has the form
dE -_
_ = cEu
(12)
where ~ Is the accelerating proton velocity ~ ~ c. Solution (12) accounting
for (11) gives:
E1s = 0.2(A/B12) /,
if it is the characteristic time of the proton synchrotron losses.
Coulomb collisions only slightly influence the propagation of protons.
Nuclear collisions become important for them. Hence, the presence of a
very inhomogeneous distribution of plasma Is needed, for instance, in the
region of the accretion column, to provide for the escape of ultrarelativ}stic
protons from the acceleration region.
It should be noted that an analysis of observational data on X-ray
pulsars lead many authors (Basko and Sunyaev 1976; Bai 1980) to the
conclusion that the plasma distribution is inhomogeneous in the Alfv~n
range and within the accretion column. In X-ray binary systems where the
compact object is a magnetized white dwarf (objects of AM Her type or
"polars") a noticeable excess of soft X-ray radiation in comparison with
the hard X-ray radiation, i.e., Lath > 1~ observed. Rota ~ al. (19~)
interpreted this result in a model of very inhomogeneous accretion, when
the accreting matter arrives in either magnetic pole region of the white
dwarf as separate blobs elongated along the magnetic field lines.
Note, that the mechanism of soliton generation causes the accretion
inhomogeneity, because the plasma density inside a soliton is noticeably
greater than outside of the soliton: Lip ~ (/\B)2.
The difficulty of the ultrarelativistic protons escape from the generation
region can be overcome, if one assumes that the source of gamma rays is
neutrons, not protons. The neutrons are formed in the generation region as
a result of nuclear collisions formed in the generation region as a result of
nuclear collisions of ultrarelativistic protons with the surrounding plasma.
In conclusion, we would like to emphasize the fact that soliton mech-
anism explains also the freezing-in of the Secreting plasma to the strong
magnetic field of the neutron star, since the magnetic field will penetrate
quickly to plasma blobs, formed by solitons.
OBSERVATIONAL CONSEQUENCES
OF THE PROPOSED MECHANISM
The lllrninosity of the X-ray pulsar in a binary is fully determined by
the rate of accretion on the neutron star according to the traditional theory
(13)
OCR for page 151
HIGH-ENERGY ASTROPHYSICS 151
Lo = GM~M/R5. (14)
The main parameter of our model is the ratio of the power of ultra-high
energy protons to the X-ray luminosity:
WE (Rg (Rgen ) R
Lo AWgr(R) Rgen
(15)
The value ~W,v(Rgen) takes into consideration the resection of the ac-
creting plasma in the region of the interaction (e.g., polar cusp) and can
considerably exceed the portion of the gravitational energy released in the
X-ray range. Hence, the coefficient ~ can be larger than unit 77(Rgen) > 1.
Let us analyse the case when the ultrarelativ~stic protons are generated
on the Aliven surface: Rgen ~ RA. Then from most typical conditions for
X-ray pulsars: M = 10-8 Midyear, B. = 10~2 the ratio is
LF/L~ ~ Rs/RA ~ 10-2
.
(16)
This ratio is characteristic for a number of sources from Table 1, if one
accepts ~ 10% for efficiency of Me generation of gamma rays. As to pyg
X-3, this ratio is close to 1. This means that according to (17) the Elfin
radius RA ~ RS, which corresponds to the value of the magnetic field on
the neutron starts surface Bs ~ 109 Gauss. This result is well confirmed by
the recent observational data, which indicate that the neutron star in the
Cyg X-3 system is a millisecond pulsar (Watson 1987; Zyskin et al. 1987~.
In accordance with (15) and (163 one should expect noticeable fluxes
of ultrahigh-gamma-rays from such X-ray binanes, whose compact com-
panions are neutron stars with comparatively weak magnetic fields (= 109
Gauss). Possible candidates of that We can be Car X-1, SS433, Sco X-1,
LSI+61°30~. Recent there was an announcement concerning the discov-
e~y of a variable gamma-ray radiation of ultrahigh energy from Cir X-1 and
2A 1822-37,1 (Ciampa and Clay 198~, Ciampa et al. 1989~.
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Representative terms from entire chapter:
gamma rays
