Ionized matter falling onto an isolated, rotating black hole will be heated sufficiently that proton-proton collisions will produce mesons, including neutral pions, which decay into gamma rays. For massive (1000 M sub circled dot), black holes, the resulting gamma-ray luminosity may exceed 10 to the 36th power engs/s, with a spectrum peaked near 20 MeV

Collins, M. S.

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ix
NASA
Technical Memorandum 79649
(NASA-Tr-79649) GAMMA RAYS FFOPI ACCFETICN
	
N79-23854
ONTO ROTATING BLACK HOLES (NASA) 10 p BC
A02/MF A01
	 CSCL 03A
Onclas
G3/89 25913
Gamma Rays from Accretion
onto Rotating Black Holes
M. S. Collins
September 1978
0
^!r
National Aeronautics and ^'	 F
Space Administration s	 rry
Goddard Space Flight Center
Greenbelt, Maryland 20771
f
1
Z
GAMMA RAYS FROM ACCRETION ONTO
ROTATING BLACK HOLES
M. S. Collins*
Gamma Ray and Nuclear Emulsions Branch, Code 662
NASA/Goddard Space Flight Center
Greenbelt, Maryland 20771
Running Title:	 Gamma Rays from Rotating Black Holes
Offprint Requests to: 	 D. J. Thompson, Code 662
NASA/Goddard Space Flight Center
Greenbelt, Maryland 20771 U.S.A.
Subdivision:	 Stars and Stellar Evolution
Submitted to:	 Main Journal
*Presently at
Physics Department
Virginia Polytechnic Institute
Blacksburg, VA 24060
SUMMARY
Ionized matter falling onto an isolated, rotating black hole will
be heated sufficiently that proton-proton collisions will produce mesons,
including neutral pions, which decay into Y rays. For massive (10 3 MO)
black holes, the resulting 7-ray luminosity may exceed 10 36 ergs s 1,
with a spectrum peaked near 20 MeV.
Key Words:
	
Gamma-ray astronomy, gamma-ray sources, black holes
,` d
1INTRODUCTION
The discovery of several localized 7-ray sources which have no
apparent x-ray counterparts (Thompson et al. 1977; Hermsen et al. 1977)
has led to renewed interest in physical mechanisms which would produce
a significant flux of 7-rays without an energy spectrum extending into
the x-ray energy band. Dahlbacka, Chapline, and Weaver (1974) have
shown that accretion of matter onto an isolated, non-rotating
(Schwarzschild) black hole may produce 7 rays with a spectrum pe-ked
near 18 MeV. The present work extends this calculation to the case of
matter accreting onto an isolated, rotating (Kerr) black hole and shows
that the 7-ray luminosity may exceed 10 36
 ergs s 1 for accretion onto a
rapidly rotating 10 3MG) black hole.
CALCULATION OF GAMMA-RAY PRODUCTION
As interstellar gas falls onto a black hole, it may be heated by
compression. If a weak magnetic field is frozen into the gas, the
accretion may be regarded aL a : ►ydrodynamic flow (Schwartzman 1971;
Shapiro 1973). A significant fraction of the gravitational potential
of the gas is then converted to thermal energy. If the black hole is
4
not too massive( s 10 Me), very little of this thermal energy is radiated
away, and hence the compression n.ay be considered as nearly adiabatic
(Schwartzman 1971; Shapiro 1973).. The x-ray luminosity of this process
is, therefore, relatively small.. If the infalling gas is initially
ionized, its temperature may exceed 10 11
 K near the Schwarzschild
radius (Shapiro 1973). These temperatures are sufficiently large that
]	 '
2
proton-proton collisions have energy above the threshold for pion pro-
duction. Gamma rays will then be produced by the decay of the neutral
pions.
The above description is the same as for the static case (Dahlbacka,
Chapline, and Weaver 1974). A rotating black hole, however, is sur-
rounded by an ergosphere (the region inside the static limit but outside
the event horizon) in which the infalling matter will spiral and accumulate
before falling through the event horizon. The density of matter (and
hence the temperature and probability of pion producing collisions) is
very much greater in the ergosphere than in the region surrounding a
static black hole. As a good approximation, then, it is possible to
treat the region outside the static limit of the rotating black hole in
exactly the same way as the static case, while the region within the
ergosphere must be treated more carefully.
The equation for radial infall along the equator of the black
hole is (Bardeen 1973)
dr
2 
= r-3 { (r(r 2+a 2 ) + 2a2m) E2-4amE^ -(r-2m)^ 2 -Arµ2}	 (1)
where	 r = radial distance from the black hole
m = mass of the black hole
a = angular momentum of the black hole per unit mass of the
black hole, taken to be - m for an extreme example
T = proper time per unit mass
E = energy with respect to infinity = 1.3 GeV
u = rest mass of the infalling particle = 1 GeV
= angular momentum with respect to infinity = 0.5 mµ
= r2 - 2 mr +a2
s3
Integrating this equation by binomial expansion of the bracket func-
tion to fourth order yields a value for the infall time of 1.25x10-3 M B.
	 k
This time is short compared to the electron-ion coupling time. The pro-
duct of this infall time and the spherical accretion rate (Novikov and
Thorne 1973) gives a total mass in the ergosphere of
3
	
,^,	 8 MM
	
a 2 x 10 () p"	 (2)
where M is the mass of the black hole in units of solar mass and pm is the
density of the gas before accretion. The assumption has been made that the
interstellar gas has no net velocity with respect to the black hole. The
average density of protons in the ergosphere for this extreme case is, there-
fore, - 2 x 1015
 PC= protons cm 3 . Since the accretion is nearly adiabatic,
the average temperature in this region is determined from the adiabatic
temperature-density relationship
	
TCX p t-1
	
(3)
where t is the adiabatic index. For these non -relativistic protons,
t may be taken to be 513, and the average temperature in the ergosphere
is Tergosphere	 1 GeV, for pm lcm-3.	 The rate of n° production
in a hot gas with proper density is given by (Dahlbacka, Chapline, and
Weaver 1974)	 2
RTT o = 2 <rro> ov (8 )	 (4)
where <rro> is the average number of neutral pions produced per col-
lision and av(8)	 is related to the laboratory pion cross section by (Dahlbacka,
Chapline and Weaver
	 1974)
	
Me) 
= ff 6(EL)vL F (p 1 ) F (p2 ) dpl 02 •	 (5)
4where vL is the laboratory velocity and F is the relativistic Maxwellian
distribution. Taking av(8)
	
1016 cm  sec -1 	and <rr°> — 1 for T
— 1 GeV one can estimate the total number of 7-rays released from the
ergosphere by
15	 M 3 2
NY = 2 x 10 J Verg nescape cone d Verg ( I^ ) Pao photons/sec (6)
where Verg is the volume of the ergosphere and the escape cone (Zeldovich
and Novikov 1971) takes into account the fact that some of the T rays
will follow trajectories into the black hole while others will escape.
The fraction of those which escape is about 0.5.
Because a detailed density distribution has not been developed in
this treatment, it is impossible to obtain a characteristic energy spec-
trum. However, the peak of the spectrum can b^ determined. If the radial
and gravitational redshifts are considered
11
lU = up	 2	 1 - r	 (7 )
  
J
r
where S = V/C corresponds to the 1 GeV kinetic energy of the protons,
r  is the gravitational radius and^;. o corresponds to 68 MeV, the
rest frame energy of the 7 rays resulting from rr° decay. Assuming that
the density - escape cone product is a maximum near r — r  = m, the
peak of the spectrum is found to be 	 20 MeV for a 1 GeV proton.
Assuming an average photon energy of 20 NeV, the 7-ray luminosity
of an accreting, rotating black hole of mass M is given by
L ft 2 x 1027	 leV11
f M 32
Y	 Tom, 
	
M	
p^	 ergs sec-1	(8)
I	 t
5
where Tm and p,, are the temperature (in eV) and density (in protons
..-I )
 
of the gas before infall. Hence, for a 103 MO rotating (a e' m)
black hole in a typical interstellar ionized cloud (p. - 1, Ti. - 1 eV)
we would expect a luminosity of y rays — 2 x 1036 ergs sec-1 . Such
luminosities would be consistent with the recently-identified 7-ray
sources (Hermsen et al. 1977). Clearly the test for this mechanism
would be the measurement of the spectrum at energies near 20 MeV to
search for the predicted peak.
CONCLUSIONS
In summary, accretion of interstellar gas onto an isolated,
rotating black hole could provide a high luminosity T-ray source with
a spectrum peaked near 20 MeV. Further calculations, including the
density distribution of matter in the ergosphere, will be needed before
the shape of the spectrum can be determined accurately.
ACKNOWLEDGMENT
I would like to thank Dr. Carl Fichtel and Dr. David Thompson
of the 7-Ray Astronomy Group at Goddard Space Flight Center without
whose support and encouragement this work would not have been suc-
cessfully completed.
REFERENCES
Bardeen, J. M. 1973, in Black Holes (ed. Dewitt, C., and Dewitt, B. S,),
Gordon and Breach, New York.
Dahlbacka, G. G., Chapline, G. F., Weaver, T. A. 1974, Nature 250, 37.
Hermsen, W. et `l. 1.977, Nature 269, 494.
Novikov, I., and Thorne, K. S. 1973, in Black Holes (ed. Dewitt, C.,
and Dewitt, B. S.), Gordon and Breach, New York.
Schwartzmann, V. C. 1971, Soviet Astr. A. J. 15, 377.
Shapiro, S. L. 1973, Ap. J. 180, 531.
Thompson, D. J., Fichtel, C. E., Hartman, R. C., Kniffen, D. A., and
Lamb, R. C. 1977, Ap. J. 213, 252.
Zeldovich, Y. B., and Novikov, I. D. 1971, Relativistic Astrophysics,
University of Chicago Press, Chicago.
E


Gamma rays from accretion onto rotating black holes

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