A model for emission of the hard photons of gamma bursts is presented. The model assumes accretion at nearly the Eddington limited rate onto a neutron star without a magnetic field. Initially soft photons are heated as they are compressed between the accreting matter and the star. A large electric field due to relatively small charge separation is required to drag electrons into the star with the nuclei against the flux of photons leaking out through the accreting matter. The photon number is not increased substantially by Bremsstrahlung or any other process. It is suggested that instability in an accretion disc might provide the infalling matter required

Colgate, S. A.

Petschek, A. G.

Sarracino, R.

English

A model for emission of the hard photons of gamma bursts is presented. The model assumes accretion at nearly the Eddington limited rate onto a neutron star without magnetic a field. Initially soft photons are heated as they are compressed between the accreting matter and the star. A large electric field due to relatively small charge separation is required to drag electrons into the star with the nuclei against the flux of photons leaking out through the accreting matter. The photon number is not increased substantially by bremsstrahlung or any other process. Instability in an accretion disc might provide the infalling matter required

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Gamma-burst emission from neutron-star accretion

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TITLE:	 GAMMA-BURST MISSION FROM NEUTRON-STAR ACCRETION
	AUTHOR ;S1
	 S*_irlink A. Colgate, T-6
Albert G. Petscnek, P-DO
Robert Sarracino, NASA
	
SUBMITTED TO
	 For publication in the Pioceeaing^ of the Summer Workshop
in Astronomy and Astrophysics, Santo Cruz, CA, July 10-22, 1983
DISCLAIMER
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	 August 30, 1983
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The lot Alamos National Laboratory repuests that the publisher identify this article as work pe r formed under the auspices o f the U S Depa rtment of Energy
Los Alamos National La^oyLrt1 ^	 Los Alamos,New Mexico 87545
FORM No on 94
67 000 Na s eat	 DIS^RIBII^IGti OF ili!S DOCU^EM^ i$ UNL!MI1
involved. For Alfven waves to propagate a^ong ca yed field lies,
the minimum rest mass density becomes p > B 12 /(4n c ) - 40 g cm a
value that violates the assumption of a vacuum magnetic field.
Similarly if one postulates a high temperature region free of mag-
netic field as would be required by Fenimore et al l to Compton heat
a soft photon flux, one has the problem of how to keep these
electrons hct using a source of energy that does not introduce more
electrons than is allowed by the "thin" approximation.
For these reasons we have spent some time attempting to find an
emission mechanism for gamma bursts that converts a reasonable
source of energy into the hard photon spectrum observed. We believe
we have found such a mechanism as the t,ormal consequence of moder-
ately thin (T = 1 to 4) accretion onto a field free neutron star.
The model is that photons of nearly constant number are sequentially
compressed, heated, diffused, further compressed, heated, diffused
and ultimately escape in a hzrd spectrum at an average flux near the
Eddington limit, but with wide fluctuations.
The physics of such accretion is complex.
	 To begin with:
1. The mass flux corresponding to steady state Eddington limit
accretion corresponds to a thickness of T ? 2. The accreting
matter cannot be much thicker, else the energy flux of radia-
tion will be less than the kinetic energy flux of infalling
matter.
2. In a transient state when the initial instantaneous photon flux
corresponds to a value much less than the Eddington limit flux,
OEdd' the free fall time is very much less than the time neces-
sary to multiply the photon number by bremsstrahlung. There-
fore, accretion with T = 2 to 4 occurs without increase in the
photon number.
CALCULATIONS
We have modeled this phenomenon with a one-dimensional (radial)
multi-energy group numerical calculation with mass layers and photon
diffusion in both energy ar_d radius. Both radi.,tion -tress and
gravity accelerate the accreting matter. The neutron star surface
is assumed to have an albedo of unity, mass layers are merged w?til
the surface when they get within LR of it and each layer is treated
as a semi-transparent diffuse scattering layer with zero heat
capacity and therefore no defined temperature. 	 A photon number
density corresponding to a small temper ire initially seeds the
problem. A typical resulting spectrum is shown in the figure_ where
the initial seed temperature was 0.355 keV, Ti . = 2.2 (integrated
to infinity) and the initial velocity distribuntion corresponded to
free fall. The curve drawn through the points is that corresponding
to a thin bremsstrahlung distribution with kTe = 139 keV.
involved. For Alfven waves to propagate a2 ong ca yed field liges,
the minimum rest mass density becomes p > B 12/(4n c ) = 40 g cm , a
value that violates the assumption of a vacuum magnetic field.
Similarly if one postulates a high temperature region free of mag-
netic field as would be required by Fenimore et al l to Compton heat
a soft photon flux, one has the problem of how to keep these
electrons hct using a source of energy that does not introduce more
electrons than is allowed by the "thin" approximation.
For these reasons we have spent some time attempting to find an
emission mechanism for gamma bursts that converts a reasonable
source of energy into the hard photon spectrum observed. We believe
we have found such a mechanism as the t,ormal consequence of moder-
ately thin (T = 1 to 4) accretion onto a field free neutron star.
The model is that photons of nearly constant number are sequentially
compressed, heated, diffused, further compressed, heated, diffused
and ultimately escape in a hzrd spectrum at an average flux near the
Eddington limit, but with wide fluctuations.
The physics of such accretion is complex.
	 To begin with:
1. The mass flux corresponding to steady state Eddington limit
accretion corresponds to a thickness of T ? 2. The accreting
matter cannot be much thicker, else the energy flux of radia-
tion will be less than the kinetic energy flux of infalling
matter.
2. In a transient state when the initial instantaneous photon flux
corresponds to a value much less than the Eddington limit flux,
OEdd' the free fall time is very much less than the time neces-
sary to multiply the photon number by bremsstrahlung. There-
fore, accretion with T = 2 to 4 occurs without increase in the
photon number.
CALCULATIONS
We have modeled this phenomenon with a one-dimensional (radial)
multi-energy group numerical calculation with mass layers and photon
diffusion in both energy at_d radius. Both radi.,tion --tress and
gravity accelerate the accreting matter. The neutron star surface
is assumed to have an albedo of unity, mass layers are merged w4til
the surface when they get within LR of it and each layer is treated
as a semi-transparent diffuse scattering layer with zero heat
capacity and therefore no defined temperature. 	 A photon nwnber
density corresponding to a small temper ire initially seeds the
problem. A typical resulting spectrum is shown in the figure_ where
the initial seed temperature was 0.355 keV, Ti . = 2.2 (integrated
to infinity) and the initial velocity distribuntion corresponded to
free fall. The curve drawn through the points is that corresponding
to a thin bremsstrahlung distribution with kT e = 139 keV.
z::szzzz
e
W
c0y0t
CL
-aft
Gii.o
inw
W
Ld g
c0
Y^
0.000	 0.500
	
1.000	 1.5m	 2.000	 2.500
	
a. o00
log energy (rev)
Fig. A y-burst spectrum from field free matter accreting
onto a neutron star. The curve is a bremsstrahlung fit
with kT = 139 keV.
e
The justification for the set of assumptions leading to the
calculations are:
1. In steady state Eddington flux limited accretion the gravita-
tional field of the neutron star acting on the ions drags the
electrons by a 2
 charge separation electric field E < gpm /e
where g = MNSG/R S^ p is the molecular weight per el-ctron, End
M the mass of tFe proton. This electric field, E = :00 v/cm
A small enou^y that charge neutrality almost prevails,
On /n = 3 x 10 This ensures that the electrons are
dragged by :he ions against the photon stress even for stopping
distances that are infinitesimal compared to the neutron star
radius.
2. The seed photon number density, generally characterized by a
black body temperature kT. t < 1 keV is small compared to the
Eddington limit value of W t: 2 keV for a neutron star of mass
I MW This ensures initial free fall of the plasma.
3. The photon number density always greatly 4exceeds the e}Ectrog
number density since n is of ^rder3 10	 T/RNS or 10	 cm
while at 1 keV, n
	 = T.5 x 10	 cm	 Therefore the electron
specific heat is negligibl 	 compared to that of the photons.
4. Provided the electrons do not run away in the charge separation
electric field, the electron temperature will be an average of
the local photon energy. Hence electron recoil and comptoniza-
tion where the thermal energy content of the hot or cold elec-
trons heats or cools the photons can be neglected In fact,
runaway will not occur because an electron undergoes many
photon collisions in a distance equal to its energy multiplica-
tion	 dista %e	 A =	 kT ! Ee,	 Ee < nh < hv>	 ac /3T, t =
2,k/(2 kT /m ) and hence Ae number of collisions in A becomes
nhv ac A 
e (c/ve ) sufficient to ensure against runaway. This
assumes that kTe
 = <hv>/3 consistent with the large number of
collisions.
5. Sigci for matter freely falling at a constant rate, j R^ pdR a
R // , the thickness pR - R	 and so photons will scatter and
be heated within several radii of the neutron star. From this
distance the free :all time is roughly equal to the diffusion
time. This ensures that some photons are trapped and raised in
energy by compression, yet also ensures that leakage allows the
large photon heating without exceeding the 
T 
ddington limit.
Since the gravitational potential is roughly c /5, the limiting
free fall velocity is = c/2. The diffusion "velocity" is
roughly (c/3T) so that T = 1 to 2 meets the criterion.
6. The neutron star surface has an albedo of the order of unity.
Since bremsstrahlung is small compared to Compton scattering,
the "surface" is where there first exists an additionA scat-
tering mean free path. Therefore a photon reaching the
"surface" from larger radius has a high probability of being
scattered back out, rather than being absorbed and reemitted as
is necessary to establish a black body spectrum.
7. The photons added to the accreting matter during free fall due
to the neutron star surface emission are not large compared to
the assumed in situ number density. Since the free fall time
is comparable to the escape time, the net addition of photons
after the start of free fall is nct greater than several fold.
8. Photons that remain local, i.e., trapped, are compressed by a
factor no greater than the local matter comer%ssian ratij, n,
so that photons that remain trapped within a	 en laver of
matter are increased in energy by the factor rl	 This is a
constraint in the numerical calculation. If the problem con-
sists of n layers and a minimum R/OR = r] , the maximum
increaS7 3 in energy of a given photon becomes of the order
(R/AR)
9. The Eddington limit flux just balances radiatiopressure
against the gravitational force, which is GM NS/R per unit
mass.	 Tc decelerate freely falling matter in a distance OR
requires an impulse per unit mass of the momentum v 2 t be
supplied in a time 2AR/v and therefore requires a force v /2AR.
The ratio of the flux rc,; ljired to decelerate the matter to the
Eddington flux is therefore v 2R2 /2GMNSAR which is R/AR taking
account of v2 = 2G^/R. The bremsstrahlung rate is propur-
tional to n2 or AR	 and the time of deceleration is propor-
e
tional to AR so that the total number of photons produced by
bremsstrahlung is proportional to 1/AR the same as the decel-
eration flux.	 Therefore, for all AR and the previous con-
ditions, the photon heating rate by the free fall matter will
exceed the photon multiplication rate by bremsstrahlung.
10. Double Compton scattering will increase the photon number at a
rate compared to Compton scattering:
a
double c = (1/137) aC(hv2)2
me
The highest energy photons have on the average undergone the
most scatterings and so are the most likely to have made a
second photon, along the way. The number of scatterings per
doubling is2 roughly 3, so the number of scatterings going from
(3 keV 4 me ) - 3 log2 (160) = 22. Then
22 adouble c - 1/6 <(hv2)2>
CY
c	 me
which is < 1 so that double Comytoa does not limit photon
energy significantly until by > me .
11. The free falling matter decelerated only when the photon
energy exceeds the matter energy. Neither bremsstrahlung nor
double Compton scattering affect the total photon energy, the
first because of limited time, and the second because it merely
redistributes the photon energy, i.e., mal.es a softer spectrum.
We have chosen our thickness such that compression heating
proceeds at just about the rate that photon energy is lost by
diffusion. To illustrate this point we take the diffusion
photon density distribution between at a reflector at x = 0 and
an outer boundary at X:
p = cos (nx/2X)
The collision rate is
Ncoll = f X cap dx
and the escape flux is
cc ddp
F = 3 dx X
The escape per collision is n 2/(121 2 ). Hence if it requires 3
collisions on the average to double the photon energy, then the
total retained photon energy will remain s gnstant if the prob-
ability of escape per collision is 2
	
, corresponding to
T = 1. Hence a modest increase in 1, will effectively trap the
photons and theirl/3total energy can increase without limit
proportional to q	 Hence we feel a natural limit tc com-
pression will be reached when y-y collisions lead to pairs that
then substantially increase T.
	
This offers a natural photor,
energy limit to tiie spectrum that is flux sensitive.
It seems reasonable to assume that the photon diffusion
terminates when pair production doubles the lepton density.
The calculations do not include pair production or this limit.
CALCULATION PARAMETERS
The calculation of the figure is relatively insensitive (- 20°,x)
to changes in energy group size (W. /W.) < V2, number of zonev
n > 10, and AR/k < 0.005.
	
If the initials seed temperature of .35
keV is reduced, then the energy group size, and AR must pie smaller
and n greater to obtain a result not grossly sensitive to the Dis-
creteness of variables.
ASTROPHYSICS
The maximum magnetic field that can be pe„,utted can be esti-
mated from Liang s who estimates the electron density for equal
emission from bremsstrahlung and synchrotron radiation to be
ne = 2.3 x 
1031 T3/2 F(T) B1 2 Z-1 cm
where T is kT /mc 2 and F(T) is of order unity for T ^_:- 1. Hence to
keep synchrotrorL radiation below bremsstr^h ung in the low 5density
plasma (n = 10 cm ) requires B < 10 or B < 3 x 10 gauss.
Since bremsstrahlung is rather a weak limit on the process and the
high energy photons come from compressed layers, a field of several
10 gauss would be acceptable. However, the limiting V eld is far
less than what would control or funnel accretion, 3 x 10 gauss. In
any event magnetic field precludes the usual interpretation of the
spectral structure as due to a cyclotron line. Some of our calcu-
lations show features similar to the observed dips at a few tens of
keV.	 Another possibility is that a parallel softer photon source
gives rise to these features.11
We feel that one possible astrophysical circumstance in which
the field-free accretion we describe could occur is the instability
of a Keplerian disc when it intersects, i.e. touches, the neutron
star surface.	 Friction and turbulence will then cause some low
density mast to accrete. Other possible candidates are super-
Eddington thermal conduction to the surface from the interior of the
neutron star or shocks that sequentially blow off surface layers
that subsequently fall back. In both these possible examples one
difficulty is the high atomic number of the neutron star matter
results in high opacity and high photon emission. Comet accretion
into an orbit that subsequently decays by gravitational wave
emission is another possibility.
It is a pleasure to acknowledge the many discussions with our
colleagues - part?cularly Ed Fenimor--, R. Ramaty, Don and Fred Lamb,
S. Woosley, David Pines and many others. This work was supported
both by the Astronomy Section of the National Science Foundaticn and
by DOE.
F.EFERENCES
1. D. Gilman, A. E. Metzger, R. H. "arker, L. G. Evans, and
J. I. Trombka, Astrophys. J. 2_36, 951 (1980).
2. T. L. Cline, Ann. N.Y. Acad. Sci. 262, 159 (1975).
3. T. L. Cline, and U. D. Desai, Astrophys. J. Lett. 196, L43
(1975).
4. F. K. Lamb, Gamma Ray Transients, edited by Lingenfelter,
Hudson, and Worrall (American Institute of Physics, 1981) p. 249.
5. E. P. Liang, Nature 299,-321 (1982).
6. E. P. Liang, Astrophys. J. 268, L89 (1983).
7. E.	 E.	 Fenimore,	 R.	 W.	 Klebesadel,	 J.	 G.	 Laros,	 and
R. E. Stockdale, Nature, 297, 665 (1982).
8. J. I. Katz, Astrophys. J. 260, 371 (1982).
9. W. D. Evans, E. E. Fenimore, R. W. Klebesadel, J. G. Laros,
and N. J. Terrell, Astrophys. +Space Science 75, 35 (1981).
10. E. P. Liang, in Proceedings of e e Workshop, "Emission Model of
Gamma-Ray Bursts," ( G oddard Space Flight Center, January 1983)
11. J. P. Lasota and B. M. Belli, Nature 304. 139 (1983).
SAC/rep:70A


Gamma-burst emission from neutron-star accretion

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