A Lagrangian, fully implicit, one dimensional hydrodynamic computer code was used to investigate the evolution of a gas cloud impacting the surface of a 20 km, 1 Msub solar neutron star. This gas is initially at rest with respect to the surface of the neutron star, extends to 185 km above the surface, and is optically thick. The infall results in a burst which lasts about 0.1 seconds and reached a peak luminosity and effective temperature of 240,000 Lsub solar and 9 million; respectively. The burst was followed by a phase of oscillations with a period 0.2 seconds

Kenyon, S.

Sparks, W. M.

Starrfield, S. G.

Truran, J. W.

English

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TITLE: A NUMERICAL SIMULATION OF THE MAGNETOSPHERIC GATE MODEL
FOR THE X-RAY BURSTERS
AUTHOR(S): Sumner G. Starrfie^
S. Kenyon	
SUWJ. W. Truran 
W. M. Sparks
SUBMITTED TO: Proceedings of the La Jolla Conference on
Y-Ray Bursters
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A NUMERV AL SIMULATION OF THE MAGNETOSPHER:C GATE MODEL
FOR THE X-RAY BURSTERS
S. Starrfield
Department of Physics, Arizona State University
Tempe, AZ 85287
and
Theoretical Division
Los Alamos National Laboratory, University of California
Los Alamos, NM 85745
S. Kenyon and J. W. Truran
Department of Astronomy, University of Illinois
Urbana, IL 61801
W. M. Sparks
Laboratory for Astronomy and Solar Physics
N.A.S.A. - Goddard Space Flight Center
Greenbelt, MY 20771
ABSTRACT
We have used a Lagrangian, full y imp licit, one-dimensional
hydrod ynamic computer code to investi gate the evolution of a gas
cloud impactin g
 the surface of a 20 km, 1 M  neutron star. This
gas is initially at rest with respect to the surface of the neutron,
star, extends to 185 km above the surface, and is optically thick.
The infall results in a burst which lasts about 0.1 seconds and
G
reaches a peak luminosity and effective tem perature of 2.4 x 10" Lo
and 9 x 10 6 K; res pectively. The burst was followed b y a phase of
oscillations with a period 0.2 seconds.
INTRODUCTION
One of the more interesting scenarios for the cause of the X-
ray Bursts is the maonetospheric gate theory of Lamb, et al.' In
this scenario we have a rapidly rotatin g neutron star with a strong
ma g netic field in a binary system with a companion that is losing
mass toward the neutron star. This material is im peded b y the .;a g
-nezic field in such a fashion that accretion is not continuous but
occurs in episodic events. To our knowledge there have been no
previous numerical simulations of th;s phenomena.
We use the same hydrodynamic code described in the last paper2.
Because it is a Lagran g ian, stellar interior, computer code which
assumes radiation trarsport by diffusion; we cannot place a hole in
the mesh and so assume that the blob of gas extenas from the surface
of the neutron star to a radius of '85 km. This blob is optically
thick, has a mass of 10 -11 "O , and is initially at rest with resoect
to the surface of the neutron star. The mass of this blot, was cho-
sen so as tc simulate a much smaller amount of material falling
only onto the polar caps. The gas initially has a temperature of
10^ K and a surface luminosity of 0.1 L . We begin the 	 calcula-
tion by allowin g the material to fall and the surface.
RESULTS
Once the infall has begun, an accretion shock forms  at the
boundary of the core. After about 100;: sec of evolution, the in-
fail velocities have reached free fall and the tem perature behind
the shock has reached 10 9 K. ?t takes 3.5 milliseconds for the
ou'^er edge of the shock to reach the surface of the blob which has
now fallen inward to 80 ktr. The entire envelope bounces imparting
enoug h enercv to the two outermost zones (2 x 10 -14 Ma ) for them to
reach escape velocity. The light curve for the burst is shown. in
Figure 1 . The peak luminosity and effective temperature produced
by the infalling material is 2.4 x 10 5
 Lo and 9 A 10
6
 K, respective-
ly. Although, this effective temperature is too low for any of the
O 11r`	 - C^ L_	 -
too- —
cc—
f
—
.00— —
_	 — — 5.00 - —
4 00 -
I11
^	 vv
^— 00— jl	 —
.^ v
=C'
:: C : z:	 :3C	 _	 C ^.c:	 x	 z.CC	 3.0c	 CC	 :.oc
-.,..
	 St 	 nos
she lurinosit y of the Fic.	 2. The lum i nosity of the
infallinc :,,Eterial	 as	 a	 function surface as a function of tine.
of,,e.
observed bursts, we could raise this tem perature by recuc'nc the
;nner ratios of t;e neutron star and reducin g the amount cf infall-
nc Taterla'..
-he temperature in the shell source at the core-envelope inter-
.	 a
=ace (CCI) has remained at 10' K and enou gh tri p le-a reactions are
occurrin g to keep the rate of nuclear energy generation at 10 18 erg
gm	 sec -1 . In addition, the deeper layers of the envelo p e are
convective, which is mixing fresh unburned nuclei into the shell
source which also is maintaining the large rate of nuclear burning.
However, the outer layers are expandin g too ra p idly for the energy
orocucec in the shell source to reach thee: and their luminosity
cross rapidly. For a short period the 21 ""-decays in the surface
layers are able to halt the decreasing luminosity but the rapiC ex-
pansion again overcomes this energy source. The entire burst lasts
about 0.3 sec.
The decline in luminosity continues until the esca p ing shells
become Optically thin. At this time the energy fro g' the interior
can now escape and the luminosity 4egins to increase. Now that we
can see into the deeper lavers we find that the accreted material
re^aininc on the neutron star is pulsatin g with a period of 0.2
sec (ricure 2). The average luminosity or this object is -,10' La
and the effective temperature is 0.3 kev. It has a radius of 150km
(average).
These pulsations are a direct result of the infail and are not
caused by a partial ionization mechanism such as in the Cepheids or
2Z Ceti variables. We also find that these pulsations must be
occurring in hi gh overtones since we find a number of nodes in the
eiaenfunction and the lar gest amplitudes are in the surface zones.
ne closely followed these pulsations for 4 seconds of star
time. However, the cor:.puter time was becomin g prohibitive and we
ended this Part of the calculation. We removed the escaping zones
and followed the resulting evciution for ano'her thousand seconds.
No further chances occurred and we ended the calculation. It is
estimated that at least one day of further evolution would be nec-
essar y to completely burn the h ydrogen in the envelope.
l•,l e also studied a purel y coolin g sequenc e in which we followed
the contraction of the extended envelope cS5l.. no onl y neutrino
losses - no nuclear energy production. The envelope contracts from
atcut 200 km to 100 km in 10 3 Jec with the luminosit y c1imbino to 2
X 7 0 - L c and the effective temperature to about 1 kev. It takes
anotner 40 minutes to contract to 20 km. During the cooling phase
the surface luminosity reaches a -)eak luminosity of 2 x 10' Lo and
a peak effective temperature of 1.9 kev.
COD NCLUS 10NS
:e find that our Burst teas too cool and tot ra p id to resemble
I	 -. 4	 1
the nor-,al bursts altnough the time scale is in acree^ent with
so,-,.e of the racid bursts that have oeen observed for some objects-.
.t is certainly Possible tnat More realistic initial Conditions,
six h as assuming the material was already infallin g , could im-
prove the correspondence between our calculations and the observa-
tions.
.:e also found that the infall produced a rin g ing of the enve-
lope which showed short period pulsations. Such pulsations have
been observed in at least one burst event".
REFERENCES
i.	 ..K. 6a7,b, A.C. Fabian, J.E. Princle, D.Q Lamb, Ap.J. 217, 197
(19i7)
2. S. Starrfield, S. Kenyon, J..^. Truran, ^d.^i. Sparks, this volume
(1981).
3. S. Starrfield, S. Kenyon, W.M. Sparks, Ap.J. (submitted 1981).
!^.	 :;.H. G. Lewin, P.C. Joss, 'nature 270, 211 (1977).
^. T. Murakami, private communication (1981).


Numerical simulation of the magnetospheric gate model for X-ray bursters

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