The motions of comets and neutron stars have been integrated over five
billion years in the Galactic potential to determine a gamma-ray burst
distribution, presuming that bursts are the result of interactions between
these two families of objects. The comets originate in two distinct populations
- one from ejection by stars in the Galactic disk, and the other from ejection
by stars in globular clusters. No choice of the free parameters resulted in
agreement with both the isotropy data and the $\log(N>F) - \log(F)$ data.Comment: 4 pages LaTex and two style files, tarred, compressed, and uuencoded.
  One postscript figure. To appear in Astrophysics and Space Science as part of
  the proceedings of the 29th ESLAB Symposium 'Toward the Source of Gamma-Ray
  Bursts' held in Noordwijk, 1995. A postscript version can be found at
  http://astro.queensu.ca/~mark/preprints.htm

Henriksen, R. N.

Higgins, M. G.

English

arXiv

The motions of comets and neutron stars have been integrated over five billion years in the Galactic potential to determine a gamma-ray burst distribution, presuming that bursts are the result of interactions between these two families of objects. The comets originate in two distinct populations - one from ejection by stars in the Galactic disk, and the other from ejection by stars in globular clusters. No choice of the free parameters resulted in agreement with both the isotropy data and the \log(N>F)-\log(F) data

Higgins, M G

Henriksen, R N

CERN Document Server

DISTRIBUTION OF GAMMA-RAY BURSTS
IN HALO NEUTRON STAR-COMET MODELS
M.G. HIGGINS and R.N. HENRIKSEN
Queen’s University at Kingston
Kingston, Ontario, Canada
Abstract.
The motions of comets and neutron stars have been integrated over five billion years in the
Galactic potential to determine a gamma-ray burst distribution, presuming that bursts
are the result of interactions between these two families of objects. The comets originate
in two distinct populations - one from ejection by stars in the Galactic disk, and the other
from ejection by stars in globular clusters. No choice of the free parameters resulted in
agreement with both the isotropy data and the log(N > F )-log(F ) data.
Key words: Gamma-ray bursts – Neutron stars – Comets – Globular clusters
1. Introduction
There have been many models over the years which try to identify gamma-
ray bursts (GRBs) with neutron stars (NSs) in an extended Halo around
the Galaxy which interact in some way with passing comets (e.g. Pineault
and Duquet (1993) or Mitrofanov and Sagdeev (1990)). The details of the
environment which would allow such a scenario involving interstellar comets
have not been worked out in detail.
Over the age of the solar system, it has been estimated that approximately
1012 comets have escaped the Sun’s gravitational well (Stern (1990)). If other
solar systems behave in a similar manner, there should be a large number
of free comets in globular clusters (GCs), which, after escaping the clusters
by scattering, could seed an extended Halo.
This work evolved a population of 106 NSs born in the disk. It also
evolved 107 comets ejected from GCs, and assumed a population of disk
comets which follow the mass density of the disk. Using these results, a
sample of GRBs was created.
2. The Model of Galactic Potential
The model used was taken from Paczynski (1990), with some modications.
It assumes three contributions to the total potential: a disk, a spheroid, and
a spherical dark matter halo. The values used for the constants in his model,
relating to the oblateness of the spheroid (a1 and b1) and disk (a2 and b2),
are: a1 = 0, b1 = 0.277 kpc, a2 = 3.7 kpc, and b2 = 0.2 kpc. A dark matter
halo with constant density inside a radius rc = 8 kpc, and density falling
o like r−2.25 outside rc, replaced Paczynski’s halo. The masses used are:
2 M.G. HIGGINS AND R.N. HENRIKSEN
M1 = 1.12  1010M (the spheroid mass), M2 = 8.07  1010M (the disk
mass), Mc = 1.75 1010M (the dark halo mass inside rc).
Other components contributing to the Galactic potential, such as satellite
galaxies or the globular cluster population, were ignored for simplicity. Over
the course of the simulation, roughly 10 % of the comets would be aected by
such objects; this is not expected to change the results to any great degree.
In addition, it is assumed that the Galactic dark matter does not interact
with the comets to any appreciable degree. This assumption would fail if
the dark matter is mainly molecular clouds, for example.
3. The Three Populations
The GC population comets were ejected from the GC stellar systems with
small relative speeds. A small fraction of these comets escaped from the GC
without scattering; however, a much larger fraction were scattered by stars
in the GC (for simplicity, all scattering stars were taken to have a mass
M), and were ejected from the GC with speeds approximately 10-20 km/s.
140 typical GCs were used in the simulation. The GC population was found
by assuming a radial distribution which falls o like r−0.85 (Kulessa and
Lynden-Bell (1992)), and a velocity distribution with gaussian form, with
average value v0 = 220− 2rkpc km/s, and standard deviation σ = 120− rkpc
km/s. Here, rkpc is the radial distance from the centre of the Galaxy in kpc,
allowed to range from 6-110 kpc. Each GC was taken to have mass 105 M,
and the Plummer model, with a radial distance scale of 1 pc, was used for
the gravitational potential.
The disk population of comets was taken to follow the disk component
of the total density. The total number of disk comets was set to the total
number of GC comets multiplied by the ratio of the disk mass to the total
mass of GCs, and a factor f (one of the free parameters in the work), which
is a ratio of the eciencies of comet ejection in the disk to comet ejection
in the GCs.
The NSs were started in the disk, with a position distribution which
follows the observed pulsar distribution, taken from Johnston (1994). The
initial speeds considered ranged from 350 km/s to 2000 km/s in a frame of
reference rotating around the Galactic centre.
4. Estimating the Interaction Probability
The probability of interaction between the NS and comet populations was
taken to be (e.g. Pineault and Poisson (1989)) P = Annsncvrel . Here, A is a
constant relating to the cross-section for collisions, nns is the NS number
density, normalised to unity at the maximum value, nc is the normalised total
comet number density (disk comets plus GC comets), and vrel is the average
9507072.tex - Date: January 22, 2003 Time: 0:29
DISTRIBUTION OF GRBS IN HALO NEUTRON STAR-COMET MODELS 3
Fig. 1. Projected sky map of 5000 sample GRBs for NS birth velocities of 700 km/s,
f = 0
relative speed of the two populations at the point in question, determined in
the simulations. This includes only gravitational focussing in the collisions.
The burst frequency in this model can be roughly estimated, but since
much of the physics is unknown, assigning values to the constants should
be taken as tentative at best. Very approximately, dNburstsdt = Nc~nNSσintvrel,
where Nc is the total number of comets, ~nNS is an average number density
of NSs, and σint is the interaction cross-section.
The total number of comets is given by Nc = NsGCNcGC+NsdNcd, where
NsGC is the total number of GC stars (’ 107), Nsd is the total number of
disk stars (’ 1010), Ncd is the number of comets produced by a disk star, and
NcGC is the number of comets produced by a GC star; using the eciency
ratio f from section 3, NcGC = Ncd/f .
As a rough estimate, we can use the number of comets estimated to have
been ejected from our solar system as an approximation to Ncd. Assuming a
total population of 109 NSs, most inside a sphere of radius 40 kpc, relative
speeds on the order of 103 km/s, and that the cross-section is just the square
of the light-cylinder radius for a NS spinning with an angular velocity of 0.1
rad/s, the number of bursts per day is roughly dNdt ’ 4bursts/day(10
−6
f ).
5. Simulated Gamma-Ray Burst Distribution
Figure 1 shows a sky map of 5000 sample GRB positions, using a NS
birth velocity of 700 km/s and eciency ratio f = 0 (no disk comets).
The anisotropy toward the Galactic disk is obvious, even without including
the eect of the disk comet population. The clustering is evident with as
few as 585 bursts (as in the BATSE 2B catalog). Including a disk popula-
tion rapidly (for any f > 10−5) makes clumping toward the Galactic plane
extremely ecient. Changing the birth velocities of NSs has little eect,
9507072.tex - Date: January 22, 2003 Time: 0:29
4 M.G. HIGGINS AND R.N. HENRIKSEN
due to the clumped comet population. Note that increasing f beyond 10−5
not only causes clumping toward the disk, but also decreases the number of
bursts/day to numbers much smaller than are observed. The requirement of
such a discrepancy in the ejection eciencies is another strike against this
model.
The flux of a burst was calculated by letting the total energy E of a burst
follow a gaussian distribution in logarithmic space, with the average burst
energy set so that a burst with this energy, located at 100 kpc, would have
a flux equal to the \instrumental" minimum observable flux. A standard
deviation of half an order of magnitude was used. This is a somewhat ad-
hoc value; the true distribution in E likely depends on distributions of NS
magnetic eld strength and spin rate, which are unknown for the burster
population. The results are not very sensitive to this spread as along as it
is less than two orders of magnitude, where it becomes comparable to the
spread in flux due to the range in distances of the bursts.
The relation log(N > F ) / −3/2 log F holds for an isotropic distribu-
tion of standard candles, where log(N > F ) is the number of bursts with
flux greater than F . The simulation data are roughly consistent with this
distribution for large values of flux, though a slope of -1.44 is the best t.
The flattening of the slope observed in the BATSE data is also seen in the
simulation data.
6. Conclusions
These results suggest that models of GRBs as comet-NS collisions in an
extended Halo are untenable for a wide range of free parameters. While
simulation data, with a somewhat unphysical choice for the ejection e-
ciency of GC stars, roughly meet the distribution in flux of real GRBs, no
values of the free parameters allow a t to the isotropy data. However, this
work does assume that the NSs are ejected from the Galactic disk, and are
not relics from the initial formation of the Galaxy. Choosing an appropriate
distribution of relic NSs may allow a model in agreement with the observa-
tions. In addition, replacing the spherical dark matter halo with an oblate
one might reduce the clumping toward the Galactic centre.
References
Johnston, S.: 1994, Monthly Not. Roy. Astr. Soc. 268, 595.
Kulessa, A.S., and Lynden-Bell, D.: 1992, Monthly Not. Roy. Astr. Soc. 255, 105.
Mitrofanov, I.G., and Sagdeev, R.Z.: 1990, Nature 344, 313.
Paczynksi, B.: 1990, Astrophys. J. 348, 485.
Pineault, S., and Duquet, J.-R.: 1993, Monthly Not. Roy. Astr. Soc. 261, 246.
Pineault, S., and Poisson, E.: 1989, Astrophys. J. 347, 1141.
Stern, S.A.: 1990, Publ. Astron. Soc. Pacific 102, 793.
9507072.tex - Date: January 22, 2003 Time: 0:29


Distribution of gamma-ray bursts in halo neutron star-comet models

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.316.856

Distribution of Gamma-Ray Bursts in Halo Neutron Star-Comet Models

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