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Spatial distribution of accreting isolated neutron
stars in the Galaxy
S.B.Popov and M.E.Prokhorov
Sternberg Astronomical Institute, Moscow State University
Abstract
We present here the computer model of the distribution of the lumi­
nosity, produced by old isolated neutron stars (OINSs) accreting from the
interstellar medium (ISM). We show, that for different mean velocities of
OINSs the distribution of the luminosity has a torus­like structure, with
the maximum at ú 5kpc.
1 Introduction
In the last several years, the spatial distribution of old isolated neutron stars
(OINSs) became of great interest (see, for example, Treves and Colpi (1991)).
Several sources of this size were observed by ROSAT. Different regimes of in­
teraction of the interstellar medium (ISM) and OINSs can appear: Ejector,
Propeller (with possible transient source), Accretor, Georotator and supercrit­
ical regimes (see, Popov (1994) and Lipunov and Popov (1995)). Here we are
interested only in accreting OINSs.
We use direct calculations of trajectories in the Galaxy potential, taken in
the form (Paczynski (1990) ):
\Phi i (R; Z) = GM i =
i
R 2 + [a i + (Z 2 + b 2
i ) 1=2 ] 2
j 1=2
.
In the articles of Postnov and Prokhorov (1993, 1994) it was shown, that
OINSs in the Galaxy form a torus­like structure. If one looks at their distri­
bution and at the distribution of the ISM (see, for example, Bochkarev (1993)
), it is clearly seen, that the maximums of two distributions roughly coincides.
It means, that most part of OINSs is situated in dence regions of ISM. So, the
luminosity there must be higher. Here we represent computer simulations of
this situation.
2 Model
We made calculations on the grid with the cell size 100 pc in R­direction and 10
pc in Z­direction (centered at R=50 pc, Z=5 pc and so on). Stars were born in
the Galactic plane. The system of differential equations was solved numerically.
In our model we assumed, that the birthrate of NSs is proportional to the
square of local density. Local density was calculated using data and formulaes
from Bochkarev (1993) and Zane et al. (1995).
1

Figure 1: The density distribution in R­Z plane
Figure 2: The luminosity distribution in R­Z plane for Maxwellian kick velocity
(75 km/s)
2

Figure 3: The luminosity distribution in R­Z plane for Maxwellian kick velocity
(150 km/s)
n(R; Z) = nHI + 2 \Delta nH2
nH2 = n 0 \Delta exp
Ÿ
\GammaZ 2
2 \Delta (70pc) 2
–
If 2kpc Ÿ R Ÿ 3:4kpc, then
nHI = n 0 \Delta exp
Ÿ
\GammaZ 2
2 \Delta (140pc \Delta R=2kpc) 2
–
;
For R Ÿ 2kpc n(R; Z) was assumed to be constant:
n(R ! 2kpc; Z) = n(R = 2kpc; Z)
Of course, it is not accurate, so for the very central part of the Galaxy our
results are only a rough estimation.
If 3:4kpc Ÿ R Ÿ 8:5kpc, then
nHI = 0:345 \Delta exp
Ÿ
\GammaZ 2
2 \Delta (212pc) 2
–
+0:107 \Delta exp
Ÿ
\GammaZ 2
2 \Delta (530pc) 2
–
+0:064 \Delta exp
Ÿ
\GammaZ
403pc
–
If 8:5 Ÿ R Ÿ 16kpc, then
3

Figure 4: The luminosity distribution in R­Z plane for ffi ­function kick velocity
(75 km/s)
nHI = n1 \Delta exp
Ÿ
\GammaZ 2
2 \Delta (530pc \Delta R=8:5kpc) 2
–
The density distribution is shown in the figure 1.
Kick velocity was taken both: in the Maxwellian form with the maximum
velocity 150 km/s, 75 km/s and 35 km/s and as a ffi ­function with V=150 km/s,
75 km/s and 35 km/s (see discussion in Lipunov et al. (1996) ).
Sound velocity was taken to be 10 km/s. Luminosity was calculated using
Bondi formula:
L =
`
GMNS
RNS
'
2ú
`
(GMNS ) 2 n(R; Z)
(V 2
s + V 2 ) 3=2
'
.
3 Results
On the figures 2­7 we represent the results for two velocity distributions. On
the figure 8 the slice at Z=+5 pc for the maxwellian kick (V max = 150 km/s) is
shown.
As it is clearly seen from the figures, the distribution of the luminosity
density (shown in arbitrary units) in R­Z plane forms a torus­like structure
with the maximum at approximatelly 5 kpc.
4

Figure 5: The luminosity distribution in R­Z plane for ffi ­function kick velocity
(150 km/s)
Figure 6: The luminosity distribution in R­Z plane for ffi ­function kick velocity
(35 km/s)
5

Figure 7: The luminosity distribution in R­Z plane for maxwellian kick velocity
(35 km/s)
Figure 8: Slice at Z=+5 pc for maxwellian kick velocity (150 km/s)
6

Figure 9: Total velocity (in arbitrary units) vs. kick velocity
4 Discussion and concluding remarks
The torus­like structure of that distribution is an interesting and important
feature of the Galactic potential. Local maximums in the ISM distribution are
smoothed (compare figures 1­7). As one can suppose, for low velocities we get
greater luminosity. Stars with the Maxwellian distribution can penetrate deeper
into the inner regions than stars with ffi ­function velocity distribution (especially
it is clear for high Z ­ 200­400 pc for low velocity distributions) because we for
maxwellian kick we have both: more low velocity and more high velocity stars.
On fig.9 we show dependence of the total luminosity of the galaxy (in arbi­
trary units) from the kick velocity for two types of distributions. We mark very
interesting feature: intersection of the curves at ú 125 km/s.
As me made very general assumptions, we argue, that such a distribution is
not unique for our Galaxy, and all spiral galaxies must have such a distribution
of the luminosity density, associated with accreting OINSs.
5 Aknowledgements
The work was supported by the RFFI (95­02­6053) and the INTAS (93­3364)
grants. The work of S.P. was also supported by the ISSEP.
7

References
[1] N.G. Bochkarev, ''Basics of the ISM physics'', 1992, Moscow, Moscow State
Univ. Press
[2] V.M. Lipunov and S.B. Popov, AZh, 71, 711, 1995
[3] V.M. Lipunov, K.A. Postnov and M.E. Prokhorov, A&A, 310, 489, 1996
[4] B. Paczynski, ApJ 348, 485, 1990
[5] S.B. Popov, Astr. Circ., N1556, 1, 1994
[6] M.E. Prokhorov and K.A. Postnov, A&A, 286, 437, 1994
[7] M.E. Prokhorov and K.A. Postnov, Astr. Astroph. Trans., 4, 81, 1993
[8] A. Treves and M. Colpi, A&A, 241, 107, 1991
[9] S. Zane, R. Turolla, L. Zampieri, M. Colpi and A. Treves, ApJ, 1995, 451,
739
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