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Dim ROSAT isolated neutron star candidates: old accretors
or young coolers?
S. B. Popov
Sternberg Astronomical Institute
Universitetskii pr.13, 119899, Moscow, Russia
e-mail: polar@sai.msu.ru
M. Colpi
University of Milan
Via Celoria 16, 20133 Milan, Italy
e{mail: colpi@uni.mi.astro.it
M. E. Prokhorov
Sternberg Astronomical Institute
Universitetskii pr.13, 119899, Moscow, Russia
e-mail: mystery@sai.msu.ru
A. Treves
University of Insubria
Via Lucini 3, 22100, Como, Italy
e{mail: treves@mi.infn.it
and
R. Turolla
University of Padova
Via Marzolo 8, 35131 Padova, Italy
e{mail: turolla@pd.infn.it
1

Abstract
We model populations of isolated neutron stars in order to investigate them as progenitors
of dim soft X-ray sources. We discuss both: old accreting and young cooling neutron stars.
For accretors realistic magneto-rotational evolution and evolution in the Galactic potential
are taken into account together with a realistic large scale distribution of the interstellar
medium. Cooling neutron stars are explored with a simpler model of local sources, but
interstellar absorption is additionly taken into account.
In the standard assumptions (maxwellian initial velocity distribution with the mean value
about 200-300 km s 1 , initial magnetic eld distribution similar to radiopulsar, no eld decay,
small initial spin periods) we obtain accretors only if their magnetic eld is > 10 11 {10 12 G.
So, for polar cap accretion X-ray sources are relatively hard with typical temperature about
300-400 eV. For them interstellar absorption is not very signicant, and we predict about 1
source per square degree for uxes about 10 15 {10 16 erg cm 2 s 1 for energy range 0.5-2
keV. For young cooling neutron stars, which are soft sources (T  50 eV), absorption is very
important, and they are signicantly less abundant at low uxes. For them we predict < 0:1
sources per square degree.
With these standard assumptions we cannot explain observed properties of the ROSAT
candidates (relatively large number of close bright sources; low temperatures; periods about
10-20 s, which are observed for two candidates: RX J0420.0-5022 and RX J0720{3125). We
argue, that most part of these sources can be young cooling neutron stars with typical age
about 10 6 yrs or less, if the total number of neutron stars in the Galaxy is signicantly higher,
than it comes from radiopulsars statistics.
The source RX J0420.0-5022 with the spin period 22.7 s can't be explained as a "standard"
accretor or a "standard" cooling neutron star. In this case most probably magnetic eld decay
is operating.
Keywords: Accretion | stars: kinematics | stars: neutron | stars: magnetic
eld | X{rays: stars
2

1 Introduction
The existence of isolated accreting neutron stars (IANSs) among observed X-
ray sources is still under doubt. Also the nature of 6-7 ROSAT INS candidates
is unclear (Treves et al. 2000), and two competive hypothesis (accretion and
cooling) exist.
Here we try to explore in more details this situation, and to give some pre-
dictions for observations at very low uxes with such satellites as Chandra and
XMM (Newton).
In our previous paper (Popov et al, 2000, P2000 hereafter) we didn't discuss
log N { log S distribution for IANSs. In the present paper we make an attempt
to do it.
In Section 2 we describe calculations of log N { log S for IANSs. In general
they are similar to calculations in P2000, but some dierences exist and we brie y
discuss them.
In Section 3 we describe a simple model which was used to obtain log N { log
S distribution for cooling INSs with interstellar absorption.
In Section 4 we discuss all these results, and in the last section we present our
conclusions.
3

2 Accreting isolated neutron stars
Population synthesis of IANSs in the Galaxy and similar investigations were made
previously by dierent authors (see, for example, Treves and Colpi 1991 (TC91
hereafter), Manning et al 1996, Madau and Blaes 1994). This attempt is closely
connected with our previous work (P2000). In the following subsection we brie y
discuss the model we use, and dierences with the previous work.
2.1 Model
In general the present model is similar to the one used in P2000. INSs are born
in the Galactic plane. In our calculations they are initially uniformly distributed
in some range of radii from the Galactic center, but for each point a coeфcient
(weight) proportional to the square of the local interstellar medium (ISM) density
is calculated. And all statistics is calculated for a specied track with this weight.
So, in our calculations starformation rate is proportional to the square of the
ISM density and is constant in time. If there was initial starformation burst in
our Galaxy, when signicant part of INS population was formed, then our results
should be shifted towards higher number of accretors.
In order to increase statistics we make calculations only for initial positions
from which a NS with initial velocity about 100 km s 1 (or less) can appear in
the volume for which log N { log S is calculated. For dierent volumes we take
dierent ranges of birth places.
We don't use a spatial grid as in P2000, instead we input a timestep, i.e. all
parameters of an INS are recalculated not on the grid cell boundaries, but with
after some timeinterval, фt. It is dierent for dierent stages of NSs evolution
4

and dierent regions of the Galaxy. The timeinterval is shorter for short living
stages (propeller and georotator) and inside the volume, where log N { log S is
calculated. Typical value of the timestep | 10 5 yrs.
Each track is used for NSs of dierent ages, i.e. it is "shifted" in time. So,
a single track actually represents a population of NSs born in the same place
with the same initial conditions, but at dierent moments: from the birth of the
Galaxy to the present time. Number of these "shifts" can be roughly estimated
as T calc =T step  10 5 , where T calc = 10 10 yrs { the age of the Galaxy.
ISM distribution, as previously, is taken from Bochkarev (1992) and Zane et al
(1995).
The important feature of our approach is detailed calculation of magneto-
rotational evolution of INSs. Magneto-rotational evolution is calculated as before,
but critical periods (ejector period, PE (E !P), for ejector ! propeller tran-
sition; ejector period, PE (P !E), for propeller ! ejector transition; accretor
period, PA ) are very slightly changed:
PE (E ! P ) = 10:21 s  1=2
30
n 1=4
v 1=2
10
;
PE (P ! E) = 2:623 s  4=7
30
n 2=7 v 6=7
10
;
PA = 302:105 s  6=7
30
n 3=7 v 9=7
10
M 11=7
1:4
:
Here  30
- magnetic moment in units 10 30 G cm 3 , v 10
- INS's spatial velocity
in 10 km s 1 , n - ISM concentration, M 1:4
- INS's mass in units 1.4 M .
For spindown on the ejector stage we use the following equation:
5

P = P 0
+ 3
10 4 t 1=2  30
;
where t is in yrs and as usual  = 1=2 B p R 3
NS (RNS - NS's radius, B p - polar
magnetic eld).
For the propeller stage we use, as in P2000, Shakura's formula (Shakura 1975).
At the accretor stage spin period is set to be equal to the "equilibrium" period
(Lipunov and Popov 1995, Konenkov and Popov 1997).
We don't take into account the possibility of formation of temporal accretion
disk around accreting INS, when its velocity relative to ISM is small. It should
have signicant in uence on spin periods, p, and _
p distribution of IANS (and
"equilibrium" periods can be slightly dierent from the values we use), but it is
not the question of this paper (from the point of view of luminosity and spectrum
it can be very important, for example, for isolated accreting black holes, which
are not discussed here).
We assume high accretion eфciency: L = _
M GM=RNS . Which is reasonable
for accretion onto NSs at low accretion rates. We don't take into account any
eects of heating of the accreting matter by radiation of the IANS.
Galactic potential is also taken in the same form as in P2000, but parameters
are slightly changed in order to t better solar distance from the Galactic center,
which is assumed to be equal to 8.5 kpc (see Madau and Blaes 1994).
Initially a NSs has a circular velocity, with a value corresponding to its birth-
place, and additional kick velocity, which had a maxwellian distribution, is added.
To increase statistics (we are able to calculate about 15,000 tracks, compare
with  1; 000 in P2000) we calculate only low-velocity stars (v < 100 km s 1 ) from
6

the maxwellian distribution for the mean velocity about 300 km s 1 (calculations
for dierent mean kick velocities are presented in P2000). All INSs with initial
velocities > 100 km s 1 are assumed to be on the ejector stage (or much less
probably on the propeller or on the georotator stages). This assumption is based
on the estimate:
t E  10 10 yrs  1
30
n 1=2
v 100 ;
and on the note, that very strongly magnetized INSs (which are able to leave the
ejector stage in less than 10 10 yrs even for high spatial velocities) can leave the
propeller stage not as accretors, but as georotators.
Our results can be easily renormalized for any mean velocity > 200 km s 1
(for 200 km s 1 , for example, log N { log S curve should be higher by a factor of
3.12 than it is for the mean velocity 300 km s 1 , for which we plot all our graphs
here).
Magnetic elds of INSs are taken to have log-gaussian distribution, similar to
the radiopulsar magnetic eld (in contrary to P2000, where we used only two
single values of the initial magnetic eld). For each track we calculate 6 dierent
magneto-rotational histories (for 6 dierent values of initial magnetic elds), and
then results are merged and normalized according to this log-gaussian distribution:
f() =
1
p
2
e (lg  lg  0 ) 2 =(2 2
)
;
where  = 1=2 B p R 3
NS , RNS - NS's radius, B p - polar magnetic eld;  = 0:32,
lg  0
= 30:06 (which corresponds to lgB 0
= 12:36). Our results are sensitive to
the initial eld distribution.
7

Nearly all strongly magnetized INSs come to the stage of accretion, and for log
N { log S we obtain good statistics for uxes < 10 11 erg cm 2 s 1 . For higher
uxes our results can be well extrapolated as a line with the slope -3/2.
All our results are normalized for the total number of NSs in the Galaxy N =
10 9 (see discussion on this number below).
2.2 Results
Our main results are presented in gures 1 and 2.
To compare calculations with observations it is useful to produce log N { log S
distribution. In P2000 we could produce only a very naive log N { log S, plotting
our single point (for limiting distance 140 pc and limiting ux 10 13 erg cm 2 s
1 ) and adding lines with slopes -1 and -3/2. It is clearly well below observed
points (see g. 2) due to a small volume (r < 140 pc) for which the number of
bright accretors was estimated. Here we try to obtain realistic log N { log S for
IANSs. We calculate log N { log S only for stars in some vicinity of the Sun (two
values were used: 500 pc and 5 kpc).
In the gure 1 we show log N { log S distribution for accretors inside 5 kpc
sphere around the Sun and distributions of temperature, velocity and accretion
rate for all accretors, which appear in our calculations. In all graphs the realistic
initial magnetic eld distribution is taken into account. Mostly all strong magnetic
eld NSs in our calculations, i.e. for v < 100 km s 1 , become accretors. But the
plotted distribution are mainly determined by the most abundant NSs in the
accepted population with elds about 2
10 12 G. INSs with elds < 0:5
10 11 G
never appears as accretors in dierent runs of the program.
The brightest accretors have luminosities about 10 32 erg s 1 , but the majority
8

of them has luminosities about 10 29 10 30 erg s 1 .
To compare results with ROSAT sources we use conversion factor 0:01cts s 1 =
3
10 13 erg cm 2 s 1 (Neuhauser and Trumper 1999, NT99 hereafter).
Calculations show, that for relatively high uxes (> 10 12 {10 13 erg cm 2 s 1 )
we can use results for 500 pc vicinity, as far as they are undistinguished from 5
kpc sample (only for very bright sources we don't have enough statistics for 5 kpc
sample).
We calculate log N { log S distribution for the total ux (L = _
M GM=RNS ,
S total = L=4r 2 ) and ux in the range 0.5-2 keV for polar cap accretion. In
the later case the spectrum is assumed to be black-body and polar cap radius is
calculated with known magnetic eld and accretion rate (R cap = RNS
q
RNS=RA ,
RA - Alfven radius).
Flattening of the log N { log S curves (g. 2), which are calculated in the 500
pc vicinity, shows that nearly at f < 10 14 erg cm 2 s 1 we see signicant part of
all accretors in that volume. Steep decrease of log N { log S at very high uxes
appears simply due to low statistics for bright (i.e. rare: very close or very low
velocity) sources.
If absorption is negligible, then one expects about 1 source per square degree for
the range 0.5-2 keV for limiting uxes about 10 16 {10 15 erg cm 2 s 1 (i.e. about
3:4
10 4 sources for the whole sky, but they should be signicantly concentrated
to the Galactic plane, and asymmetry center-anticenter should also appear).
We also compare our new results with P2000 when it is possible, and both sets
of results are in very good correspondence.
9

3 Cooling neutron stars
Cooling INSs can be a reasonable explanation for ROSAT INS candidates. But,
as for accretors, in that case some problems also exist.
3.1 Model
We assume, that INSs are uniformly distributed in the disk with a semithickness
of 450 pc. Spatial density of INSs was varied. We take two values: nNS =
0:33
10 3 pc 3 and nNS = 3:3
10 3 pc 3 . The rst value corresponds to the
density which was used, for example, in NT99, and it is connected with the
radiopulsar statistics. The second value corresponds to the total number of NSs
in the Galaxy N  10 9 and comes from nucleosynthesis calculations (Arnett et
al. 1989). This higher value was used, for example, in TC91. These two values
can be compared, for example, with n  1:4
10 3 pc 3 in Paczynski (1990). For
high kick velocities the value nNS = 3:3
10 3 pc 3 seems to be high, but as we
show below it is necessary to explain the observed data.
All INSs are taken as the "standard candles" with L = 10 32 erg s 1 and black-
body spectrum. Time of NS cooling was taken to be 10 6 yrs. It corresponds to the
"slow cooling" (Page et al. 2000). In the "fast cooling" models (Yakovlev et al.
1999) numbers of observable cooling INSs should be much smaller. So, potentially,
observations of INSs can help to distinguish between models of cooling of NSs.
ISM is treated in a very simple way:
1. spherical local Bubble of radius r l (it can be varied) and density n = 0:07 cm 3
around the Sun.
2. uniform ISM with density n = 1 cm 3 in the disc with 450 pc semithickness.
10

After the column density, NH , is calculated we run standard ROSAT routine to
calculate count rate for a given luminosity, temperature and column density.
This simple model reproduces the most important feature: " attening" of log
N { log S distribution outside the Local Bubble, which is important to explain
the ROSAT data for bright uxes. More sophisticated models with realistic dis-
tribution of ISM and INSs give nearly the same results, and more detailed study
of log N { log S for coolers will be presented in a separate paper.
3.2 Results
Results are shown in gures 3 and 4.
In the rst of them we plot observed sources, calculations for accretors and
a line from NT99. The later one is obtained with an assumption of a total NSs
number about (1 3)
10 8 and has the slope -1. Curves for accretors are plotted
for 10 9 INSs in the Galaxy. For comparable numbers it is clear, that at bright
uxes coolers dominate. It happens due to much higher average luminosity of
coolers (10 32 vs. 10 29 10 30 erg s 1 ).
In the second { we add two our curves for coolers for dierent spatial densities of
INSs, which were calculated with absorption in the way described in the previous
subsection, instead of the curves for accretors.
In these calculations we take r l = 140 pc (equal to the radius of the Local
Bubble in our calculations for accretors), which is in the range suggested by Sfeir
et al. (1999).
A clear "knee" appears due to absorption. Such strong attening can help to
explain the observed data, if one assumes, that most of INS are identied, as far
as we deal with relatively bright sources (> 0:1 cts s 1 ).
11

The position of the "knee" can be tted varying r l and densities in and outside
the Local Bubble. When r l is smaller the "knee" moves to the right, to higher
count rates.
We note, that one also can play with other parameters: time of the cooling,
luminosity distribution of INSs etc. Especially, time of the cooling is important, as
far as there is some evidence for a shorter value of this parameter ("fast cooling"
models). Increase of luminosity of cooling INSs can also help to explain the data
without very signicant increase of INSs number, but any way, this number should
be higher, than it comes from the radiopulsar statistics.
In general, if we take high spatial density of INSs, then we can explain in this
model both: the number of bright sources and the " attening" of the observed
log N { log S distribution.
4 Discussion
The task to explain ROSAT observations of INS candidates is not an easy one,
as far as all "standard" assumptions can't produce enough of such sources:
1. Bright (high count rates, > 0:1 cts s 1 ).
2. Close (low NH  10 20 cm 2 ).
3. Soft (T  50 100 eV).
4. With spin periods about 10-20 s (two candidates have periods of 8.4 and 22.7
s).
Polar cap accretion for "standard" magnetic eld ( 10 12 G) can't produce so
soft sources, and so short periods are impossible for those eld values (period of
accretion, p A , is  100 1000 s). Young NSs can't slow down to  20 s in < 10 6
12

(when they are still hot) for "standard" elds and even for elds about 10 14 G
(p  15 sec B 14
(t=10 6 yrs) 1=2 ).
If we assume, that all NSs are initially active as radiopulsars, it gives us, that
the total number of NSs in the Galaxy is about (1 3)
10 8 (we exclude possible
initial starformation burst). For these numbers one can't have enough bright INSs
in the solar vicinity for both: accretion and cooling scenarios.
So, we need something "non-standard" in order to explain ROSAT candidates
as one unique population:
1. Higher numbers of NSs in the Galaxy.
In this case coolers can explain high number of bright close sources and their
temperatures. But it is diфcult to explain the observed periods. And if the
cooling time is signicantly shorter than the value we use ("fast cooling" models),
then it is impossible to explain high number of bright sources even for high total
number of INSs. To obtain reasonable number of accretors higher total number
of INSs in the Galaxy ( 10 9 ) is also necessary.
Note, that actually in the cooling model it is necessary to have only local
(both: in time and space) excess of INSs relative to radiopulsar statistics. Such
excess is in correspondence with historical SN rate (van den Bergh & Tammann
1991). Also the structure of local ISM (Local Bubble, North Polar Spur etc.)
and even geophysical data (isotope history in antarctic ice etc.) favors recent
close SN explosions, but we don't know close (d < 100 pc) young (t < 10 6 yrs)
radiopulsars. Close regions of starformation (Sco-Cen association and Perseus-
Taurus association) can be birth places of these young INSs.
13

2. Magnetic eld decay.
In this scenario accretors can explain low temperatures and periods. We are not
sure about exact numbers of close bright sources: to obtain them it is necessary
to produce population synthesis calculations. Field decay can both: increase and
decrease numbers of accretors (see Colpi et al. 1998, Livio et al. 1998, P2000).
INSs, in general, can be very important for models of eld decay (see Popov
and Prokhorov 2000). In these objects eld decay appears in the most "pure"
form (Konenkov & Popov 1997, Wang 1997), as far as strong accretion from the
secondary companion does not in uence the process of eld decay. Extensive cal-
culations of population synthesis of IANSs with realistic models of eld decay and
taking into account ISM absorption (these accretors should be soft, so absorption
is important) are necessary.
3. Strong decaying magnetic elds
It can help to explain in the cooling model periods of candidates. And if decaying
eld can increase the lifetime of such an object as bright X-ray source, it can also
help to explain numbers without huge increasing of the total number of INSs.
But detailed population synthesis is necessary, because this hypothesis should
be also in correspondence with other observations of NSs (radiopulsars, close
binaries, compact X-ray sources in supernova remnants (SNR) etc.), so probably
the fraction of strong eld stars cannot be high, and relatively high number of
observed bright candidates can be unexplained in this model.
In principle, one can also play with non-standard distributions of spin periods
(long initial period, longer than in Spruit & Phinney 1998) or initial magnetic
elds (second maximum on very low values,  10 7 G, or on high values,  10 14 G).
14

There is no observational (and even theoretical) evidence for high numbers of NSs
with so unusual period distribution. Probable high numbers of NSs with strong
magnetic elds were discussed by several authors (see, for example, Gotthelf and
Vasisht 2000). These authors argue, that "at least half of the observed young
neutron stars follow an evolutionary path quite distinct from that of the Crab
pulsar", i.e. they most probably have strong (magnetar scale) initial magnetic
elds, which are decaying in order to produce observed luminosity (which cannot
be explained by magnetodipole losses). Probably, there can be INSs with strong
initial magnetic eld, which is not signicantly decaying on short time scale, so
they'll spin-down as magnetars, but their X-ray luminosity will be 1-2 orders of
magnitude lower. For our knowledge nobody tried to make population synthesis
of close binary stars including about 50% magnetars with eld decay at the rate
which is necessary to produce enough X-rays. It should be done, because otherwise
we are not sure, that wonderful idea about magnetars is "universal".
Observations of Cas A (Chakrabarty et al. 2000, Pavlov et al. 2000) showed
a central compact X-ray source which is not a classical young pulsar, and, most
probably, it can't be a magnetar. There is a possibility, that this NS was born
with a very low (< 10 8 G) magnetic eld. So, "low-eld" hypothesis also can be
discussed.
Anyway, the enigma of ROSAT candidates and IANSs should have solution,
which is in correspondence with radiopulsars observations, observations of NSs
in close binaries, AXPs, and compact radiosilent sources in SNRs (also the small
number of radiopulsars in SNRs should be taken into account). All, probably
bright, ideas, which satisfy only part of the data are not very useful, and one must
15

think about in uence of every accepted hypothesis on all known populations of
NSs.
It is diфcult to explain the ROSAT data simply increasing the number of IANSs
(for example, decreasing mean velocity of population, or taking non-maxwellian
velocity distributions). It is so, because accretors have wide distribution of tem-
peratures and velocities and they are hotter and dimmer on average than coolers,
so the attening of the log N { log S due to absorption (even if for some reasons
sources are soft as coolers) is not so signicant, and at 0.1 cts s 1 (and brighter)
one expects signicant number of sources (hundreds), which are not identied as
INS candidates for some reasons.
We also note, that due to wider distributions in temperature towards higher
values accretors can dominate at low uxes, when one reaches distance, where all
coolers are completely absorbed, but the most hot and bright accretors still can
be observed.
We don't take into account very detailed (and complicated) structure of the lo-
cal ISM. Probably, that discovery of hot (300-400 eV) accretors in close molecular
clouds with deep Chandra observations is possible as far as absorption is not as
important for them as for softer sources discussed previously (Colpi et al. 1993,
Manning et al. 1996), but of course due to large initial mean velocity numbers
should be smaller than predicted previously by Colpi et al. (1993). Note, that in
this new picture molecular clouds are not the best places to search for IANSs, be-
cause new satellites can observe very dim sources, and the most important point
is to have a large sample, i.e. to observe sources at large distances, not in close
molecular clouds, which obscure distant sources behind them.
16

Bright ROSAT candidates, being close (and not numerous) sources, don't show
any concentration to the Galactic plane or to the Galactic center (see g. 5) . For
fainter sources this concentration should be observed. Usually deep pointings
are made in the direction perpendicular to the Galactic plane (see for example,
Mushotzky et al. 2000). In these observations we don't expect a lot of accretors
(only the closest ones can appear: far from the Galactic plane there is no fuel
for accretion). The same is true for coolers, because even if in principle a cooler
can be observed from large distance if absorption is low, a young NS can't travel
farther than  1 kpc from the Galactic plane during its cooling time, and even if
halo is lled with INSs, they are old cold objects, non-emitting X-rays.
5 Conclusions
We modeled populations of INSs in order to investigate them as possible dim
x-ray sources (especially in the ROSAT data). We discussed both: old accreting
and young cooling NSs. For accretors realistic magneto-rotational evolution and
evolution in the Galactic potential were taken into account together with realistic
large scale distribution of the ISM. Cooling neutron stars were explored with a
simpler model of local sources, and interstellar absorption was taken into account
also in a simplied way.
In the standard assumptions (maxwellian initial velocity distribution with the
mean value about 200-300 km s 1 , initial eld distribution similar to radiopulsar,
no magnetic eld decay, small initial spin periods) we obtained accretors only
if INS's magnetic eld was > 10 11 {10 12 G. So, for polar cap accretion X-ray
sources were relatively hard with typical temperature about 300-400 eV. For them
17

interstellar absorption is not very signicant (on the scale of hundreds pc), and
we predict about 1 source per square degree for uxes about 10 15 {10 16 erg cm 2
s 1 for energy range 0.5-2 keV, which can be observed, for example, by Chandra.
As far as at low uxes IANSs will show concentration towards the Galactic plane
(and the Galactic center) our average prediction of 1 per square degree should be
nearly an order of magnitude higher for regions close to the Galactic plane, and
correspondently lower for direction perpendicular to this plane.
Number of coolers can not be high at these low uxes due to strong absorption
of these very soft objects (mean free path  100 pc).
We note also, that accretors can appear as dim sources not only because they
are very far, but because of wide luminosity distribution. Coolers vice versa have
very "sharp" luminosity distribution, and dim coolers should be far (not close,
but with low luminosity), which means strong absorption.
So, we predict  0:01 0:1 coolers per square degree in deep Chandra obser-
vations. Which means, that it is nearly impossible to nd them serendipiously in
these pointings with very small covered area of the sky.
If XMM (Newton) is able to observe in deep (200 ks) pointings all coolers with
T  10 6 K inside 5 kpc (Helfand 1998), than the prediction will be about 1 per
square degree also for coolers. This is an average value, and in direction towards
the Galactic center of course it'll be higher (as for accretors).
Anyway, number of accretors (of all luminosities) in the Galaxy is about two
orders of magnitude larger than the number of observable coolers (few percents
vs. 0.01%). But an "average" accretor is 3 orders of magnitude dimmer than a
typical cooler.
18

Accretors become more abundant than coolers at uxes about 10 13 {10 12 erg
cm 2 s 1 . But we note again, that these accretors are hotter than coolers (300-400
eV vs. 50-100 eV).
With standard assumptions we can't explain observed properties of the ROSAT
candidates (large number of close bright sources, low temperatures, periods about
10 s) in the frame of the accretion scenario. We argue, that most part of these
sources can be young cooling neutron stars with typical age about 10 6 yrs, if the
total number of INSs in the Galaxy is much higher, than it comes from radiopulsar
statistics. So, probably X-ray observations of INS candidates are in favor of high
number of NSs in the Galaxy, most of which never were active as radiopulsars.
This conclusion is in correspondence with nucleosynthesis investigations (Arnett
et al. 1989) and observations of SNRs (Gotthelf and Vasisht 2000).
The source RX J0420.0-5022 with spin period 22.7 s can't be explained as a
"standard" accretor or a "standard" cooling neutron star as far as its period is
not typical for both of these populations. In this case most probably magnetic
eld decay is operating.
So, to explain ROSAT data on INSs candidates one have to introduce some
"non-standard" (but reasonable and relatively popular) ideas about NSs astro-
physics.
Acknowledgements We wish to thank J. Lattimer, E. van den Heuvel, V.M.
Lipunov, and S. Campana for useful discussions. SBP and MEP also thank the
University of Insubria for nancial support and the Universities of Milano-Bicocca
and Padova together with the Brera Observatory (Merate) for their kind hospi-
tality. The work of SBP and MEP was supported through the grant RFBR
19

00-02-17164 and NTP Astronomy grants 1.4.4.1. and 1.4.2.3. Support from the
European Commission under contract ERBFMRXCT98-0195 and from MURST
under contract COFIN98021541 is acknowledged.
20

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Figure captions
Figure 1.
On the upper left panel we show log N { log S distribution for accretors inside 5
kpc sphere around the Sun. Two curves are shown: for the total ux, and for polar
cap black-body emission in the range 0.5-2 keV. For comparison we add lines with
the slopes -1 and -3/2. On the upper right panel we show distribution of velocities
of all accretors in our calculation. On this panel (as on all others) distribution is
normalized to be equal to 1 in the maximum, and log-gaussian distribution of the
magnetic eld is taken into account. On the lower left panel we show temperature
distribution for polar cap accretion. Maximum corresponds to lg T  6:8. And on
the last panel we show _
M distribution. Maximum corresponds to the accretion
rate  10 9:5 g s 1 .
Figure 2.
On the gure we compare log N { log S for 500 pc and 5 kpc spheres around
the Sun. Also we plot log N { log S for observed sources and naive log N { log S
based on calculations in P2000 (\census point").
Figure 3.
Here we show bright part of calculated log N { log S for accretors. Fluxes are
converted to count rate. For comparison we show observed sources and a line with
the slope -1 proposed in NT99 as a simple estimate of log N { log S for cooling
INSs.
Figure 4.
The same as in the previous gure, but we add our calculations of log N { log
S for cooling NSs instead of calculations for accretors. Our upper (lled circles)
23

curve for coolers corresponds to NSs density 0.0033 pc 3 . And lower (opaque
circles) { to 0.00033 pc 3 ; r l = 140 pc.
Figure 5.
Distribution of ROSAT INS candidates in the Galaxy. For all sources the unit
distance was accepted. On the upper panel x-z distribution is shown (projection to
the plane perpendicular to the Galactic plane), and on the lower { x-y distribution
(projection onto the Galactic plane).
Figure 6.
Combined gure of dierent log N { log S for bright sources. We show our
calculations, observational points and the naive log N { log S distribution from
P2000 calculations.
24