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Hot Points in Astrophysics
JINR, Dubna, Russia, August 22-26, 2000
Isolated Neutron Stars in the Galaxy
Sergei B. Popov y , Mikhail E. Prokhorov y , Monica Colpi z , Aldo Treves  , Roberto
Turolla  and Vladimir M. Lipunov y
y Sternberg Astronomical Institute, Universitetski pr. 13, 119899, Moscow, Russia
z University Milano-Bicocca, Milan, Italy
 Universita dell'Insubria, 22100, Como, Italy
 University of Padova, Via Marzolo 8, 35131, Padova, Italy
Abstract
In this article we brie y review our recent results on evolution and properties of
isolated neutron stars (INSs) in the Galaxy.
As the rst step we calculate a census of INSs in our Galaxy. We infer a lower
bound for the mean kick velocity of NSs, < V >(200-300) km s 1 . The same
conclusion is reached for both a constant magnetic eld (B  10 12 G) and for a
magnetic eld decaying exponentially with a timescale  10 9 yr. These results,
moreover, constrain the fraction of low velocity stars, which could have escaped
pulsar statistics, to few percents.
Then we show that the range of minimum value of magnetic moment,  b : 
10 29:5   b  10 28 Gcm 3 , and the characteristic decay time, t d :  10 8  t d 
10 7 yrs, can be excluded assuming the standard initial magnetic momentum,  0
=
10 30 Gcm 3 , if accreting INSs are observed. For these parameters an INS would
never reach the stage of accretion from the interstellar medium even for a low space
velocity of the star and high density of the ambient plasma. The range of excluded
parameters increases for lower values of  0
.
It is shown that old accreting INSs become more abundant than young cooling
INSs at X-ray uxes below  10 13 erg cm 2 s 1 . We can predict that about one
accreting INS per square degree should be observed at the Chandra and Newton ux
limits of  10 16 erg cm 2 s 1
: The weak ROSAT sources, associated with INSs,
can be young cooling objects, if the NSs birth rate in the solar vicinity during the
last  10 6 yr was much higher than inferred from radiopulsar observations.

Introduction
Despite intensive observational campaigns, no irrefutable identication of an isolated ac-
creting neutron star (IANS) has been presented so far. Although six soft, weak sources,
which are associated with isolated NSs, have been found in ROSAT elds, present X-ray
and optical data do not allow an unambiguous determination of the physical mechanism
responsible for their emission. These sources can be powered either by accretion of the
interstellar gas onto old ( 10 10 yr) INSs or by the release of internal energy in relatively
young ( 10 6 yr) cooling INSs (see [14] for recent review). ROSAT candidates, although
relatively bright (up to  1 cts s 1 ), are intrinsically dim and their inferred luminosity
(L  10 31 erg s 1 ) is close to that expected from both close-by cooling and (most lu-
minous) accreting INSs. Up to now only two optical counterparts have been possibly
identied (RX J 1856-3754, [15]; RX J 0720-3125, [2]) and in both cases an optical excess
over the low-frequency tail of the black body X-ray spectrum has been reported. While
detailed multiwavelength observations with next-generation instruments may indeed be
the key for assessing the true nature of these sources, other, indirect, approaches may be
used to discriminate in favor of one of the two scenarios proposed so far.
Since early 90 s , when in [13] it was suggested to search for IANSs with ROSAT satellite,
several investigations on INSs have been done (see for exapmle [6], [7], and [14] for a
review). Here we present our recent results in that eld.
Neutron Star Census
We have investigated, [9], how the present distribution of NSs in the dierent stages
(Ejector, Propeller, Accretor and Georotator, see [3]) depends on the star mean velocity
at birth (see Fig. 1). The fraction of Accretors was used to estimate the number of
sources within 140 pc from the Sun which should have been detected by ROSAT. Most
recent analysis of ROSAT data indicate that no more than  10 non{optically identied
sources can be accreting old INSs. This implies that the average velocity of the INSs
population at birth has to exceed  200 km s 1 , a gure which is consistent with those
derived from radio pulsars statistics. We have found that this lower limit on the mean
kick velocity is substantially the same either for a constant or a decaying B{eld, unless
the decay timescale is shorter than  10 9 yr. Since observable accretion{powered INSs are
slow objects, our results exclude also the possibility that the present velocity distribution
of NSs is richer in low{velocity objects with respect to a Maxwellian. The paucity of
accreting INSs seem to lend further support in favor of NSs as fast objects.

0.0 200.0 400.0 600.0
Velocity, km/s
1
10
100
Accretors
0.0 200.0 400.0 600.0
0.0
20.0
40.0
60.0
80.0
100.0
Ejectors
0.0 200.0 400.0 600.0
Velocity, km/s
0.00
0.20
0.40
0.60
Georotators
0.0 200.0 400.0 600.0
0.00
0.05
0.10
0.15
0.20
0.25
Propellers
Figure 1: Fractions of NSs (in percents) on dierent stages vs. the mean kick velocity
for  30
= 0:5 (open circles) and  30
= 1 (lled circles); typical statistical uncertainty for
ejectors and accretors is  1-2%. Figures are plotted for constant magnetic eld.
Magnetic Field Decay
Magnetic eld decay can operate in INSs. Probably, some of observed ROSAT INS can-
didates represent such exapmples ([1], [16]) We tried to evaluate the region of parameters
which is excluded for models of the exponential magnetic eld decay in INSs using the
possibility that some of ROSAT soft X-ray sources are indeed old AINSs.
In this section we follow the article [11].
Here the eld decay is assumed to have an exponential shape:
 =  0
e t=t d ; for  >  b (1)
where  0
is the initial magnetic moment ( = 1
2
B p R 3
NS , here B p is the polar magnetic
eld, RNS is the NS radius), t d is the characteristic time scale of the decay, and  b is the
bottom value of the magnetic momentum which is reached at the time

10 26
10 27
10 28
10 29
Bottom magnetic momentum
10 7
10 8
10 9
10 10
Decay
time
scale,
yrs
Figure 2: The characteristic time scale of the magnetic eld decay, t d , vs. bottom magnetic
moment,  b . In the hatched region Ejector life time, t E , is greater than 10 10 yrs. The
dashed line corresponds to t H = t d
ln ( 0
= b ), where t H = 10 10 years. The solid line
corresponds to p E ( b ) = p(t = t cr ), where t cr = t d
ln ( 0 = b ). Both the lines and hatched
region are plotted for  0
= 10 30 Gcm 3 . The dash-dotted line is the same as the dashed
one, but for  0 = 5
10 29 Gcm 3 . The dotted line shows the border of the \forbidden"
region for  0
= 5
10 29 Gcm 3 . See details in [11].
t cr = t d
ln

 0
 b
!
(2)
and does not change after that.
The intermediate values of t d ( 10 7 10 8 yrs) in combination with the intermediate
values of  b ( 10 28 10 29:5 Gcm 3 ) for  0
= 10 30 Gcm 3 can be excluded for progenitors
of isolated accreting NSs because NSs with such parameters would always remain on the
Ejector stage and never pass to the accretion stage (see Fig. 2). Even if all modern
candidates are not accreting objects, the possibility of limitations of magnetic eld decay
models based on future observations of isolated accreting NSs should be addressed.
For higher  0
NSs should reach the stage of Propeller (i.e. p = p E , where p E { is the

Ejector period) even for t d < 10 8 yrs, for weaker elds the \forbidden" region becomes
wider. Critical period, p E , corresponds to transision from the Propeller stage to the stage
of Ejector, and is about 10-25 seconds for typical parameters. The results are dependent
on the initial magnetic eld,  0
, the ISM density, n, and NSs velocity, V . So here dierent
ideas can be investigated.
In fact the limits obtained above are even stronger than they could be in nature,
i.e. \forbidden" regions can be wider, because we did not take into account that NSs
can spend some signicant time (in the case with eld decay) at the propeller stage (the
spin-down rate at this stage is very uncertain, see the list of formulae, for example, in [4]
or [3]). The calculations of this eect for dierent models of non-exponential eld decay
were studied separately in [10].
Note that there is another reason due to which a very fast decay down to small values
of  b can also be excluded, because this would lead to a huge amount of accreting isolated
NSs in drastic contrast with observations. This situation is similar to the \turn-o" of
the magnetic eld of an INS (i.e., quenching any magnetospheric eect on the accreting
matter). So for any velocity and density distributions we should expect signicantly
more accreting isolated NSs than we know from ROSAT observations (of course, for high
velocities X-ray sources will be very dim, but close NSs can be observed even for velocities
 100 km s 1 ).
Log N { Log S distribution
In this section we brie y present our new results on INSs, [12].
We compute and compare the log N { log S distribution of both accreting and cooling
NSs, to establish the relative contribution of the two populations to the observed number
counts. Previous studies derived the log N { log S distribution of accretors ([13]; [6]; [7])
assuming a NSs velocity distribution rich in slow stars (v < 100 km s 1 ). More recent
measurements of pulsar velocities (e.g. [5]) and upper limits on the observed number of
accretors in ROSAT surveys point, however, to a larger NS mean velocity (see [14] for
a critical discussion). Recently Neuhauser & Trumper ([8]) compared the number count
distribution of the ROSAT isolated NS candidates with those of accretors and coolers. In
[12] we address these issues in greater detail, also in the light of the latest contributions
to the modeling of the evolution of Galactic NSs.
Our main results for AINSs are presented in Fig. 3.
Using \standard" assumptions on the velocity, spin period and magnetic eld param-
eters, the accretion scenario can not explain the observed properties of the six ROSAT

100 1000
Tcap eV
0
0.2
0.4
0.6
0.8
1
fraction
Temperature distribution
-16 -14 -12 -10
log S
10 -3
10 -1
10 1
10 3
10 5
N
(>S)
Log N - Log S for accretors
Polar caps
Total flux
10 7
10 8
10 9
10 10
10 11
10 12
Accretion rate g/s
0
0.2
0.4
0.6
0.8
1
fraction
Accretion rate distribution
0 50 100 150
Velocity km/s
0
0.2
0.4
0.6
0.8
1
fraction
Velocity distribution
-3/2
-1
Figure 3: Upper left panel: the log N { log S distribution for accretors within 5 kpc
from the Sun. The two curves refer to total emission from the entire star surface and
to polar cap emission in the range 0.5-2 keV; two straight lines with slopes -1 and -3/2
are also shown for comparison. From top right to bottom right: the velocity, eective
temperature and accretion rate distributions of accretors; all distributions are normalized
to their maximum value.
candidates.
A key result of our statistical analysis is that accretors should eventually become more
abundant than coolers at uxes below 10 13 erg cm 2 s 1 .
Conclusions
INSs are now a real Hot Point in Astrophysics. We tried to show how these objects are
related with models of magnetic eld decay, and with recent anf future X-ray observations.
Observed candidates propose \non-standard" properties of NSs. And future observa-
tions with XMM (Newton) and Chandra satellites can give more important facts.

Acknowledgments
We wish to thank J. Lattimer, E. van den Heuvel and S. Campana for useful discussions.
SBP and MEP also thank the University of Insubria for nancial support and the Uni-
versities of Milano-Bicocca and Padova together with the Brera Observatory (Merate) for
their kind hospitality. The work of SBP, VML and MEP was supported through grant
RFBR 00-02-17164 and NTP Astronomy grants 1.4.4.1. and 1.4.2.3.
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