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arXiv:astro­ph/0011564
v2
30
Dec
2001
X-ray astronomy 2000
ASP Conference Series, Vol. 3  10 8 , 2001
R. Giacconi, L. Stella, S. Serio eds.
The Magnicent Seven: Close-by Cooling Neutron Stars ?
Aldo Treves
Dipartimento di Scienze, Universita dell'Insubria, Via Valleggio 11,
22100, Como, Italy; e{mail: treves@mi.infn.it
Sergei B. Popov
Sternberg Astronomical Institute, Universitetskii Pr. 13, 119899,
Moscow, Russia; e{mail: polar@sai.msu.ru
Monica Colpi
Dipartimento di Fisica, Universita di Milano Bicocca, P.zza della
Scienza 3, 20126 Milano, Italy; e{mail: colpi@uni.mi.astro.it
Mikhail E. Prokhorov
Sternberg Astronomical Institute, Universitetskii Pr. 13, 119899,
Moscow, Russia; e{mail: mystery@sai.msu.ru
Roberto Turolla
Dipartimento di Fisica, Universita di Padova, Via Marzolo 8, 35131
Padova, Italy; e{mail: turolla@pd.infn.it
Abstract.
We model Galactic populations of accreting and cooling isolated neu-
tron stars in the attempt to explore their link with a new class of dim soft
X-ray sources revealed by ROSAT. For accretors we follow the magneto-
rotational and dynamical evolution in the Galactic potential and a real-
istic large scale distribution of the interstellar medium is used. Under
standard assumptions old neutron stars enter the accretor stage only if
their magnetic eld exceeds  10 11 {10 12 G. We predict about 1 source
per square degree for uxes  10 15 {10 16 erg cm 2 s 1 in the energy
range 0.5-2 keV.
Cooling neutron stars are explored within a simpler model of local
sources, including however interstellar absorption. They are found to
be signicantly less abundant at low uxes, < 0:1 sources per square
degree, but dominate over accretors at higher ux levels ( 10 12 {10 11
erg cm 2 s 1 ). We suggest that the faint sources observed by ROSAT
may be young cooling neutron stars with typical age  < 10 6 yrs, if the
total number of young neutron stars in the Solar proximity is  10 times
higher than inferred from radiopulsars statistics.
1

2 Treves et al.
1. The Magnicent Seven
Seven soft sources, The Magnicent Seven, have been found in ROSAT elds
which are most probably associated with isolated radio-quiet NSs. A summary of
their main observational properties is reported in the table (see e.g. Neuhauser
& Trumper 1999, NT99; Motch 2000; Treves et al. 2000, T2000, and references
therein; see also Burwitz et al. at this conference).
Table 1. Properties of ROSAT Isolated NS Candidates
Source PSPC T bb NH log f X =f V Period
count s 1 eV 10 20 cm 2 s
MS 0317.7-6647 0.03 200 40 > 1:8 {
RX J0420.0-5022 0.11 57 1.7 > 3:3 22.7
RX J0720.4-3125 1.69 79 1.3 5.3 8.37
RX J0806.4-4132 0.38 78 2.5 > 3:4 {
RBS1223 0.29 118  1 > 4:1 5.2 a
RBS1556 0.88 100 < 1 > 3:5 {
RX J185635-3754 3.64 57 2 4.9 {
a Hambaryan et al. (2001)
Present X-ray and optical data however do not allow an unambiguous iden-
tication 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)
NSs or by the release of internal energy in relatively young ( 10 6 yr) cooling
NSs (T2000 for a recent review). The ROSAT candidates, although relatively
bright (up to  1 count s 1 ), are intrinsically dim and their inferred luminosity
(L  10 31 erg s 1 ) is near to that expected from either a close-by cooling NS
or from an accreting NS among the most luminous. Their X-ray spectrum is
soft and thermal, again as predicted for both accretors and coolers (T2000).
Up to now only two optical counterparts have been identied: RXJ 1856-37,
Walter & Matthews (1997), for which a distance estimate of  60 pc has been
very recently obtained, and RXJ 0720-31, Kulkarni & Van Kerkwick (1998). In
both cases an optical excess over the low-frequency tail of the black body X-ray
spectrum has been reported.
A statistical approach, based on the comparison of the predicted and ob-
served source counts may provide useful informations on the nature of these
objects. Previous studies derived the log N { log S distribution of accretors
(Treves & Colpi 1991; Madau & Blaes 1994; Manning et al. 1996) assuming
a NSs velocity distribution rich in slow stars (v  < 100 km s 1 ). Recent mea-
surements of pulsar velocities (e.g. Lyne & Lorimer 1994; Hansen & Phinney
1997) and upper limits on the observed number of accretors in ROSAT surveys
(Danner 1998) point, however, to a larger NS mean velocity (T2000). Neuhauser
& Trumper (NT99) compared the number count distribution of the ROSAT iso-
lated NS candidates with those of accretors and coolers. Here we address these
issues in greater detail, in the light of the latest contributions to the modeling

APS Conf. Ser. Style 3
of the evolution of Galactic NSs (Popov et al. 2000, P2000a). A more compre-
hensive discussion can be found in Popov et al. (2000, P2000b).
2. Accreting isolated neutron stars
An important feature of our approach is the detailed calculation of the magneto-
rotational evolution of isolated NSs, calculated as in P2000a (see Lipunov 1992
for the basic concepts), but with slightly revised values for the critical periods
governing the Ejector-Propeller and Propeller-Accretor transitions. When the
accretor stage is reached, the NS spin period is set equal to the \equilibrium"
period (Konenkov & Popov 1997). The form of the Galactic potential is taken as
in Paczynski (1990; see also P2000a); some parameters were upgraded in order
to t better solar distance from the Galactic center (see Madau and Blaes 1994).
Initially each NS has a circular velocity corresponding to its birthplace, and an
additional kick velocity, selected from a Maxwellian distribution, is added. NSs
are assumed to be born in the Galactic plane and their birthrate is constant
in time and proportional to the the square of the local gas density. The NS
magnetic eld is taken to follow a log-gaussian distribution. For each evolution-
ary track we calculate six dierent magneto-rotational histories, corresponding
to dierent values of the initial magnetic eld. Results were then merged and
normalized. The total number of NSs in the Galaxy is taken N tot = 10 9 .
In order to compare theoretical predictions with observations it is useful to
produce the log N { log S distribution. The brightest accretors in our calcula-
tions have luminosities L  10 32 erg s 1 , but the majority of them cluster around
L = 10 29 10 30 erg s 1 . To compare our results with observations of ROSAT
sources a conversion factor 0:01 count s 1 = 310 13 erg cm 2 s 1 was used (e.g.
NT99). We calculate the log N { log S distribution for the frequency intergrated
ux (S total = L total =4D 2 , here D is the source distance, L total = _
MGM=R) and
for the ux in the range 0.5-2 keV. In latter case the spectrum is assumed to
be a blackbody and the polar cap radius is calculated with the current values of
the magnetic eld and accretion rate (R cap = RNS
p
RNS=RA , where RA is the
Alfven radius). If absorption is negligible, then one expects about 1 source per
square degree in the range 0.5-2 keV for limiting uxes about 10 16 {10 15 erg
cm 2 s 1 . This should be compared with a total numer of sources presently de-
tected by Chandra of  10 3 {10 4 (see e.g. Giacconi at this conference). Results
are presented in the gure.
3. Cooling neutron stars
Although in principle the evolution of coolers should be computed exactly in
the same way as for accretors, they are much more short-lived and hence less
numerous. This poses a severe problem about the reliability of our sample
which is based on a limited number of evolutionary tracks. This can be avoided
exploiting the fact that coolers are a local population of sources. We assume
that NSs are uniformly distributed in the disk with half-thickness of 450 pc. The
NSs spatial density is a free parameter and can be varied. We used two values,
nNS = 0:33  10 3 pc 3 and nNS = 3:3  10 3 pc 3 . The rst value corresponds

4 Treves et al.
to the density adopted by NT99, and comes from radiopulsars statistics. The
second one corresponds to N tot  10 9 and is suggested by considerations on
supernova nucleosynthetic yields (e.g. Arnett et al. 1989). These two values can
be compared, for example, with nNS  1:4  10 3 pc 3 as derived by Paczynski
(1990).
All NSs are assumed to be \standard candles" with L = 10 32 erg s 1 and
blackbody spectrum. The duration of the cooling phase was taken to be 10 6
yrs, as suggested by the slow cooling scenario. In the fast cooling model (e.g.
Yakovlev et al. 1999) the number of observable coolers should be much smaller,
so, potentially, observations of isolated NSs may help in shedding light on their
cooling history. The ISM structure is treated in a very simple way: a spherical
local Bubble of radius r l (which can be varied) and density n = 0:07 cm 3
centered at the Sun and a uniform medium with density n = 1 cm 3 in the
Galactic disc (with scaleheight 450 pc) at larger distances. After the column
density NH is calculated, we compute the source count rate for given luminosity,
temperature and column density. Results are shown in the gure.
10 -3 10 -2 10 -1 10 0 10 1
counts/s
10 -2
10 -1
10 0
10 1
10 2
10 3
10 4
N
(>S)
per
steradian
Log N - Log S
ROSAT points
absorbed coolers
Polar caps accretion
-14 -13 -12 -11
Figure 1. Comparison of the log N { log S distributions for accretors
and coolers. Top and bottom axes give the ux in erg cm 2 s 1 and in
ROSAT counts/s.
This simple model reproduces a key feature: the attening of the log N
{log S distribution outside the Local Bubble, which is important to explain
ROSAT data at large uxes. More sophisticated models with a realistic distri-
bution of both the ISM and the coolers give nearly the same results, and will
be presented in a separate paper. In the actual calculation we took r l = 140 pc
(equal to the radius of the Local Bubble in our calculations for accretors, see
also Sfeir et al. 1999). A clear knee appears due to the eect of absorption. Such
strong attening can help to explain the observed data, if one assumes that the

APS Conf. Ser. Style 5
the vast majority of bright (> 0:1 count s 1 ) isolated NSs are already identied.
The position of the knee can be adjusted varying r l , nNS and the ISM density;
for smaller values of r l the knee moves to the right, towards higher count rates.
By taking a high enough spatial density of NSs these results are able to account
for both: i) the number of bright sources, and ii) the attening of the observed
log N { log S distribution.
4. Discussion
The task of explaining the observed properties of the seven ROSAT isolated NS
candidates within a single model based on standard assumptions is not easy.
The ROSAT sources are in fact: i) relatively bright,  > 0:1 count s 1 ; ii) close,
NH  10 20 cm 2 ; iii) soft, T eff  50 100 eV; iv) slowly rotating, for RX J0720,
RX J0420 and RBS1223 the periods are about 5{20 s.
The accretion stage can be reached only if NS magnetic eld is  > 10 11 {
10 12 G. For polar cap accretion the X-ray spectrum is then relatively hard with
a typical temperature around 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. While accretors may
indeed represent the bulk of a still undetected low-luminosty population of X-ray
sources, it is diфcult to reconcile them with the relatively bright ROSAT sources,
as shown in the gure. On the contrary, the number distribution of coolers is in
agreement with that of the seven isolated NS sources discovered so far, only if
the total number of young close-by NSs is a factor  10 larger than what implied
by radiopulsar statistics. Taken at face value, this implies that the majority of
NSs do not experience an active radiopulsar phase, a major implication which
is also supported by other evidences (see e.g. Gotthelf & Vasisht 2000). The
interpretation of the observed periods of some of the Magnicent Seven remains
problematic and seems to require special conditions on the evolution of the
magnetic eld and spin.
Acknowledgements The work of SBP and MEP was supported through the
grant RFBR 00-02-17164. Support from the European Commission under con-
tract ERBFMRXCT98-0195 and from MURST under contract COFIN98021541
is acknowledged.
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