

The most recent use of the scale factor approach to derive the
characteristics of the true normal and millisecond pulsar
populations is based on the sample of pulsars within 1.5 kpc
of the Sun [152
]. The rationale for this cut-off is that, within this region,
the selection effects are well understood and easier to quantify
by comparison with the rest of the Galaxy. These calculations
should give reliable estimates for the
local pulsar population
.
Figure 17:
Left: The corrected luminosity distribution (solid histogram
with error bars) for normal pulsars. The corrected distribution
before
the beaming model has been applied is shown by the dot-dashed
line. Right: The corresponding distribution for millisecond
pulsars. In both cases, the observed distribution is shown by the
dashed line and the thick solid line is a power law with a slope
of -1. The difference between the observed and corrected
distributions highlights the severe under-sampling of
low-luminosity pulsars.
The luminosity distributions obtained from this analysis are
shown in Fig.
17
. For the normal pulsars, integrating the corrected distribution
above 1
and dividing by
yields a local surface density, assuming Biggs' beaming
model [32] of
pulsars
. The same analysis for the millisecond pulsars, assuming a mean
beaming fraction of 75% [122], leads to a local surface density of
pulsars
for luminosities above 1
.
Integrating the local surface densities of pulsars over the whole
Galaxy requires a knowledge of the presently rather uncertain
Galactocentric radial distribution [153,
107]. One approach is to assume that pulsars have a radial
distribution similar to that of other stellar populations and
scale the local number density with this distribution to estimate
the total Galactic population. The corresponding
local-to-Galactic scaling is
[200]. With this approach we estimate there to be
active normal pulsars and
millisecond pulsars in the Galaxy. Based on these estimates, we
are in a position to deduce the corresponding rate of formation
or birth-rate. From the
P
-
diagram in Fig.
7, we infer a typical lifetime for normal pulsars of
yr, corresponding to a Galactic birth rate of
per 60 yr - consistent with the rate of supernovae [253]. As noted in §
2.4, the millisecond pulsars are much older, with ages close to that
of the Universe
(we assume here
Gyr [104]). Taking the maximum age of the millisecond pulsars to be
, we infer a mean birth rate of at least
. This is consistent, within the uncertainties, with the
birth-rate of low-mass X-ray binaries [135
].
The estimates of the local surface density of active pulsars
allow us to deduce the likely distance of the nearest neutron
star to Earth. For the combined millisecond and normal pulsar
populations, with a surface density of
pulsars
, the nearest neutron star is thus likely to be
. This number is of interest to those building gravitational wave
detectors, since it determines the likely amplitude of
gravitational waves emitted from nearby rotating neutron
stars [213]. According to Thorne [244
], currently planned detectors will be able to detect neutron
stars with ellipticities greater than
, where
P
is the rotation period in ms and
d
is the distance in kpc. The recent probable detection of free
precession in the radio pulsar B1828-11 [221] does indicate that ellipticities exist in neutron stars so that
nearby objects may be continuous sources of gravitational
radiation.
Thus, in order to detect small ellipticities, nearby sources
with short spin periods are required. One of the best candidates
is the nearby 5.75-ms pulsar J0437-4715 [108
]. At a distance of
[208
] this is currently the closest known millisecond pulsar to the
Earth. The closest known neutron star is RX J185635-3754
discovered in the ROSAT all-sky survey [261]. Multi-epoch HST observations show that this isolated neutron
star is located at a distance of
[260]. In keeping with other radio-quiet isolated neutron stars, the
period of this pulsar is likely to be several seconds [176].


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Binary and Millisecond Pulsars at the New Millennium
Duncan R. Lorimer
http://www.livingreviews.org/lrr-2001-5
© Max-Planck-Gesellschaft. ISSN 1433-8351
Problems/Comments to
livrev@aei-potsdam.mpg.de
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