], contains up-to-date parameters for some 706 pulsars. Most of
these are ``normal'' in the sense that their pulse periods are of
order one second and, with few exceptions, are observed to
increase secularly at rates of typically
s/s. A growing fraction of the observed sample are the so-called
``millisecond pulsars'', which have spin periods primarily in the
range 1.5 and 30 ms and have rates of slowdown
s/s. The first millisecond pulsar discovered, PSR B1937+21 [20], with a period of 1.5578 ms, remains the most rapidly rotating
neutron star presently known to man.
A very useful means of demonstrating the distinction between
these two classes is the ``
'' diagram - a logarithmic scatter plot of the observed pulse
period versus the period derivative. This is shown in Fig.
5, in which normal pulsars occupy the majority of the upper right
hand part of the diagram, whilst the millisecond pulsars reside
in the lower left hand part of the diagram.
The differences in
P
and
imply different ages and surface magnetic field strengths. By
treating the pulsar as a rotating magnetic dipole, one may show
that the surface magnetic field strength is proportional to
[113]. Lines of constant magnetic field strength are drawn on
Fig.
5, together with lines of constant
characteristic age
(
). From these, one infers typical magnetic fields and ages of
G and
yr for the normal pulsars and
G and
yr for the millisecond pulsars respectively.
A very important additional difference between normal and
millisecond pulsars is the presence of an orbiting companion.
Presently, about 7% of all known pulsars are members of binary
systems. Timing measurements (§
4) place useful constraints on the masses of the companions which,
supplemented by observations at other wavelengths, tell us a
great deal about their nature. The present sample of orbiting
companions are either white dwarfs, main sequence stars, or other
neutron stars. A notable additional hybrid system is the
so-called ``planets pulsar'' PSR B1257+12 -- a 6.2 ms pulsar
accompanied by at least two
Earth-mass bodies [168,
2]. Orbital companions are much more commonly observed around
millisecond pulsars (
% of the observed sample) than the normal pulsars (< 1%). The
sample of binary pulsars is delineated in Fig.
6
as orbital eccentricity against mass of the companion. The
dashed line serves merely to guide the eye in this figure. From
this we note that the binary systems below the line are those
with low-mass companions (
-- predominantly white dwarfs) and essentially circular orbits:
. The binary pulsars with high-mass companions (
-- neutron stars or main sequence stars) are in much more
eccentric orbits: 0.2 >
e
> 0.9 and lie above the line.
The presently favoured model to explain the formation of the
various types of systems has been developed over the years by a
number of authors [34,
59,
143,
14] and can be qualitatively summarised as follows: Starting with a
binary star system, the neutron star is formed during the
supernova explosion of the initially more massive star which has
an inherently shorter main sequence lifetime. From the virial
theorem, it follows that the binary system gets disrupted if more
than half the total pre-supernova mass is ejected from the system
during the explosion. In addition, the fraction of surviving
binaries is affected by the magnitude and direction of the
impulsive ``kick'' velocity the neutron star receives at birth [76,
21]. Those binary systems that disrupt produce a high velocity
isolated neutron star and an OB runaway star [35]. Over the next
yr or so after the explosion, the neutron star may be observable
as a normal radio pulsar spinning down to periods of several
seconds or longer. The high disruption probability explains why
so few normal pulsars have companions.
For those few binaries that remain bound, and in which the
companion is sufficiently massive to evolve into a giant and
overflow its Roche lobe, the old spun-down neutron star can gain
a new lease on life as a pulsar by accreting matter and therefore
angular momentum from its companion [14]. The term ``recycled pulsar'' is often used to describe such
objects. During this accretion phase, the X-rays liberated by
heating the infalling material onto the neutron star mean that
such a system is expected to be visible as an X-ray binary
system. Two classes of X-ray binaries relevant to binary and
millisecond pulsars exist,
viz:
neutron stars with high-mass or low-mass companions. For a
detailed review of the X-ray binary population, including systems
likely to contain black holes rather than neutron stars, the
interested reader is referred to [32].
The high-mass companions are massive enough to explode
themselves as a supernova, producing a second neutron star. If
the binary system is lucky enough to survive
this
explosion, it ends up as a double neutron star binary. The
classic example is PSR B1913+16 [78], a 59 ms radio pulsar with a characteristic age of
yr which orbits its companion every 7.75 hr [151,
152]. Other examples include PSR B2303+46, a 1 s pulsar with a
characteristic age of
yr in a 12 day orbit [146]. Within the framework of this formation scenario, PSR B1913+16
is an example of the older, first-born, neutron star that has
subsequently accreted matter from its companion. PSR B2303+46 is,
on the other hand, likely to be the younger, second-born neutron
star in its binary system. As we shall see (§
3.4), double neutron star binary systems are very rare in the
Galaxy, a direct indication that the majority of binary systems
get disrupted by the exploding star.
Although no such system has yet been found in which both
neutron stars are visible as radio pulsars, timing measurements
(§
4.3) show that the companion masses are
M
-- exactly that expected for a neutron star [140]. In addition, no optical counterparts are seen. Thus, we
conclude that these unseen companions are neutron stars that are
either too weak to be seen/no longer active as radio pulsars or
their emission beams do not intersect our line of sight. The two
known radio pulsars with main sequence companions may well
represent the ``missing link'' between high-mass X-ray binaries
and double neutron star systems [83,
86].
By definition, the companions in the low-mass X-ray binaries evolve and transfer matter onto the neutron star on a much longer time-scale, spinning it up to periods as short as a few ms [14]. This model has recently gained strong support from the discoveries of kHz quasi-periodic oscillations in a number of low-mass X-ray binaries [164], as well as Doppler-shifted 2.49 ms X-ray pulsations from the transient X-ray burster SAX J1808.4-3658 [165, 42].
At the end of the spin-up phase, the secondary sheds its outer
layers to become a white dwarf in orbit around a rapidly spinning
millisecond pulsar. Presently
of these systems have compelling optical identifications of the
white dwarf companion [27,
29,
101,
100]. Perhaps the best example is the white dwarf companion to the
5.25 ms pulsar J1012+5307 [119,
97]. This
magnitude white dwarf is bright enough to allow precise
measurements of its surface gravity, as well as the Doppler
shifts of its spectral lines as it moves in its orbit [161].
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Binary and Millisecond Pulsars
D. R. Lorimer (dunc@mpifr-bonn.mpg.de) http://www.livingreviews.org/lrr-1998-10 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |