A very useful means of demonstrating the distinction between
these two classes is the ``
P
-
diagram'' - a logarithmic scatter plot of the observed pulse
period versus the period derivative. As shown in Fig.
7, normal pulsars occupy the majority of the upper right hand part
of the diagram, while 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
[163
]. Lines of constant magnetic field strength are drawn on
Fig.
7, together with lines of constant
characteristic age
(
). Typical inferred magnetic fields and ages are
and
for the normal pulsars and
and
for the millisecond pulsars.
A very important additional difference between normal and
millisecond pulsars is the presence of an orbiting companion.
Orbital companions are much more commonly observed around
millisecond pulsars (
% of the observed sample) than around the normal pulsars (
%). Fig.
8
is a scatter plot of orbital eccentricity versus mass of the
companion. The dashed line serves merely to guide the eye in this
figure. Binary systems lying below the line are those with
low-mass companions (
- predominantly white dwarfs) and essentially circular orbits:
. Binary pulsars with high-mass companions (
- neutron stars or main sequence stars) are in eccentric orbits,
, and lie above the line.
Starting with a binary star system, a 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 [98,
31
]. In addition, the fraction of surviving binaries is affected by
the magnitude and direction of any impulsive ``kick'' velocity
the neutron star receives at birth [98,
18]. Those binary systems that disrupt produce a high-velocity
isolated neutron star and an OB runaway star [35]. The high binary disruption probability during the explosion
explains, qualitatively at least, why so few normal pulsars have
companions. Over the next
yr or so after the explosion, the neutron star may be observable
as a normal radio pulsar spinning down to a period
several seconds. After this time, the energy output of the star
diminuishes to a point where it no longer produces significant
radio emission.
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 of life as a pulsar by accreting matter and therefore
angular momentum at the expense of the orbital angular momentum
of the binary system [2]. The term ``recycled pulsar'' is often used to describe such
objects. During this accretion phase, the X-rays produced by the
liberation of gravitational energy of the infalling matter 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 [31
].
The high-mass companions are massive enough to explode 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 [102], a 59-ms radio pulsar with a characteristic age of
yr which orbits its companion every 7.75 hr [239
,
240
]. In this formation scenario, PSR B1913+16 is an example of the
older, first-born, neutron star that has subsequently accreted
matter from its companion. So far there are no clear examples of
systems where the second-born neutron star is observed as a radio
pulsar. In the case of {PSR B1820-11 [155
], which may be an example, the mass of the companion is not well
determined, so either a main-sequence [193
] or a white dwarf companion [194] are plausible alternatives. This lack of observation of
second-born neutron stars as radio pulsars is probably reasonable
when one realises that the observable lifetimes of recycled
pulsars are much larger than those of normal pulsars. As
discussed in §
3.4.1, double neutron star binary systems are very rare in the Galaxy
- another indication that the majority of binary systems get
disrupted when one of the components explodes as a supernova.
Systems disrupted after the supernova of the secondary form a
mildly-recycled isolated pulsar and a young pulsar formed during
the explosion of the secondary.
Although no system has so far been found in which both neutron
stars are visible as radio pulsars, timing measurements of three
systems show that the companion masses are
- as expected for neutron stars [215]. In addition, no optical counterparts are seen. Thus, we
conclude that these unseen companions are neutron stars that are
either too weak to be detected, no longer active as radio
pulsars, or their emission beams do not intersect our line of
sight. The two known young radio pulsars with main sequence
companions massive enough to explode as a supernova probably
represent the intermediate phase between high-mass X-ray binaries
and double neutron star systems [110
,
115].
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 [2]. This model has gained strong support in recent years from the
discoveries of quasi-periodic kHz oscillations in a number of
low-mass X-ray binaries [266], as well as Doppler-shifted 2.49-ms X-ray pulsations from the
transient X-ray burster SAX J1808.4-3658 [267,
53]. 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 [25,
27,
139,
138]. Perhaps the best example is the white dwarf companion to the
5.25-ms pulsar J1012+5307 [177
,
133]. This 19th magnitude white dwarf is bright enough to allow
measurements of its surface gravity and orbital velocity [257].
The range of white dwarf masses observed is becoming broader.
Since this article originally appeared in 1998, the number of
``intermediate-mass binary pulsars'' [43] has grown significantly [49]. These systems are distinct to the ``classical'' millisecond
pulsar-white dwarf binaries like PSR J1012+5307 in several ways:
(1) the spin period of the radio pulsar is generally longer
(9-200 ms); (2) the mass of the white dwarf is larger
(typically close to
); (3) the orbital eccentricity, while still essentially
circular, is often significantly larger (
). It is not presently clear whether these systems originated
from either low- or high-mass X-ray binaries. It was suggested by
van den Heuvel [254] that they have more in common with high-mass systems, the
difference being that the secondary star was not sufficiently
massive to explode as a supernova. Instead it formed a white
dwarf. Detailed studies of this sub-population of binary pulsars
are required for further understanding in this area.
Another relatively poorly understood area is the existence of
solitary millisecond pulsars in the Galactic disk (which comprise
just under 20% of all Galactic millisecond pulsars). Although it
has been proposed that the millisecond pulsars have got rid of
their companion by ablation, as appears to be happening in the
PSR B1957+20 system [83], it is not clear whether the time-scales for this process are
feasible. There is some observational evidence that suggests that
solitary millisecond pulsars are less luminous than binary
millisecond pulsars [20
,
122
]. If confirmed by future discoveries, this would need to be
explained by any viable evolutionary model.
Such large velocities are perhaps not surprising, given the
violent conditions under which neutron stars are formed.
Shklovskii [217] demonstrated that, if the explosion is only slightly
asymmetric, an impulsive ``kick'' velocity of up to 1000
is imparted to the neutron star. In addition, if the neutron
star progenitor was a member of a binary system prior to the
explosion, the pre-supernova orbital velocity will also
contribute to the resulting speed of the newly-formed pulsar.
High-velocity pulsars born close to the Galactic plane quickly
migrate to higher Galactic latitudes. This migration is seen in
Fig.
10, a dynamical simulation of the orbits of 100 neutron stars in a
model of the Galactic gravitational potential. Given such a broad
velocity spectrum, as much as half of all pulsars will eventually
escape the gravitational potential of the Galaxy and end up in
intergalactic space [148
,
58
].
Based on the proper motion data, recent studies have
demonstrated that the mean birth velocity of normal pulsars is
450
([148,
132,
58,
84]; see, however, also [93,
91]). This is significantly larger than the velocities of
millisecond and binary pulsars. Recent studies suggest that their
mean birth velocity is likely to be in the range
[129,
57,
152
]. The main reason for this difference surely lies in the fact
that about 80% of the millisecond pulsars are members of binary
systems (§
2.4) which could not have survived had the neutron star received a
substantial kick velocity.
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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 |