has a negative derivative
(
).
is easily observable and is
traditionally used to determine the age of the pulsar.
1 On leave from the Department of Physics & Astronomy, University of Nigeria, Nsukka
Abstract. Timing observations of glitches in radio pulsars is currently one of the best probes of the neutron star interior. Such observations have led to a number of models describing the various components of the neutron star and their mutual coupling. Here, we briefly summarize some of our current work in this regard.
Sommaire. Les observations des changements soudains de fréquence des pulsars radio sont de nos jours un des meilleurs sondages de l'intérieur d'une étoile à neutrons. De telles observations ont conduit à plusieurs modèles qui décrivent les différentes composantes de l'étoile à neutrons et leur couplage mutuel. Nous résumons ici brièvement nos recherches actuelles à cet égard.
Radio pulsars were discovered as sequences of rapid (~ 1Hz) and regular radio pulses in 1967, by Jocelyn Bell and Anthony Hewish (Hewish et al., 1968). Currently about 1000 pulsars are known and the galactic population is estimated at around 105.
Shorly after their discovery, the pulses were firmly associated with highly magnetized, rapidly rotating, neutron stars. Neutron stars are one of the final evolutionary stages of stars formed by the collapse of a massive star in a supernova explosion. Containing typically 1.4 solar masses within a diameter of about 15 km, they are also the densest known form of directly-observable matter in the Universe.
Although neutron stars have now been recognized in a variety of stellar systems such as X-ray binaries, radio pulsars are by far the most common observable manifestation of the fascinating neutron star. The emitted radio pulses allow us to directly measure the rotation of the underlying star. This rotation rate is, in comparison with most other astronomical measurements, exceptionally stable and easy to measure with high accuracy. Glitches are perturbations to this regular behaviour which give us a window into the interior of the neutron star, as described below.
Pulsars slow down steadily, due to the loss of kinetic (rotational)
energy via the emission of high-energy particles and radiation. In other
words, the pulsar spin rate, has a negative derivative
(
).
is easily observable and is
traditionally used to determine the age of the pulsar.
Outside the steady decrease in all pulsars exhibit to some
extent rotational irregularities known as timing noise, which is
observable as random wandering in either the pulse phase or its
frequency. Sudden changes in the rotational frequency are known as
glitches, and may or may not be related to timing noise. Glitches
involve relative increases in the pulsar rotational frequency of up to 1
part in 106. Since the rotation rate can be measured to an accuracy
of up to 10-12, such events are easy to recognize.
| PSR | P (s) |  |
Log  (yr) |
| B1046-58 | 0.1236526 | 96.93 | 4.31 |
| B1737-30 | 0.6066433 | 465.67 | 4.31 |
| Vela | 0.0892991 | 126.68 | 4.05 |
While the slow-down is believed to be caused by processes above the surface of the neutron star, pulsars are (unusual amongst stars) almost all isolated bodies, and the glitch is generally attributed to internal processes. The few intensive observations of post-glitch behaviour reveal recovery over a range of time scales. These observations have been used to study the pulsar interior, in particular the various components of the interior and the manner in which they couple with each other.
To date about eighty glitches have been noted, involving over thirty pulsars. The extremely young PSR 0531+21 (Crab) and the adolescent PSRs 0833-45 (Vela) and 1737-30 are responsible for almost half of these glitches. Evidence is growing in support of the view that glitch characteristics such as frequency of occurrence and rate of post-glitch recovery are dependent on the age of the pulsar. Unfortunately, only in the Crab and Vela pulsars have multiple glitches been monitored intensively. Similarly, intense observations from a larger sample of pulsars is required to distinguish between competing theories of the neutron star interior.
Figure 1:
Integrated pulse profiles showing: (a) 72,750
integrations of 1046-58 at 18 cm; and
(b) 18,000 integrations of 1737-30 at 13 cm.
Pulsar observations using the Hartebeesthoek Radio Astronomy Observatory (HartRAO) 26-m radio telescope commenced in 1984. Observations are made at 1.7 and 2.3 GHz. In 1988, software was installed to analyse observations in near-real time and then initiate continuous observations should a glitch be detected. The Observatory also has software that allows short observations of a range of astronomical objects to be scheduled automatically at selected times. These developments allow for a rapid and automatic response to glitches, and the Vela pulsar became the first target of a new ``glitch detection'' project. The project has been quite successful in providing good observational coverage of immediate postglitch behaviour of five glitches in the Vela pulsar (Flanagan, 1995). Recently, two more young pulsars (1046-58 and 1737-30) have been included in the list of frequently-observed pulsars, although the low signal-to-noise ratio of these observations prevented on-line glitch-detection with automatically-scheduled follow-up observations.
Figure 2:
The rotational parameters of PRS B1046-58 showing the glitch
that occured on MJD 50791.5 ± 0.5.
(a) shows the residual frequency after subtracting the pre-glitch model
while (b) is the frequency derivative.
In panel (a) the uncertainties are much smaller than the
size of the symbols.
PSRs 1737-30 and 1046-58 are of similar age to Vela (Table 1). The former is the most frequently-glitching pulsar known, although its post-glitch behaviour has not yet been observed as well as that of Vela. No glitch observations of the more southern PSR 1046-58 appear to have been published; because of its age and the similarity of its spin-down rate to that of Vela, we expect it also to undergo frequent glitches. PSR 1046-58 is observed twice daily at approximately 8-hourly intervals while PSR 1737-30 is observed three times daily at approximately 5-hourly intervals. A single integration consists of 5000 samples of PSR 1737-30 and 1089 samples of PSR 1046-58; the integration lasting 10-20 minutes depending on the frequency of observation. Fig. 1 shows samples of integrated pulse profiles for these pulsars.
Manual checks of phase drift are done after most of the observations for any evidence of a glitch. The first glitch in PSR 1046-58 was observed in this monitoring programme. It occurred on December 9, 1997, about 200 days after the commencement of intensive observations on this pulsar. The spin-up was rather large in magnitude and was accompanied by an increase in spin-down rate. We also observed a large glitch on PSR 1737-30 (the largest so far on this pulsar) on May 3, 1998. Figs. 2 and 3 show the rotational behaviour of the two pulsars over a 400-day period.
Early observations of pulsar response to a glitch on time scales of weeks provided strong evidence for a superfluid interior(e.g. Baym et al., 1969) - all forms of ``normal'' matter would respond to such a disturbance on unobservably short time-scales. A neutron star, as shown in Fig. 4, is believed to have a rigid outer crust which consists primarily of iron nuclei; an inner crust of neutron-rich nuclei, electrons and 1S0 neutron superfluids; an outer (fluid) core containing 3P2 superfluid neutrons with an admixture of 1S0 super-conducting protons and normal electrons; and an inner (plasma) core that may possibly contain pion condensate, condensed kaons or matter in some exotic state (Alpar, 1989).
Figure 3:
The rotational parameters of PRS B1737-58 showing the glitch
that occured on MJD 50936.8 ± 0.1.
(a) shows the residual frequency after subtracting the pre-glitch model
while (b) is the frequency derivative.
In panel (a) the uncertainties are much smaller than the
size of the symbols.
Pulsar glitch recovery is now known to occur over all observed time scales, from a few hours to years. These recovery time scales have been explained in terms of the superfluid components of the neutron star interior and their coupling to the lattice crust. As the quality and number of observations has increased, so too has the number of proposed possible mechanisms of inter-component coupling. Some of the currently surviving models are, briefly: the vortex creep model (Alpar et al., 1984, 1993, 1996); the core ``shell'' model (Sedrakian et al., 1995); the three-component model (Takatsuka & Tamagaki, 1989) and the vortex corotating model (Jones, 1990). In both the vortex creep and the vortex corotating models, glitch behaviours are attributed to the interaction between the crustal superfluid and the rest of the star while the core ``shell'' model is based on the core superfluid coupling/decoupling from the rest of the star. In the three-component model both the core and crust superfluids contribute to glitch behaviours. These and other models are yet to provide adequate explanations for all the observed glitch characteristics - glitch sizes, recovery, interval, etc.
In a modified three-component model we extended the original three-component model to accomodate all the observed glitch recovery time scales (Urama & Okeke, 1999). The model is based on the principle of the corotation of both the core and crust superfluids which are not pinned. Here, the shortest recovery timescale has been attributed to the core superfluid while the interglitch period is seen to result from the crust superfluid.
Figure 4:
A schematic representation of a possible cross-section of a
neutron star.
The Vela and Crab pulsars are the only pulsars whose glitch recoveries
have been monitored in sufficient detail. While the Vela pulsar has
generally shown giant glitches, all the Crab pulsar glitches have been
small. For the Crab pulsar, it is shown that the spin-down rate,
never returns to its preglitch value; there is a
permanent offset in
The issue of whether the same
mechanisms are involved in Vela-type and Crab-type glitches continues to
be contentious. The differences in their glitch characteristics have
been too easily attributed to the age difference between them.
Unfortunately all the data on real-time glitch detection have been
obtained only on these two. The HartRAO pulsar project has contributed to
the debate on component interaction with the first observation of short
(~ hours) recovery following a glitch in the Vela pulsar (Flanagan,
1990), and of a pair of glitches with atypical characteristics. We hope
that by extending this project to include other young pulsars we can
also shed some light on the structural evolution of the pulsar interior.
Acknowledgements
One of us, J.O.U., acknowledges the support of HartRAO and an IAU Commission 38 travel grant towards his visit to South Africa. He also wishes to thank the staff of HartRAO and Claire Flanagan for hospitality and wonderful assistance with this work.
References
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