Rotation Rates Of Pulsars Research Articles

THE ROLE OF THE MAGNETOROTATIONAL INSTABILITY IN MASSIVE STARS

The magnetorotational instability (MRI) is key physics in accretion disks and is widely considered to play some role in massive-star core collapse. Models of rotating massive stars naturally develop very strong shear at composition boundaries, a necessary condition for MRI instability, and the MRI is subject to triply-diffusive destabilizing effects in radiative regions. We have used the MESA stellar evolution code to compute magnetic effects due to the Spruit-Taylor mechanism and the MRI, separately and together, in a sample of massive star models. We find that the MRI can be active in the later stages of massive star evolution, leading to mixing effects that are not captured in models that neglect the MRI. The MRI and related magneto-rotational effects can move models of given ZAMS mass across "boundaries" from degenerate CO cores to degenerate O/Ne/Mg cores and from degenerate O/Ne/Mg cores to iron cores, thus affecting the final evolution and the physics of core collapse. The MRI acting alone can slow the rotation of the inner core in general agreement with the observed "initial" rotation rates of pulsars. The MRI analysis suggests that localized fields ~10^{12} G may exist at the boundary of the iron core. With both the ST and MRI mechanisms active in the 20 solar mass model, we find that the helium shell mixes entirely out into the envelope. Enhanced mixing could yield a population of yellow or even blue supergiant supernova progenitors that would not be standard SN IIP.

Neutron star glitches have a substantial minimum size

Glitches are sudden spin-up events that punctuate the steady spin down of pulsars and are thought to be due to the presence of a superfluid component within neutron stars. The precise glitch mechanism and its trigger, however, remain unknown. The size of glitches is a key diagnostic for models of the underlying physics. While the largest glitches have long been taken into account by theoretical models, it has always been assumed that the minimum size lay below the detectability limit of the measurements. In this paper we define general glitch detectability limits and use them on 29 years of daily observations of the Crab pulsar, carried out at Jodrell Bank Observatory. We find that all glitches lie well above the detectability limits and by using an automated method to search for small events we are able to uncover the full glitch size distribution, with no biases. Contrary to the prediction of most models, the distribution presents a rapid decrease of the number of glitches below ~0.05 $\mu$Hz. This substantial minimum size indicates that a glitch must involve the motion of at least several billion superfluid vortices and provides an extra observable which can greatly help the identification of the trigger mechanism. Our study also shows that glitches are clearly separated from all the other rotation irregularities. This supports the idea that the origin of glitches is different to that of timing noise, which comprises the unmodelled random fluctuations in the rotation rates of pulsars.

The GSF instability and turbulence do not account for the relatively low rotation rate of pulsars

<i>Aims. <i/>We examine the effects of the horizontal turbulence in differentially rotating stars on the Goldreich-Schubert-Fricke (GSF) instability and apply our results to pre-supernova models.<i>Methods. <i/>We derive the expression for the GSF instability with account of the thermal transport and smoothing of the <i>μ<i/>-gradient by the horizontal turbulence. We apply the new expressions in numerical models of a 20 star.<i>Results. <i/>We show that if <i><<i/> 0 the Rayleigh-Taylor instability cannot be killed by the stabilising thermal and <i>μ<i/>-gradients, so that the GSF instability is always there and we derive the corresponding diffusion coefficient. The GSF instability grows toward the very latest stages of stellar evolution. Close to the deep convective zones in pre-supernova stages, the transport coefficient of elements and angular momentum by the GSF instability can, in small parts of the star, be larger than the shear instability and even as large as the thermal diffusivity. However, the zones in which the GSF instability is acting are extremely narrow and there is not enough time left before the supernova explosion for a significant mixing to occur. Thus, the GSF instability remains insignificant for the evolution even when the inhibiting effects of the <i>μ<i/>-gradient are reduced by the horizontal turbulence.<i>Conclusions. <i/>We conclude that the GSF instability in pre-supernova stages is not responsible for the relatively low rotation rate of pulsars compared to the predictions of rotating star models.

Presupernova Evolution of Rotating Massive Stars and the Rotation Rate of Pulsars

Rotation in massive stars has been studied on the main sequence and during helium burning for decades, but only recently have realistic numerical simulations followed the transport of angular momentum that occurs during more advanced stages of evolution. The results affect such interesting issues as whether rotation is important to the explosion mechanism, whether supernovae are strong sources of gravitational radiation, the star's nucleosynthesis, and the initial rotation rate of neutron stars and black holes. We find that when only hydrodynamic instabilities (shear, Eddington-Sweet, etc.) are included in the calculation, one obtains neutron stars spinning at close to critical rotation at their surface – or even formally in excess of critical. When recent estimates of magnetic torques (Spruit 2002) are added, however, the evolved cores spin about an order of magnitude slower. This is still more angular momentum than observed in young pulsars, but too slow for the collapsar model for gamma-ray bursts.

Mixing and Rotation

The inclusion of rotation in massive star models improves the agreement between theory and observations on at least three important points: 1) rotational mixing allows to produce variations of the surface abundances already during the Main-Sequence phase as is observed. The changes of the surface abundances are more important when, for a given initial velocity, the initial masses are larger, and/or the metallicities are lower; 2) the observed number of red supergiants at the metallicity of the Small Magellanic Cloud (SMC) can be accounted for; 3) the observed variation of the number ratio of Wolf-Rayet to O-type stars as a function of the metallicity can be reproduced. For all these comparisons non-rotating models give unsatisfactory fits. Rotating models results also give interesting insights on questions such as the origin of Be stars, the mechanisms responsible for the huge mass loss rates undergone by the Luminous Blue Variables, the rotation rates of pulsars, the progenitors of collapsars and the sources of primary nitrogen at low metallicity.

Effects of stellar winds and rotation on the evolution of massive stars

We discuss the impact of the inclusion of both mass loss and rotation in massive star models at different metallicities. Rotation much improves the agreement between theory and observation. In particular rotational mixing allows to produce variations of the surface abundances already during the Main-Sequence phase. The changes of the surface abundances are more important when, for a given initial velocity, the initial mass increases, and/or the initial metallicity decreases. Also the observed high number of red supergiants at low metallicity can be accounted for by rotating stellar models, as well as the observed variation of the number ratio of Wolf-Rayet to O-type stars as a function of the metallicity and the variation with the metallicity of the number ratio of type Ibc to type II supernovae. In all these questions non-rotating models give unsatisfactory fits. Rotating models can also give interesting insights on questions as the origin of the Be stars, the mechanisms responsible for the huge mass loss rates undergone by the Luminous Blue Variables, the sources of primary nitrogen at low metallicity, the rotation rate of pulsars and the progenitors of the collapsars.

PSR1737–30 and period discontinuities in young pulsars

THE rotation rate of pulsars decreases as kinetic energy is lost by the emission of electromagnetic radiation and particles. This gradual spin-down is sometimes interrupted, however, by abrupt increases in rotational frequency. Such discontinuities—known as glitches—arise because of structural changes in neutron stars, and can provide valuable information on their interiors. Glitches generally occur more frequently in younger pulsars1. A timing program has been monitoring the periods of the forty predominantly young pulsars found in the Jodrell Bank 1,400-MHz survey2,3,4. As part of this study, we report here the observation that one pulsar, PSR1737–30, has undergone no fewer than five glitches in the past three years. Although not especially young, this pulsar is glitching at a rate nearly an order of magnitude greater than any other known pulsar. We speculate that the higher temperatures associated with the youngest pulsars might prevent the build-up of the stresses the sudden release of which is the cause of glitches. If so, this might explain the lower glitch activity now evident in those pulsars that are less than 2,000 years old.

Binary pulsar with a very small mass function

Much of the interesting physics concerning neutron stars and their evolution depends for its experimental foundation on observations of the rotation rates of pulsars. To continue recent efforts of our group in this area1–3, we began a series of pulse-arrival-time observations of ∼70 pulsars in January 1985. Most of the pulsars in this study were discovered in the Princeton/NRAO pulsar survey of the preceding two years4,5. Soon after we began these observations it became clear that PSR2303+46 was a binary pulsar2; it is now evident that PSR1831–00 is also a member of a binary system, the seventh such radio pulsar known. It moves in an orbit with a period of 1.81 days, a small eccentricity, and an unusually small mass function of 0.00012 M⊙ (where M⊙ is the mass of the Sun). With a period P = 0.521 s and period derivative P≲ 10−17 s s−1, PSR1831–00, like the other known binary pulsars, has a relatively weak magnetic field. We discuss the features of this system that provide clues to its evolutionary history and outline possible models for its formation.