MILLISECOND radio pulsars, which are old (∼109yr), rapidly rotating neutron stars believed to be spun up by accretion of matter from their stellar companions, are usually found in binary systems with other degenerate stars1. Using the 305-m Arecibo radiotelescope to make precise timing measurements of pulses from the recently discovered 6.2-ms pulsar PSR1257 +12 (ref. 2), we demonstrate that, rather than being associated with a stellar object, the pulsar is orbited by two or more planet-sized bodies. The planets detected so far have masses of at least 2.8 M⊕ and 3.4 M⊕ where M⊕ is the mass of the Earth. Their respective distances from the pulsar are 0.47 AU and 0.36 AU, and they move in almost circular orbits with periods of 98.2 and 66.6 days. Observations indicate that at least one more planet may be present in this system. The detection of a planetary system around a nearby (∼500 pc), old neutron star, together with the recent report on a planetary companion to the pulsar PSR1829–10 (ref. 3) raises the tantalizing possibility that a non-negligible fraction of neutron stars observable as radio pulsars may be orbited by planet-like bodies. The utility of the clock-like pulses emitted by pulsars [see Nature 217, 709-713 (1968)] did not end with the insights they have yielded into the properties of neutron stars, and hence of high-density matter. In 1992, Wolszczan and Frail reported precise pulsar timing measurements which exhibited periodic variations. Unlike similar observations reported in the previous year (cited as ref. 3 in the paper), these variations were not an artefact, but revealed the presence of two or more planet-sized objects orbiting the neutron star — the first such objects to be detected outside the Solar System.

A planetary system around the millisecond pulsar PSR1257 + 12

The structure of neutron stars is considered from theoretical and observational perspectives We demonstrate an important aspect of neutron star structure: the neutron star radius is primarily determined by the behavior of the pressure of matter in the vicinity of nuclear matter equilibrium density In the event that extreme softening does not occur at these densities, the radius is virtually independent of the mass and is determined by the magnitude of the pressure For equations of state with extreme softening or those that are self-bound, the radius is more sensitive to the mass Our results show that in the absence of extreme softening, a measurement of the radius of a neutron star more accurate than about 1 km will usefully constrain the equation of state We also show that the pressure near nuclear matter density is primarily a function of the density dependence of the nuclear symmetry energy, while the nuclear incompressibility and skewness parameters play secondary roles In addition, we show that the moment of inertia and the binding energy of neutron stars, for a large class of equations of state, are nearly universal functions of the star's compactness These features can be understood by considering two analytic, yet realistic, solutions of Einstein's equations, by, respectively, Buchdahl and Tolman We deduce useful approximations for the fraction of the moment of inertia residing in the crust, which is a function of the stellar compactness and, in addition, the pressure at the core-crust interface

https://iopscience.iop.org/article/10.1086/319702/pdf

Neutron Star Structure and the Equation of State

Formation and evolution of binary and millisecond radio pulsars

Neutron Stars 1: Equation of State and Structure

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About these proceedings

It is proposed that the quasi-periodic behavior of the bright galactic bulge source GX5 - 1 results from fluctuations in accretion rate onto a millisecond pulsar which has been spun up by accretion to its steady-state spin rate. According to models that use spin-up by accretion to bring the neutron stars to steady-state fast short periods, galactic bulge sources are likely progenitors of millisecond pulsars. After steady state is achieved in these systems, accretion may continue without further spin-up, so that for a substantial fraction of the lifetime of a galactic bulge X-ray source, the neutron star may already be spinning rapidly at the equilibrium spin. The behavior of GX5 - 1 can be explained in terms of deviations from this equilibrium state resulting from changes in the accretion rate.

Is GX5 – 1 a millisecond pulsar?

We present a comprehensive reevaluation of eight of the nine glitches observed to date from the Vela pulsar, and the postglitch relaxation following each glitch. All glitch data sets can be described in terms of three distinct components of short and intermediate time scale exponential relaxation, followed by a long-term recovery of the glitch-induced change in the spin-down rate that is linear in t, ΔΩ˙ c (t)∞t. We interpret the short and the intermediate time scale exponential relaxation, characterized by relaxation times of 10 hr, 3 d .2, and 32 d as the linear response of vortex creep in those regions of the pinned superfluid in the neutron star crust through which no sudden vortex motion occurred at the time of the glitch

Postglitch Relaxation of the VELA Pulsar after Its First Eight Large Glitches: A Reevaluation with the Vortex Creep Model

Pinning and Threading of Quantized Vortices in the Pulsar Crust Superfluid

The anomalous X-ray pulsar 4U 0142+61 was recently detected in the mid infrared bands with the SPITZER Observatory (Wang, Chakrabarty & Kaplan 2006). This observation is the first instance for a disk around an AXP. From a reanalysis of optical and infrared data, we show that the observations indicate that the disk is likely to be an active disk rather than a passive dust disk beyond the light cylinder, as proposed in the discovering paper. Furthermore, we show that the irradiated accretion disk model can also account for all the optical and infrared observations of the anomalous X-ray pulsars in the persistent state.

Anomalous X-ray pulsars: Persistent States with Fallback Disks

Vortex creep theory is used to construct model noise power spectra for three physically distinct types of events which might give rise to pulsar timing noise These are 'pure' events, in which vortex unpinning is the source of the initial frequency jump; 'mixed' events, in which the initial frequency jump is produced by some physical process other than vortex unpinning but leads to the unpinning of some vortices; and 'external' events, in which the initial frequency jumps responsible for noise do not involve any vortex unpinning For the first two types of events, it is found that relaxation processes in the region responsible for the noise will give rise to structure in the observed power spectra, while for external events, the resulting noise spectra will not be influenced by vortex creep The theoretical results are compared with observed power spectra for 25 pulsars The absence of structure in the observed power spectra of the Crab and Vela pulsars within the range of time scales which characterize their postglitch behavior indicates that the pinning regions which play a role in postglitch behavior do not experience the small unpinning events leading to timing noise

M. Ali Alpar

Papers

Is GX5 – 1 a millisecond pulsar?

Postglitch Relaxation of the VELA Pulsar after Its First Eight Large Glitches: A Reevaluation with the Vortex Creep Model

Pinning and Threading of Quantized Vortices in the Pulsar Crust Superfluid

Anomalous X-ray pulsars: Persistent States with Fallback Disks

Vortex creep and the internal temperature of neutron stars : timing noise in pulsars.