Equilibrium spin pulsars unite neutron star populations

Many pulsars are formed with a binary companion from which they can accrete matter. Torque exerted by accreting matter can cause the pulsar spin to increase or decrease, and over long times, an equilibrium spin rate is achieved. Application of accretion theory to these systems provides a probe of the pulsar magnetic field. We compare the large number of recent torque measurements of accreting pulsars with a high-mass companion to the standard model for how accretion affects the pulsar spin period. We find that many long spin period (P > 100 s) pulsars must possess either extremely weak (B < 10^10 G) or extremely strong (B > 10^14 G) magnetic fields. We argue that the strong-field solution is more compelling, in which case these pulsars are near spin equilibrium. Our results provide evidence for a fundamental link between pulsars with the slowest spin periods and strong magnetic fields around high-mass companions and pulsars with the fastest spin periods and weak fields around low-mass companions. The strong magnetic fields also connect our pulsars to magnetars and strong-field isolated radio/X-ray pulsars. The strong field and old age of our sources suggests their magnetic field penetrates into the superconducting core of the neutron star.Comment: 6 pages, 4 figures; to appear in MNRA

Spin period change and the magnetic fields of neutron stars in Be X-ray binaries in the Small Magellanic Cloud

We report on the long-term average spin period, rate of change of spin period and X-ray luminosity during outbursts for 42 Be X-ray binary systems in the Small Magellanic Cloud. We also collect and calculate parameters of each system and use these data to determine that all systems contain a neutron star which is accreting via a disc, rather than a wind, and that if these neutron stars are near spin equilibrium, then over half of them, including all with spin periods over about 100 s, have magnetic fields over the quantum critical level of 4.4x10^13 G. If these neutron stars are not close to spin equilibrium, then their magnetic fields are inferred to be much lower, of the order of 10^6-10^10 G, comparable to the fields of neutron stars in low-mass X-ray binaries. Both results are unexpected and have implications for the rate of magnetic field decay and the isolated neutron star population.Comment: 22 pages, 50 figures; to appear in MNRA

Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces

Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions. Operators acting on such spaces are, for instance, required to embed conditional probability distributions in order to implement the kernel Bayes rule and build sequential data models. It was recently shown that transfer operators such as the Perron-Frobenius or Koopman operator can also be approximated in a similar fashion using covariance and cross-covariance operators and that eigenfunctions of these operators can be obtained by solving associated matrix eigenvalue problems. The goal of this paper is to provide a solid functional analytic foundation for the eigenvalue decomposition of RKHS operators and to extend the approach to the singular value decomposition. The results are illustrated with simple guiding examples

Swift J045106.8-694803: A Highly Magnetised Neutron Star in the Large Magellanic Cloud

We report the analysis of a highly magnetised neutron star in the Large Magellanic Cloud (LMC). The high mass X-ray binary pulsar Swift J045106.8-694803 has been observed with Swift X-ray telescope (XRT) in 2008, The Rossi X-ray Timing Explorer (RXTE) in 2011 and the X-ray Multi-Mirror Mission - Newton (XMM-Newton) in 2012. The change in spin period over these four years indicates a spin-up rate of 5.010.06 s/yr, amongst the highest observed for an accreting pulsar. This spin-up rate can be accounted for using Ghosh and Lambs (1979) accretion theory assuming it has a magnetic field of (1.2 +/= 0.20/0.7) x 10(exp 14) Gauss. This is over the quantum critical field value. There are very few accreting pulsars with such high surface magnetic fields and this is the first of which to be discovered in the LMC. The large spin-up rate is consistent with Swift Burst Alert Telescope (BAT) observations which show that Swift J045106.8-694803 has had a consistently high X-ray luminosity for at least five years. Optical spectra have been used to classify the optical counterpart of Swift J045106.8-694803 as a B0-1 III-V star and a possible orbital period of 21.631 +/- 0.005 days has been found from MACHO optical photometry

Resonances in a chaotic attractor crisis of the Lorenz Flow

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle--Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises