Segal's spectral sequence in twisted equivariant k-teory for proper and discrete actions

AbstractWe use a spectral sequence developed by Graeme Segal in order to understand the twisted G-equivariant K-theory for proper and discrete actions. We show that the second page of this spectral sequence is isomorphic to a version of Bredon cohomology with local coefficients in twisted representations. We furthermore explain some phenomena concerning the third differential of the spectral sequence, and recover known results when the twisting comes from finite order elements in discrete torsion.</jats:p

Ermakov Systems with Multiplicative Noise

Using the Euler-Maruyama numerical method, we present calculations of the Ermakov-Lewis invariant and the dynamic, geometric, and total phases for several cases of stochastic parametric oscillators, including the simplest case of the stochastic harmonic oscillator. The results are compared with the corresponding numerical noiseless cases to evaluate the effect of the noise. Besides, the noiseless cases are analytic and their analytic solutions are briefly presented. The Ermakov-Lewis invariant is not affected by the multiplicative noise in the three particular examples presented in this work, whereas there is a shift effect in the case of the phasesComment: 12 pages, 4 figures, 22 reference

The enigmatic spin evolution of PSR J0537-6910: r-modes, gravitational waves and the case for continued timing

We discuss the unique spin evolution of the young X-ray pulsar PSR J0537-6910, a system in which the regular spin down is interrupted by glitches every few months. Drawing on the complete timing data from the Rossi X-ray Timing Explorer (RXTE, from 1999-2011), we argue that a trend in the inter-glitch behaviour points to an effective braking index close to $n=7$, much larger than expected. This value is interesting because it would accord with the neutron star spinning down due to gravitational waves from an unstable r-mode. We discuss to what extent this, admittedly speculative, scenario may be consistent and if the associated gravitational-wave signal would be within reach of ground based detectors. Our estimates suggest that one may, indeed, be able to use future observations to test the idea. Further precision timing would help enhance the achievable sensitivity and we advocate a joint observing campaign between the Neutron Star Interior Composition ExploreR (NICER) and the LIGO-Virgo network.Comment: 10 pages, 4 figures, emulate ApJ forma

The glitch activity of neutron stars

We present a statistical study of the glitch population and the behaviour of the glitch activity across the known population of neutron stars. An unbiased glitch database was put together based on systematic searches of radio timing data of 898 rotation-powered pulsars obtained with the Jodrell Bank and Parkes observatories. Glitches identified in similar searches of 5 magnetars were also included. The database contains 384 glitches found in the rotation of 141 of these neutron stars. We confirm that the glitch size distribution is at least bimodal, with one sharp peak at approximately $20\, \rm{\mu\,Hz}$, which we call large glitches, and a broader distribution of smaller glitches. We also explored how the glitch activity $\dot{\nu}_{\rm{g}}$, defined as the mean frequency increment per unit of time due to glitches, correlates with the spin frequency $\nu$, spin-down rate $|\dot{\nu}|$, and various combinations of these, such as energy loss rate, magnetic field, and spin-down age. It is found that the activity is insensitive to the magnetic field and that it correlates strongly with the energy loss rate, though magnetars deviate from the trend defined by the rotation-powered pulsars. However, we find that a constant ratio $\dot\nu_{\rm{g}}/|\dot\nu| = 0.010 \pm 0.001$ is consistent with the behaviour of all rotation-powered pulsars and magnetars. This relation is dominated by large glitches, which occur at a rate directly proportional to $|\dot{\nu}|$. The only exception are the rotation-powered pulsars with the highest values of $|\dot{\nu}|$, such as the Crab pulsar and PSR B0540$-$69, which exhibit a much smaller glitch activity, intrinsically different from each other and from the rest of the population. The activity due to small glitches also shows an increasing trend with $|\dot\nu|$, but this relation is biased by selection effects.Comment: Accepted for publication in A&

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.Comment: 8 pages; 4 figures. Accepted for publication in MNRA

Fixing the U-band photometry of Type Ia supernovae

We present previously unpublished photometry of supernovae 2003gs and 2003hv. Using spectroscopically-derived corrections to the U-band photometry, we reconcile U-band light curves made from imagery with the Cerro Tololo 0.9-m, 1.3-m and Las Campanas 1-m telescopes. Previously, such light curves showed a 0.4 mag spread at one month after maximum light. This gives us hope that a set of corrected ultraviolet light curves of nearby objects can contribute to the full utilization of rest frame U-band data of supernovae at redshift ~0.3 to 0.8. As pointed out recently by Kessler et al. in the context of the Sloan Digital Sky Survey supernova search, if we take the published U-band photometry of nearby Type Ia supernovae at face value, there is a 0.12 mag U-band anomaly in the distance moduli of higher redshift objects. This anomaly led the Sloan survey to eliminate from their analyses all photometry obtained in the rest frame U-band. The Supernova Legacy Survey eliminated observer frame U-band photometry, which is to say nearby objects observed in the U-band, but they used photometry of high redshift objects no matter in which band the photons were emitted.Comment: 25 pages, 9 figures, accepted for publication in the Astronomical Journa

The Mass-Radius Relationship for Very Low Mass Stars: Four New Discoveries from the HATSouth Survey

We report the discovery of four transiting F-M binary systems with companions between 0.1-0.2 Msun in mass by the HATSouth survey. These systems have been characterised via a global analysis of the HATSouth discovery data, combined with high-resolution radial velocities and accurate transit photometry observations. We determined the masses and radii of the component stars using a combination of two methods: isochrone fitting of spectroscopic primary star parameters, and equating spectroscopic primary star rotation velocity with spin-orbit synchronisation. These new very low mass companions are HATS550-016B (0.110 -0.006/+0.005 Msun, 0.147 -0.004/+0.003 Rsun), HATS551-019B (0.17 -0.01/+0.01 Msun, 0.18 -0.01/+0.01 Rsun), HATS551-021B (0.132 -0.005/+0.014 Msun, 0.154 -0.008/+0.006 Rsun), HATS553-001B (0.20 -0.02/+0.01 Msun, 0.22 -0.01/+0.01 Rsun). We examine our sample in the context of the radius anomaly for fully-convective low mass stars. Combining our sample with the 13 other well-studied very low mass stars, we find a tentative 5% systematic deviation between the measured radii and theoretical isochrone models.Comment: 17 pages, 8 figures, accepted for publication in MNRA

Measuring Dislocation Density in Aluminum with Resonant Ultrasound Spectroscopy

Dislocations in a material will, when present in enough numbers, change the speed of propagation of elastic waves. Consequently, two material samples, differing only in dislocation density, will have different elastic constants, a quantity that can be measured using Resonant Ultrasound Spectroscopy. Measurements of this effect on aluminum samples are reported. They compare well with the predictions of the theory.Comment: 4 pages, 2 figure