Expansion properties of a random regular graph after random vertex deletions

We investigate the following vertex percolation process. Starting with a random regular graph of constant degree, delete each vertex independently with probability p, where p=n^{-alpha} and alpha=alpha(n) is bounded away from 0. We show that a.a.s. the resulting graph has a connected component of size n-o(n) which is an expander, and all other components are trees of bounded size. Sharper results are obtained with extra conditions on alpha. These results have an application to the cost of repairing a certain peer-to-peer network after random failures of nodes.Comment: 14 page

The optical counterpart of SAX J1808.4-3658, the transient bursting millisecond X-ray pulsar

A set of CCD images have been obtained during the decline of the X-ray transient SAX J1808.4-3658 during April-June 1998. The optical counterpart has been confirmed by several pieces of evidence. The optical flux shows a modulation on several nights which is consistent with the established X-ray binary orbit period of 2 hours. This optical variability is roughly in antiphase with the weak X-ray modulation. The source mean magnitude of V=16.7 on April 18 declined rapidly after April 22. From May 2 onwards the magnitude was more constant at around V=18.45 but by June 27 was below our sensitivity limit. The optical decline precedes the rapid second phase of the X-ray decrease by 3 +/- 1 days. The source has been identified on a 1974 UK Schmidt plate at an estimated magnitude of ~20. The nature of the optical companion is discussed.Comment: 5 pages, 3 figures; published in MNRAS, March 15th 199

A GPU based real-time software correlation system for the Murchison Widefield Array prototype

Modern graphics processing units (GPUs) are inexpensive commodity hardware that offer Tflop/s theoretical computing capacity. GPUs are well suited to many compute-intensive tasks including digital signal processing. We describe the implementation and performance of a GPU-based digital correlator for radio astronomy. The correlator is implemented using the NVIDIA CUDA development environment. We evaluate three design options on two generations of NVIDIA hardware. The different designs utilize the internal registers, shared memory and multiprocessors in different ways. We find that optimal performance is achieved with the design that minimizes global memory reads on recent generations of hardware. The GPU-based correlator outperforms a single-threaded CPU equivalent by a factor of 60 for a 32 antenna array, and runs on commodity PC hardware. The extra compute capability provided by the GPU maximises the correlation capability of a PC while retaining the fast development time associated with using standard hardware, networking and programming languages. In this way, a GPU-based correlation system represents a middle ground in design space between high performance, custom built hardware and pure CPU-based software correlation. The correlator was deployed at the Murchison Widefield Array 32 antenna prototype system where it ran in real-time for extended periods. We briefly describe the data capture, streaming and correlation system for the prototype array.Comment: 11 pages, to appear in PAS

Pulse Profiles, Accretion Column Dips and a Flare in GX 1+4 During a Faint State

The Rossi X-ray Timing Explorer (RXTE) spacecraft observed the X-ray pulsar GX 1+4 for a period of 34 hours on July 19/20 1996. The source faded from an intensity of ~20 mCrab to a minimum of <~0.7 mCrab and then partially recovered towards the end of the observation. This extended minimum lasted ~40,000 seconds. Phase folded light curves at a barycentric rotation period of 124.36568 +/- 0.00020 seconds show that near the center of the extended minimum the source stopped pulsing in the traditional sense but retained a weak dip feature at the rotation period. Away from the extended minimum the dips are progressively narrower at higher energies and may be interpreted as obscurations or eclipses of the hot spot by the accretion column. The pulse profile changed from leading-edge bright before the extended minimum to trailing-edge bright after it. Data from the Burst and Transient Source Experiment (BATSE) show that a torque reversal occurred <10 days after our observation. Our data indicate that the observed rotation departs from a constant period with a Pdot/P value of ~-1.5% per year at a 4.5 sigma significance. We infer that we may have serendipitously obtained data, with high sensitivity and temporal resolution about the time of an accretion disk spin reversal. We also observed a rapid flare which had some precursor activity, close to the center of the extended minimum.Comment: 19 pages, 6 figures, accepted for publication in Astrophysical Journal (tentatively scheduled for vol. 529 #1, 20 Jan 2000

Accretion column eclipses in the X-ray pulsars GX 1+4 and RX J0812.4-3114

Sharp dips observed in the pulse profiles of three X-ray pulsars (GX 1+4, RX J0812.4-3114 and A 0535+26) have previously been suggested to arise from partial eclipses of the emission region by the accretion column occurring once each rotation period. We present pulse-phase spectroscopy from Rossi X-ray Timing Explorer satellite observations of GX 1+4 and RX J0812.4-3114 which for the first time confirms this interpretation. The dip phase corresponds to the closest approach of the column axis to the line of sight, and the additional optical depth for photons escaping from the column in this direction gives rise to both the decrease in flux and increase in the fitted optical depth measured at this phase. Analysis of the arrival time of individual dips in GX~1+4 provides the first measurement of azimuthal wandering of a neutron star accretion column. The column longitude varies stochastically with standard deviation 2-6 degrees depending on the source luminosity. Measurements of the phase width of the dip both from mean pulse profiles and individual eclipses demonstrates that the dip width is proportional to the flux. The variation is consistent with that expected if the azimuthal extent of the accretion column depends only upon the Keplerian velocity at the inner disc radius, which varies as a consequence of the accretion rate Mdot.Comment: 7 pages, 5 figures, accepted by MNRAS. Included reference

VLBI Imaging of Water Maser Emission from the Nuclear Torus of NGC 1068

We have made the first VLBI synthesis images of the H2O maser emission associated with the central engine of the Seyfert galaxy NGC 1068. Emission extends about +/-300 km/s from the systemic velocity. Images with submilliarcsecond angular resolution show that the red-shifted emission lies along an arc to the northwest of the systemic emission. (The blue-shifted emission has not yet been imaged with VLBI.) Based on the maser velocities and the relative orientation of the known radio jet, we propose that the maser emission arises on the surface of a nearly edge-on torus, where physical conditions are conducive to maser action. The visible part of the torus is axially thick, with comparable height and radius. The velocity field indicates sub-Keplerian differential rotation around a central mass of about 1e7 Msun that lies within a cylindrical radius of about 0.65 pc. The estimated luminosity of the central engine is about 0.5 of the Eddington limit. There is no detectable compact radio continuum emission near the proposed center of the torus (T_B< 5e6 K on size scales of about 0.1 pc), so that the observed flat-spectrum core cannot be direct self-absorbed synchrotron radiation.Comment: 12 pages, 4 figures. To appear in ApJ Part 2. Also available at http://www.physics.ucsb.edu/~vlbiweb

Spectral variation in the X-ray pulsar GX 1+4 during a low-flux episode

The X-ray pulsar GX 1+4 was observed with the RXTE satellite for a total of 51ks between 1996 July 19 - 21. During this period the flux decreased smoothly from an initial mean level of ~ 6 X 10^36 erg/s to a minimum of ~ 4 X 10^35 erg/s (2-60 keV, assuming a source distance of 10 kpc) before partially recovering towards the initial level at the end of the observation. BATSE pulse timing measurements indicate that a torque reversal took place approximately 10 d after this observation. Both the mean pulse profile and the photon spectrum varied significantly. The observed variation in the source may provide important clues as to the mechanism of torque reversals. The single best-fitting spectral model was based on a component originating from thermal photons with kT ~ 1 keV Comptonised by a plasma of temperature kT \~ 7 keV. Both the flux modulation with phase during the brightest interval and the evolution of the mean spectra over the course of the observation are consistent with variations in this model component; with, in addition, a doubling of the column density nH contributing to the mean spectral change. A strong flare of duration 50 s was observed during the interval of minimum flux, with the peak flux ~ 20 times the mean level. Although beaming effects are likely to mask the true variation in Mdot thought to give rise to the flare, the timing of a modest increase in flux prior to the flare is consistent with dual episodes of accretion resulting from successive orbits of a locally dense patch of matter in the accretion disc.Comment: 8 pages, 3 figures, submitted to MNRA

Direction-Dependent Polarised Primary Beams in Wide-Field Synthesis Imaging

The process of wide-field synthesis imaging is explored, with the aim of understanding the implications of variable, polarised primary beams for forthcoming Epoch of Reionisation experiments. These experiments seek to detect weak signatures from redshifted 21cm emission in deep residual datasets, after suppression and subtraction of foreground emission. Many subtraction algorithms benefit from low side-lobes and polarisation leakage at the outset, and both of these are intimately linked to how the polarised primary beams are handled. Building on previous contributions from a number of authors, in which direction-dependent corrections are incorporated into visibility gridding kernels, we consider the special characteristics of arrays of fixed dipole antennas operating around 100-200 MHz, looking towards instruments such as the Square Kilometre Array (SKA) and the Hydrogen Epoch of Reionization Arrays (HERA). We show that integrating snapshots in the image domain can help to produce compact gridding kernels, and also reduce the need to make complicated polarised leakage corrections during gridding. We also investigate an alternative form for the gridding kernel that can suppress variations in the direction-dependent weighting of gridded visibilities by 10s of dB, while maintaining compact support.Comment: 15 pages, 4 figures. Accepted for publication in JA