Pancyclicity of Hamiltonian line graphs

Let f(n) be the smallest integer such that for every graph G of order n with minimum degree 3(G)>f(n), the line graph L(G) of G is pancyclic whenever L(G) is hamiltonian. Results are proved showing that f(n) = ®(n 1/3)

Could 2S 0114+650 be a magnetar?

We investigate the spin evolution of the binary X-ray pulsar 2S 0114+650, which possesses the slowest known spin period of $\sim 2.7$ hours. We argue that, to interpret such long spin period, the magnetic field strength of this pulsar must be initially \gsim 10^{14} G, that is, it was born as a magnetar. Since the pulsar currently has a normal magnetic field $\sim 10^{12}$ G, our results present support for magnetic field decay predicted by the magnetar model.Comment: 7 pages, 1 figure, accepted for publication in ApJ

Long Gamma-Ray Burst Progenitors: Boundary Conditions and Binary Models

The observed association of Long Gamma-Ray Bursts (LGRBs) with peculiar Type Ic supernovae gives support to Woosley`s collapsar/hypernova model, in which the GRB is produced by the collapse of the rapidly rotating core of a massive star to a black hole. The association of LGRBs with small star-forming galaxies suggests low-metallicity to be a condition for a massive star to evolve to the collapsar stage. Both completely-mixed single star models and binary star models are possible. In binary models the progenitor of the GRB is a massive helium star with a close companion. We find that tidal synchronization during core-helium burning is reached on a short timescale (less than a few millennia). However, the strong core-envelope coupling in the subsequent evolutionary stages is likely to rule out helium stars with main-sequence companions as progenitors of hypernovae/GRBs. On the other hand, helium stars in close binaries with a neutron-star or black-hole companion can, despite the strong core-envelope coupling in the post-helium burning phase, retain sufficient core angular momentum to produce a hypernova/GRB.Comment: 8 pp., 2 figs, Proceedings of 5th Stromlo Symposiu

New Direct Observational Evidence for Kicks in SNe

We present an updated list of direct strong evidence in favour of kicks being imparted to newborn neutron stars. In particular we discuss the new cases of evidence resulting from recent observations of the X-ray binary Circinus X-1 and the newly discovered binary radio pulsar PSR J1141-6545. We conclude that the assumption that neutron stars receive a kick velocity at their formation is unavoidable (van den Heuvel & van Paradijs 1997).Comment: 2 pages, to appear in the proceedings of the IAU Colloq. 177 "Pulsar Astronomy - 2000 and beyond

A catalogue of low-mass X-ray binaries in the Galaxy, LMC, and SMC (Fourth edition)

We present a new edition of the catalogue of the low-mass X-ray binaries in the Galaxy and the Magellanic Clouds. The catalogue contains source name(s), coordinates, finding chart, X-ray luminosity, system parameters, and stellar parameters of the components and other characteristic properties of 187 low-mass X-ray binaries, together with a comprehensive selection of the relevant literature. The aim of this catalogue is to provide the reader with some basic information on the X-ray sources and their counterparts in other wavelength ranges ($\gamma$-rays, UV, optical, IR, and radio). Some sources, however, are only tentatively identified as low-mass X-ray binaries on the basis of their X-ray properties similar to the known low-mass X-ray binaries. Further identification in other wavelength bands is needed to finally determine the nature of these sources. In cases where there is some doubt about the low-mass nature of the X-ray binary this is mentioned. Literature published before 1 October 2006 has, as far as possible, been taken into account.Comment: 45 pages, catalogue include

Discovery of Two Relativistic Neutron Star-White Dwarf Binaries

We have discovered two recycled pulsars in relativistic orbits as part of the first high-frequency survey of intermediate Galactic latitudes. PSR J1157-5112 is a 44 ms pulsar and the first recycled pulsar with an ultra-massive (M > 1.14 Mo) white dwarf companion. Millisecond pulsar J1757-5322 is a relativistic circular-orbit system which will coalesce due to the emission of gravitational radiation in less than 9.5 Gyr. Of the ~40 known circular orbit pulsars, J1757-5322 and J1157-5112 have the highest projected orbital velocities. There are now three local neutron-star/white-dwarf binaries that will coalesce in less than a Hubble time, implying a large coalescence rate for these objects in the local Universe. Systems such as J1141-6545 (Kaspi et al. 2000) are potential gamma-ray burst progenitors and dominate the coalescence rate, whilst lighter systems make excellent progenitors of millisecond pulsars with planetary or ultra-low mass companions.Comment: 4 pages, to appear in ApJ Letters. Uses aastex v 5.0, emulateapj5.sty, apjfonts.st

Degree Sequences and the Existence of kk-Factors

We consider sufficient conditions for a degree sequence $\pi$ to be forcibly $k$-factor graphical. We note that previous work on degrees and factors has focused primarily on finding conditions for a degree sequence to be potentially $k$-factor graphical. We first give a theorem for $\pi$ to be forcibly 1-factor graphical and, more generally, forcibly graphical with deficiency at most $\beta\ge0$. These theorems are equal in strength to Chv\'atal's well-known hamiltonian theorem, i.e., the best monotone degree condition for hamiltonicity. We then give an equally strong theorem for $\pi$ to be forcibly 2-factor graphical. Unfortunately, the number of nonredundant conditions that must be checked increases significantly in moving from $k=1$ to $k=2$, and we conjecture that the number of nonredundant conditions in a best monotone theorem for a $k$-factor will increase superpolynomially in $k$. This suggests the desirability of finding a theorem for $\pi$ to be forcibly $k$-factor graphical whose algorithmic complexity grows more slowly. In the final section, we present such a theorem for any $k\ge2$, based on Tutte's well-known factor theorem. While this theorem is not best monotone, we show that it is nevertheless tight in a precise way, and give examples illustrating this tightness.Comment: 19 page

The Peculiar Evolutionary History of IGR J17480-2446 in Terzan 5

The low mass X-ray binary (LMXB) IGR J17480-2446 in the globular cluster Terzan 5 harbors an 11 Hz accreting pulsar. This is the first object discovered in a globular cluster with a pulsar spinning at such low rate. The accreting pulsar is anomalous because its characteristics are very different from the other five known slow accreting pulsars in galactic LMXBs. Many features of the 11 Hz pulsar are instead very similar to those of accreting millisecond pulsars, spinning at frequencies >100 Hz. Understanding this anomaly is valuable because IGR J17480-2446 can be the only accreting pulsar discovered so far which is in the process of becoming an accreting millisecond pulsar. We first verify that the neutron star (NS) in IGR J17480-2446 is indeed spinning up by carefully analyzing X-ray data with coherent timing techniques that account for the presence of timing noise. We then study the present Roche lobe overflow epoch and the two previous spin-down epochs dominated by magneto dipole radiation and stellar wind accretion. We find that IGR J17480-2446 is very likely a mildly recycled pulsar and suggest that it has started a spin-up phase in an exceptionally recent time, that has lasted less than a few 10^7 yr. We also find that the total age of the binary is surprisingly low (<10^8 yr) when considering typical parameters for the newborn NS and propose different scenarios to explain this anomaly.Comment: Accepted by ApJ, in pres