The arithmetic of hyperelliptic curves

We summarise recent advances in techniques for solving Diophantine problems on hyperelliptic curves; in particular, those for finding the rank of the Jacobian, and the set of rational points on the curve

Effective renormalized multi-body interactions of harmonically confined ultracold neutral bosons

We calculate the renormalized effective 2-, 3-, and 4-body interactions for N neutral ultracold bosons in the ground state of an isotropic harmonic trap, assuming 2-body interactions modeled with the combination of a zero-range and energy-dependent pseudopotential. We work to third-order in the scattering length a defined at zero collision energy, which is necessary to obtain both the leading-order effective 4-body interaction and consistently include finite-range corrections for realistic 2-body interactions. The leading-order, effective 3- and 4-body interaction energies are U3 = -(0.85576...)(a/l)^2 + 2.7921(1)(a/l)^3 + O[(a/l)^4] and U4 = +(2.43317...)(a/l)^3 + O[(a\l)^4], where w and l are the harmonic oscillator frequency and length, respectively, and energies are in units of hbar*w. The one-standard deviation error 0.0001 for the third-order coefficient in U3 is due to numerical uncertainty in estimating a slowly converging sum; the other two coefficients are either analytically or numerically exact. The effective 3- and 4-body interactions can play an important role in the dynamics of tightly confined and strongly correlated systems. We also performed numerical simulations for a finite-range boson-boson potential, and it was comparison to the zero-range predictions which revealed that finite-range effects must be taken into account for a realistic third-order treatment. In particular, we show that the energy-dependent pseudopotential accurately captures, through third order, the finite-range physics, and in combination with the multi-body effective interactions gives excellent agreement with the numerical simulations, validating our theoretical analysis and predictions.Comment: Updated introduction, correction of a few typos and sign error

A New Method for Obtaining Binary Pulsar Distances and its Implications for Tests of General Relativity

We demonstrate how measuring orbital period derivatives can lead to more accurate distance estimates and transverse velocities for some nearby binary pulsars. In many cases this method will estimate distances more accurately than is possible by annual parallax, as the relative error decreases as t^-5/2. Unfortunately, distance uncertainties limit the degree to which nearby relativistic binary pulsars can be used for testing the general relativistic prediction of orbital period decay to a few percent. Nevertheless, the measured orbital period derivative of PSR B1534+12 agrees within the observational uncertainties with that predicted by general relativity if the proper-motion contribution is accounted for.Comment: 4 pages, latex, uuencoded compressed postscript + source, no figures, uses aaspptwo.sty and dec.sty, accepted for publication in ApJL, omitted reference now include

Cosmology on a Mesh

An adaptive multi grid approach to simulating the formation of structure from collisionless dark matter is described. MLAPM (Multi-Level Adaptive Particle Mesh) is one of the most efficient serial codes available on the cosmological 'market' today. As part of Swinburne University's role in the development of the Square Kilometer Array, we are implementing hydrodynamics, feedback, and radiative transfer within the MLAPM adaptive mesh, in order to simulate baryonic processes relevant to the interstellar and intergalactic media at high redshift. We will outline our progress to date in applying the existing MLAPM to a study of the decay of satellite galaxies within massive host potentials.Comment: 3 pages, 2 figures, to appear in the proceedings of "The IGM/Galaxy Connection - The Distribution of Baryons at z=0", ed. M. Putman & J. Rosenber

Are the distributions of Fast Radio Burst properties consistent with a cosmological population?

High time resolution radio surveys over the last few years have discovered a population of millisecond-duration transient bursts called Fast Radio Bursts (FRBs), which remain of unknown origin. FRBs exhibit dispersion consistent with propagation through a cold plasma and dispersion measures indicative of an origin at cosmological distances. In this paper we perform Monte Carlo simulations of a cosmological population of FRBs, based on assumptions consistent with observations of their energy distribution, their spatial density as a function of redshift and the properties of the interstellar and intergalactic media. We examine whether the dispersion measures, fluences, inferred redshifts, signal-to-noises and effective widths of known FRBs are consistent with a cosmological population. Statistical analyses indicate that at least 50 events at Parkes are required to distinguish between a constant co-moving FRB density, and a FRB density that evolves with redshift like the cosmological star formation rate density.Comment: 11 pages, 7 figures, 3 table

Relativistic spin precession in the binary PSR J1141−-6545

PSR J1141$-$6545 is a precessing binary pulsar that has the rare potential to reveal the two-dimensional structure of a non-recycled pulsar emission cone. It has undergone $\sim 25 \deg$ of relativistic spin precession in the $\sim18$ years since its discovery. In this paper, we present a detailed Bayesian analysis of the precessional evolution of the width of the total intensity profile, to understand the changes to the line-of-sight impact angle ($\beta$) of the pulsar using four different physically motivated prior distribution models. Although we cannot statistically differentiate between the models with confidence, the temporal evolution of the linear and circular polarisations strongly argue that our line-of-sight crossed the magnetic pole around MJD 54000 and that only two models remain viable. For both these models, it appears likely that the pulsar will precess out of our line-of-sight in the next $3-5$ years, assuming a simple beam geometry. Marginalising over $\beta$ suggests that the pulsar is a near-orthogonal rotator and provides the first polarization-independent estimate of the scale factor ($\mathbb{A}$) that relates the pulsar beam opening angle ($\rho$) to its rotational period ($P$) as $\rho = \mathbb{A}P^{-0.5}$ : we find it to be $> 6 \rm~deg~s^{0.5}$ at 1.4 GHz with 99\% confidence. If all pulsars emit from opposite poles of a dipolar magnetic field with comparable brightness, we might expect to see evidence of an interpulse arising in PSR J1141$-$6545, unless the emission is patchy.Comment: Accepted for publication in Astrophysical Journal Letter

Half-life of the electron-capture decay of 97Ru: Precision measurement shows no temperature dependence

We have measured the half-life of the electron-capture (ec) decay of 97Ru in a metallic environment, both at low temperature (19K), and also at room temperature. We find the half-lives at both temperatures to be the same within 0.1%. This demonstrates that a recent claim that the ec decay half-life for 7Be changes by $0.9% +/- 0.2% under similar circumstances certainly cannot be generalized to other ec decays. Our results for the half-life of 97Ru, 2.8370(14)d at room temperature and 2.8382(14)d at 19K, are consistent with, but much more precise than, previous room-temperature measurements. In addition, we have also measured the half-lives of the beta-emitters 103Ru and 105Rh at both temperatures, and found them also to be unchanged.Comment: 6 pages, 6 figure