Magneto-elastic oscillations of neutron stars: exploring different magnetic field configurations

We study magneto-elastic oscillations of highly magnetized neutron stars (magnetars) which have been proposed as an explanation for the quasi-periodic oscillations (QPOs) appearing in the decaying tail of the giant flares of soft gamma-ray repeaters (SGRs). We extend previous studies by investigating various magnetic field configurations, computing the Alfv\'en spectrum in each case and performing magneto-elastic simulations for a selected number of models. By identifying the observed frequencies of 28 Hz (SGR 1900+14) and 30 Hz (SGR 1806-20) with the fundamental Alfv\'en QPOs, we estimate the required surface magnetic field strength. For the magnetic field configurations investigated (dipole-like poloidal, mixed toroidal-poloidal with a dipole-like poloidal component and a toroidal field confined to the region of field lines closing inside the star, and for poloidal fields with an additional quadrupole-like component) the estimated dipole spin-down magnetic fields are between 8x10^14 G and 4x10^15 G, in broad agreement with spin-down estimates for the SGR sources producing giant flares. A number of these models exhibit a rich Alfv\'en continuum revealing new turning points which can produce QPOs. This allows one to explain most of the observed QPO frequencies as associated with magneto-elastic QPOs. In particular, we construct a possible configuration with two turning points in the spectrum which can explain all observed QPOs of SGR 1900+14. Finally, we find that magnetic field configurations which are entirely confined in the crust (if the core is assumed to be a type I superconductor) are not favoured, due to difficulties in explaining the lowest observed QPO frequencies (f<30 Hz).Comment: 21 pages, 16 figures, 6 tables, matched to version accepted by MNRAS with extended comparison/discussion to previous wor

The Closest Look at 1H0707-495: X-ray Reverberation Lags with 1.3 Ms of Data

Reverberation lags in AGN were first discovered in the NLS1 galaxy, 1H0707-495. We present a follow-up analysis using 1.3 Ms of data, which allows for the closest ever look at the reverberation signature of this remarkable source. We confirm previous findings of a hard lag of ~100 seconds at frequencies v ~ [0.5 - 4] e-4 Hz, and a soft lag of ~30 seconds at higher frequencies, v ~ [0.6 - 3] e-3 Hz. These two frequency domains clearly show different energy dependences in their lag spectra. We also find evidence for a signature from the broad Fe K line in the high frequency lag spectrum. We use Monte Carlo simulations to show how the lag and coherence measurements respond to the addition of Poisson noise and to dilution by other components. With our better understanding of these effects on the lag, we show that the lag-energy spectra can be modelled with a scenario in which low frequency hard lags are produced by a compact corona responding to accretion rate fluctuations propagating through an optically thick accretion disc, and the high frequency soft lags are produced by short light-travel delay associated with reflection of coronal power-law photons off the disc.Comment: 11 pages, 10 figures. Accepted for publication in MNRA

On The Evolution of Magnetic White Dwarfs

We present the first radiation magnetohydrodynamics simulations of the atmosphere of white dwarf stars. We demonstrate that convective energy transfer is seriously impeded by magnetic fields when the plasma-beta parameter, the thermal to magnetic pressure ratio, becomes smaller than unity. The critical field strength that inhibits convection in the photosphere of white dwarfs is in the range B = 1-50 kG, which is much smaller than the typical 1-1000 MG field strengths observed in magnetic white dwarfs, implying that these objects have radiative atmospheres. We have then employed evolutionary models to study the cooling process of high-field magnetic white dwarfs, where convection is entirely suppressed during the full evolution (B > 10 MG). We find that the inhibition of convection has no effect on cooling rates until the effective temperature (Teff) reaches a value of around 5500 K. In this regime, the standard convective sequences start to deviate from the ones without convection owing to the convective coupling between the outer layers and the degenerate reservoir of thermal energy. Since no magnetic white dwarfs are currently known at the low temperatures where this coupling significantly changes the evolution, effects of magnetism on cooling rates are not expected to be observed. This result contrasts with a recent suggestion that magnetic white dwarfs with Teff < 10,000 K cool significantly slower than non-magnetic degenerates.Comment: 11 pages, 12 figures, accepted for publication in the Astrophysical Journa

A Probabilistic Analysis of Kademlia Networks

Kademlia is currently the most widely used searching algorithm in P2P (peer-to-peer) networks. This work studies an essential question about Kademlia from a mathematical perspective: how long does it take to locate a node in the network? To answer it, we introduce a random graph K and study how many steps are needed to locate a given vertex in K using Kademlia's algorithm, which we call the routing time. Two slightly different versions of K are studied. In the first one, vertices of K are labelled with fixed IDs. In the second one, vertices are assumed to have randomly selected IDs. In both cases, we show that the routing time is about c*log(n), where n is the number of nodes in the network and c is an explicitly described constant.Comment: ISAAC 201

BE Ursae Majoris: A detached binary with a unique reprocessing spectrum

New infrared photometry, optical and UV spectrophotometry, and a photographic ephemeris are presented for the detached binary BE UMa. Results show the primary to be a DO white dwarf with an effective temperature of 80,000 + or - 15,000 K and a mass of 0.6 + or - 0.1 solar masses. No evidence is found for variability of the primary. The main sequence secondary star is shown to be of early M spectral type, with a formal range of M1 to M5 being possible. A reflection effect in reprocessed line and continuum radiation is produced by EUV radiation from the primary incident on the secondary atmosphere. It is suggested that the temperature of the reprocessed component of the secondary's atmosphere is in the 5000 to 8500 K range, and that emission lines of decreasing ionization form deeper in the irradiated envelope. Relatively narrow He II and high excitation metal lines are formed from recombination and continuum fluorescence processes

The Mass of the Black Hole in LMC X-3

We analyze a large set of new and archival photometric and spectroscopic observations of LMC X-3 to arrive at a self-consistent dynamical model for the system. Using echelle spectra obtained with the MIKE instrument on the 6.5m Magellan Clay telescope and the UVES instrument on the second 8.2m Very Large Telescope we find a velocity semiamplitude for the secondary star of $K_2=241.1\pm 6.2$ km s$^{-1}$, where the uncertainty includes an estimate of the systematic error caused by X-ray heating. Using the spectra, we also find a projected rotational velocity of $V_{\rm rot}\sin i=118.5\pm 6.6$ km s$^{-1}$. From an analysis of archival $B$ and $V$ light curves as well as new $B$ and $V$ light curves from the SMARTS 1.3m telescope, we find an inclination of $i=69.84\pm 0.37^{\circ}$ for models that do not include X-ray heating and an inclination of $i=69.24\pm 0.72^{\circ}$ for models that incorporate X-ray heating. Adopting the latter inclination measurement, we find masses of $3.63\pm 0.57\,M_{\odot}$ and $6.98\pm 0.56\,M_{\odot}$ for the companion star and the black hole, respectively. We briefly compare our results with earlier work and discuss some of their implications.Comment: 31 pages, 15 figures, substantial revisions, ApJ, accepte

The Spin of the Black Hole Microquasar XTE J1550-564 via the Continuum-Fitting and Fe-Line Methods

We measure the spin of XTE J1550-564 in two ways: by modelling the thermal continuum spectrum of the accretion disc, and independently by modeling the broad red wing of the reflection fluorescence Fe-K line. We find that the spin measurements conducted independently using both leading methods are in agreement with one another. For the continuum-fitting analysis, we use a data sample consisting of several dozen RXTE spectra, and for the Fe-K analysis, we use a pair of ASCA spectra from a single epoch. Our spin estimate for the black hole primary using the continuum-fitting method is -0.11 < a* < 0.71 (90 per cent confidence), with a most likely spin of a* = 0.34. In obtaining this result, we have thoroughly explored the dependence of the spin value on a wide range of model-dependent systematic errors and observational errors; our precision is limited by uncertainties in the distance and orbital inclination of the system. For the Fe-line method, our estimate of spin is a* = 0.55(+0.15,-0.22). Combining these results, we conclude that the spin of this black hole is moderate, a* = 0.49(+0.13,-0.20), which suggests that the jet of this microquasar is powered largely by its accretion disc rather than by the spin energy of the black hole.Comment: 19 pages, 15 figures, submitted to MNRAS, updated abstrac

The Theory of the Interleaving Distance on Multidimensional Persistence Modules

In 2009, Chazal et al. introduced $\epsilon$-interleavings of persistence modules. $\epsilon$-interleavings induce a pseudometric $d_I$ on (isomorphism classes of) persistence modules, the interleaving distance. The definitions of $\epsilon$-interleavings and $d_I$ generalize readily to multidimensional persistence modules. In this paper, we develop the theory of multidimensional interleavings, with a view towards applications to topological data analysis. We present four main results. First, we show that on 1-D persistence modules, $d_I$ is equal to the bottleneck distance $d_B$. This result, which first appeared in an earlier preprint of this paper, has since appeared in several other places, and is now known as the isometry theorem. Second, we present a characterization of the $\epsilon$-interleaving relation on multidimensional persistence modules. This expresses transparently the sense in which two $\epsilon$-interleaved modules are algebraically similar. Third, using this characterization, we show that when we define our persistence modules over a prime field, $d_I$ satisfies a universality property. This universality result is the central result of the paper. It says that $d_I$ satisfies a stability property generalizing one which $d_B$ is known to satisfy, and that in addition, if $d$ is any other pseudometric on multidimensional persistence modules satisfying the same stability property, then $d\leq d_I$. We also show that a variant of this universality result holds for $d_B$, over arbitrary fields. Finally, we show that $d_I$ restricts to a metric on isomorphism classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in Foundations of Computational Mathematics. 36 page