On problem of polarization tomography, I

The polarization tomography problem consists of recovering a matrix function f from the fundamental matrix of the equation $D\eta/dt=\pi_{\dot\gamma}f\eta$ known for every geodesic $\gamma$ of a given Riemannian metric. Here $\pi_{\dot\gamma}$ is the orthogonal projection onto the hyperplan $\dot\gamma^{\perp}$. The problem arises in optical tomography of slightly anisotropic media. The local uniqueness theorem is proved: a $C^1$- small function f can be recovered from the data uniquely up to a natural obstruction. A partial global result is obtained in the case of the Euclidean metric on $R^3$

Discovery Of A 552 Hz Burst Oscillation In The Low-Mass X-Ray Binary Exo 0748–676

We report the detection of pulsations at 552 Hz in the rising phase of two type-I (thermonuclear) X-ray bursts observed from the accreting neutron star EXO 0748–676 in 2007 January and December, by the Rossi X-ray Timing Explorer. The fractional amplitude was 15% (rms). The dynamic power density spectrum for each burst revealed an increase in frequency of ≈1-2 Hz while the oscillation was present. The frequency drift, the high significance of the detections and the almost identical signal frequencies measured in two bursts separated by 11 months, confirms this signal as a burst oscillation similar to those found in 13 other sources to date. We thus conclude that the spin frequency in EXO 0748 – 676 is within a few Hz of 552 Hz, rather than 45 Hz as was suggested from an earlier signal detection by Villarreal & Strohmayer. Consequently, Doppler broadening must significantly affect spectral features arising from the neutron star surface, so that the narrow absorption features previously reported from an XMM-Newton spectrum could not have arisen there. The origin of both the previously reported 45 Hz oscillation and the X-ray absorption lines is now uncertain

X-ray timing of the accreting millisecond pulsar SAX J1808.4-3658

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2007.Includes bibliographical references (p. 105-114).We present a 7 yr timing study of the 2.5 ms X-ray pulsar SAX J1808.4-3658, an X-ray transient with a recurrence time of =2 yr, using data from the Rossi X-ray Timing Explorer covering 4 transient outbursts (1998-2005). Substantial pulse shape variability, both stochastic and systematic, was observed during each outburst. Analysis of the systematic pulse shape changes suggests that, as an outburst dims, the X-ray "hot spot" on the pulsar surface drifts longitudinally and a second hot spot may appear. The overall pulse shape variability limits the ability to measure spin frequency evolution within a given X-ray outburst (and calls previous zi measurements of this source into question), with typical upper limits of Jil < 2.5 x 10-14 Hz s-1 (2a). However, combining data from all the outbursts shows with high (6 a) significance that the pulsar is undergoing long-term spin down at a rate /i = (-5.6 ± 2.0) x 10-16 Hz s-1, with most of the spin evolution occurring during X-ray quiescence. We discuss the possible contributions of magnetic propeller torques, magnetic dipole radiation, and gravitational radiation to the measured spin down, setting an upper limit of B < 1.5 x 108 G for the pulsar's surface dipole magnetic field and Q < 4.4 x 1036 g cm2 for the mass quadrupole moment. We also measured an orbital period derivative of Porb = (3.5 + 0.2) x 10-12 s s-1 We identify a strong anti-correlation between the fractional amplitude of the harmonic (r2) and the X-ray flux (fx) in the persistent pulsations of four sources: SAX J1808.4-3658, IGR J00291+5934, and XTE J1751-305, XTE J1807-294. These sources exhibit a powerlaw relationship r2 x( fx7 with slopes ranging from y = -0.47 to -0.70. The three other accreting millisecond pulsars that we analyzed, XTE J0929-314, XTE J1814-338, and HETE J1900.1-2455, do not as fully explore a wide range of fluxes, but they too seem to obey a similar relation. We argue that these trends may be evidence of the recession of the accretion disk as the outbursts dim. We examine the energy dependence of the persistent pulsations and thermonuclear burst oscillations from SAX J1808.4-3658.We confirm the soft phase lags previously discovered from this source, and we discover that these phase lags increase as the source flux decays slowly following its peak flux. When the source decay becomes rapid and the outburst enters its flaring tail stage, this relationship reverses, and the phase lags diminish as the flux dims further. This result, along with the pulse profile changes observed at the beginning of the flairing tail stage, suggests an abrupt change in the geometry of the accretion disk and column at this time in the outburst. In contrast, the thermonuclear burst oscillation timing does not show appreciable lags, and the burst oscillation phases and fractional amplitudes appear to be relatively independent of energy.by Jacob M. Hartman.Ph.D

Normal frames and the validity of the equivalence principle

We investigate the validity of the equivalence principle along paths in gravitational theories based on derivations of the tensor algebra over a differentiable manifold. We prove the existence of local bases, called normal, in which the components of the derivations vanish along arbitrary paths. All such bases are explicitly described. The holonomicity of the normal bases is considered. The results obtained are applied to the important case of linear connections and their relationship with the equivalence principle is described. In particular, any gravitational theory based on tensor derivations which obeys the equivalence principle along all paths, must be based on a linear connection.Comment: 14 pages, LaTeX 2e, the package amsfonts is neede

ACCRETION TORQUES AND MOTION OF THE HOT SPOT ON THE ACCRETING MILLISECOND PULSAR XTE J1807-294

We present a coherent timing analysis of the 2003 outburst of the accreting millisecond pulsar (AMXP) XTE J1807-294. We find a 95% confidence interval for the pulse frequency derivative of (+0.7, + 4.7) × 10⁻¹⁴ Hz s⁻¹ and (-0.6, + 3.8) × 10⁻¹⁴ Hz s⁻¹ for the fundamental and second harmonics, respectively. The sinusoidal fractional amplitudes of the pulsations are the highest observed among AMXPs and can reach values of up to 27% (2.5-30 keV). The pulse arrival time residuals of the fundamental frequency follow a linear anti-correlation with the fractional amplitudes that suggests hot spot motion both in longitude and latitude over the surface of the neutron star. An anti-correlation between residuals and X-ray flux suggests an influence of the accretion rate on pulse phase and casts doubts on the interpretation of pulse frequency derivatives in terms of changes of spin rates and torques on the neutron star

General technique of calculating drift velocity and diffusion coefficient in arbitrary periodic systems

We develop a practical method of computing the stationary drift velocity V and the diffusion coefficient D of a particle (or a few particles) in a periodic system with arbitrary transition rates. We solve this problem both in a physically relevant continuous-time approach as well as for models with discrete-time kinetics, which are often used in computer simulations. We show that both approaches yield the same value of the drift, but the difference between the diffusion coefficients obtained in each of them equals V*V/2. Generalization to spaces of arbitrary dimension and several applications of the method are also presented.Comment: 12 pages + 2 figures, RevTeX. Submitted to J. Phys. A: Math. Ge

Normal frames and the validity of the equivalence principle. III. The case along smooth maps with separable points of self-intersection

The equivalence principle is treated on a mathematically rigorous base on sufficiently general subsets of a differentiable manifold. This is carried out using the basis of derivations of the tensor algebra over that manifold. Necessary and/or sufficient conditions of existence, uniqueness, and holonomicity of these bases in which the components of the derivations of the tensor algebra over it vanish on these subsets, are studied. The linear connections are considered in this context. It is shown that the equivalence principle is identically valid at any point, and along any path, in every gravitational theory based on linear connections. On higher dimensional submanifolds it may be valid only in certain exceptional cases.Comment: 15 standard LaTeX 2e (11pt, A4) pages. The package amsfonts is require

Normal frames and the validity of the equivalence principle. I. Cases in a neighborhood and at a point

A treatment in a neighborhood and at a point of the equivalence principle on the basis of derivations of the tensor algebra over a manifold is given. Necessary and sufficient conditions are given for the existence of local bases, called normal frames, in which the components of derivations vanish in a neighborhood or at a point. These frames (bases), if any, are explicitly described and the problem of their holonomicity is considered. In particular, the obtained results concern symmetric as well as nonsymmetric linear connections.Comment: LaTeX2e, 9 pages, to be published in Journal of Physics A: Mathematical and Genera

The Effects of Binary Evolution on the Dynamics of Core Collapse and Neutron-Star Kicks

We systematically examine how the presence in a binary affects the final core structure of a massive star and its consequences for the subsequent supernova explosion. Interactions with a companion star may change the final rate of rotation, the size of the helium core, the strength of carbon burning and the final iron core mass. Stars with initial masses larger than \sim 11\Ms that experiece core collapse will generally have smaller iron cores at the time of the explosion if they lost their envelopes due to a previous binary interaction. Stars below \sim 11\Ms, on the other hand, can end up with larger helium and metal cores if they have a close companion, since the second dredge-up phase which reduces the helium core mass dramatically in single stars does not occur once the hydrogen envelope is lost. We find that the initially more massive stars in binary systems with masses in the range 8 - 11\Ms are likely to undergo an electron-capture supernova, while single stars in the same mass range would end as ONeMg white dwarfs. We suggest that the core collapse in an electron-capture supernova (and possibly in the case of relatively small iron cores) leads to a prompt explosion rather than a delayed neutrino-driven explosion and that this naturally produces neutron stars with low-velocity kicks. This leads to a dichotomous distribution of neutron star kicks, as inferred previously, where neutron stars in relatively close binaries attain low kick velocities. We illustrate the consequences of such a dichotomous kick scenario using binary population synthesis simulations and discuss its implications. This scenario has also important consequences for the minimum initial mass of a massive star that becomes a neutron star. (Abbreviated.)Comment: 8 pages, 3 figures, submitted to ApJ, updated versio