Relaxation of spins due to a magnetic field gradient, revisited; Identity of the Redfield and Torrey theories

There is an extensive literature on magnetic gradient induced spin relaxation. Cates, Schaefer and Happer (CSH) in a seminal paper, have solved the problem in the regime where diffusion theory (the Torrey equation is applicable using an expansion of the density matrix in diffusion equation eigenfunctions and angular momentum tensors. McGregor has solved the problem in the same regime using a slightly more general formulation using Redfield theory formulated in terms of the auto-correlation function of the fluctuating field seen by the spins and calculating the correlation functions using the diffusion theory Green's function. The results of both calculations were shown to agree for a special case. In the present work we show that the eigenfunction expansion of the Torrey equation yields the expansion of the Green's function for the diffusion equation thus showing the identity of this approach with that of Redfield theory. The general solution can also be obtained directly from the Torrey equation for the density matrix. Thus the physical content of the Redfield and Torrey approaches are identical. We then introduce a more general expression for the position autocorrelation function of particles moving in a closed cell, extending the range of applicability of the theory.Comment: 2 figure

Bounds on Compactness for LMXB Neutron Stars from X-ray Burst Oscillations

We have modelled X-ray burst oscillations observed with the Rossi X-ray Timing Explorer (RXTE) from two low mass X-ray binaries (LMXB): 4U 1636-53 with a frequency of 580 Hz, and 4U 1728-34 at a frequency of 363 Hz. We have computed least squares fits to the oscillations observed during the rising phase of bursts using a model which includes emission from either a single circular hot spot or a pair of circular antipodal hot spots on the surface of a neutron star. We model the spreading of the thermonuclear hot spots by assuming that the hot spot angular size grows linearly with time. We calculate the flux as a function of rotational phase from the hot spots and take into account photon deflection in the relativistic gravitational field of the neutron star assuming the exterior spacetime is the Schwarzschild metric. We find acceptable fits with our model and we use these to place constraints on the compactness of the neutron stars in these sources. For 4U 1636-53, in which detection of a 290 Hz sub-harmonic supports the two spot model, we find that the compactness (i.e., mass/radius ratio) is constrained to be M/R < 0.163 at 90% confidence (G = c = 1). This requires a relatively stiff equation of state (EOS) for the stellar interior. For example, if the neutron star has a mass of 1.4 Msun then its radius must be > 12.8 km. Fits using a single hot spot model are not as highly constraining. We discuss the implications of our findings for recent efforts to calculate the EOS of dense nucleon matter and the structure of neutron stars.Comment: 27 pages, 6 figures, AASTeX. Revised and expanded version. Resubmitted to Astrophysical Journa

Models of the hard X-ray spectrum of AM Herculis and implications for the accretion rate

Phenomenological fits to the hard X-ray spectrum of AM Herculis left unexplained the high equivalent width (0.8 + or - 0.1 keV) of Fe K alpha emission. A purely thermal origin implies a much steeper spectrum than was observed. With Monte Carlo calculations, scattering and fluorescent line production in a cold or partially ionized accretion column of hard X-rays emitted at the base were investigated. The strength of the iron emission and the flat spectral continuum can be explained by the effects of fluorescence and absorption within the accretion column and the surface of the white dwarf on a thermal X-ray spectrum. Thomson optical depths across the column in the range 0.2 to 0.7 are acceptable. The accretion rate and gravitational power can be deduced from the optical depth across the column, if the column size is known, and, together with the observed hard X-ray and polarized light luminosities, imply a lower limit for the luminosity in the UV to soft X-ray range, for which the observations give model-dependent values. Estimates of the column size differ by a factor of 40. Small spot sizes and low luminosities would be consistent with the soft component being the expected reprocessed bremsstrahlung and cyclotron radiation, although the constraint of matching the spectrum confines one to solutions with fluxes exceeding 20% the Eddington limits

Discovery of the Orbit of the Transient X ray Pulsar SAX J2103.5+4545

Using X-ray data from the Rossi X-Ray Timing Explorer (RXTE), we carried out pulse timing analysis of the transient X-ray pulsar SAX J2103.5+4545. An outburst was detected by All Sky Monitor (ASM) October 25 1999 and reached a peak X-ray brightness of 27 mCrab October 28. Between November 19 and December 27, the RXTE/PCA carried out pointed observations which provided us with pulse arrival times. These yield an eccentric orbit (e= 0.4 \pm 0.2) with an orbital period of 12.68 \pm 0.25 days and light travel time across the projected semimajor axis of 72 \pm 6 sec. The pulse period was measured to be 358.62171 \pm 0.00088 s and the spin-up rate (2.50 \pm 0.15) \times 10^{-13} Hz s^{-1}. The ASM data for the February to September 1997 outburst in which BeppoSAX discovered SAX J2103.5+4545 (Hulleman, in't Zand and Heise 1998) are modulated at time scales close to the orbital period. Folded light curves of the 1997 ASM data and the 1999 PCA data are similar and show that the intensity increases at periastron passages.Comment: To appear in The Astrophysical Journal (Letters

Rapid X-ray variability in the Seyfert galaxy NGC 6814

The HEAO-1 A-2 high time resolution X-ray observations of the X-ray emitting Seyfert I Galaxy NGC 6814 are reported. In sharp distinction with a sample of over 30 active galactic nuclei this object showed strong X-ray variability on timescales less than 3 hours. The mean flux on a timescale of 90 minutes varied by a factor of approximately 2.5 corresponding to Delta L sub x being approximately 1 x 10 to the 43rd power ergs/sec. An autocorrelation analysis shows a characteristic time for variability of 100 (+60 or -25) seconds. There is no indication of spectral variability with an upper limit on a change in the power law spectral index of the absolute value of Delta gamma .37, for a factor two change in intensity. The constraints of such rapid variability on a wide variety of X-ray source mechanisms are considered

The MXB1916-053/4U1915-05: Burst properties and constraints on a 50 minute binary secondary

Results are presented from OSO-8 and HEAO-1 A2 observations of 34 bursts from the X-ray burster MXB1916-053/4U1915-05 recently discovered to show a 50 minute binary period. While 11 burst previously reported all had similar light curves, 22 observed two years later show a factor of 3 range of peak fluxes and decay times between 3 and 20 s. Recurrence times between successive bursts vary between 3 and 6 hours. A ratio of steady flux to average burst flux of equiv 120 is developed. A burst observed with the HEAO-1 A2 experiment showed an initial temperature rise to a peak black body temperature of equiv 3 keV followed by the cooling typical of type I bursts. The burst was unusual in that the apparent projected size of a blackbody source increased by a factor of 3 during the cooling phase

The X-ray absorption spectrum of 4U1700-37 and its implications for the stellar wind of the companion HD153919

The first high resolution non-dispersive 2-60 KeV X-ray spectra of 4U1700-37 is presented. The continuum is typical of that found from X-ray pulsars; that is a flat power law between 2 and 10 keV and, beyond 10 keV, an exponential decay of characteristic energy varying between 10 and 20 keV. No X-ray pulsations were detected between 160 ms and 6 min with an amplitude greater than approximately 2%. The absorption measured at binary phases approximately 0.72 is comparable to that expected from the stellar wind of the primary. The gravitational capture of material in the wind is found to be more than enough to power the X-ray source. The increase in the average absorption after phi o approximately 0.5 is confirmed. The minimum level of adsorption is a factor of 2 or 3 lower than that reported by previous observers, which may be related to a factor of approximately 10 decline in the average X-ray luminosity over the same interval. Short term approximately 50% variations in adsorption are seen for the first time which appear to be loosely correlated with approximately 10 min flickering activity in the X-ray flux. These most likely originate from inhomogeneities in the stellar wind of the primary

The CHANDRA HETGS X-ray Grating Spectrum of Eta Car

Eta Car may be the most massive and luminous star in the Galaxy and is suspected to be a massive, colliding wind binary system. The CHANDRA X-ray observatory has obtained a calibrated, high-resolution X-ray spectrum of the star uncontaminated by the nearby extended soft X-ray emisssion. Our 89 ksec CHANDRA observation with the High Energy Transmission Grating Spectrometer (HETGS) shows that the hot gas near the star is non-isothermal. The temperature distribution may represent the emission on either side of the colliding wind bow shock, effectively ``resolving'' the shock. If so, the pre-shock wind velocities are ~ 700 and ~ 1800 km/s in our analysis, and these velocities may be interpreted as the terminal velocities of the winds from Eta Car and from the hidden companion star. The forbidden-to-intercombination (f/i) line ratios for the He-like ions of S, Si and Fe are large, indicating that the line forming region lies far from the stellar photosphere. The iron fluorescent line at 1.93 Angstrom, first detected by ASCA, is clearly resolved from the thermal iron line in the CHANDRA grating spectrum. The Fe fluorescent line is weaker in our CHANDRA observation than in any of the ASCA spectra. The CHANDRA observation also provides an uninterrupted high-time resolution lightcurve of the stellar X-ray emission from Eta Car and suggests that there was no significant, coherent variability during the CHANDRA observation. The Eta Car CHANDRA grating spectrum is unlike recently published X-ray grating spectra of single massive stars in significant ways and is generally consistent with colliding wind emission in a massive binary.Comment: revised after comments from referee and includes a new variability analysis, taking into account the effects of CCD pileu

Milli-second Oscillations in the Persistent and Bursting Flux of Aql X-1 During an Outburst

The Rossi X-Ray Timing Explorer observed the soft X-Ray transient Aql X-1 during its outburst in February and March 1997. We report the discovery of quasi-periodic oscillations (QPOs) in its persistent flux with frequencies in the range of 740 to 830 Hz, Q-value of over 100, and a fractional RMS amplitude of (6.8 +- 0.6)%, and nearly coherent oscillations (NCOs) during a Type-I burst with a frequency of 549 Hz. The frequency of the QPOs in the persistent flux is correlated with the mass accretion rate on time scale of hours, but not on time scale of days. This is most likely the manifestation in a single source of the kHz QPO puzzle observed among many sources, i.e., on the one hand, individual sources show a correlation between the QPO frequency and the inferred mass accretion rate, on the other hand, the dozen or so sources with luminosities spanning two decades have essentially the same QPO frequencies. We propose that this multi-valued QPO frequency and mass accretion rate correlation indicates the existence of many similar regimes of the accretion disk. These regimes, with a very similar energy spectrum and QPO frequency, are distinguished from each other by the mass accretion rate or the total X-ray flux. The NCOs during the burst can be made almost perfectly coherent by taking into account a large frequency derivative. This strongly suggests that this frequency is related to the neutron star spin frequency. The large frequency derivative is attributable to the expansion or contraction of the neutron star photosphere during the burst.Comment: 6 pages, LaTex (aas2pp4), Accepted for publication in ApJ Let