Analyzing X-ray variability by State Space Models

In recent years, autoregressive models have had a profound impact on the description of astronomical time series as the observation of a stochastic process. These methods have advantages compared with common Fourier techniques concerning their inherent stationarity and physical background. If autoregressive models are used, however, it has to be taken into account that real data always contain observational noise often obscuring the intrinsic time series of the object. We apply the technique of a Linear State Space Model which explicitly models the noise of astronomical data and allows to estimate the hidden autoregressive process. As an example, we have analysed a sample of Active Galactic Nuclei (AGN) observed with EXOSAT and found evidence for a relationship between the relaxation timescale and the spectral hardness.Comment: 4 pages, Latex, uses Kluwer Style file crckapb.cls To appear in Proc. of Astronomical Time Series, Tel Aviv, 199

Quantifying Rapid Variability in Accreting Compact Objects

I discuss some practical aspects of the analysis of millisecond time variability X-ray data obtained from accreting neutron stars and black holes. First I give an account of the statistical methods that are at present commonly applied in this field. These are mostly based on Fourier techniques. To a large extent these methods work well: they give astronomers the answers they need. Then I discuss a number of statistical questions that astronomers don't really know how to solve properly and that statisticians may have ideas about. These questions have to do with the highest and the lowest frequency ranges accessible in the Fourier analysis: how do you determine the shortest time scale present in the variability, how do you measure steep low-frequency noise. The point is stressed that in order for any method that resolves these issues to become popular, it is necessary to retain the capabilities the current methods already have in quantifying the complex, concurrent variability processes characteristic of accreting neutron stars and black holes.Comment: To be published in the Proceedings of "Statistical Challenges in Modern Astronomy II", University Park PA, USA, June 199

Updating the orbital ephemeris of Her X-1; rate of decay and eccentricity of the orbit

We present an update of the orbital ephemeris of the binary X-ray pulsar Her X-1 and determine an improved value for the rate of orbital decay. In addition, we report the first measurement of the orbital eccentricity. We have analyzed pulse timing data of Her X-1 from X-ray observations by RXTE (Rossi X-Ray Timing Explorer) and INTEGRAL over the period 1996-2007. Accurate pulse arrival times were determined from solar system bary-centered photon arrival times by generating pulse profiles averaged over appropriately short integration times. Applying pulse phase connection techniques, it was possible to determine sufficiently accurate local ephemeris data for seven observation periods distributed over 12 years. Combining the new local T90 values with historical values from the literature we update the orbital ephemeris of Her X-1 to T90 = MJD 46359.871940(6) and Porb = 1.700167590(2) d and measure a continuous change of the orbital period of dPorb/dt = -(4.85 +/- 0.13) x 10-11 s/s. For the first time, a value for the eccentricity of the orbit of Her X-1 is measured to be e = (4.2 +/- 0.8) x 10-4.Comment: 7 pages, 4 figures, accepted by A&A on 30.03.200

Discovery of orbital decay in SMC X-1

The results are reported of three observations of the binary X ray pulsar SMC X-1 with the Ginga satellite. Timing analyses of the 0.71 s X ray pulsations yield Doppler delay curves which, in turn, provide the most accurate determination of the SMC X-1 orbital parameters available to date. The orbital phase of the 3.9 day orbit is determined in May 1987, Aug. 1988, and Aug. 1988 with accuracies of 11, 1, and 3.5 s, respectively. These phases are combined with two previous determinations of the orbital phase to yield the rate of change in the orbital period: P sub orb/P sub orb = (-3.34 + or - 0.023) x 10(exp -6)/yr. An interpretation of this measurement and the known decay rate for the orbit of Cen X-3 is made in the context of tidal evolution. Finally, a discussion is presented of the relation among the stellar evolution, orbital decay, and neutron star spinup time scales for the SMC X-1 system

Correlation between X-ray flux and rotational acceleration in Vela X-1

The results of a search for correlations between X-ray flux and angular acceleration for the accreting binary pulsar Vela X-1 are presented. Results are based on data obtained with the Hakucho satellite during the interval 1982 to 1984. In undertaking this correlation analysis, it was necessary to modify the usual statistical method to deal with conditions imposed by generally unavoidable satellite observing constraints, most notably a mismatch in sampling between the two variables. The results are suggestive of a correlation between flux and the absolute value of the angular acceleration, at a significance level of 96 percent. The implications of the methods and results for future observations and analysis are discussed

Study of the cyclotron feature in MXB 0656-072

We have monitored a type II outburst of the Be/X-ray binary MXB 0656−072 in a series of pointed RXTE observations during October through December 2003. The source spectrum shows a cyclotron resonance scattering feature at 32.8 +0.5 −0.4 keV, corresponding to a magnetic field strength of 3.67 +0.06 −0.04 × 10 12 G and is stable through the outburst and over the pulsar spin phase. The pulsar, with an average pulse period of 160.4 ± 0.4s,shows a spin-up of 0.45 s over the duration of the outburst. From optical data, the source distance is estimated to be 3.9 ± 0.1 kpc and this is used to estimate the X-ray luminosity and a theoretical prediction of the pulsar spin-up during the outburst

Two ~35 day clocks in Her X-1: evidence for neutron star free precession

We present evidence for the existence of two ~35 day clocks in the Her X-1/HZ Her binary system. ~35 day modulations are observed 1) in the Turn-On cycles with two on- and two off-states, and 2) in the changing shape of the pulse profiles which re-appears regularly. The two ways of counting the 35 day cycles are generally in synchronization. This synchronization did apparently break down temporarily during the long Anomalous Low (AL3) which Her X-1 experienced in 1999/2000, in the sense that there must have been one extra Turn-On cycle. Our working hypothesis is that there are two clocks in the system, both with a period of about ~35 days: precession of the accretion disk (the less stable "Turn-On clock") and free precession of the neutron star (the more stable "Pulse profile clock"). We suggest that free precession of the neutron star is the master clock, and that the precession of the accretion disk is basically synchronized to that of the neutron star through a feed-back mechanism in the binary system. However, the Turn-On clock can slip against its master when the accretion disk has a very low inclination, as is observed to be the case during AL3. We take the apparent correlation between the histories of the Turn-Ons, of the Anomalous Lows and of the pulse period evolution, with a 5 yr quasi-periodicity, as evidence for strong physical interaction and feed-back between the major components in the system. We speculate that the 5 yr (10 yr) period is either due to a corresponding activity cycle of HZ Her or a natural ringing period of the physical system of coupled components. The question whether free precession really exists in neutron stars is of great importance for the understanding of matter with supra-nuclear density.Comment: 6 pages, 5 figures, accepted for publication by A&

Warped accretion discs and the long periods in X-ray binaries

Precessing accretion discs have long been suggested as explanations for the long periods observed in a variety of X-ray binaries, most notably Her X-1/HZ Her. We show that an instability of the disc's response to the radiation reaction force from the illumination by the central source can cause the disc to tilt out of the orbital plane and precess in something like the required manner. The rate of precession and disc tilt obtained for realistic values of system parameters compare favourably with the known body of data on X-ray binaries with long periods. We explore other possible types of behaviour than steadily precessing discs that might be observable in systems with somewhat different parameters. At high luminosities, the inner disc tilts through more than 90 degrees, i.e. it rotates counter to the usual direction, which may explain the torque reversals in systems such as 4U 1626-67.Comment: submitted to MNRAS, 17-Dec-97, revised submit 2-Nov-98. 15 pages LaTeX, 11 postscript figures in-tex