Analysis and interpretation of X-ray pulsars

By careful measurements of the fluctuations in pulsar pulse periods on time scales of days and longer, researchers determined that these fluctuations are caused by changes in the rotation rate of the stellar crust apparently arising from matter accretion. The study of these fluctuations is a particularly promising way to determine the properties of accreting pulsars, because stellar rotation is relatively simple in comparison to much other X-ray source physics and can be investigated in detail. Rotation rates can be determined precisely

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

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

The Timing Noise of PSR 0823+26, PSR 1706-16, PSR 1749-28, PSR 2021+51 and The Anomalous Braking Indices

We have investigated the stability of the pulse frequency second derivatives ($\ddot \nu$) of PSR 0823+26, PSR 1706-16, PSR 1749-28, PSR 2021+51 which show significant quadratic trends in their pulse frequency histories in order to determine whether the observed second derivatives are secular or they arise as part of noise processes. We have used TOA data extending to more than three decades which are the longest time spans ever taken into account in pulse timing analyses. We investigated the stability of pulse frequency second derivative in the framework of low resolution noise power spectra (Deeter 1984) estimated from the residuals of pulse frequency and TOA data. We have found that the $\ddot \nu$ terms of these sources arise from the red torque noise in the fluctuations of pulse frequency derivatives which may originate from the external torques from the magnetosphere of pulsar

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

A Systems Analysis Experiential Case Study: Repeatable Real World Problem Solving

Many business schools today are emphasizing experiential education, particularly in undergraduate instruction, where students often have had limited exposure to business settings. While a business problem can be presented in the form of a written case study, real world projects for external clients are increasingly being incorporated into the classroom. However finding suitable clients and projects for multiple student teams each semester can be difficult

A Comprehensive Study on RXTE & INTEGRAL Observations of the X-ray Pulsar 4U 1907+09

We analyse \emph{INTEGRAL} (between 2005 October and 2007 November) and \emph{RXTE} (between 2007 June and 2011 March) observations of the accretion powered pulsar 4U 1907+09. From \emph{INTEGRAL} IBIS-ISGRI and \emph{RXTE}-PCA observations, we update pulse period history of the source. We construct power spectrum density of pulse frequencies and find that fluctuations in the pulse frequency derivatives are consistent with the random walk model with a noise strength of $1.27\times10^{-21}$ Hz s$^{-2}$. From the X-ray spectral analysis of \emph{RXTE}-PCA observations, we find that Hydrogen column density is variable over the binary orbit, tending to increase just after the periastron passage. We also show that the X-ray spectrum gets hardened with decreasing X-ray flux. We discuss pulse-to-pulse variability of the source near dipping ingress and egress. We find that the source more likely undergoes in dipping states after apastron until periastron when the accretion from clumpy wind might dominate so that occasional transitions to temporary propeller state might occur.Comment: 19 pages, 8 figures, accepted for publication in MNRA