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

Optimal Estimation of Several Linear Parameters in the Presence of Lorentzian Thermal Noise

In a previous article we developed an approach to the optimal (minimum variance, unbiased) statistical estimation technique for the equilibrium displacement of a damped, harmonic oscillator in the presence of thermal noise. Here, we expand that work to include the optimal estimation of several linear parameters from a continuous time series. We show that working in the basis of the thermal driving force both simplifies the calculations and provides additional insight to why various approximate (not optimal) estimation techniques perform as they do. To illustrate this point, we compare the variance in the optimal estimator that we derive for thermal noise with those of two approximate methods which, like the optimal estimator, suppress the contribution to the variance that would come from the irrelevant, resonant motion of the oscillator. We discuss how these methods fare when the dominant noise process is either white displacement noise or noise with power spectral density that is inversely proportional to the frequency ($1/f$ noise). We also construct, in the basis of the driving force, an estimator that performs well for a mixture of white noise and thermal noise. To find the optimal multi-parameter estimators for thermal noise, we derive and illustrate a generalization of traditional matrix methods for parameter estimation that can accommodate continuous data. We discuss how this approach may help refine the design of experiments as they allow an exact, quantitative comparison of the precision of estimated parameters under various data acquisition and data analysis strategies.Comment: 16 pages, 10 figures. Accepted for publication in Classical and Quantum Gravit

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

Pulse-Timing Studies of X Ray Pulsars

The pulse-timing projects supported by NASA Grant NAG8-695 were motivated in large part by our long-standing interest in the physics of rotating neutron stars and particularly the variations in rotation due to internal and external fluctuating torques. For accretion-powered pulsars, observed as compact galactic X-ray sources, our work has been motivated by questions regarding the physics of matter accretion, mass transfer, and mass loss in these X-ray binary systems. For rotation-powered pulsars using X-ray, optical, and radio observations, we have examined the internal structure of neutron stars and mechanisms for secular spin-down. These issues are still central to the continuing process of understanding the complex behavior of these fascinating systems. The work supported by this grant is based mainly on Ginga observations of three pulsating X-ray sources. We observed two of these sources (Her X-1 and SMC X-1) within the framework of a NASA-ISAS program for U.S.-Japan collaborations to obtain and analyze Ginga observations. In addition, we joined with members of the Ginga team to apply our pulse-timing methods to PSR 0540-69 data obtained as a collateral benefit of the regular monitoring by Ginga of SN 1987A. In addition to these Ginga observations, there exist other relevant data on all three of these sources. The direction of our investigations has been affected by the necessity of including these supporting data in our analyses, and setting up the necessary collaborations has sometimes entailed extra work that was not anticipated in our proposals. Indeed, we have often taken the initiative in establishing these joint projects

Spin period evolution of GX 1+4

We aim both to complement the existing data on the spin history of the peculiar accreting X-ray pulsar GX 1+4 with more past and current data from BeppoSAX, INTEGRAL, and Fermi and to interpret the evolution in the framework of accretion theory. We used source light curves obtained from BeppoSAX/WFC and INTEGRAL/ISGRI to derive pulse periods using an epoch-folding analysis. Fermi/GBM data were analyzed by fitting a constant plus a Fourier expansion to background-subtracted rates, and maximizing the Y2 statistic. We completed the sample with hard X-ray light curves from Swift/BAT. The data were checked for correlations between flux and changes of the pulsar spin on different timescales. The spin-down of the pulsar continues with a constant change in frequency, i.e., an apparently accelerating change in the period. Over the past three decades, the pulse period has increased by about ~50%. Short-term fluctuations on top of this long-term trend do show anti-correlation with the source flux. Possible explanations of the observed long-term frequency and its dependence on flux are discussed.Comment: Accepted for publication in A&