Building X-ray pulsar timing model without the use of radio parameters

This paper develops a timing solution for the X-ray pulsar timing model without the use of the initial radio model parameters. First, we address the problem of phase ambiguities for the pre-fit residuals in the construction of pulsar timing model. To improve the estimation accuracy of the pulse time of arrival (TOA), we have deduced the general form of test statistics in Fourier transform, and discussed their estimation performances. Meanwhile, a fast maximum likelihood (FML) technique is presented to estimate the pulse TOA, which outperforms cross correlation (CC) estimator and exhibits a performance comparable with maximum likelihood (ML) estimator in spite of a much less reduced computational complexity. Depending on the strategy of the difference minimum of pre-fit residuals, we present an effective forced phase-connected technique to achieve initial model parameters. Then, we use the observations with the Rossi X-Ray Timing Explorer (RXTE) and X-ray pulsar navigation-I (XPNAV-1) satellites for experimental studies, and discuss main differences for the root mean square (RMS) residuals calculated with the X-ray and radio ephemerides. Finally, a chi-square value (CSV) of pulse profiles is presented as a complementary indicator to the RMS residuals for evaluating the model parameters. The results show that the proposed timing solution is valid and effective, and the obtained model parameters can be a reasonable alternative to the radio ephemeris.