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High frequency quasi-periodic oscillations (QPOs) from weakly magnetizedneutron stars display rapid frequency variability and high coherence withquality factors up to at least 200 at frequencies around 850 Hz. Theirparameters have been estimated so far from standard min(chi2) fittingtechniques, after combining a large number of Power Density Spectra (PDS), asto have the powers normally distributed. Accounting for the statisticalproperties of PDS, we apply a maximum likelihood method to derive the QPOparameters in the non Gaussian regime. The method presented is general, easy toimplement and can be applied to fitting individual PDS, several PDSsimultaneously or their average, and is obviously not specific to the analysisof kHz QPO data. It applies to the analysis of any PDS optimized in frequencyresolution and for low frequency variability or PDS containing features whoseparameters vary on short timescales, as is the case for kHz QPOs. It isequivalent to the standard chi^2 minimization fitting when the number of PDSfitted is large. The accuracy, reliability and superiority of the method isdemonstrated with simulations of synthetic PDS. We show that the maximumlikelihood estimates of the QPO parameters are asymptotically unbiased, andhave negligible bias when the QPO is reasonably well detected. By contrast, weshow that the standard min(chi2) fitting method gives biased parameters withlarger uncertainties. The maximum likelihood fitting method is applied to asubset of archival Rossi X-ray Timing Explorer (RXTE) data of the neutron starX-ray binary 4U1608-522. We show that the kHz QPO parameters can be measured on8 second timescales and that the time evolution of the frequency is consistentwith a random walk. This enables us to estimate the intrinsic quality factor ofthe QPO to be around 260, whereas previous analysis indicated a maximum valuearound 200 (abridged).

astrophysical journal/the astrophysical journal

Maximum likelihood fitting of X-ray power density spectra: Application  to high-frequency quasi-periodic oscillations from the neutron star X-ray  binary 4U1608-522