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

Abstract

High frequency quasi-periodic oscillations (QPOs) from weakly magnetized neutron stars display rapid frequency variability and high coherence with quality factors up to at least 200 at frequencies around 850 Hz. Their parameters have been estimated so far from standard min(chi2) fitting techniques, after combining a large number of Power Density Spectra (PDS), as to have the powers normally distributed. Accounting for the statistical properties of PDS, we apply a maximum likelihood method to derive the QPO parameters in the non Gaussian regime. The method presented is general, easy to implement and can be applied to fitting individual PDS, several PDS simultaneously or their average, and is obviously not specific to the analysis of kHz QPO data. It applies to the analysis of any PDS optimized in frequency resolution and for low frequency variability or PDS containing features whose parameters vary on short timescales, as is the case for kHz QPOs. It is equivalent to the standard chi^2 minimization fitting when the number of PDS fitted is large. The accuracy, reliability and superiority of the method is demonstrated with simulations of synthetic PDS. We show that the maximum likelihood estimates of the QPO parameters are asymptotically unbiased, and have negligible bias when the QPO is reasonably well detected. By contrast, we show that the standard min(chi2) fitting method gives biased parameters with larger uncertainties. The maximum likelihood fitting method is applied to a subset of archival Rossi X-ray Timing Explorer (RXTE) data of the neutron star X-ray binary 4U1608-522. We show that the kHz QPO parameters can be measured on 8 second timescales and that the time evolution of the frequency is consistent with a random walk. This enables us to estimate the intrinsic quality factor of the QPO to be around 260, whereas previous analysis indicated a maximum value around 200 (abridged).

24 pages, 8 figures, Accepted for publication in the Astrophysical Journal

References in corpus (2)

• Error estimation in astronomy: A guide
• A crash course on data analysis in asteroseismology

Cited by in corpus (49)

• Generating artificial light curves: Revisited and updated
• The ultraluminous X-ray sources NGC 1313 X-1 and X-2: a broadband study with NuSTAR and XMM-Newton
• No Time for Dead Time: Timing analysis of bright black hole binaries with NuSTAR
• A ~3.8 hour Periodicity from an Ultrasoft Active Galactic Nucleus Candidate
• Waves in the lower solar atmosphere: the dawn of next-generation solar telescopes
• Gamma-ray quasi-periodicities of blazars. A cautious approach
• NuSTAR Observations of the State Transition of Millisecond Pulsar Binary PSR J1023+0038
• Gamma-ray and Optical Oscillations of 0716+714, MRK 421, and BL Lac
• Quasi-periodicities of BL Lac Objects
• Quasi-Periodic Oscillations and broadband variability in short magnetar bursts
• Phase-resolved spectroscopy of a quasi-periodic oscillation in the black hole X-ray binary GRS 1915+105 with NICER and NuSTAR
• Individual power density spectra of Swift gamma-ray bursts
• Accretion in Strong Field Gravity with eXTP
• Looking at Blazar Light Curve Periodicities with Gaussian Processes
• An X-ray periodicity of $\sim$1.8 hours in a narrow-line Seyfert 1 galaxy Mrk 766
• Soft lags in neutron star kHz Quasi Periodic Oscillations: evidence for reverberation?
• Highly Significant Detection of X-Ray Polarization from the Brightest Accreting Neutron Star Sco X-1
• The 2021 outburst of the recurrent nova RS Ophiuchi observed in X-rays by the Neil Gehrels Swift Observatory: a comparative study
• Two transient X-ray Quasi-Periodic Oscillations separated by an intermediate state in 1H 0707-495
• Random time series in Astronomy
• No Time for Dead Time: Use the Fourier Amplitude Differences to Normalize Dead-time-affected Periodograms
• Timescale of twin-peak quasi-periodic oscillations and mass of accreting neutron stars
• Damping of Propagating Kink Waves in the Solar Corona
• Power density spectra of modes of orbital motion in strongly curved spacetime: obtaining the observable signal
• X-ray timing analysis of the quasar PG 1211+143
• A deep X-ray view of the bare AGN Ark 120. III. X-ray timing analysis and multiwavelength variability
• A Radio Quasi-periodic Oscillation of 176 day in the Radio-loud Narrow-line Seyfert 1 Galaxy J0849+5108
• Quasi-periodic dipping in the ultraluminous X-ray source, NGC 247 ULX-1
• Searching for Quasi-Periodic Modulations in $\gamma$-ray Active Galactic Nuclei
• Searching for quasi-periodic oscillations in astrophysical transients using Gaussian processes
• The spectral-timing properties of upper and lower kHz QPOs
• Pitfalls of periodograms: The non-stationarity bias in the analysis of quasi-periodic oscillations
• A Systematic Spectral-Timing Analysis of Kilohertz Quasi-Periodic Oscillations in the Rossi X-ray Timing Explorer Archive
• Detection of Very Low-Frequency Quasi-Periodic Oscillations in the 2015 Outburst of V404 Cygni
• The time derivative of the kilohertz quasi-periodic oscillations in 4U 1636-53
• X-Ray Variability and the Inner Region in Active Galactic Nuclei
• Fitting FFT-derived Spectra: Theory, Tool, and Application to Solar Radio Spike Decomposition
• On the area of accretion curtains from fast aperiodic time variability of the intermediate polar EX Hya
• AstroSat observations of GRO J2058+42 during the 2019 outburst
• On Detecting Transient Phenomena
• Probing X-ray burst -- accretion disk interaction in low mass X-ray binaries through kilohertz quasiperiodic oscillations
• X-ray variability analysis of a large series of XMM-Newton + NuSTAR observations of NGC 3227
• The nature of the broadband X-ray variability in the dwarf Seyfert galaxy NGC 4395
• A double-period oscillation signal in millimeter emission of the radio galaxy NGC 1275
• An 85-s X-ray quasi-periodicity after a stellar tidal disruption by a candidate intermediate-mass black hole
• Fourier Domain
• A NuSTAR study of quasi-periodic oscillations from the ultraluminous X-ray sources in M82
• Searching for unresolved massive black hole pairs through AGN photometric variability
• Lense-Thirring precession of neutron-star accretion flows: Relativistic versus classical precession