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Register a new userThe time derivative of the kilohertz quasi-periodic oscillations in 4U 1636-53
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Andrea Sanna
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We analysed all archival RXTE observations of the neutron-star low-mass X-ray binary 4U 1636-53 up to May 2010. In 528 out of 1280 observations we detected kilohertz quasi-periodic oscillations (kHz QPOs), with ~ 65% of these detections corresponding to the so-called lower kHz QPO. Using this QPO we measured, for the first time, the rate at which the QPO frequency changes as a function of QPO frequency. For this we used the spread of the QPO frequency over groups of 10 consecutive measurements, sampling timescales between 320 and 1600 s, and the time derivative of the QPO frequency over timescales of 32 to 160 s. We found that: (i) Both the QPO-frequency spread and the QPO time derivative decrease by a factor ~ 3 as the QPO frequency increases. (ii) The average value of the QPO time derivative decreases by a factor of ~ 2 as the timescale over which the derivative is measured increases from less than 64 s to 160 s. (iii) The relation between the absolute value of the QPO time derivative and the QPO frequency is consistent with being the same both for the positive and negative QPO-frequency derivative. We show that, if either the lower or the upper kHz QPO reflects the Keplerian frequency at the inner edge of the accretion disc, these results support a scenario in which the inner part of the accretion disc is truncated at a radius that is set by the combined effect of viscosity and radiation drag.
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We present for the neutron-star low-mass X-ray binary 4U 1636$-$53, and for the first time for any source of kilohertz quasi-periodic oscillations (kHz QPOs), the two-dimensional behaviour of the fractional rms amplitude of the kHz QPOs in the parameter space defined by QPO frequency and photon energy. We find that the rms amplitude of the lower kHz QPO increases with energy up to $sim12$ keV and then decreases at higher energies, while the rms amplitude of the upper kHz QPO either continues increasing or levels off at high energies. The rms amplitude of the lower kHz QPO increases and then decreases with frequency, peaking at $sim 760$ Hz, while the amplitude of the upper kHz QPO decreases with frequency, with a local maximum at around $sim 770$ Hz, and is consistent with becoming zero at the same QPO frequency, $sim1400$ Hz, in all energy bands, thus constraining the neutron-star mass at $M_{NS} leq 1.6 M_{odot}$, under the assumption that this QPO reflects the Keplerian frequency at the inner edge of the accretion disc. We show that the slope of the rms energy spectrum is connected to the changing properties of the kHz QPOs in different energy bands as its frequencies change. Finally, we discuss a possible mechanism responsible for the radiative properties of the kHz QPOs and, based on a model in which the QPO arises from oscillations in a Comptonising cloud of hot electrons, we show that the properties of the kHz QPOs can constrain the thermodynamic properties of the inner accretion flow.
(abridged) We studied the energy and frequency dependence of the Fourier time lags and intrinsic coherence of the kHz QPOs in the NS LMXBs 4U 1608-52 and 4U 1636-53 using RXTE data. In both sources we confirmed energy-dependent soft lags of 10-100 mu s for the lower kHz QPO. We also found that the time lags of the upper kHz QPO are independent of energy and inconsistent with the soft lags of the lower kHz QPO. The intrinsic coherence of the lower kHz QPO remains constant at 0.6 from 5 to 12 keV, and then drops to zero, while for the upper kHz QPO the intrinsic coherence is consistent with zero across the full energy range. The intrinsic coherence of the upper kHz QPO is consistent with zero over the full frequency range of the QPO, except in 4U 1636-53 at ~780 Hz where it increases to 0.13. In 4U 1636-53, for the lower kHz QPO the 4-12 keV photons lag the 12-20 keV ones by 25 mu s in the QPO frequency range 500-850 Hz, with the lags decreasing to 15 mu s at higher frequencies. In 4U 1608-52 the soft lags of the lower kHz QPO remain constant at 40 mu s. In 4U 1636-53, for the upper kHz QPO the 12-20 keV photons lag the 4-12 keV ones by 11 +/- 3 mu s, independent of QPO frequency; we found consistent results for the time lags of the upper kHz QPO in 4U 1608-52. The intrinsic coherence of the lower kHz QPO increases from ~0-0.4 at 600 Hz to 1 and 0.6 at 800 Hz in 4U 1636-53 and 4U 1608-52, respectively. In 4U 1636-53 it decreases to 0.5 at 920 Hz, while in 4U 1608-52 we do not have data above 800 Hz. We discuss our results in the context of scenarios in which the soft lags are either due to reflection off the accretion disc or up-/down-scattering in a hot medium close to the neutron star. We finally explore the connection between, on one hand the time lags and the intrinsic coherence of the kHz QPOs, and on the other the QPOs amplitude and quality factor in these two sources.
Inverse Compton scattering dominates the high energy part of the spectra of neutron star (NS) low mass X-ray binaries (LMXBs). It has been proposed that inverse Compton scattering also drives the radiative properties of kilohertz quasi periodic oscillations (kHz QPOs). In this work, we construct a model that predicts the energy dependence of the rms amplitude and time lag of the kHz QPOs. Using this model, we fit the rms amplitude and time lag energy spectra of the lower kHz QPO in the NS LMXB 4U 1636-53 over 11 frequency intervals of the QPO and report three important findings: (i) A medium that extends 1-8 km above the NS surface is required to fit the data; this medium can be sustained by the balance between gravity and radiation pressure, without forcing any equilibrium condition. (ii) We predict a time delay between the oscillating NS temperature, due to feedback, and the oscillating electron temperature of the medium which, with the help of phase resolved spectroscopy, can be used as a probe of the geometry and the feedback mechanism. (iii) We show that the observed variability as a function of QPO frequency is mainly driven by the oscillating electron temperature of the medium. This provides strong evidence that the Comptonising medium in LMXBs significantly affects, if not completely drives, the radiative properties of the lower kHz QPOs regardless of the nature of the dynamical mechanism that produces the QPO frequencies.
Both the broad iron (Fe) line and the frequency of the kilohertz quasi-periodic oscillations (kHz QPOs) in neutron star low-mass X-ray binaries (LMXBs) can potentially provide independent measures of the inner radius of the accretion disc. We use XMM-Newton and simultaneous Rossi X-ray Timing Explorer observations of the LMXB 4U 1636-53 to test this hypothesis. We study the properties of the Fe-K emission line as a function of the spectral state of the source and the frequency of the kHz QPOs. We find that the inner radius of the accretion disc deduced from the frequency of the upper kHz QPO varies as a function of the position of the source in the colour-colour diagram, in accordance with previous work and with the standard scenario of accretion disc geometry. On the contrary, the inner disc radius deduced from the profile of the Fe line is not correlated with the spectral state of the source. The values of the inner radius inferred from kHz QPOs and Fe lines, in four observations, do not lead to a consistent value of the neutron star mass, regardless of the model used to fit the Fe line. Our results suggest that either the kHz QPO or the standard relativistic Fe line interpretation does not apply for this system. Furthermore, the simultaneous detection of kHz QPOs and broad Fe lines is difficult to reconcile with models in which the broadening of the Fe line is due to the reprocessing of photons in an outflowing wind.
We studied the harmonics of the millihertz quasi-periodic oscillations (mHz QPOs) in the neutron-star low-mass X-ray binary 4U 1636-53 using the Rossi X-ray Timing Explorer observations. We detected the harmonics of the mHz QPOs in 73 data intervals, with most of them in the transitional spectra state. We found that the ratio between the rms amplitude of the harmonic and that of the fundamental remains constant in a wide range of the fundamental frequency. More importantly, we studied, for the first time, the rms amplitude of the harmonics vs. energy in 4U 1636-53 in the 2-5 keV range. We found that the rms amplitude of both the harmonic and the fundamental shows a decreasing trend as the energy increases, which is different from the behaviors reported in QPOs in certain black hole systems. Furthermore, our results suggest that not all observations with mHz QPOs have the harmonic component, although the reason behind this is still unclear.
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