Relation between the properties of the kilohertz quasi-periodic oscillations and spectral parameters in 4U 1636−53

Abstract

We investigate the relation between the parameters of the energy spectrum and the frequency and amplitude of the kilohertz quasi-periodic oscillations (kHz QPOs) in the low-mass X-ray binary 4U 1636−53. We fit the 3 − 180-keV spectrum of this source with a model that includes a thermal Comptonisation component. We show that the frequencies of both kHz QPOs follow the same relation as a function of the parameters of this spectral component, except for a systematic frequency shift, whereas the rms fractional amplitude of each QPO follows a different relation with respect to those same parameters. This implies that, while the dynamical mechanism that sets the frequencies of the QPO can be the same for both kHz QPOs, the radiative mechanisms that set the amplitudes of the lower and the upper kHz QPO are likely different. We discuss the implications of these results to the modelling of the kHz QPOs and the possibility that the lower kHz QPO reflects a resonance between the Comptonising medium and the photons from the accretion disc and/or the neutron star surface.

The Comptonizing medium of the neutron star in 4U 1636 − 53 through its lower kilohertz quasi-periodic oscillations

“…Gilfanov et al (2003), proposed that the lower kHz QPO originates in a boundary layer close to the NS surface, and it is associated with Comptonisation, and de Avellar et al (2013) proposed that, regardless of the dynamical mechanism that explains the kHz QPO frequencies, the radiative mechanism that governs the timing properties of the lower and upper kHz QPOs should be different. Recently, Ribeiro et al (2017) showed that the frequency dependence of the fractional rms amplitude of the upper kHz QPO, although in general different from that of the lower kHz QPO, exhibits the same behaviour as that of the lower kHz QPO around certain QPO frequencies. The latter finding indicates that when the lower and upper kHz QPOs are (separately) observed within a certain QPO frequency range, their variability could be caused by the same radiative mechanism.…”

“…For the cold-seed case model, Γ increases from around 1.5 at 570 Hz to around 2.2 at 860 Hz and then decreased to 1.7 at 920 Hz. In Figure 4 we plot the observed Γ values from Zhang et al (2017) and Ribeiro et al (2017) together with the predicted values of Γ, given the best-fitting values of kTe τT and their MCMC uncertainties. The values of Γ, alongside their propagated uncertainties, are given in Table 2.…”

“…Given the fact that |δḢext| plays the role of a normalization for the modulus of the QPO amplitude, |δnγ |, it is not surprising that |δḢext| is correlated to the energy averaged rms (Figure 7), since the latter may be thought of us approximately the area under the curve of rms as a function of energy. A direct comparison between our bestfitting cold-and hot-seed model and the energy averaged rms and time lags presented in Ribeiro et al (2017) and de Avellar et al (2013) respectively is shown in Figures 7 and 8. We calculated the energy averaged rms in the full energy band (nominally 2-60 keV).…”

“…However, Zhang et al (2017) fitted the spectra of NS 4U 1636 − 53, during the occurence of the kHz QPOs, using the model nthcomp of XSP EC with a disc blackbody seed source and a simple blackbody on top of that. The timing data that are used in this work come from Ribeiro et al (2017) and Ribeiro et al (2019), the first of which used the best-fitting specral parameters of Zhang et al (2017). Thus any comparison between our best-fitting values of kTe, kTs and τT , or their dependence on QPO frequency, to the results of Ribeiro et al (2017) must take into account the different spectral approaches.…”

“…The timing data that are used in this work come from Ribeiro et al (2017) and Ribeiro et al (2019), the first of which used the best-fitting specral parameters of Zhang et al (2017). Thus any comparison between our best-fitting values of kTe, kTs and τT , or their dependence on QPO frequency, to the results of Ribeiro et al (2017) must take into account the different spectral approaches. In fact, it is physically more accurate for our model to use a factor of 1 2 instead of 1 3 in equation (3), because the former is correct when the seed source intensity is a delta-like function at the center of the corona, while the latter is correct when the source intensity is distributed sinusoidally from the center of the corona, as was suggested by Sunyaev & Titarchuk (1980).…”