Modeling the Upper kHz QPOs of 4U 1728-34 with X-Ray Reverberation

Abstract

While kilohertz quasi-periodic oscillations (kHz QPOs) have been well studied for decades since their initial discovery, the cause of these signals remains unknown, as no model has been able to accurately predict all of their spectral and timing properties. Separately, X-ray reverberation lags have been detected in AGN and stellar-mass black hole binaries, and reverberation may be expected to occur in neutron star systems as well, producing lags of the same amplitude as the lags measured of the kHz QPOs. Furthermore, the detection of a relativistically reflected Fe K line in the time-averaged spectra of many neutron star systems provides an additional motivation for testing reverberation. While it has been shown that the lag-energy properties of the lower kHz QPOs are unlikely to be produced by X-ray reverberation, the upper kHz QPOs have not yet been explored. We therefore model the upper kHz QPO lag-energy spectra using relativistic ray-tracing functions and apply them to archival RXTE data on 4U 1728−34 where upper kHz QPOs have been detected. By modeling the time-averaged spectra in which upper kHz QPOs had been significantly detected, we determine the reflected flux fraction across all energies and produce a model for the lag-energy spectra from X-ray reverberation. We explore the dependence of the modeled lag properties on several different types of reflection models, but are unable to successfully reproduce the measured lags of 4U 1728−34. We conclude that reverberation alone does not explain the measured time lags detected in upper kHz QPOs.

Kilohertz quasi-periodic oscillations in neutron-star X-ray binaries: Flattening of the lag spectrum with increasing luminosity

“…Observations show the opposite trend, suggesting that reverberation is not the mechanism producing the soft lags of the lower kHz QPOs in 4U 1608−52; by extension, the same must be true for the lower kHz QPOs in the other sources in this paper. It is worth mentioning that Coughenour et al (2020) performed a similar study of the lags of the upper kHz QPO in the source 4U 1728−34, finding that reverberation alone cannot be responsible for those lags either.…”

High-Frequency Variability in Neutron-Star Low-Mass X-ray Binaries

“…This led to the conclusion [30] that the lags of the lower kHz QPO in 4U 1608−52 cannot be due only to reverberation. Subsequently, the same idea was tested on the upper kHz QPO in 4U 1728−34 [36]; the result of the fits of a reverberation model to the lags of this QPO is shown in Fig. 6.30b.…”

“…Contrary to those expectations, inverse Compton scattering could work, and produce soft lags, if there is feedback from the corona to the disc ( [92], see also [91]). In this scenario, soft photons from the disc are up-scattered in the corona; part of those up-scattered photons go to the observer, and produce the power-law like component in the 6 in [30]) and the upper kHz QPO in 4U 1728−34 (bottom (b); originally published as Figure 6 in [36]) as a function of energy, with the best-fitting reverberation model spectrum, but a fraction of those corona photons will illuminate back the disc, increasing the disc temperature [55]. If the photon flux that is originally produced in the disc is modulated (e.g., at the QPO frequency), the flux that returns to the disc after being scattered in the corona will also be modulated and, as those photons reheat the disc, the disc temperature will vary at the frequency of that modulation.…”

“…Fig.6 30. Time lags of the lower kHz QPO in 4U 1608−52 (top (a); originally published as Figure6in[30]) and the upper kHz QPO in 4U 1728−34 (bottom (b); originally published as Figure6in[36]) as a function of energy, with the best-fitting reverberation model…”

High-frequency variability in neutron-star low-mass X-ray binaries

“…This led to the conclusion (30) that the lags of the lower kHz QPO in 4U 1608-52 cannot be due only to reverberation. Subsequently, the same idea was tested on the upper kHz QPO in 4U 1728-34 (36); the result of the fits of a reverberation model to the lags of this QPO is shown in Figure 30b. From this Figure it is apparent that, while the lags of the QPO first decrease with energy up to E∼5 − 6 keV, and increase again above that energy, the model predicts that the lags should follow the opposite behaviour.…”