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.

This paper describes the design and implementation of stingray, a library in Python built to perform time series analysis and related tasks on astronomical light curves. Its core functionality comprises a range of Fourier analysis techniques commonly used in spectral-timing analysis, as well as extensions for analyzing pulsar data, simulating data sets, and statistical modeling. Its modular build allows for easy extensions and incorporation of its methods into data analysis workflows and pipelines. We aim for the library to be a platform for the implementation of future spectral-timing techniques. Here, we describe the overall vision and framework, core functionality, extensions, and connections to high-level command-line and graphical interfaces. The code is Corresponding author: Daniela Huppenkothen dhuppenk@uw.edu arXiv:1901.07681v2 [astro-ph.IM] 9 Aug 2019 2 HUPPENKOTHEN ET AL.well-tested, with a test coverage of currently 95%, and is accompanied by extensive API documentation and a set of step-by-step tutorials.

We fitted the 3 − 180-keV spectrum of all the observations of the neutron-star lowmass X-ray binary 4U 1636−53 taken with the Rossi X-ray Timing Explorer using a model that includes a thermal Comptonisation component. We found that in the lowhard state the power-law index of this component, Γ, gradually increases as the source moves in the colour-colour diagram. When the source undergoes a transition from the hard to the soft state Γ drops abruptly; once the source is in the soft state Γ increases again and then decreases gradually as the source spectrum softens further. The changes in Γ, together with changes of the electron temperature, reflect changes of the optical depth in the corona. The lower kilohertz quasi-periodic oscillation (kHz QPO) in this source appears only in observations during the transition from the hard to the soft state, when the optical depth of the corona is high and changes depends strongly upon the position of the source in the colour-colour diagram. Our results are consistent with a scenario in which the lower kHz QPO reflects a global mode in the system that results from the resonance between, the disc and/or the neutron-star surface, and the Comptonising corona.

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 twodimensional 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 ∼ 12 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 ∼ 760 Hz, while the amplitude of the upper kHz QPO decreases with frequency, with a local maximum at around ∼ 770 Hz, and is consistent with becoming zero at the same QPO frequency, ∼ 1400 Hz, in all energy bands, thus constraining the neutron-star mass at M N S ≤ 1.6M , 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.

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.