The amplitude of the kilohertz quasi-periodic oscillations in 4U 1636$-$53 in the frequency-energy space

TL;DR

This study maps the two-dimensional behavior of kHz QPOs in neutron star 4U 1636-53, revealing energy and frequency dependencies that constrain neutron star mass and inner accretion flow properties.

Contribution

First to analyze the 2D rms amplitude behavior of kHz QPOs in energy and frequency space, linking QPO properties to neutron star mass and accretion flow characteristics.

Findings

RMS amplitude of lower kHz QPO peaks at ~12 keV then decreases

Upper kHz QPO amplitude either increases or levels off at high energies

QPO properties constrain neutron star mass to ≤ 1.6 M_sun

Abstract

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.