Spectral-timing analysis of the kilohertz quasi-periodic oscillations and constraints on the mass of the neutron star in 4U 1636-536 using AstroSat observations

TL;DR

This study presents a broadband spectral–timing analysis of 4U 1636-536 with AstroSat, combining SXT+LAXPC data to model 0.7–25 keV emission as a combination of thermal Comptonization, boundary-layer blackbody, and a relativistic reflection component with a disk. Timing results reveal LFQPOs near ~30 Hz and twin kHz QPOs whose frequency correlations are interpreted with the Relativistic Precession Model, yielding NS masses around $M\approx 2.37\pm0.02\,M_\odot$ (for $\nu_s\approx300$ Hz) and $M\approx2.50\pm0.04\,M_\odot$ (for $\nu_s=581$ Hz), implying a large NS mass in this system. The energy-dependent lag and rms analyses support a mainly Comptonization-driven origin for the kHz QPOs, with soft lags (~$200$–$300\;\mu$s) and increasing rms (~$15$-$18\%$) toward higher energies, which can be explained by a compact corona of order ~$5$ km with a variable heating rate and modest feedback. Overall, the work links spectral-state evolution to timing properties and provides a self-consistent framework to constrain NS mass and inner-disk/coronal geometry, while acknowledging the model-dependence and limitations inherent to QPO interpretations.

Abstract

Kilohertz quasi-periodic oscillations (kHz QPOs) are believed to originate from the orbital timescales of the inner accretion flow, reflecting the dynamics of the innermost disk regions under strong gravitational forces. Despite numerous radiative and geometric models proposed so far, a comprehensive explanation of the observed properties of these variability components remains elusive. This study systematically examines kHz QPOs, their variability, and their connection to spectral properties in $4U 1636-536$ using AstroSat data. Our analysis tracks the source transition from hard to soft states in the hardness-intensity diagram. Broad spectral analysis (0.7-25 keV) using SXT and LAXPC data indicates a spectrum shaped by reflection from a thermal corona, with contributions from boundary layer emission and a soft disk component. We find significant changes in optical depth, blackbody temperature, and inner disk temperature that likely drive state transitions. Power density spectra reveal three variability types: a low frequency QPO (LFQPOs) (~30 Hz), and two simultaneous kHz QPOs. The LFQPOs and the upper kHz QPOs appear more prominently in soft spectral states. The presence of LFQPOs and twin kHz QPOs in soft spectral states enable us to estimate the neutron star mass at (2.37 $\pm$ 0.02) $M_\odot$ using the relativistic precession model (RPM). Additionally, time-lag and root mean square (rms) analysis provide insights into the size of the corona and the radiative origin of these variability components.

Figures (7)

• Figure 1: Hardness vs Intensity diagram using LAXPC PCU 20 to see the evolution of 4U 1636$-$536. The bin time is 1024 sec.
• Figure 2: The $\Delta \chi$ of the spectral fitting using only Const * Tbabs * (Thcomp * bbodyrad). Excess around 6-10 keV can be seen out from this figure which needs to be taken care of.
• Figure 3: The spectra of Observation 1 (Hard) and Observation 2 (Soft). The blue and violet colour represents the SXT and LAXPC for Obs 1. Similarly, the orange and lightcoral shade represents the SXT and LAXPC for Obs 2.
• Figure 4: PDS of 4U 1636$-$536 from Obs$-$1 to Obs$-$4 with in 3$-$20 keV range employing all the PCUs. Obs 2 and Obs 3 show a clear presence of twin QPOs where as Obs 1 has a signature of a lower kHz QPO, and Obs 4 has a signature of an upper kHz QPO.
• Figure 5: The dynamic power density spectrum of 4U 1636$-$536 in Obs 2, captured between 49,000 and 52,500 seconds, is shown. The right-hand axis of the figure represents the Leahy-normalised power.