In this letter, we develop a model formalism to study the structure of a relativistic, viscous, optically thin, advective accretion flow around a rotating black hole in presence of radiative coolings. We use this model to examine the physical parameters of the Ultra-luminous X-ray sources (ULXs), namely mass (MBH), spin (ak) and accretion rate (${\dot{m}}$), respectively. While doing this, we adopt a recently developed effective potential to mimic the spacetime geometry around the rotating black holes. We solve the governing equations to obtain the shock induced global accretion solutions in terms of ${\dot{m}}$ and viscosity parameter (α). Using shock properties, we compute the Quasi-periodic Oscillation (QPO) frequency (νQPO) of the post-shock matter (equivalently post-shock corona, hereafter PSC) pragmatically, when the shock front exhibits Quasi-periodic variations. We also calculate the luminosity of the entire disc for these shock solutions. Employing our results, we find that the present formalism is potentially promising to account the observed νQPO and bolometric luminosity (Lbol) of a well studied ULX source IC 342 X-1. Our findings further imply that the central source of IC 342 X-1 seems to be rapidly rotating and accretes matter at super-Eddington accretion rate provided IC 342 X-1 harbors a massive stellar mass black hole (MBH < 100 M⊙) as indicated by the previous studies.
We present a comprehensive temporal and spectral analysis of the ‘softer’ variability classes (i.e. θ, β, δ, ρ, κ, ω and γ) of the source GRS 1915+105 observed by AstroSat during the 2016−2021 campaign. Wide-band (3−60 keV) timing studies reveal the detection of high-frequency quasi-periodic oscillations (HFQPOs) with frequencies of 68.14−72.32 Hz, significance of 2.75−11σ and rms amplitude of 1.48–2.66 per cent in δ, κ, ω and γ variability classes. Energy-dependent power spectra show that HFQPOs are detected only in the 6−25 keV energy band and rms amplitude is found to increase (1–8 per cent) with energy. The dynamical power spectra of the κ and ω classes demonstrate that HFQPOs seem to be correlated with high count rates. We observe that wide-band (0.7−50 keV) energy spectra can be described by the thermal Comptonization component (nthComp) with a photon index (Γnth) of 1.83−2.89 along with an additional steep (ΓPL ∼ 3) power-law component. The electron temperature (kTe) of 1.82−3.66 keV and optical depth (τ) of 2−14 indicate the presence of a cool and optically thick corona. In addition, nthComp components, 1.97 ≲ Γnth ≲ 2.44 and 1.06 × 10−8 ≲ Fnth (erg cm−2 s−1) ≲ 4.46 × 10−8, are found to dominate in the presence of HFQPOs. Overall, these findings infer that HFQPOs are possibly the result of the modulation of the ‘Comptonizing corona’. Further, we find that the bolometric luminosity (0.3−100 keV) of the source lies within the sub-Eddington (3–34 per cent LEdd) regime. Finally, we discuss and compare the obtained results in the context of existing models on HFQPOs.
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