Long-term evolution of BH-ULX candidates: an ‘unusual’ <i>L</i>disc–<i>T</i>col correlation associated with spectral states

ABSTRACT We present the long-term spectral evolution of eight black hole ultraluminous X-ray sources (BH-ULXs), namely NGC 1313 X-1, NGC 5408 X-1, NGC 6946 X-1, IC 342 X-1, NGC 55 ULX-1, NGC 4395 ULX-1, NGC 5204 X-1, and NGC 4190 ULX-1 using XMM–Newton monitoring data spanning over a decade or more. An in-depth spectral modelling with thermal Comptonization (nthComp) and standard disc (diskbb) components reveals NGC 5204 X-1, IC 342 X-1, NGC 4190 ULX-1, and NGC 1313 X-1 exhibiting harder spectral characteristics with dominant effect of Comptonization ($F_{\rm nth}&amp;gt;F_{\rm disc}$, $\Gamma _{\rm nth}\lesssim 2$). However, NGC 6946 X-1 and NGC 55 ULX-1 remain in a disc-dominated state ($F_{\rm disc}\sim 2F_{\rm nth}$, $\Gamma _{\rm nth}\gtrsim 2$), while NGC 5408 X-1 shows intermediate spectral characteristics. The spectral analyses indicate an anticorrelation between disc luminosity ($L_{\rm disc}$) and temperature ($T_{\rm col}$) for all sources except NGC 5204 X-1. These anticorrelations follow a relation $L_{\rm disc} \propto T_{\rm col}^{\alpha }$ with steeper exponents of $\alpha =-6.01\pm 0.25$ (NGC 55 ULX-1), $\alpha = -8.93\pm 0.11$ (NGC 6946 X-1), and $\alpha = -10.31\pm 0.10$ (NGC 5408 X-1) for sources with softer or intermediate spectral characteristics. For harder sources, NGC 1313 X-1 and IC 342 X-1, the combined results provide $\alpha =-3.58\pm 0.04$. However, for NGC 5204 X-1, a positive correlation is found, yielding $\alpha =1.4\pm 0.1$, suggesting that the emission mechanism is associated with the transition from the ‘standard disc’ to the ‘slim disc’ scenario. These findings suggest that the observed $L_{\rm disc} \!-\! T_{\rm col}$ correlations, along with the overall spectrotemporal properties of BH-ULXs, seem to be governed by disc–corona–wind-driven accretion processes at various inclinations. Finally, we report a quasi-periodic oscillation like feature (${\sim} 20$ mHz) with rms percentage $\sim 6.6$, Q-factor $\sim 6.7$, and significant $2.8\sigma$ in NGC 55 ULX-1.