Title: Long-term evolution of BH-ULX candidates: An `unusual' $L_{\rm disc}$-$T_{\rm col}$ correlation associated with spectral states Show Chinese title

Title: 黑洞极亮X射线源候选体的长期演化：与光谱状态相关的“不寻常”的$L_{\rm disc}$-$T_{\rm col}$相关性

Abstract: We present the long-term spectral evolution of eight black hole ultra-luminous X-ray sources (BH-ULXs), namely NGC1313 X-1, NGC5408 X-1, NGC6946 X-1, IC342 X-1, NGC55 ULX1, NGC4395 ULX1, NGC5204 X-1 and NGC4190 ULX1 using {\it XMM-Newton} monitoring data spanning over a decade or more. An in-depth spectral modeling with thermal Comptonization ({\it nthComp}) and standard disc ({\it diskbb}) components reveals NGC5204 X-1, IC342 X-1, NGC4190 ULX1 and NGC1313 X-1 exhibiting harder spectral characteristics with dominant effect of Comptonization ($F_{nth}>F_{disc}$, $\Gamma_{nth}\lesssim2$). However, NGC6946 X-1 and NGC55 ULX1 remain in a disc-dominated state ($F_{disc}\sim2F_{nth}$, $\Gamma_{nth}\gtrsim2$), while NGC5408 X-1 shows intermediate spectral characteristics. The spectral analyses indicate an anti-correlation between disc luminosity ($L_{disc}$) and temperature ($T_{col}$) for all sources except NGC5204 X-1. These anti-correlations follow a relation $L_{disc}\propto T_{col}^{\alpha}$ with steeper exponents of $\alpha=-6.01\pm0.25$ (NGC55 ULX1), $-8.93\pm0.11$ (NGC6946 X-1), and $-10.31\pm0.10$ (NGC5408 X-1) for sources with softer or intermediate spectral characteristics. For harder sources, NGC1313 X-1 and IC342 X-1, the combined results provide $\alpha=-3.58\pm0.04$. However, for NGC5204 X-1, a positive correlation is found, yielding $\alpha=1.4\pm0.1$, 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 $L_{disc}-T_{col}$ correlations, along with the overall spectro-temporal properties of BH-ULXs, seems to be governed by disc-corona-wind driven accretion processes at various inclinations. Finally, we report a QPO-like feature ($\sim20$ mHz) with $rms\%\sim6.6$, Q-factor $\sim6.7$ and significant $2.8\sigma$ in NGC55 ULX1. Show Chinese abstract

Abstract: 我们展示了八个黑洞超亮X射线源（BH-ULXs）的长期光谱演化，即NGC1313 X-1、NGC5408 X-1、NGC6946 X-1、IC342 X-1、NGC55 ULX1、NGC4395 ULX1、NGC5204 X-1和NGC4190 ULX1，使用了跨越十年或更长时间的{\it XMM-Newton}监测数据。通过热康普顿化（{\it 第n次组合}）和标准盘（{\it 盘状黑体}）组分的深入光谱建模，发现NGC5204 X-1、IC342 X-1、NGC4190 ULX1和NGC1313 X-1表现出更硬的光谱特征，康普顿化占主导作用（$F_{nth}>F_{disc}$，$\Gamma_{nth}\lesssim2$）。然而，NGC6946 X-1和NGC55 ULX1仍处于盘主导状态（$F_{disc}\sim2F_{nth}$，$\Gamma_{nth}\gtrsim2$），而NGC5408 X-1表现出中间光谱特征。 光谱分析表明，除了NGC5204 X-1以外的所有源都存在盘亮度（$L_{disc}$）和温度（$T_{col}$）之间的反相关性。这些反相关性遵循关系$L_{disc}\propto T_{col}^{\alpha}$，对于具有较软或中等光谱特性的源，其指数更陡，分别为$\alpha=-6.01\pm0.25$（NGC55 ULX1）、$-8.93\pm0.11$（NGC6946 X-1）和$-10.31\pm0.10$（NGC5408 X-1）。对于较硬的源，NGC1313 X-1和IC342 X-1，综合结果提供$\alpha=-3.58\pm0.04$。 然而，对于NGC5204 X-1，发现存在正相关，得到$\alpha=1.4\pm0.1$，表明发射机制与从“标准盘”到“瘦盘”情景的转变有关。 这些发现表明，观测到的$L_{disc}-T_{col}$相关性，以及BH-ULXs的整体光谱-时变特性，似乎由在不同倾角下的盘-冕-风驱动的吸积过程所支配。 最后，我们在NGC55 ULX1中报告了一个类似QPO的特征（$\sim20$ mHz），具有$rms\%\sim6.6$，Q值为$\sim6.7$，并且有显著的$2.8\sigma$。