标题： 关于在建模超快外流时特殊相对论效应的重要性 显示英文标题

标题： On the importance of special relativistic effects in modelling ultra-fast outflows

摘要： 外流现象在各种天体物理源中被观测到。值得注意的是，在紫外线和X射线波段中，超快速（$v\geq 0.1c$）外流经常出现在活动星系核（AGNs）中。根据它们的能量和质量外流率（分别用$\dot{E}_{out}, \dot{M}_{out}$表示），这种外流可能在宇宙时间尺度上通过调节AGN-宿主星系的共同演化过程发挥关键作用。因此，提供风属性的准确估计至关重要。在这里，我们专注于相对论速度的物质与辐射源相比时，光与物质相互作用中的特殊相对论效应。我们的目标是评估这些效应对观测到的外流性质的影响，并在现有的光谱建模程序中实施相对论修正。我们定义了一个简单的程序，用于在辐射传输代码中纳入相对论效应。按照这个程序，我们运行了一系列模拟，以探索这些效应对不同（$v$）和外流柱密度的影响。通常认为，观测到的光学深度可以作为风的（$N_H$）的一个代理，而不管其速度如何。然而，我们的模拟表明，具有特定柱密度（$N_H$）的外流的观测光学深度会随着风速接近相对论值迅速减小。这反过来又意味着，在从光学深度估计（$N_H$）时，即使是对于中等速度（例如$v \geq 0.05c$），也需要包括一个与速度相关的修正。 这一校正线性传播到导出的$\dot{M}_{out}, \dot{E}_{out}$。 作为这些效应的一个例子，我们计算了文献中提取的$\sim 30$组超快外流的相对论校正值$\dot{M}_{out}$和$\dot{E}_{out}$，并发现校正因子在观测到的外流速度范围内为$20-120 \%$。 显示英文摘要

摘要： Outflows are observed in a variety of astrophysical sources. Remarkably, ultra-fast ($v\geq 0.1c$), outflows in the UV and X-ray bands are often seen in AGNs. Depending on their energy and mass outflow rate, respectively $\dot{E}_{out}, \dot{M}_{out}$, such outflows may play a key role in regulating the AGN-host galaxy co-evolution process through cosmic time. It is therefore crucial to provide accurate estimates of the wind properties. Here, we concentrate on special relativistic effects concerning the interaction of light with matter moving at relativistic speed relatively to the source of radiation. Our aim is to assess the impact of these effects on the observed properties of the outflows and implement a relativistic correction in the existing spectral modelling routines. We define a simple procedure to incorporate relativistic effects in radiative transfer codes. Following this procedure, we run a series of simulations to explore the impact of these effects on the simulated spectra, for different $v$ and column densities of the outflow. The observed optical depth is usually considered a proxy for the wind $N_H$, independently on its velocity. However, our simulations show that the observed optical depth of an outflow with a given column density $N_H$ decreases rapidly as the velocity of the wind approaches relativistic values. This, in turn, implies that when estimating $N_H$ from the optical depth, it is necessary to include a velocity-dependent correction, already for moderate velocities (e.g. $v \geq 0.05c$). This correction linearly propagates to the derived $\dot{M}_{out}, \dot{E}_{out}$. As an example of these effects, we calculate the relativistically corrected values of $\dot{M}_{out}$ and $\dot{E}_{out}$ for a sample of $\sim 30$ Ultra-Fast Outflows taken from the literature, and find correction factors of $20-120 \%$ within the observed range of outflowing velocities.