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arXiv 0904.2804astro-ph.HE
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相对论平面平行流中的可变Eddington因子

Variable Eddington Factor in a Relativistic Plane-Parallel Flow

J. Fukue

摘要:

我们研究爱丁顿因素在光学厚,相对论性流在垂直方向上加速。当气流被辐射加速时,存在速度梯度,也存在密度梯度。同向运动的观察者看到来自封闭表面的辐射,其中从观察者测量的光学深度是1。这样的表面,称为{ \it one-tau photo-oval},在流动方向上是细长的。通常,由光椭圆发射的辐射强度是不均匀的,并且光椭圆表面相对于同向运动的观察者的位置具有相对速度。这两种效应都在共动坐标系中观察到的辐射场中引入了一定程度的各向异性。结果,由共动观察者观察到的辐射场变为{ \it各向异性},并且爱丁顿因子必须偏离通常的1/3值。因此,相对论性爱丁顿因子通常取决于光学深度$τ$和速度梯度$du/dτ$,$u$是四个速度。%在平行平面垂直流的情况下,我们得到了光椭圆的形状,并计算了光学厚区的爱丁顿因子。我们发现,爱丁顿因子$f$是很好的近似$f(τ, \frac{du}{dτ}) = {1/3} \exp (\frac{1}{u} \frac{du}{dτ}) $。这个相对论变量爱丁顿因子可以用于各种相对论辐射驱动流。

英文摘要:

We examine the Eddington factor in an optically thick, relativistic flow accelerating in the vertical direction. % When the gaseous flow is radiatively accelerated and there is a velocity gradient, there also exists a density gradient. The comoving observer sees radiation coming from a closed surface where the optical depth measured from the observer is unity. Such a surface, called a {\it one-tau photo-oval}, is elongated in the flow direction. In general, the radiation intensity emitted by the photo-oval is non-uniform, and the photo-oval surface has a relative velocity with respect to the position of the comoving observer. Both effects introduce some degree of anisotropy in the radiation field observed in the comoving frame. As a result, the radiation field observed by the comoving observer becomes {\it anisotropic}, and the Eddington factor must deviate from the usual value of 1/3. Thus, the relativistic Eddington factor generally depends on the optical depth $τ$ and the velocity gradient $du/dτ$, $u$ being the four velocity. % In the case of a plane-parallel vertical flow, we obtain the shape of the photo-oval and calculate the Eddington factor in the optically thick regime. We found that the Eddington factor $f$ is well approximated by $f(τ, \frac{du}{dτ}) = {1/3} \exp (\frac{1}{u} \frac{du}{dτ}) $. % This relativistic variable Eddington factor can be used in various relativistic radiatively-driven flows.

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