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arXiv 0904.2803astro-ph.HE
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相对论变量爱丁顿因子

Relativistic Variable Eddington Factor

J. Fukue

备注：
9 pages, 9 figures
发表信息：
PASJ, 60, 377 (2008)
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摘要：

我们解析地导出了相对论辐射流中的一个相对论变量爱丁顿因子，发现爱丁顿因子不仅依赖于流速，而且依赖于{ \it速度梯度}。当气流被加速并且存在速度梯度时，也存在密度梯度。结果，由共动观察者的无阻碍的观察范围，其中从共动观察者测量的光学深度是1，不是球体，而是变成在流动方向上伸长的椭圆形状;我们称之为{ \it one-tau photo-oval}。对于同向运动的观察者，光椭圆的内壁通常以不均匀的强度发射，并且具有相对速度。因此，由共动观测器观测到的共动辐射场变为{ \it各向异性}，并且爱丁顿因子必须偏离各向同性辐射场的值。在平行平面垂直流的情况下，我们检查了照片椭圆，并获得了爱丁顿因子。在足够光学厚的线性区域中，爱丁顿因子解析地表示为$f (τ, β, \frac{dβ}{dτ}) = {1/3} (1 + {16/15} \frac{dβ}{dτ})$，其中$τ$是光学深度，$β$（$=v/c$）是通过光速归一化的流速。%即，爱丁顿因子取决于速度梯度。我们还研究了线性和半线性制度，并发现爱丁顿因子一般取决于速度和它的梯度。

英文摘要：

We analytically derive a relativistic variable Eddington factor in the relativistic radiative flow, and found that the Eddington factor depends on the {\it velocity gradient} as well as the flow velocity. When the gaseous flow is accelerated and there is a velocity gradient, there also exists a density gradient. As a result, an unobstructed viewing range by a comoving observer, where the optical depth measured from the comoving observer is unity, is not a sphere, but becomes an oval shape elongated in the direction of the flow; we call it a {\it one-tau photo-oval}. For the comoving observer, an inner wall of the photo-oval generally emits at a non-uniform intensity, and has a relative velocity. Thus, the comoving radiation fields observed by the comoving observer becomes {\it anisotropic}, and the Eddington factor must deviate from the value for the isotropic radiation fields. % In the case of a plane-parallel vertical flow, we examine the photo-oval and obtain the Eddington factor. In the sufficiently optically thick linear regime, the Eddington factor is analytically expressed as $f (τ, β, \frac{dβ}{dτ}) = {1/3} (1 + {16/15} \frac{dβ}{dτ})$, where $τ$ is the optical depth and $β$ ($=v/c$) is the flow speed normalized by the speed of light. %i.e., the Eddington factor depends on the velocity gradient. We also examine the linear and semi-linear regimes, and found that the Eddington factor generally depends both on the velocity and its gradient.

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