薄吸积盘内部区域的粘性力矩和耗散：对测量黑洞自旋的意义
Viscous Torque and Dissipation in the Inner Region of a Thin Accretion Disk: Implications for Measuring Black Hole Spin
摘要：
我们考虑一个简单的牛顿模型的稳定吸积盘周围的黑洞。该模型是基于高度集成的流体动力学方程，α-粘度，和一个伪牛顿的潜力，结果在一个最内层的稳定的圆形轨道（ISCO），非常接近GR预测的一个。我们发现，流体动力学模型表现出越来越大的偏差，从标准的磁盘模型的Shakura和Sunyaev磁盘厚度H/R或α值的增加。后者是一个分析模型，其中的粘性扭矩被假定为消失在ISCO。我们考虑的影响，试图估计黑洞自旋的标准盘模型，以适应连续谱的黑洞吸积盘的结果。我们发现，只要H/R < 0.1和α < 0.2，自旋估计的误差是相当适度的。在最坏的情况下，对于不旋转的黑洞，自旋参数的估计值误差为0.1;对于快速旋转的黑洞，误差要小得多。我们还考虑了密度和磁盘之间的气体和内部的ISCO的厚度对比。如果要通过拟合从吸积盘反射的荧光铁发射的相对论加宽的X射线线轮廓来成功地估计黑洞的自旋，则需要大的对比度。在我们的流体动力学模型中，当H/R>0.1时，密度和厚度的对比度很低，这表明在极薄的圆盘中，铁线技术可能是最可靠的。我们提醒说，这些结果已经获得了粘性流体动力学模型，并需要证实与辐射冷却薄磁盘的MHD模拟。
英文摘要：
We consider a simple Newtonian model of a steady accretion disk around a black hole. The model is based on height-integrated hydrodynamic equations, alpha-viscosity, and a pseudo-Newtonian potential that results in an innermost stable circular orbit (ISCO) that closely approximates the one predicted by GR. We find that the hydrodynamic models exhibit increasing deviations from the standard disk model of Shakura & Sunyaev as disk thickness H/R or the value of alpha increases. The latter is an analytical model in which the viscous torque is assumed to vanish at the ISCO. We consider the implications of the results for attempts to estimate black hole spin by using the standard disk model to fit continuum spectra of black hole accretion disks. We find that the error in the spin estimate is quite modest so long as H/R < 0.1 and alpha < 0.2. At worst the error in the estimated value of the spin parameter is 0.1 for a non-spinning black hole; the error is much less for a rapidly spinning hole. We also consider the density and disk thickness contrast between the gas in the disk and that inside the ISCO. The contrast needs to be large if black hole spin is to be successfully estimated by fitting the relativistically-broadened X-ray line profile of fluorescent iron emission from reflection off an accretion disk. In our hydrodynamic models, the contrast in density and thickness is low when H/R>0.1, sugesting that the iron line technique may be most reliable in extemely thin disks. We caution that these results have been obtained with a viscous hydrodynamic model and need to be confirmed with MHD simulations of radiatively cooled thin disks.
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