2018年USAAAO短问题第11道
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英文题目
11. [5 pt] When a gravitationally bound system (such as a galaxy) forms, it transitions from a just bound state ($$E_{kin} = |E_{pot}|$$) to a virialized state ($$E_{kin} = 0.5|E_{pot}|$$) and the excess binding energy has to be radiated away. Consider an idealized disk galaxy with an exactly flat rotation curve with a rotation speed of $$v_{circ} = 220 km/s$$ (you can neglect the kinetic energy in random motions). Its density profile cuts off abruptly at a radius of $$R_{max} = 50 kpc$$. Assume that it took 500 million years for this galaxy to collapse to its present state. What was its mean luminosity (in units of solar luminosity) due to the release of the binding energy during that period?
中文翻译
11. [5 pt] 当一个引力束缚系统（例如星系）形成时，它会从刚刚束缚状态（$$E_{kin} = |E_{pot}|$$）过渡到维里化状态（$$E_{kin} = 0.5|E_{pot}|$$），多余的束缚能必须以辐射的形式释放。考虑一个理想化的盘状星系，其旋转曲线完全平坦，旋转速度为 $$v_{circ} = 220 { km/s}$$（可以忽略随机运动的动能）。其密度分布在半径 $$R_{max} = 50 kpc$$ 处突然截止。假设这个星系花了5亿年时间塌缩到现在的状态。在此期间由于释放束缚能量，它的平均光度（以太阳光度为单位）是多少？
