2018年USAAAO短问题第11道 - 版本历史

RT.x：改错

2026-07-07T03:43:37Z

改错

Astro Yuan：/* 英文题目 */

2026-07-04T02:46:02Z

‎英文题目

Jingsong Guo：创建页面，内容为“==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 viri…”

2020-03-09T13:25:13Z

创建页面，内容为“==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 viri…”

新页面

==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?

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 ==英文题目==
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 that period?
 ==中文翻译==
-. [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 $$v_{circ} = 220 	ext{ km/s}$$（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？
+. [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？
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←上一版本		2026年7月4日 (六) 02:46的版本
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	What was its mean luminosity (in units of solar luminosity) due to the release of the binding energy during		What was its mean luminosity (in units of solar luminosity) due to the release of the binding energy during
	that period?		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 $$v_{circ} = 220 ext{ km/s}$$（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？
		+	<br />