题型概述：星系、宇宙学与系外行星Question types: galaxies, cosmology & exoplanets
本专题把星系观测与系外行星的物理模型连起来。所选真题中，Section A 每题 1 分，Section B 每题 5 分；本页共 13 分。选择题考单位、数量级和面积比例，分步题要求从图像或光度推到物理量。常见失分来自星等符号、nm 与 μm 的换算，以及把高红移当成低速多普勒效应。This topic links observations of galaxies and exoplanets to physical models. In the selected papers, Section A questions carry 1 mark each and Section B questions 5 marks each, giving 13 marks here. MCQs test units, scale and area ratios; written questions connect graphs or luminosity to physical quantities. Common errors involve magnitude signs, nm-to-μm conversion, and treating high redshift as a low-speed Doppler shift.
1从观测量到几何量From observation to geometry
光谱线的伸长比例给出红移；凌星损失的通量比例给出面积比。两种观测都要先分清“测到了什么”。Spectral stretching gives redshift; lost transit flux gives an area ratio. Start by identifying exactly what was measured.
星等增大代表变暗；波长变长对应正红移。Increasing magnitude means dimming; longer wavelength means positive redshift.
2用单位和尺度检验模型Check models with units and scaling
哈勃常数的量纲是时间的倒数；视界半径随质量增大，但平均密度反而降低。先看幂次再按计算器，可提前发现错误。The Hubble constant has dimensions of inverse time. Horizon radius increases with mass, while mean density decreases. Check powers before entering numbers.
高红移必须使用题给的宇宙学转换图；H₀ 不是在所有时刻都恒定。Use the supplied cosmological conversion at high redshift; H₀ is not constant at every epoch.
3能量守恒决定平衡温度Energy conservation sets equilibrium temperature
行星以迎光圆盘截获星光，再由整个球面辐射。零反照率、均匀温度的模型中，温度与半径无关，与距离的平方根成反比。A planet intercepts starlight with its projected disc and emits over its whole sphere. With zero albedo and uniform temperature, temperature is independent of radius and scales as inverse square root of distance.
辐射温度不一定等于有温室大气时的地表温度。Radiating temperature need not equal surface temperature under a greenhouse atmosphere.
| 子题型Sub-type | 识别特征How to spot it | 核心步骤Core step | 真题Past paper |
|---|---|---|---|
| 量纲估算Dimensional estimate | a、H₀、da, H₀, d | 检查 LT⁻²Check LT⁻² | 2024 Q3 |
| 凌星半径Transit radius | 星等下降Magnitude dip | 通量 → 面积 → 半径Flux → area → radius | 2020 Q8 |
| 黑洞平均密度Black-hole mean density | 史瓦西半径Schwarzschild radius | M / 球体体积M / sphere volume | 2020 Q9 |
| 光谱红移Spectral redshift | 多条氢线Multiple hydrogen lines | 匹配线 → 读图 → 距离Match → read graph → distance | 2022 Q12 |
| 行星温度Planet temperature | 光度、轨道半径Luminosity and orbit | 吸收功率 = 辐射功率Absorption = emission | 2020 Q11 |