📚 IB & Edexcel Physics: Astrophysics Key Points Revision | IB Edexcel 物理：天体物理考点精讲
Astrophysics is a fascinating option in both IB Physics (Option D) and Edexcel A Level Physics (Paper 9: Astrophysics and Cosmology). It links stellar properties, galactic motion, and the evolution of the entire universe. Mastering this topic requires a clear understanding of observational quantities, theoretical models, and the evidence that underpins modern cosmology. This article distils every essential concept, formula, and diagram you must know for your exam.
天体物理是IB物理（Option D）和Edexcel A Level物理（Paper 9: Astrophysics and Cosmology）中极具魅力的选修模块，它将恒星性质、星系运动与宇宙整体演化紧密联结。掌握该主题需要透彻理解观测量、理论模型以及支撑现代宇宙学的证据。本文提炼了考试中必须掌握的每一个核心概念、公式和图像。
1. Stellar Classification and the Hertzsprung-Russell Diagram | 恒星分类与赫罗图
Stars are classified by spectral type O, B, A, F, G, K, M, based on surface temperature and absorption lines. O stars are the hottest (>30 000 K) and appear blue, while M stars are the coolest (<3 500 K) and appear red. Our Sun is a G2 star with a surface temperature of about 5 800 K.
恒星根据表面温度和吸收线光谱型分为O、B、A、F、G、K、M。O型星最热（>30 000 K），呈蓝色；M型星最冷（<3 500 K），呈红色。太阳是一颗G2型恒星，表面温度约为5 800 K。
The Hertzsprung-Russell (HR) diagram plots luminosity against surface temperature (decreasing left to right). Most stars lie on the Main Sequence, where they fuse hydrogen into helium. Giants and supergiants are luminous and cool, while white dwarfs are faint and hot. The diagram reveals stellar evolution paths and allows distance and mass estimates.
赫罗图以光度为纵轴、表面温度（从右向左递减）为横轴绘制。绝大多数恒星位于主序星带上，在那里进行氢到氦的核聚变。巨星和超巨星光度高但温度低，白矮星则光度低但温度高。赫罗图揭示了恒星演化轨迹，并可用来估算距离和质量。
2. Stellar Evolution: Life Cycle of Stars | 恒星演化：生命周期
Low-mass stars (M < 8 M☉) spend ~10 billion years on the main sequence, then expand into red giants. Helium fusion in the core may ignite in a helium flash, after which outer layers are ejected as a planetary nebula, leaving behind a white dwarf remnant supported by electron degeneracy pressure.
小质量恒星（M < 8 M☉）在主序阶段停留约100亿年，随后膨胀为红巨星。氦闪可能点燃核心的氦聚变，之后外层被抛射为行星状星云，核心留下由电子简并压支撑的白矮星。
High-mass stars (M > 8 M☉) evolve rapidly, fusing heavier elements up to iron. Iron fusion absorbs energy, causing core collapse and a supernova explosion. The remnant is either a neutron star (if core mass < 3 M☉) or a black hole. Neutron stars are supported by neutron degeneracy pressure.
大质量恒星（M > 8 M☉）演化迅速，依次聚变更重元素直至铁。铁的聚变吸收能量，导致核心坍缩，引发超新星爆发。残余天体为中子星（核心质量 < 3 M☉）或黑洞。中子星由中子简并压支撑。
3. Neutron Stars and Black Holes | 中子星与黑洞
Neutron stars are incredibly dense objects, with radii of only about 10 km and masses up to ~2 M☉. Rapidly rotating neutron stars emitting beams of radiation are observed as pulsars. The period of rotation is extremely stable, making them useful astronomical clocks.
中子星密度极高，半径仅约10 km，质量可达约2 M☉。快速旋转并发射辐射束的中子星被称为脉冲星，其自转周期极其稳定，可用作高精度天文钟。
A black hole has an event horizon at the Schwarzschild radius Rs = 2GM/c². Any mass compressed within this radius prevents light from escaping. The formula can be expressed as:
黑洞的事件视界位于史瓦西半径 Rs = 2GM/c² 处。任何质量被压缩至该半径内，光都将无法逃逸。该公式可表示为：
Rₛ = 2GM / c²
For a solar-mass black hole, Rs ≈ 3 km. The escape velocity at the event horizon equals the speed of light.
对一颗太阳质量的黑洞，Rs ≈ 3 km。事件视界处的逃逸速度等于光速。
4. Apparent and Absolute Magnitude | 视星等与绝对星等
Apparent magnitude m quantifies a star’s brightness as seen from Earth. A difference of 5 magnitudes corresponds to a brightness ratio of exactly 100. The smaller the magnitude, the brighter the object.
视星等 m 量化从地球观测到的恒星亮度。星等每差5等，亮度相差100倍。星等数值越小，天体越亮。
Absolute magnitude M is defined as the apparent magnitude a star would have if placed at a distance of 10 parsecs. The distance modulus equation relates m, M, and distance d (in pc):
绝对星等 M 定义为将恒星置于10秒差距处所应具有的视星等。距离模数方程将 m、M 与距离 d（单位 pc）联系起来：
m − M = 5 log₁₀(d/10)
Alternatively, d = 10^((m−M+5)/5). This is crucial for determining stellar distances from photometric measurements.
或写作 d = 10^((m−M+5)/5)。该公式对于通过测光确定恒星距离至关重要。
5. Standard Candles and Distance Determination | 标准烛光与距离测定
A standard candle is an astrophysical object of known absolute magnitude. Cepheid variable stars exhibit a precise period-luminosity relationship: the longer the period, the higher the absolute luminosity. By measuring their period and apparent brightness, astronomers can calculate distance.
标准烛光是指绝对星等已知的天体。造父变星具有严格的周期-光度关系：周期越长，绝对光度越高。通过测量其光变周期和视亮度，天文学家便可计算距离。
Type Ia supernovae are even more luminous standard candles, with a consistent peak absolute magnitude of about −19.3. They allow distance measurements to remote galaxies, forming the basis of the cosmic distance ladder.
Ia 型超新星是更亮的标准烛光，峰值绝对星等稳定在约 −19.3 等。它们使遥远星系的距离测量成为可能，构成了宇宙距离阶梯的基础。
6. The Expanding Universe: Redshift and Hubble’s Law | 膨胀宇宙：红移与哈勃定律
Cosmological redshift z is given by z = Δλ/λ₀ = (λᵒᵇˢ − λ₀)/λ₀, where λ₀ is the rest wavelength. For distant galaxies, the redshift arises from the expansion of space itself, not from proper motion.
宇宙学红移 z 由 z = Δλ/λ₀ = (λᵒᵇˢ − λ₀)/λ₀ 给出，其中 λ₀ 为静止波长。对于遥远星系，红移源自空间本身的膨胀，而非星系的自行运动。
Hubble’s Law states that the recessional velocity v of a galaxy is proportional to its distance d: v = H₀ d. H₀ is the Hubble constant, currently measured at approximately 70 km s⁻¹ Mpc⁻¹. The law provides the primary evidence for an expanding universe.
哈勃定律指出，星系的退行速度 v 与其距离 d 成正比：v = H₀ d。H₀ 为哈勃常数，目前测量值约为 70 km s⁻¹ Mpc⁻¹。该定律是宇宙膨胀的主要证据。
7. Cosmic Microwave Background Radiation | 宇宙微波背景辐射
The Cosmic Microwave Background (CMB) is isotropic blackbody radiation with a temperature of 2.725 K, peaking at microwave wavelengths. It is the afterglow of the Big Bang, dating from the epoch of recombination when electrons and protons combined to form neutral hydrogen, about 380 000 years after the Big Bang.
宇宙微波背景辐射（CMB）是各向同性的黑体辐射，温度为 2.725 K，峰值位于微波波段。它是大爆炸的余辉，产生于电子与质子复合形成中性氢的复合时期，约在大爆炸后38万年。
Tiny temperature fluctuations (ΔT/T ~ 10⁻⁵) observed in the CMB correspond to density fluctuations in the early universe, which later seeded the formation of galaxies. The CMB is one of the strongest pillars of Big Bang cosmology.
观测到的微幅温度涨落（ΔT/T ~ 10⁻⁵）对应于早期宇宙的密度涨落，这些涨落后来成为星系形成的种子。CMB 是大爆炸宇宙学最坚实的支柱之一。
8. Dark Matter and Dark Energy | 暗物质与暗能量
Galaxy rotation curves show that orbital speeds remain constant or even increase with distance from the centre, implying the presence of unseen dark matter extending far beyond the visible disk. Gravitational lensing provides further evidence: massive dark matter halos bend light from background sources.
星系旋转曲线显示，轨道速度随到中心距离的增加而保持不变甚至上升，暗示着大量不可见的暗物质存在于可见盘面之外。引力透镜效应提供了进一步证据：大质量暗物质晕偏折了背景光源的光线。
Dark energy is hypothesised to explain the observed accelerated expansion of the universe, discovered via Type Ia supernova distance measurements. It behaves like a repulsive force and can be modelled by a cosmological constant Λ.
暗能量被用来解释观测到的宇宙加速膨胀，该现象通过 Ia 型超新星距离测量发现。暗能量表现为斥力，可用宇宙学常数 Λ 建模。
9. Stellar Parallax and Distance Measurement | 恒星视差与距离测量
Stellar parallax is the apparent shift of a nearby star against distant background stars as Earth orbits the Sun. The parallax angle p (in arcseconds) and distance d (in parsecs) are related by d = 1/p. A parsec is the distance at which a star shows a parallax of one arcsecond.
恒星视差是指地球绕日公转时，较近恒星相对于远背景恒星的视位置移动。视差角 p（角秒）与距离 d（秒差距）满足 d = 1/p。1秒差距是恒星视差为1角秒时所对应的距离。
Parallax is reliable only for nearby stars (d < 100 pc). Combining parallax with apparent magnitude yields absolute magnitude via the distance modulus, calibrating the first rung of the cosmic distance ladder.
视差法仅适用于近距离恒星（d < 100 pc）。将视差与视星等结合，通过距离模数可获得绝对星等，从而校准宇宙距离阶梯的第一级。
10. Fate of the Universe | 宇宙的命运
The ultimate fate of the universe depends on its density parameter Ω. If Ω > 1, the universe is closed and will eventually recollapse in a Big Crunch. If Ω < 1, it is open and will expand forever. With Ω = 1, a flat universe expands asymptotically to a halt.
宇宙的最终命运取决于密度参数 Ω。若 Ω > 1，宇宙封闭，最终将在大坍缩中收缩；若 Ω < 1，宇宙开放，将永远膨胀；若 Ω = 1，平坦宇宙膨胀速率渐趋于零。
Observations combining CMB data, supernovae, and large-scale structure indicate that Ω ≈ 1, with dark energy contributing about 68% and dark matter about 27%. The current evidence favours an accelerating expansion leading to a ‘Big Freeze’ or heat death.
综合 CMB 数据、超新星和大尺度结构的观测表明，Ω ≈ 1，其中暗能量约占68%，暗物质约占27%。当前证据支持宇宙加速膨胀，最终走向“大冻结”或热寂。
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