Lecture 1 Chemodynamics and other

约 2151 字大约 7 分钟

2026-07-28

Prof. Chiaki Kobayashi, from the University of Hertfordshire

警告

由于第一天不太适应加上听不太懂教授的发音，而且前半段试图用手写方式记录但是后来发现效率不够高，漏记错记想必数不胜数，本篇权当试水.

Wolf–Rayet Stars

Wolf–Rayet (WR) stars are evolved massive stars with extremely powerful stellar winds.

These winds strip away most or all of the hydrogen envelope, exposing helium-burning products beneath.

Binary Evolution: Binary mass transfer can also remove the hydrogen envelope. Consequently, even stars with somewhat lower initial masses can become Wolf–Rayet stars.

Supernova Classification

Chemical Enrichment

( $f_g$ 是气体分数)

\frac{\mathrm{d}(Zf_g)}{\mathrm{d}t} = \underbrace{E_{\text{SW}}+E_{\text{SNcc}}+E_{\text{SNIa}}}_{\text{Metal ejection rates}}\underbrace{\underset{\text{decreased by star evolution}}{\underline{-Z\psi}}\underset{\text{inflow}}{\underline{+Z_{\text{inflow}}}}\underset{\text{outflow}}{\underline{-ZR_{\text{outflow}}}}}_{\text{Galaxy Evolution}}

Initial Mass Function (IMF)：一般而言这是一个 power law，它是一个经验性的概率分布函数，描述恒星的质量分布. 一般而言它来源于恒星的光度分布，然后再用恒星演化模型来导出.

Is IMF universal？

Ejection rates from SWs and SNe

一颗星，初始质量 $m$ ，lifetime $\tau_m$ ，剩下的质量 $w_m$ ，在时刻 $(t-\tau_m)$ 出生、在时刻 $t$ 死亡. 终止质量 ( $\tau_m=t$ ) 为 $m_t$ .

E=\int_{m_t}^{m_u}(1-w_m)\psi(t-\tau_m)\phi(m)\mathrm{d}m

大于终止质量的星体是死掉的星体. SNe 由 nucleosynthesis yields (核合成产率) $p_{zm}$ 给出，

E_{Z,\text{cc}} = \int_{m_t}^{m_u}p_{zm}\psi(t-\tau_m)\phi(m)\mathrm{d}m

同理，SW 也是一样.

Galactic terms

Star formation rate: $\psi\propto f_g$
Inflow rate: $R_{\text{in}}\propto e^{-t/\tau}$ or $te^{-t/\tau}$
Outflow rate: $R_{\text{out}}\propto\psi$ (SN-driven) or $\psi=0$ for $t>t_w$ (AGN-driven)

Numerical Solutions

这里有三种模型：

Closed：封闭的状态
Infall：系统不断吸收气体，气体向中心塌缩
Outflow：气体塌缩的同时还存在 ejection，失去 metal

初始情况都是 $f_{g,0}=1$ . 三种模型的演化曲线有很大的差异. 我们只讨论 one-zone model 情况下的结论，从观测数据来看， $[\text{O}/\text{Fe}]$ - $[\text{Fe}/\text{H}]$ 关系有一个开始时比较慢、之后比较快的下降，拟合最好的模型是 infall model.

The Origin of Elements

这里 $\text{Be}$ 和 $\text{B}$ 不包含在模型内，因为它们很多来源于高能量宇宙射线的作用.

NS-NS Merger Model

为了解释银河系内部的 r-process (也就是快中子捕获过程，被认为是产生一半以上重于铁的元素的过程)，有一种思路是双中子星并合事件. 但是仍然有很多争议.

GPT's Explanation

The Neutron Star Merger (NSM) model is currently the leading explanation for the production of the heaviest r-process elements (e.g. Au, Pt, Th, U), especially after the discovery of the kilonova associated with GW170817. However, it faces several challenges, and a number of alternative or complementary models have been proposed.

A useful way to organize them is:

Origin of heavy r-process elements
│
├── Neutron Star Mergers (standard model)
│
├── Magnetorotational Supernovae
│
├── Collapsars (Hypernovae)
│
├── Electron-Capture Supernovae
│
├── Neutrino-driven Winds
│
└── Exotic Models
    ├── Quark nova
    ├── Primordial black holes
    └── Others

Below are the major competing models.

Magnetorotational Supernovae (Jet Supernovae)

The basic idea is a rapidly rotating massive star with an extremely strong magnetic field collapses.

Instead of producing a roughly spherical explosion, rotation and magnetic fields launch bipolar relativistic jets.

Massive star
    ↓
Core collapse
    ↓
Rapid rotation
+ Strong magnetic field
    ↓
Jet explosion
    ↓
Neutron-rich ejecta
    ↓
r-process

Advantages
Very early in Galactic history. Unlike neutron star mergers, so no binary evolution and merger delay. Therefore they naturally explain extremely metal-poor stars and large star-to-star scatter in Eu abundances.

Problems
Very rare.
Requires rapid rotation and magnetic field. Both conditions are uncommon. Simulations still disagree about whether enough neutron-rich material is ejected.

Collapsars

Currently the strongest competitor. The basic idea is a very massive star $M\gtrsim25\sim30,M_\odot$ collapses directly into a black hole. An accretion disk forms.

Massive star
    ↓
Black hole
    ↓
Accretion disk
    ↓
Disk wind
    ↓
r-process

This is closely related to

Hypernovae
Long Gamma-Ray Bursts (GRBs)

Advantages
Produces enormous r-process mass. Typically $0.05-0.3,M_\odot$ per event, much larger than many core-collapse supernovae. Occurs immediately after star formation.
Can explain
early Eu enrichment
high [Eu/Fe]
Galactic chemical evolution.

Problems
Event rate is uncertain. Need enough collapsars without overproducing GRBs.

Neutrino-driven Winds

This was the "classical" model before neutron star mergers became popular.

After core collapse,

Proto-neutron star
    ↓
Neutrino heating
    ↓
Neutrino wind
    ↓
Heavy nuclei

The idea was that neutrino winds become neutron rich.

Problems
Modern simulations generally find $Y_e$ is too high.
The ejecta become proton-rich rather than neutron-rich.
Usually only produce Sr, Y, Zr instead of Au, Pt, U.
Thus today they are thought to produce the weak r-process, not the main r-process.

Electron-Capture Supernovae (ECSNe)

Occurs in stars of roughly $8-10,M_\odot.$

Core collapse begins when $e^-+{}^{24}\mathrm{Mg}$ or $e^-+{}^{20}\mathrm{Ne}$ captures reduce electron pressure.

Advantages
More common than magnetorotational SNe.

Problems
Ejecta are usually not neutron rich enough.

Mostly produce light trans-iron elements rather than heavy r-process nuclei.

Quark Nova

Very speculative.

Idea

Neutron star
    ↓
Quark matter transition
    ↓
Second explosion
    ↓
Neutron-rich ejecta

Could in principle create ideal r-process conditions.

No convincing observational evidence exists.

Primordial Black Hole Scenarios

Another speculative idea. Tiny primordial black holes interact with neutron stars. This can eject neutron-rich matter.

But current observational support is essentially absent.

Why was NSM challenged?

The biggest historical problem was time delay.

Neutron star mergers require

Massive binary
    ↓
Two supernovae
    ↓
Binary inspiral
    ↓
Merger

The inspiral time may be $10^8-10^9\ \text{yr}.$

However, very metal-poor stars $[\mathrm{Fe}/\mathrm{H}]<-3$ already contain Eu and Ba, indicating r-process enrichment almost immediately after star formation.

This motivated prompt sources like magnetorotational supernovae or collapsars.

Today, population synthesis and the discovery of fast-merging binaries suggest that some neutron star mergers can occur within only a few to tens of Myr, reducing (though not completely eliminating) this tension.

Current Consensus

Rather than a single source, most researchers now favor multiple r-process sites.

Heavy r-process
│
├── Neutron star mergers
│      ✔ Main contributor today
│
├── Collapsars
│      ✔ Possibly important in early galaxies
│
├── Magnetorotational SNe
│      ✔ Rare but prompt
│
└── Ordinary CCSNe
    ✔ Weak r-process only

The main debate today is not whether neutron star mergers produce r-process elements —— GW170817 established that they do —— but whether they are sufficient to explain all Galactic r-process enrichment, especially in the earliest generations of stars. Many recent Galactic chemical evolution models therefore combine neutron star mergers with a prompt source, most commonly collapsars or magnetorotational supernovae, to reproduce both the abundance patterns and the observed evolution of Eu with metallicity.

Chemodynamics

对于一个 UV 背景辐射，考虑一团正在冷却的气体，星体形成条件为

$\nabla\cdot\vec{v}<0$
$t_{\text{cool}}<t_{\text{dyn}}$
$t_{\text{dyn}}<t_{\text{sound}}$

有多个过程构成一个循环，进行元素的生成.

这里有好几种模拟方法：

Direct summation —— $\mathcal{O}(N^2)$

m_i\frac{\mathrm{d}^2x_i}{\mathrm{d}t^2}=\sum_{j\neq i}Gm_im_j\frac{x_j-x_i}{|x_j-x_i|^3}

网格数值法
……
SPH Method (Smoothed-particle hydrodynamics，平滑粒子流体力学)：处理大尺度的流体模拟比较有效，不需要建立一个网格来进行计算.

Cosmological 'Zoom in' Simulation

展示了一个完整的星系形成过程：从最初的气体到形成 disk，最终的结构中能看到 thin disk 和中间的 bulge，以及 halo (通过卫星星系来体现).

Inhomogenous Enrichment

The scatter of $[X/\text{Fe}]$ at given $[\text{Fe}/\text{H}]$ is increased / decreased by

动力学效应导致的 star mixing
Local variation in flows
Stellar yields depend on M, Z, E rot. of stars (intrinsic variation, 固有的差异)
ISM may be mixed before the next star formation by other effects like diffusion / turbulence (涡流)

因此，不会存在 strong age-metallicity relation；另外，大多数 metal-poor stars 不是最老的那一批恒星.

more explanation on「大多数 metal-poor stars 不是最老的那一批恒星」：
根据模拟的数据 (Age-Metallicity relation figure)，可以观察到这些恒星确实处于年龄较大的那一批恒星中，但是并不是最老的恒星.
我们说这个结论实际上是想纠正观测上的一些常识性的错误认知.