---
title: "Cosmic Reionization Interactive Lab | Sandbox Physics"
description: "How does starlight reionize cosmic hydrogen? Ultraviolet light escaping young galaxies ionizes intergalactic hydrogen."
canonical_url: "https://sandboxphysics.com/labs/reionization-photon-budget/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/reionization-photon-budget/"
last_modified: "2026-11-12"
---

# Cosmic Reionization

**How does starlight reionize cosmic hydrogen?** Ultraviolet light escaping young galaxies ionizes intergalactic hydrogen. More escaped light grows the ionized volume; recombination uses some of that supply again. As neighbouring ionized regions meet, less neutral hydrogen remains to produce a 21 cm signal.

Move sources and compare ionized regions with their ideal radio signal.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

This is a synthetic uniform-density, periodic hydrogen model in a box twenty comoving megaparsecs wide. A cell records ionized-phase volume fraction, rather than microscopic partial ionization. The adopted flat matter-plus-Lambda background has reduced Hubble constant 0.674, matter fraction 0.315, baryon density times its squared reduced Hubble constant 0.02237, and hydrogen mass fraction 0.76. Radiation and helium electrons are omitted. Sources turn on at redshift ten. A prescribed common clumping factor and ionized temperature of ten thousand kelvin set the case-B recombination budget. Instantaneous two-round allocation distributes net new ionized volume; it does not propagate light or evolve density, heating or hydrodynamics. The five saved presets use thirty-two cells per side, 512 allocation intervals, 2048 global-counter intervals and 65 saved native times. Presets compare the same native time; each record separately retains its original scientific representative nearest forty-five percent ionized volume. Dragging or changing a physical control starts a cancellable sixteen-cell-per-side exploration with 64 allocation intervals, visibly distinguished from a qualified saved record. Fixed-preset tests cover the original five-percent time/order and ten-percent thirty-two-to-sixty-four-cell finite-mode power criteria at selected ionized volumes between one fifth and four fifths. They do not establish arbitrary-source or unique-morphology convergence. The separate ideal 21 cm calculation assumes high neutral spin temperature, the Rayleigh-Jeans and optically thin limits, a coeval cube and a pure Hubble velocity gradient. This spin assumption is independent of the ionized gas temperature. Four families of low Fourier modes describe this finite box, without density, peculiar velocities, instrument response or a HERA likelihood.

Scientific sources and fixed-record methods

- [Madau, Haardt & Rees (1999), §3.1](https://arxiv.org/abs/astro-ph/9809058v1) — The global ionized-volume budget.
- [Hui & Gnedin (1997), Appendix A](https://arxiv.org/abs/astro-ph/9612232v1) — The case-B recombination fit.
- [Choudhury & Paranjape (2018), §4](https://arxiv.org/abs/1807.00836v2) — Photon counting and redistribution at overlapping regions.
- [Furlanetto, Oh & Briggs (2006), §2.1](https://arxiv.org/abs/astro-ph/0608032v2) — 21 cm transfer and the ideal high-spin-temperature limit.

The original synthetic fields and standalone Python methods include all five fixed records, 325 full-precision fields, provenance, licences and labelled numerical evidence. The scripts can inspect a field with the Python standard library or rerun the full fixed model with the declared numerical packages.

[Download the fixed-source data and methods (3.90 MB ZIP)](https://sandboxphysics.com/stories/reionization/materials/fixed-source-analysis.zip)

## Follow a photon from a galaxy to the gas

**Background** Young stars emit ultraviolet light. Some escapes the galaxy and can separate an electron from a hydrogen atom. Near a source, an ionized region grows into the surrounding neutral gas.

**Why it matters** Counting emitted photons is only the beginning: electrons and protons can recombine, requiring another photon to maintain the same ionized volume.

- **Focus question**: What changes the amount of ionized gas, and what changes its shape?
- **One-sentence intuition**: In this uniform two-phase model, the source supply and common recombination budget fix the total ionized volume. Source positions decide where that volume is allocated. Moving sources can change the map without changing the global count.

### Core mathematical model

#### Balance ionization and recombination

$$
\frac{dQ}{dt}=\frac{f_{\rm esc}\sum_s\dot N_s}{N_{\rm H}}-\frac{Q}{t_{\rm rec}},\qquad t_{\rm rec}^{-1}=C\alpha_{\rm B}\bar n_{{\rm H},0}a^{-3}
$$

The ionized volume fraction grows with escaped light. Divide the escaped photon rate by the fixed number of hydrogen nuclei in the comoving box. Recombination acts in the fully ionized phase; expansion reduces its physical density. At full ionization, additional supply becomes surplus.

#### Keep all four counts

$$
E=Q+R+U,\qquad \langle q\rangle_V=Q
$$

All counts are per hydrogen nucleus: escaped supply is split into retained ionizations, cumulative recombinations and surplus. The equal-volume cell mean must match retained ionizations at that same time. The scene distributes net new ionized volume instantaneously; it is not a finite-speed radiation front.

#### Read the remaining neutral gas

$$
\delta T_b(\mathbf x)=T_0(z)[1-q(\mathbf x)],\qquad P_T(k)=T_0(z)^2P_{1-q}(k)
$$

This ideal radio map additionally assumes high neutral spin temperature, an optically thin coeval cube and a pure Hubble velocity gradient. It comes from the same completed cell field. The power chart averages only the declared four finite-box mode families.

### Common difficulties

#### Half the volume is a phase statement

**Typical misconception** Every atom is halfway ionized.

**Better mental model** A cell contains a volume share of fully ionized gas and a share of neutral gas. This differs from treating every parcel as microscopically partially ionized, which changes recombination counting.

#### A changed shape can have the same mean

**Typical misconception** Moving two sources together must ionize more gas.

**Better mental model** The prescribed uniform budget is unchanged by source position. Overlap redistributes the available volume. Local density and local recombination would require additional physics.

#### A radio map needs its own assumptions

**Typical misconception** The ionized gas temperature establishes the neutral spin temperature.

**Better mental model** They describe different gas and different physics. High neutral spin temperature is an extra idealization here; heating, spin coupling and an instrument are not calculated.

### Run the experiment

1. 01

   #### Watch neighbouring regions meet

   Let Bubbles meet play, then pause at an intermediate time.

   **What to observe:** The gold sources stay fixed while ionized volume grows. The neutral-hydrogen slice and photon counts refer to the same completed field and time.

2. 02

   #### Compare a common cosmic time

   Compare Less light escapes and Gas recombines faster with Bubbles meet. Pause before changing a preset if you want to inspect the initial comparison.

   **What to observe:** Each preset starts at the same comparison time. Less supply or faster recombination leaves less ionized gas. Their saved scientific representative frames remain separately documented.

3. 03

   #### Move the source pattern

   Drag a gold source, or compare Starlight spread out with Bubbles meet.

   **What to observe:** The topology and finite-mode power can change while the common global budget stays fixed. Dragging uses the visibly labelled coarse exploration.

4. 04

   #### Keep the completed result

   Open Slice, resolution and download, move the slice, then download.

   **What to observe:** The result includes the whole three-dimensional Float64 cell field, settings, physical clock, counters and mode coefficients. Changing the viewing slice does not change those data.

Physical conclusion

Keep the global photon budget and the spatial map connected. Then keep the ideal neutral-hydrogen signal distinct from the additional heating, velocity and instrument physics needed to interpret a real observation.

## Related experiments and articles

Starlight and intergalactic hydrogen · Reading path

### Photons, ionized volume and a radio signal

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **How starlight changes intergalactic hydrogen**](https://sandboxphysics.com/stories/reionization/starlight-and-hydrogen/)
2. [Article **What does half ionized mean?**](https://sandboxphysics.com/stories/reionization/ionized-volume-and-local-fraction/)
3. [Article **Supplying photons to an expanding volume**](https://sandboxphysics.com/stories/reionization/photons-in-an-expanding-box/)
4. [Article **Where the photons go when ionized bubbles meet**](https://sandboxphysics.com/stories/reionization/when-ionized-bubbles-overlap/)
5. [Article **Reading ionized bubbles through neutral hydrogen**](https://sandboxphysics.com/stories/reionization/reading-a-neutral-hydrogen-map/)
6. [Article **Recompute a fixed-source ionization history**](https://sandboxphysics.com/stories/reionization/recompute-a-fixed-source-history/)
7. [Article **Reading HERA's 21 cm upper limits**](https://sandboxphysics.com/stories/reionization/reading-hera-upper-limits/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)