---
title: "Hearing the first stars in 21 cm hydrogen"
description: "Learn why early hydrogen glows or darkens at 21 cm, how radio arrays keep bright foregrounds away from it, and how to read HERA upper limits."
canonical_url: "https://sandboxphysics.com/stories/cosmic-dawn-21cm/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/cosmic-dawn-21cm/"
last_modified: "2026-11-14"
---

# Hearing the first stars in 21 cm hydrogen

Sandbox Physics · 2026-11-12

Early hydrogen left a faint radio signal at 21 cm. Start with why it glows or darkens, follow one radio baseline as it separates that signal from a sky ten thousand times brighter, then rebuild and read the published HERA limits yourself.

1. L1 · Concept

   ## [Finding faint early hydrogen under a bright radio sky](https://sandboxphysics.com/stories/cosmic-dawn-21cm/finding-hydrogen-under-radio-foregrounds/)

   Our galaxy's radio glow is about ten thousand times brighter than early hydrogen, but it changes smoothly with frequency. HERA uses that difference.

2. L1 · Chapter

   ## [Why early hydrogen glows or casts a shadow at 21 cm](https://sandboxphysics.com/stories/cosmic-dawn-21cm/spin-temperature-and-21cm-brightness/)

   Derive the 21 cm brightness temperature from spin temperature, the microwave background and optical depth, then see what sets its sign.

3. L2 · Chapter

   ## [How one baseline separates smooth foregrounds from hydrogen](https://sandboxphysics.com/stories/cosmic-dawn-21cm/delay-spectrum-and-foreground-wedge/)

   Fourier transform a visibility along frequency, find a baseline's horizon delay and see why smooth foregrounds fill a wedge.

4. L3 · Chapter

   ## [Turning delay power into a bandpower without losing the signal](https://sandboxphysics.com/stories/cosmic-dawn-21cm/power-spectrum-window-and-signal-loss/)

   Convert delay power to cosmological units, read a window function and use an injected signal to test whether a foreground filter removes hydrogen.

5. L3 · Method

   ## [Recompute HERA's upper limits and compare a model through its window](https://sandboxphysics.com/stories/cosmic-dawn-21cm/recompute-hera-window-comparison/)

   Rebuild seven Field 1 upper limits from the public HERA files, pass two model histories through the window rows and check five common mistakes.

6. L4 · Paper guide

   ## [Reading how HERA kept foregrounds out of its first limits](https://sandboxphysics.com/stories/cosmic-dawn-21cm/reading-hera-foreground-avoidance/)

   Read four sections of the HERA Phase I paper: the wedge and buffer, leakage past the horizon, instrument spectral structure and signal-loss corrections.

[Open the Lab: drag the heating history and the dish spacing](https://sandboxphysics.com/labs/cosmic-dawn-21cm-foregrounds/)