Hearing the first stars in 21 cm hydrogen
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.
Finding faint early hydrogen under a bright radio sky
Our galaxy's radio glow is about ten thousand times brighter than early hydrogen, but it changes smoothly with frequency. HERA uses that difference.
Why early hydrogen glows or casts a shadow at 21 cm
Derive the 21 cm brightness temperature from spin temperature, the microwave background and optical depth, then see what sets its sign.
How one baseline separates smooth foregrounds from hydrogen
Fourier transform a visibility along frequency, find a baseline's horizon delay and see why smooth foregrounds fill a wedge.
Turning delay power into a bandpower without losing the signal
Convert delay power to cosmological units, read a window function and use an injected signal to test whether a foreground filter removes hydrogen.
Recompute HERA's upper limits and compare a model through its window
Rebuild seven Field 1 upper limits from the public HERA files, pass two model histories through the window rows and check five common mistakes.
Reading how HERA kept foregrounds out of its first limits
Read four sections of the HERA Phase I paper: the wedge and buffer, leakage past the horizon, instrument spectral structure and signal-loss corrections.