---
title: "How distant light becomes a galaxy count"
description: "Follow early colour-selected galaxies through Keck spectroscopy, then see how infrared filters and finite noisy pixels shape a census."
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language: "en"
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  zh-CN: "https://sandboxphysics.com/zh/stories/high-redshift-galaxies/far-light-to-a-count/"
last_modified: "2026-11-12"
---

[From distant light to a galaxy census](https://sandboxphysics.com/stories/high-redshift-galaxies/)

L1 · Light, images and selection

# How distant light becomes a galaxy count

Sandbox Physics · 2026-11-12

In October 1995, the Keck telescope in Hawaii spread the light of faint targets into spectra. Their colours had put them on the observing list: longer-wavelength light remained, but a bluer band was weak. Steidel and colleagues followed that missing light to a population of distant star-forming galaxies.

## Use a spectral gap to shorten the observing list

A deep image contains many tiny patches. A nearby faint star and a distant galaxy can both look small and dim. Obtaining a detailed spectrum for every patch would take a great deal of telescope time. Astronomers needed a way to put promising distant targets near the front of the list.

Hydrogen provided a clue. A galaxy can have a bright ultraviolet continuum at longer wavelengths and a sharp loss of light toward shorter ones. Cosmic expansion shifts the spectrum to longer observed wavelengths. A suitable set of filters can test whether the gap lies between neighbouring bands.

The early ultraviolet and optical selection targeted galaxies near redshift three. At that redshift, an emitted wavelength arrives stretched by a factor of four. Searching for the corresponding kind of gap at larger redshifts moves the relevant observations farther into the infrared.

Reading: Steidel et al. (1996) · Hogg (1999)

## A spectrum gives the colour interpretation another test

Keck’s LRIS instrument separated the candidates’ light by wavelength. Absorption and emission features could then be compared at several positions in a spectrum. A common shift of several features carries more information than a difference between a few broad images.

The paper published in 1996 listed sixteen star-forming galaxies with spectroscopic redshifts from 3.01 to 3.43. Colour selected the candidates; spectra supplied more detailed identifications. The sequence turned small patches in deep images into a population that could be studied.

Such a selection naturally favours sources with ultraviolet light still visible. Dust, spectral shape and a weak signal affect which galaxies reach the list. Their selection remains part of the interpretation when the sample is used to investigate galaxy formation.

Reading: Steidel et al. (1996)

## Move the search into infrared filters

A more distant source has a greater wavelength stretch. Structure emitted in the ultraviolet can arrive in the near infrared. NIRCam on JWST provides filters covering different wavelength ranges, allowing the same sky to be compared where the source is faint and where its light returns.

A broad filter receives a range of wavelengths. Its transmission changes across that range, including at the edges. A spectral gap moving through a filter therefore usually dims its integrated light gradually. The neighbouring measurements jointly determine the observed colour.

The redder images must also contain a credible source. If every band contains only noise, absence in the blue band has supplied little information about distance. A useful dropout selection combines missing blue light with positive red detections.

Reading: STScI · Hogg (1999)

## The same total light can be harder to find

After passing a filter, the light lands in pixels. Spreading one quantity of paint over a larger patch makes each small area paler. Spreading a galaxy’s flux across more noisy pixels changes its visibility in a similar way.

A controlled image example increases the physical half-light radius from 0.3 to 1.2 kiloparsecs. This radius encloses half the source’s total light. Both sources have the same input total flux in a given infrared band. The larger source spreads it over more pixels and loses some beyond the finite field.

With its position and profile known, total flux can still be estimated with a larger uncertainty. When the position must also be found, diffuse light is more likely to merge into the background. The surviving sample can consequently favour compact sources.

Reading: Sandbox Physics

## A census carries the selection with it

A list of detections prompts another question: how many galaxies of this kind occupy a chosen redshift and brightness range? The sky area and number found provide a starting point. The missing objects and the effects of noise near the selection boundaries must also be understood.

Colour selection, spectroscopic identification and population counting each contribute a different measurement. Selection makes the search efficient. Spectra identify individual targets more closely. A census then relates those targets to a defined sample, accounting for the kinds of sources its images tend to miss.

Reading: Steidel et al. (1996) · Sandbox Physics

## Try the observation

### [Watch one source gain or lose its place in a selection](https://sandboxphysics.com/labs/high-redshift-dropout-survey/)

1. Compare The blue band disappears with Blue light remains; predict which meets the blue non-detection rule.
2. Choose Spread the same light and compare the image with its total-flux uncertainty.
3. Move the source toward the edge and explain the change in enclosed light.

The controlled example sends a prescribed continuum through four actual passbands and measures finite Gaussian pixels with the source position and profile supplied.

## Check the numerical examples

The summaries identify the specified model, saved measurements and finite independent checks used here. The figures show synthetic sources; these files do not contain an observed galaxy catalog.

- [Distances, passbands and the five saved examples (JSON)](https://sandboxphysics.com/stories/high-redshift-galaxies/materials/model-numerical-examples.json)
- [The 58 finite independent model checks (JSON)](https://sandboxphysics.com/stories/high-redshift-galaxies/materials/model-commission-summary.json)
- [Exact file sizes and SHA256 identities](https://sandboxphysics.com/stories/high-redshift-galaxies/public-reproduction.json) · [Attribution and permission](https://sandboxphysics.com/stories/high-redshift-galaxies/materials/LICENSE.txt)

[Next: How redshift turns UV luminosity into received flux](https://sandboxphysics.com/stories/high-redshift-galaxies/redshift-ab-and-spectral-density/)

## Primary sources and calculation notes

1. [Steidel et al. (1996), Spectroscopic confirmation of a population of normal star-forming galaxies at redshifts above three](https://arxiv.org/pdf/astro-ph/9602024v1)

   Sections 2–3 and Figure 1: October 1995 Keck/LRIS spectra, colour-selected candidates and the listed spectroscopic galaxy redshifts. No new reconciliation of the paper’s candidate denominators or LF estimate.

2. [Hogg (1999), Distance measures in cosmology](https://ned.ipac.caltech.edu/level5/Hogg/Hogg7.html)

   Luminosity-distance section: bolometric flux, angular/luminosity distance and spectral-density transformations. The numerical examples use the explicitly adopted radiation-free model.

3. [STScI, NIRCam filters and mean system throughput](https://jwst-docs.stsci.edu/jwst-near-infrared-camera/nircam-instrumentation/nircam-filters)

   Four frozen v7 detector-averaged total-system tables: F115W, F150W, F200W and F277W. Original table URLs and SHA256 identities accompany the numerical examples. Throughput is distinct from a PSF or an exposure/noise calibration.

4. [Sandbox Physics, specified synthetic imaging examples](https://sandboxphysics.com/stories/high-redshift-galaxies/materials/model-numerical-examples.json)

   Original synthetic examples with exact parameters, distances, native-band totals and saved noisy measurements. No observed galaxy catalog, foreign source ZIP, executable Engine or measured cosmic LF is included.