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Sandbox Physics
From distant light to a galaxy census

L1 · Light, images and selection

Why a galaxy drops out of one filter

Sandbox Physics ·

A galaxy can be visible through one infrared filter and nearly absent through a bluer one. It has not switched off between exposures. Gas along the sightline removes part of the spectrum, and expansion moves that missing light into the observed bands.

Hydrogen removes short-wavelength light from the sightline

Gas also fills the space between galaxies: the intergalactic medium. Its neutral hydrogen absorbs and scatters ultraviolet light. Gas at different distances places hydrogen absorption features at different observed wavelengths. Together, those effects can strongly suppress the shorter-wavelength side of a distant spectrum.

A simple reference cuts off all light below rest-frame 121.6 nanometres and transmits the longer-wavelength side. This captures the location of a high-redshift dropout. Real transmission varies with absorbers and sightline; Inoue and colleagues model mean attenuation from several absorber populations.

This reference lies near Lyman alpha. The classic redshift-three selections often exploited the shorter-wavelength Lyman continuum ionization edge. The spectral structures have different details, which matter when interpreting a particular sample.

Reading: Inoue et al. (2014) · Steidel et al. (1996)

A boundary crosses an entire passband

At redshift ten, wavelengths stretch by eleven, putting the declared boundary at about 1.3376 microns. It lies at 1.0944 microns for redshift eight and 1.7024 microns for redshift thirteen. Increasing redshift changes which filters lose light.

The four NIRCam curves below cover broad ranges. A passband describes how wavelengths contribute to the detected signal. When the boundary enters one filter, its longer-wavelength portion may still transmit light. The band’s integrated flux can therefore change smoothly as the boundary moves.

Four native NIRCam throughput curves and independent ideal sharp IGM references at redshifts eight, ten and thirteen
The upper panel retains the native knots of the frozen STScI v7 total-system tables. The lower panel is a separate normalized sharp-absorption reference. It marks the boundary positions without fitting an observed IGM transmission curve.

Reading: STScI · Inoue et al. (2014)

A photon detector combines the whole spectrum

The received photon signal depends on where light falls within the passband. Photon energy changes with wavelength, as does throughput. A quoted mean spectral density needs a weighting appropriate to that photon-counting response.

For a density expressed per unit frequency, the wavelength-integral weight is throughput divided by wavelength. The integrals add contributions from thin wavelength slices across the band.

⟨fν⟩T=∫fν(λ) T(λ) dλ/λ∫T(λ) dλ/λ\langle f_\nu\rangle_T=\frac{\int f_\nu(\lambda)\,T(\lambda)\,d\lambda/\lambda}{\int T(\lambda)\,d\lambda/\lambda}
The spectral density stays per hertz; wavelength is the integration coordinate. The numerator adds the actual spectrum. The denominator makes a flat frequency spectrum return the same mean through every filter. A pivot wavelength marks a representative band position; the full spectrum supplies the mean.
Specified synthetic sourceIntrinsic UV magnitudeF115W input / nJyF150W input / nJy
Redshift eight−19.518.626.8
Redshift ten−19.50.000061318.7
Redshift thirteen−20.000.00137

Reading: STScI synphot · STScI · Sandbox Physics

Combine missing blue light with red detections

A physical source has nonnegative flux, but noisy estimates fluctuate around its true value. After background subtraction, a source with almost no blue light can have a small positive or negative measured flux. Retaining flux and uncertainty preserves that information before a significance test.

Signal-to-noise here is the measured total flux divided by its uncertainty. The specified selection requires signal-to-noise below two in F115W, above five in F150W and above three in F200W. The red measurements supply a credible source alongside the blue non-detection.

Dust also reddens colours. The saved thicker-screen example still passes: its F150W signal-to-noise is about 5.29, F200W about 5.47, and the blue band remains weak. Attenuation changes the spectrum; the actual measurements determine which side of the thresholds a source occupies.

A real candidate sample must also distinguish nearer galaxies, stars and noise. Modelling those alternative sources and comparing spectra makes it possible to investigate how reliably a colour-selected list identifies distant galaxies.

Reading: Sandbox Physics · Inoue et al. (2014)

Try the observation

Follow the boundary through the four bands

  1. Hold size and screen fixed, increase redshift slowly and compare blue and red signal-to-noise.
  2. Select The next band disappears. Predict the F150W cut and compare F200W.
  3. Compare Add a dust screen with the default, distinguishing dimmer flux from a threshold crossing.

Four actual passbands, a prescribed continuum and a sharp IGM cutoff determine the pixels; the three selection rules define this controlled experiment.

Primary sources and calculation notes

  1. Steidel et al. (1996), Spectroscopic confirmation of a population of normal star-forming galaxies at redshifts above three

    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. STScI, NIRCam filters and mean system throughput

    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.

  3. STScI synphot, Photometric properties

    Bandpass weighting and the pivot-wavelength definition; a pivot is a property of the bandpass and does not replace a weighted source integral.

  4. Inoue et al. (2014), An updated analytic model for attenuation by the intergalactic medium

    Introduction and Section 3.1/Figure 5: intergalactic hydrogen and mean Lyman-alpha transmission. The controlled example uses a separate sharp 1216-Angstrom cutoff, not this paper’s full attenuation calculation.

  5. Sandbox Physics, specified synthetic imaging examples

    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.

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