From light to a selected population

High-redshift Galaxy Dropout Survey

Which distant galaxies enter a survey, and which disappear? Intergalactic absorption removes a distant galaxy’s blue light, while its remaining light is spread across finite pixels. A source can miss a survey because its signal is too diffuse or because it fails the colour cuts. Population counts need the matching selection and flux-scatter response, including objects scattered between bins.

Move and resize a distant galaxy across four noisy filter images. Then inspect a separate fixed survey of twenty-six selected sources.

F150W signal / noise $15.3$

F115W signal / noise $-0.732$

F200W signal / noise $15.7$

F150W light inside the detector $100\,\%$

Let the detector decide

Redshift

10.0

z

Physical half-light radius

0.300

r_{1/2}/\mathrm{kpc}

UV screen attenuation

0.200

A_{1500}/\mathrm{mag}

Drag the green centre or amber size grip in F150W. Each example keeps its own saved noise while you move it.

This source passes all three declared cuts.

Luminosity, spectrum and complete measurements

Intrinsic UV absolute magnitude

-19.5

M_{1500}

Continuum spectral slope

-2

\beta

Each image has thirty-two pixels along each side. All bands share one fixed asinh scale: negative noise is blue, positive flux is warm; display values above three nanojanskys per pixel saturate. The thin ring marks the prescribed intrinsic half-light radius.

$L_\lambda\propto\lambda^\beta,\quad A_\lambda=A_{1500}\left(\frac{\lambda}{0.15\,\mu\mathrm m}\right)^{-0.7}$

$\lambda_{\rm break}=0.1216(1+z)\,\mu\mathrm m$

The detector centre is the origin, with right and up positive. The ring projects the intrinsic source half-light radius through angular distance, before the Gaussian proxy blur.

$\sigma_{\rm pix}=0.15\,\mathrm{nJy},\quad\Delta\theta=0.03\,\mathrm{arcsec}$

A known-position, known-profile estimator reads the simulated noisy pixels. No fresh noise is generated by dragging. Reset restores the original first example and its saved draw.

$x_s=y_s=0\,\mathrm{arcsec}$

Band	Input total / nJy	Recovered / nJy
F115W	$6.13\times10^{-5}$	$-0.829\pm1.13$
F150W	$18.7$	$17.8\pm1.16$
F200W	$19.9$	$18.9\pm1.2$
F277W	$20.5$	$20.2\pm1.29$

The export contains all four images, profiles, noise arrays, selection rules, units and source settings. Throughputs are STScI v7 numerical tables; the Gaussian diffraction proxy is not a measured JWST PSF.

STScI NIRCam filter documentation

Hogg: luminosity distance and spectral density

Model assumptions

This is a synthetic known-source experiment. Adopted flat matter-plus-Lambda cosmology uses a Hubble constant of seventy kilometres per second per megaparsec and matter fraction three tenths, with radiation omitted, over redshift seven and a half to fifteen. An AB-normalized UV power-law continuum passes through a prescribed wavelength-dependent dust screen and a sharp opaque intergalactic cutoff at rest-frame Lyman alpha. There are no stellar populations, emission lines, AGN fit or mass estimates. Four native STScI NIRCam version-seven throughput curves supply photon-weighted band fluxes. A circular Gaussian source is integrated over a finite thirty-two by thirty-two pixel detector with a Gaussian diffraction-width proxy for an aperture of six and a half metres, not a JWST PSF or exposure calculator. Clipped light is not renormalized. Pixel noise is independent Gaussian with one fixed saved draw per example; photon noise, covariance, blending and blind source detection are omitted. The linear estimator knows the true position and profile. All four images share a fixed intensity scale; bright pixels can saturate the display. A separate five-square-arcminute synthetic survey has fixed redshift, morphology, screen and spectrum. Its selected-count response and restricted midpoint Schechter family do not follow the individual controls. Its half-unit profile interval is descriptive, not an exact small-sample confidence interval. Neither survey is an observed JADES luminosity-function measurement.

The same source through four passbands

F115WF150WF200WF277W

Grey is the prescribed continuum. Open squares are photon-weighted band means, placed at each pivot wavelength; dots and error bars come from the actual noisy pixels. The ideal expectation view changes only the displayed image.

$\mathrm{SNR}_{115}<2$

$\mathrm{SNR}_{150}>5$

$\mathrm{SNR}_{200}>3$

A separate, fixed synthetic survey

These twenty-six selected sources use a fixed five-square-arcminute calibration. Moving the individual galaxy above changes its own pixels and cuts; the survey record below has its own unchanged source population.

$9.5\leq z\leq10.5,\quad r_{1/2}=0.3\,\mathrm{kpc},\quad A_{1500}=0.2\,\mathrm{mag},\quad\beta=-2$

Selected counts and their fitted expectation

Blue bars are the saved counts. The gold curve predicts the selected counts after the full response. B and F mark bright and faint overflow. Only these detections enter the likelihood.

Selection and bin migration from the same noise law

Each column totals one when nonselection and overflow are included. Intrinsic widths are unequal. Recovered-bin labels give midpoints; the saved response retains the exact edges.

What the restricted count fit can tell us

$M_*=-20.6,\quad\widehat\alpha=-2.00,\quad\widehat\phi_*=4.43\times10^{-4}\,\mathrm{Mpc}^{-3}$

$\Delta\ln\mathcal L=0.5:\quad -2.304\leq\alpha\leq-1.725$

Densities are constant inside six intrinsic bins; the restricted Schechter-shaped family is evaluated at their midpoints. The characteristic magnitude is imposed. The half-unit likelihood-drop interval is descriptive and has no exact small-sample coverage guarantee. The faintest column is poorly recovered, so its density inherits the family assumptions.

This is an original synthetic survey, not an observed JADES luminosity function. Hidden parent objects and unselected counts are not fit observations. A real survey needs its own sensitivity, area and selection-volume calculation.

Start with the essentials

Focus question: Does a galaxy with the same total light remain equally easy to select?
One-sentence intuition: The selection acts on flux estimates recovered from the same finite noisy images. A larger image has a less precise total-flux estimate even when its total input light is unchanged.

Core mathematical model

Redshift moves a spectral density

f_{\nu,o}=\frac{(1+z)L_{\nu,e}}{4\pi D_L^2},\qquad \langle f_\nu\rangle_T=\frac{\int f_\nu T(\lambda)\,d\lambda/\lambda}{\int T(\lambda)\,d\lambda/\lambda}

The emitted spectral density is evaluated at the corresponding emitted frequency. A fixed rest-UV normalization, screen and sharp IGM break determine the photon-weighted flux in each native passband.

Estimate flux from the actual pixels

\widehat F=\frac{\sum_p w_p I_p}{\sum_p w_p^2},\qquad \sigma_F=\frac{\sigma_{\rm pix}}{\sqrt{\sum_p w_p^2}}

The weights integrate the known profile over each finite pixel. They retain lost field light. The formula assumes independent equal-variance Gaussian pixel noise and an oracle position/profile.

Keep selection and migration inside the count model

\mu_i=\sum_j A_{ij}\phi_j,\qquad \ln\mathcal L=\sum_i\left[N_i\ln\mu_i-\mu_i-\ln(N_i!)\right]

The fixed response already includes each intrinsic magnitude-bin width and volume. Only selected counts, including bright and faint overflow, enter this Poisson likelihood.

Common difficulties

A missing blue band has several explanations

Typical misconceptionEvery blue non-detection is a selected distant galaxy.

Better mental modelThis example also requires strong enough F150W and F200W measurements. Dust, size and noise affect those tests.

An ideal profile is a reference

Typical misconceptionThe smooth image is the noisy measurement with its noise perfectly removed.

Better mental modelIt is the specified model expectation. The measured pixels retain the actual saved noise draw, and the estimator uses those pixels.

The survey calibration is fixed

Typical misconceptionMoving this individual source also recalibrates the count matrix.

Better mental modelThe separate survey uses its declared fixed size, screen and redshift interval. Changing that population would require a matching new response calculation.

Run the experiment

01
Watch the blue band disappear
Compare The blue band disappears with Blue light remains.
What to observe: The sharp rest-frame break crosses the native filters; the same three cut rules can select one source and refuse the other.
02
Spread or move the light
Drag the amber grip or green centre in F150W. Watch the measurement before releasing it.
What to observe: Size spreads flux across noisy pixels; moving toward the detector edge loses field light. The clipped profile is never normalized back to unity.
03
Try the dusty record
Select Add a dust screen and inspect all three cuts.
What to observe: This actual noisy source still passes. Dust attenuates the spectrum without guaranteeing rejection.
04
Read a fixed synthetic survey
Compare the twenty-six selected counts with the predicted selected counts and the full response.
What to observe: Some intrinsic bins lose most sources and others scatter between measured bins. The faint end inherits strong assumptions about the restricted family.

High-redshift Galaxy Dropout Survey

A separate, fixed synthetic survey

Follow a galaxy from light to a count

Core mathematical model

Redshift moves a spectral density

Estimate flux from the actual pixels

Keep selection and migration inside the count model

Common difficulties

A missing blue band has several explanations

An ideal profile is a reference

The survey calibration is fixed

Run the experiment

Watch the blue band disappear

Spread or move the light

Try the dusty record

Read a fixed synthetic survey

Related experiments and articles

From distant light to a galaxy census