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Sandbox Physics
From distant light to a galaxy census

L4 · Light, images and selection

Does bright UV light imply efficient star formation?

Sandbox Physics ·

Bright UV light first establishes a large luminosity at those wavelengths. A star-formation rate, accumulated stellar mass and baryon-conversion efficiency each require additional assumptions about stellar ages, dust, active nuclei and halos. Follow those steps through specific primary-paper sections before interpreting an efficiency claim.

Compare a coeval population with continuing star formation

Open Section 3.1.1 and Figure 2 of Madau and Dickinson’s 2014 review. The left panel ages a population formed together; the right continually adds new stars. Comparing them reveals why UV brightness needs a history before it becomes a present formation rate.

The initial mass function specifies the relative numbers born at different stellar masses. Massive short-lived stars supply much UV light, while faint low-mass stars can retain substantial mass. Age, composition and dust change the luminosity associated with a given rate. Read Figure 3 and equation 10 with their stated mass function and history.

Reading: Madau & Dickinson (2014)

Change the conversion conditions one at a time

Take a UV AB absolute magnitude of minus twenty as a scalar illustration, without fitting a stellar population. The preceding 3631-jansky reference gives rest-frame luminosity density about 4.344 times ten to the twenty-eight ergs per second per hertz.

Choose one explicit reference listed in the review: a Salpeter initial mass function from 0.1 to 100 solar masses, constant formation, solar metallicity and age at least about 300 million years. Its coefficient is 1.3 times ten to the minus twenty-eight. The review’s 1.15 coefficient for a population-evolution comparison has different assumptions.

M˙⋆=KUVLν,⋆intrinsic,KUV=1.3×10−28M⊙ yr−1erg s−1 Hz−1\dot M_\star=K_{\rm UV}L_{\nu,\star}^{\rm intrinsic},\qquad K_{\rm UV}=1.3\times10^{-28}\frac{M_\odot\,\mathrm{yr}^{-1}}{\mathrm{erg}\,\mathrm{s}^{-1}\,\mathrm{Hz}^{-1}}
Apply the declared conversion to intrinsic stellar UV luminosity. Revisit it when age or formation history changes.
Specified interpretation of the same emerging UV lightRate / solar masses per year
All stellar, zero UV attenuation5.65
All stellar, one magnitude of stellar UV attenuation14.2
Half the emerging UV stellar, one magnitude of stellar attenuation7.09

Reading: Madau & Dickinson (2014) · Sandbox Physics

Distinguish a formation rate from retained stellar mass

One magnitude of attenuation multiplies intrinsic stellar luminosity by about 2.512. The final row additionally specifies half of the emerging UV as stellar. That fraction is an illustration, not a measured AGN contribution in a real galaxy. One luminosity supports different conditional answers.

A formation rate measures new mass per year. Present stellar mass accumulates past formation while accounting for gas subsequently returned. Multiplying the current rate by an age assumes an unchanged rate, and even then the mass ever formed differs from mass still retained in stars.

M⋆(t)=∫0tM˙⋆(t′) [1−R(t−t′)] dt′M_\star(t)=\int_0^t\dot M_\star(t')\,[1-R(t-t')]\,dt'
The schematic return fraction describes mass returned by a coeval stellar population and depends on its adopted physics. No return function or new stellar mass is calculated here.

Reading: Madau & Dickinson (2014) · Sandbox Physics

Read JADES spectra for another source of light

An active galactic nucleus is the luminous region around an accreting black hole. Open version two of Juodžbalis and colleagues’ 2025 JADES paper, Figure 1, Section 5.2 and Figure 4. Identify the stellar and nuclear components and ask how the spectroscopic aperture handles an extended host.

Figure 1 shows broad Balmer components, narrow lines and the wider spectrum. Check the component models, signal, residuals and whether other lines support the same kinematic interpretation. Section 5.2 specifies nuclear-plus-stellar decomposition and compares two fitting routes for host mass. Those observations and models add much more than four broad-band measurements.

Retain the sample’s redshift and selection conditions. An AGN fraction from it cannot simply be assigned to a controlled redshift-ten Gaussian source. Ask instead which additional observation could separate another continuum source from stellar light.

Reading: Juodžbalis et al. (2025)

Place a galaxy in a halo before defining efficiency

Read Sections 2.2, 3.2–3.3 and 6.6 of Shuntov and colleagues’ 2025 COSMOS-Web paper with Figures 1, 10 and 11. Follow population fitting, completeness and AGN handling before the matching of galaxy abundances to theoretical halo abundances. Halo mass on the final plot has passed through that inference.

Section 6.6 distinguishes integrated efficiency from present formation relative to halo accretion and from formation per unit gas mass. Annotate the mass range, baryon fraction and matching assumptions. This reading does not recompute the authors’ masses or halo curves.

ϵ⋆=M⋆fbMh\epsilon_\star=\frac{M_\star}{f_bM_h}
This is integrated baryon-to-star efficiency. In a separate example, specify one billion solar masses of stars, a hundred billion in the halo and baryon fraction 0.16: efficiency is 0.0625, or 6.25 percent. Both masses are assumed inputs.

Reading: Shuntov et al. (2025) · Sandbox Physics

Choose an observation for the next inference

Start with the four-band fluxes and visible pixels. A recent formation rate needs age, dust and other light sources checked. Accumulated mass needs observations constraining older stars and the formation history. An efficiency claim additionally needs an explicit route to halo mass.

Annotate JADES Figure 1 with the observed lines or continuum components constraining its model. Annotate COSMOS-Web Figure 10 with the step introducing theoretical halo abundance. Extra UV output could reflect recent formation, transmission or another source of light. A mechanism becomes testable when an additional measurement can distinguish those possibilities.

Reading: Juodžbalis et al. (2025) · Shuntov et al. (2025)

Try the observation

Separate spectral normalization from physical inference

  1. Open luminosity and spectrum; change UV magnitude and screen separately and compare the four bands.
  2. Identify changes prescribing a continuum/transmission and those needing stellar-age or nuclear observations.
  3. Use the three primary figure targets to name one additional dataset needed for mass or efficiency.

The image example measures a prescribed continuum/screen through finite pixels. This chapter adds explicit scalar conversions and primary-paper reading, without population-synthesis or mass fitting.

Exercises and explained answers

Hold one magnitude of stellar attenuation fixed and halve the stellar fraction of emerging UV. How does the scalar rate change?

Intrinsic stellar luminosity and the corresponding rate halve under that explicit assumption. Holding the same stellar attenuation is essential; this does not measure an actual AGN fraction.

Do equal present UV luminosities establish equal accumulated stellar masses?

No. Different histories, ages and gas return change the relation between current light and retained mass. Constraining those histories needs additional observations and population models.

What are the units of a formation rate divided by gas mass, and how do they differ from integrated efficiency?

The ratio has units per year, a gas-consumption rate scale. Integrated efficiency divides stellar mass by halo-associated baryonic mass and is dimensionless.

Primary sources and calculation notes

  1. Madau & Dickinson (2014), Cosmic Star-Formation History

    Sections 3/3.1.1, Figures 2–4 and equation 10: ages, stellar initial mass functions and conditional UV conversion. The illustrative coefficient 1.3e−28 uses constant formation, solar metallicity, age at least about 300 Myr and Salpeter 0.1–100 solar masses; it is distinct from their evolving-population 1.15 choice.

  2. Juodžbalis et al. (2025), JADES broad-line AGN census, v2

    Version 29 April 2025; Figure 1, Section 5.2, Figure 4 and Tables 3–4. Read broad/narrow spectra, nuclear/stellar decomposition, aperture assumptions and compared host-mass routes. No AGN fraction is transferred to the redshift-ten synthetic source; no mass fit is replayed.

  3. Shuntov et al. (2025), COSMOS-Web stellar mass assembly, A&A 695, A20

    Publisher version of record read via DTU Orbit: Sections 2.2/3.2–3.3/6.6 and Figures 1/10/11. Follow population modelling, completeness/AGN handling and simple abundance matching. The baryon fraction is an explicit separate assumption in the scalar example, not a reconstruction of these curves.

  4. Sandbox Physics, explicit stellar-reading scalar examples

    Original AB-normalization, declared UV-to-rate conversion, screen/fraction and assumed-mass efficiency arithmetic only. No SPS, stellar-mass fit or new observations.

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