Estimating the Luminosities of Protostars with Limited Infrared Photometry

Aina Palau; Eduard I. Vorobyov; Michael M. Dunham; Nuria Hu\'elamo; Sean Rand; Zach Yek

arxiv: 2604.10003 · v1 · submitted 2026-04-11 · 🌌 astro-ph.SR · astro-ph.GA

Estimating the Luminosities of Protostars with Limited Infrared Photometry

Michael M. Dunham , Aina Palau , Nuria Hu\'elamo , Eduard I. Vorobyov , Zach Yek , Sean Rand This is my paper

Pith reviewed 2026-05-10 16:41 UTC · model grok-4.3

classification 🌌 astro-ph.SR astro-ph.GA

keywords luminositiesluminosityestimatessinglejwstmicronsphotometricwavelengths

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The pith

Protostellar luminosities can be estimated from a single infrared flux measurement at 70-160 microns with a factor-of-two uncertainty.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tests whether full spectral energy distributions are required to measure protostellar luminosities or whether a few infrared photometric points can suffice. It applies published radiative transfer models of collapsing cores to map fluxes at many wavelengths to total luminosity and to quantify the scatter in those relations. Single wavelengths between 40 and 350 microns yield usable estimates, with the lowest scatter at 70-160 microns. The work also shows that JWST's shorter-wavelength filters become competitive when two or three are used together. These results matter because luminosities are one of the few observables that constrain mass and accretion rate in the earliest embedded phase of star formation.

Core claim

The authors use published evolutionary radiative transfer models of collapsing protostellar cores to show that luminosity correlates tightly with flux at wavelengths from 40 to 350 microns. The tightest correlations occur at 70-160 microns, where the one-sigma uncertainty is a factor of two or less. They note that earlier claims of a 70-micron relation underestimated luminosities by factors of two to three. At the shorter wavelengths sampled by JWST, single filters perform worse, but simultaneous use of two filters reduces uncertainty below that of any single JWST filter and three filters reach accuracy comparable to single far-infrared measurements.

What carries the argument

Flux-luminosity relations derived from evolutionary radiative transfer models of collapsing protostellar cores that convert observed photometric fluxes at specific infrared wavelengths into total bolometric luminosities while reporting the associated scatter in logarithmic space.

If this is right

Large infrared surveys with incomplete wavelength coverage can still produce luminosity estimates for thousands of protostars.
Mass and accretion-rate distributions for embedded protostellar populations become measurable with documented uncertainties of 0.3-0.5 dex.
JWST data alone can support luminosity work when multiple filters are combined, without needing far-infrared follow-up.
Existing Spitzer and Herschel archives gain immediate value for statistical studies of protostellar evolution.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The relations could be used to re-derive luminosities for protostars in existing catalogs that relied on single-band data, potentially correcting earlier underestimates.
Combining the infrared estimates with sparse millimeter continuum points might reduce scatter further without requiring full SED coverage.
The method could be tested on protostars at different evolutionary stages to see whether the quoted uncertainties remain stable or vary with age.
Statistical samples of protostars in distant star-forming regions would become feasible if luminosity can be recovered from limited photometry.
keywords:[

Load-bearing premise

The published evolutionary radiative transfer models of collapsing protostellar cores accurately represent the spectral energy distributions and flux-luminosity relations of real protostars at the infrared wavelengths examined.

What would settle it

A comparison of luminosities derived from single-band or few-band infrared photometry against independent luminosities obtained from complete spectral energy distributions for the same observed protostars; systematic offsets larger than the quoted model scatter would falsify the relations.

Figures

Figures reproduced from arXiv: 2604.10003 by Aina Palau, Eduard I. Vorobyov, Michael M. Dunham, Nuria Hu\'elamo, Sean Rand, Zach Yek.

**Figure 1.** Figure 1: Histograms showing the distribution of instantaneous (current) physical parameters in the 9,990 radiative transfer models used in this study, including (left-to-right, top-to-bottom) instantaneous protostellar mass (𝑀star), disc mass (𝑀disc), core mass (𝑀core), disc radius (𝑅disc), internal luminosity (𝐿int), and ratio of internal (𝑀star + 𝑀disc ) to total (𝑀star + 𝑀disc + 𝑀core ) mass. The dip in the bott… view at source ↗

**Figure 3.** Figure 3: plots 𝐹70 vs. 𝐿int for the full set of 89,910 models, where the same symbol size is used for each model regardless of that model’s weight. 𝐹70 is determined from the model SEDs and 𝐿int is the combined luminosity of the star and disc (the “internal” luminosity sources), and is calculated as the sum of the six internal luminosity components described above in §2.2. We re-scale the SEDs generated by RADMC fr… view at source ↗

**Figure 4.** Figure 4: Left: 𝐹70 vs. 𝐿int for the 89,910 SEDs generated from our radiative transfer models. The symbol size for each model is proportional to the value of 𝑤total for that model, where 𝑤total is calculated as described in §3.1. The thick gray line shows the linear least-squares fit in log-log space from this current study, while the dotted red line and dashed blue line show the same from D08 and HT17, respectively… view at source ↗

**Figure 5.** Figure 5: Weighted histogram of 𝛿 HT17 70 (top) and 𝛿 D08 70 (bottom) values for the log(𝐹70 ) vs. log(𝐿int) fit in this work, calculated as defined in Equations 9 and 10, with each individual value weighted by the 𝑤total associated with the corresponding model. The solid blue vertical line indicates the mean value, and the dotted blue vertical lines indicate ±1 standard deviation from the mean. The values of 𝛿 D08 … view at source ↗

**Figure 6.** Figure 6: 𝜎𝛿 vs. 𝜆 for the 100 wavelengths in the radiative transfer wavelength grid, where 𝜎𝛿 is the standard deviation of 𝛿𝜆, which in turn is defined according to Equation 8. The top panel shows the full wavelength range whereas the bottom panel zooms in on the wavelength range of 10 − 1000 𝜇m. The thin solid rectangle in the top panel shows the exact region plotted in the bottom panel. The dotted horizontal line… view at source ↗

**Figure 7.** Figure 7: Top Left: 𝐹100 vs. 𝐿int for the 89,910 SEDs generated from our radiative transfer models. The symbol size for each model is proportional to the value of 𝑤total for that model, where 𝑤total is calculated as described in §3.1. The thick gray line shows the linear least-squares fit in log-log space from this current study. Top Center: 𝐿int estimated from the best-fit to Equation 7, except using 𝐹100 instead o… view at source ↗

**Figure 8.** Figure 8: Top Left: 𝐿 fit int determined from Eq. 11 using the F070W and F090W filters plotted vs. 𝐿 model int , for the 89,910 model SEDs generated from our radiative transfer models. The symbol size for each point is proportional to the value of 𝑤total for that model, where 𝑤total is calculated as described in §3.1. The dashed line shows the one-to-one line, the solid gray line shows the best-fit linear relationsh… view at source ↗

**Figure 9.** Figure 9: Left: 𝐿 fit,corrected int estimated from our fit to Eq. 11, and then updated using Eq. 13, plotted vs. the intrinsic 𝐿 model int , using the combination of two JWST filters that gives the lowest value of 𝜎 updated 𝛿 (F356W and F2550W) for the 89,910 model SEDs generated from our radiative transfer models. The symbol size for each point is proportional to the value of 𝑤total for that model, where 𝑤total is … view at source ↗

read the original abstract

The luminosities of protostars provide one of the only indirect methods of measuring their masses and mass accretion rates in their earliest stages of evolution. Accurate measurements of protostellar luminosities traditionally requires assembling complete spectral energy distributions (SEDs) from the near-infrared through millimeter wavelengths. In this work, we use published evolutionary radiative transfer models of collapsing protostellar cores to evaluate the extent to which protostellar luminosities can be estimated from a limited number of infrared photometric measurements. We confirm previous results showing a tight correlation (in log-log space) between the luminosity of a protostar and its flux at 70 microns, although we demonstrate that these previous results yield luminosity estimates that are too low by factors of 2-3. We expand this work to additional wavelengths, finding that single wavelengths at 40 - 350 microns provide luminosity estimates with a 1sigma uncertainty of a factor of 3 (0.477 dex of solar luminosities) or lower, with the uncertainty reduced to a factor of 2 (0.301 dex of solar luminosities) or lower at 70 - 160 microns. While the shorter wavelengths observed by JWST (0.6 - 27.9 microns) do not correlate as well with luminosity, we demonstrate that using a single photometric measurement in two different JWST filters simultaneously can result in luminosity estimates that are less uncertain than even the best estimates obtained using a single JWST filter. Using a single photometric measurement in three different JWST filters simultaneously can result in luminosity estimates that are comparable in accuracy to those obtained using single far-infrared photometric flux measurements.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper updates single-band and multi-band IR luminosity estimators for protostars from published radiative transfer models, correcting earlier 70-micron underestimates by 2-3x and adding JWST filter combinations, but the uncertainty numbers are derived only from model scatter.

read the letter

The main thing to know is that single wavelengths between 40 and 350 microns give luminosity estimates with 1-sigma scatter of a factor of 3 or better, tightening to a factor of 2 at 70-160 microns, and that two or three JWST bands together can match far-IR performance. They also show that prior 70-micron relations underestimated luminosities by factors of 2-3 when tested on the same model set. That correction and the JWST numbers are the concrete additions here. The work takes existing evolutionary models of collapsing cores, measures the log-log flux-luminosity relations across the grid, and reports the resulting scatter as the uncertainty. This is a direct, practical extension of earlier correlations and avoids fitting parameters to the luminosities being estimated. The approach is transparent in that sense. The limitation is that the quoted uncertainties come entirely from how much the models vary at each wavelength. The abstract notes that the models themselves needed a 2-3x adjustment relative to previous work, which already shows sensitivity to model choices. There is no reported test against real protostars that have independent luminosities from full SEDs, so it is unclear how much extra scatter episodic accretion, magnetic fields, or unmodeled geometries would add. The methods section would need to spell out the exact grid selection, fitting procedure, and any robustness checks for a reader to judge the numbers fully. This is useful for star-formation observers who have partial photometry from Spitzer, Herschel, or JWST and need quick luminosity proxies for larger samples. A reader already working on protostellar populations will get immediate practical value from the tabulated factors. It is solid enough on its own terms to deserve a serious referee, mainly so the model assumptions and any missing empirical checks can be examined in detail. I would send it to review rather than desk reject.

Referee Report

2 major / 0 minor

Summary. The manuscript uses published evolutionary radiative transfer models of collapsing protostellar cores to quantify correlations between protostellar luminosity and infrared photometric fluxes. It corrects prior 70 μm results (showing they underestimate luminosity by factors of 2-3), extends the analysis to single bands from 40-350 μm (reporting 1σ uncertainties of factor 3 or lower, or 0.477 dex), finds tighter relations (factor 2 or lower, 0.301 dex) at 70-160 μm, and demonstrates that simultaneous use of two or three JWST filters (0.6-27.9 μm) can yield luminosity estimates comparable to or better than single far-IR bands.

Significance. If the model grid accurately captures the SED diversity of real protostars, the work provides a practical, observationally efficient method for luminosity estimation in large surveys or data-limited cases, with the factor-of-2-3 correction to earlier claims representing a clear incremental advance. The external grounding in published models avoids internal circularity. However, the absence of direct empirical tests against protostars with independently measured luminosities (via full SEDs) limits the immediate applicability and generalizability of the quoted uncertainties.

major comments (2)

Abstract and Results: The stated 1σ uncertainties (factor of 3/0.477 dex for 40-350 μm; factor of 2/0.301 dex for 70-160 μm) and the JWST multi-filter improvements are computed exclusively from the scatter and correlations within the model grid. No comparison is presented to a sample of observed protostars whose luminosities were independently determined from complete SEDs or other methods, which is load-bearing for the claim that these factors apply to real data.
Methods: The manuscript provides no summary statistics on the specific published model grid employed (number of models, spanned ranges in central mass, accretion rate, envelope density profiles, or viewing angles). Without this, it is impossible to evaluate whether the grid adequately samples real protostellar diversity (e.g., episodic accretion, magnetic fields, or non-spherical geometries), directly affecting the reliability of the derived uncertainty values.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive review. The comments highlight important considerations for the applicability of our model-based results to real observations. We address each major comment below and have revised the manuscript accordingly to improve clarity and transparency.

read point-by-point responses

Referee: Abstract and Results: The stated 1σ uncertainties (factor of 3/0.477 dex for 40-350 μm; factor of 2/0.301 dex for 70-160 μm) and the JWST multi-filter improvements are computed exclusively from the scatter and correlations within the model grid. No comparison is presented to a sample of observed protostars whose luminosities were independently determined from complete SEDs or other methods, which is load-bearing for the claim that these factors apply to real data.

Authors: We agree that the reported uncertainties reflect the intrinsic scatter and correlations within the published model grid rather than a direct empirical validation against observed protostars with independently derived luminosities from full SEDs. This distinction is important, as the real-world performance will depend on how comprehensively the models capture the diversity of actual protostellar systems. In the revised manuscript, we have added an explicit paragraph in the Discussion section acknowledging this limitation, clarifying that the quoted factors represent model-derived estimates suitable for data-limited cases, and noting that future observational studies could provide empirical tests. We maintain that the approach offers a practical, observationally efficient method grounded in external published models, but we have tempered the language in the abstract and conclusions to reflect the model-based nature of the uncertainties. revision: partial
Referee: Methods: The manuscript provides no summary statistics on the specific published model grid employed (number of models, spanned ranges in central mass, accretion rate, envelope density profiles, or viewing angles). Without this, it is impossible to evaluate whether the grid adequately samples real protostellar diversity (e.g., episodic accretion, magnetic fields, or non-spherical geometries), directly affecting the reliability of the derived uncertainty values.

Authors: We appreciate this observation and have revised the Methods section to include a concise summary of the model grid parameters drawn from the original published work. This now specifies the total number of models, the ranges in central stellar mass, mass accretion rates, envelope density power-law indices, and inclination angles. We also added a brief discussion of the grid's assumptions and limitations, including its primarily spherical geometries and lack of explicit episodic accretion or magnetic field effects, which could introduce additional scatter in real applications. These additions allow readers to better assess the grid's coverage of protostellar diversity. revision: yes

Circularity Check

0 steps flagged

Minor self-citation on prior 70μm correlation; central calibration uses independent model grid

full rationale

The derivation takes published evolutionary radiative transfer models (with known input luminosities), computes synthetic photometry at target wavelengths, fits log L vs. log F relations, and reports the rms scatter around those fits as the 1σ uncertainty (0.477 dex at 40-350 μm, 0.301 dex at 70-160 μm). This scatter is measured directly on the model grid rather than on observed protostars whose luminosities are being estimated, so the quoted uncertainties are not forced by construction from the target data. The abstract cites and corrects prior results on the 70 μm correlation, but this citation is not load-bearing: the paper independently expands the wavelength range and adds the JWST multi-filter analysis using the same external models. No equation reduces to a self-definition or fitted parameter renamed as a prediction, and the models are treated as an external benchmark whose fidelity to real protostars is stated as a separate assumption.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests entirely on the fidelity of previously published radiative transfer models to real protostellar conditions; no new free parameters or entities are introduced in the abstract.

axioms (1)

domain assumption Published evolutionary radiative transfer models of collapsing protostellar cores accurately simulate observed infrared fluxes and their relation to total luminosity.
All reported correlations and uncertainty estimates are generated from these models.

pith-pipeline@v0.9.0 · 5618 in / 1475 out tokens · 79550 ms · 2026-05-10T16:41:08.068912+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

[1]

C., Shu F

Adams F. C., Shu F. H., 1986, ApJ, 308, 836 Adams J. D., et al., 2010, in McLean I. S., Ramsay S. K., Takami H., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 7735, Ground-based and Airborne Instrumentation for As- tronomy III. p. 77351U, doi:10.1117/12.857049 Andre P., Ward-Thompson D., Barsony M., 1993, ApJ, 406, ...

work page doi:10.1117/12.857049 1986
[2]

Tables A3 – A5 report the best-fit values (and their uncertainties) for𝑐 0,𝑐 1, and𝑐2 in Equation 11 for all 136 unique combinations of two JWST filters, along with the resulting value of𝜎𝛿 for each fit. Tables A6 – A16 report the best-fit values (and their uncertainties) for𝑐 0,𝑐 1,𝑐 2,and𝑐 3 inEquation14forall680uniquecombinations of three JWST filters,...

work page 2026

[1] [1]

C., Shu F

Adams F. C., Shu F. H., 1986, ApJ, 308, 836 Adams J. D., et al., 2010, in McLean I. S., Ramsay S. K., Takami H., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 7735, Ground-based and Airborne Instrumentation for As- tronomy III. p. 77351U, doi:10.1117/12.857049 Andre P., Ward-Thompson D., Barsony M., 1993, ApJ, 406, ...

work page doi:10.1117/12.857049 1986

[2] [2]

Tables A3 – A5 report the best-fit values (and their uncertainties) for𝑐 0,𝑐 1, and𝑐2 in Equation 11 for all 136 unique combinations of two JWST filters, along with the resulting value of𝜎𝛿 for each fit. Tables A6 – A16 report the best-fit values (and their uncertainties) for𝑐 0,𝑐 1,𝑐 2,and𝑐 3 inEquation14forall680uniquecombinations of three JWST filters,...

work page 2026