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arxiv: 2606.01957 · v1 · pith:Y6TFJWXQnew · submitted 2026-06-01 · 🌌 astro-ph.GA

Radio Continuum Emission from Evolving Star-Forming Galaxies -- I. Correlations Involving the Total Synchrotron Luminosity

Sukanta Ghosh , Luke Chamandy , Charles Jose , Anvar Shukurov , Luiz Felippe S. Rodrigues , Fatemeh Tabatabaei This is my paper

Pith reviewed 2026-06-28 14:07 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords synchrotron emissionstar-forming galaxiesradio continuumgalaxy evolutionmagnetic fieldsstar formation rateTully-Fisher relation
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The pith

Models show synchrotron luminosity from star-forming galaxies correlates strongly with both star formation rate and rotation speed out to redshift 3.

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

The work combines a semi-analytic galaxy formation code with magnetic dynamo simulations to compute the radio synchrotron output of evolving galaxies. Under the assumption that cosmic-ray and magnetic-field energies are locally equal, the total synchrotron luminosity tracks the star-formation rate because gas mass itself tracks star formation. The same luminosity also tracks rotation speed because of the stellar-mass Tully-Fisher relation that links mass, size and spin. The turbulent magnetic-field component supplies most of the power at low redshift, but the ordered large-scale field grows in relative importance beyond redshift 1. The same models match existing radio data at low redshift yet produce systematically lower star-formation rates than earlier observational inferences at higher redshift.

Core claim

Strong positive correlations exist between the specific synchrotron luminosity L_ν and both the star formation rate SFR and the characteristic galaxy rotation speed V_rot for redshifts up to z ≃ 3. These correlations arise from the tight link between disc gas mass and SFR together with the stellar-mass Tully-Fisher relation. At low redshifts the turbulent magnetic field dominates the luminosity, while the contribution of the large-scale field increases with redshift and becomes important for z ≳ 1. The models agree with compiled observational data at low redshift but under-predict SFR at higher redshift.

What carries the argument

The combination of the GALFORM semi-analytic galaxy formation model with the MAGNETIZER dynamo code, used to compute synchrotron luminosity under local cosmic-ray–magnetic-field equipartition.

If this is right

  • The correlation between L_ν and SFR follows directly from the correlation between disc gas mass and SFR.
  • The additional correlation between L_ν and V_rot follows from the stellar-mass Tully–Fisher relation obeyed by main-sequence galaxies.
  • Turbulent magnetic fields dominate the synchrotron luminosity at low redshift while the large-scale field contribution rises and becomes significant for z ≳ 1.
  • Model predictions match existing radio data at low redshift but yield systematically smaller SFR values than earlier observational estimates at higher redshift.

Where Pith is reading between the lines

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

  • If the correlations hold, total radio luminosity could serve as a dust-independent proxy for star-formation rate once the high-redshift discrepancy is resolved.
  • The growing importance of the ordered field with redshift implies that polarization surveys at z > 1 will increasingly trace large-scale galactic dynamos rather than turbulence alone.
  • The same scaling relations could be inverted to estimate rotation speeds of distant galaxies from radio continuum maps alone, providing an independent check on the Tully–Fisher relation.

Load-bearing premise

Local energy equipartition between cosmic rays and magnetic fields is assumed when converting simulated magnetic-field strengths into synchrotron luminosity.

What would settle it

A set of radio observations at z > 1 that shows no correlation between total synchrotron luminosity and either SFR or V_rot would falsify the reported relations.

Figures

Figures reproduced from arXiv: 2606.01957 by Anvar Shukurov, Charles Jose, Fatemeh Tabatabaei, Luiz Felippe S. Rodrigues, Luke Chamandy, Sukanta Ghosh.

Figure 1
Figure 1. Figure 1: Schematic diagram of a galaxy disc showing the line of sight (LoS) unit vectors ˆn passing through the centre of the galaxy and an arbitrary location (r, ϕ). The galaxy is inclined at an angle i with respect to the LoS. The LoS di￾rections are parallel to the yZ-plane in the galactic reference frame. where B2 = B 2 + b 2 rms, E2 → ∞ and E1 = 8 GeV, the energy where the electron spectrum flattens in the sol… view at source ↗
Figure 2
Figure 2. Figure 2: Scatter plots of the total synchrotron luminosity Lν in the rest frame of the galaxies and the star formation rate (SFR) for two magnetizer models: J24 (left) and Fiducial (right), at 1.4 GHz and redshift z = 0. The small coloured circles represent the simulated galaxies with B/T ≤ 0.4 for Fiducial, while no such selection is applied for J24. The symbols with error bars denote the observational data. The c… view at source ↗
Figure 3
Figure 3. Figure 3: As Fig. 2b, but for the Fiducial model at four frequencies: 144 MHz (3a), 4.8 GHz (3b), 8.4 GHz (3c) and 10.7 GHz (3d). In Figs. 3a, 3c and 3d, hexagons and downward triangles represent the spiral galaxies and irregular/lenticular galaxies from F. S. Tabatabaei et al. (2017) (T17), respectively. In Fig. 3b, spiral galaxies from H22 are shown as diamonds [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The rotation speed Vrot as a function of the galac￾tocentric radius for 100 randomly selected galaxies at red￾shifts z = 0, 1 and 2. The radius is normalized by the half– mass radius r1/2. Vertical red lines are shown at 1.5 r1/2 and 2.5 r1/2, between which Vrot is measured. a higher redshift. These issues are discussed further in Section 5.3 [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Similar to figure 2, but showing the variation of the total synchrotron luminosity Lν in the rest frame of galaxies with the rotational velocity Vrot in the flat part of the rotation curve for two magnetizer models: J24 (left) and Fiducial (right), at ν = 1.4 GHz and z = 0. This correlation is shown for actively star-forming galaxies with specific star formation rates sSFR > 10−10.4 yr−1 . The colour bar r… view at source ↗
Figure 6
Figure 6. Figure 6: As Fig. 5b, for four different frequencies: 144 MHz (6a), 4.8 GHz (6b), 8.4 GHz (6c) and 10.7 GHz (6c). Plus signs in 6a, 6c and 6d and diamond signs in 6b are the spiral galaxies from T17 and H22, respectively, with sSFR > 10−10.4 yr−1 . servational data. To exclude the contamination from radio-loud AGN, we restrict B/T to be less than or equal to 0.4 in Fiducial (for details see Section 2.4). In [PITH_F… view at source ↗
Figure 7
Figure 7. Figure 7: The correlation between Lν and SFR as shown in Fig. 2b, at different redshifts up to z = 3. The observational data are taken from the MIGHTEE-COSMOS survey (F. An et al. 2021) at the observational frequency 1.3 GHz. To compare with the observations, we first subtract the thermal contribution from the observed flux and then calculate the rest-frame synchrotron luminosity (see Section 3 for details). Each pa… view at source ↗
Figure 8
Figure 8. Figure 8: The redshift evolution of the correlation between Lν and the rotational velocity Vrot corresponding to the flat part of the rotation curve, as in Fig. 5b [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Similar to Fig. 2a, but with the contributions of the large-scale (B) (panel 9a) or small-scale (b) (panel 9b) magnetic fields alone [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Redshift evolution of radio luminosity function (RLF) of SFGs at 1.4 GHz rest frame frequency. The orange curve shows the prediction from our Fiducial model, while the black dotted curve represents the prediction from the J24. The orange shaded region indicates the prediction of our Fiducial model for 0.2 ≤ B/T ≤ 0.5. The observational data are taken from J. J. Condon et al. (2002) (cyan diamonds), J. J. … view at source ↗
Figure 11
Figure 11. Figure 11: Correlations between the average magnetic field strength ⟨B⟩ and SFR (left), stellar mass M⋆ (middle) and sSFR (right). The grey circles represent the fiducial model, while the blue diamonds, red hexagons/downward arrows, yellow pluses, cyan crosses and green stars correspond to observations from R. Beck et al. (2019), K. T. Chy˙zy et al. (2011), B. C. Lacki & R. Beck (2013), K. T. Chy˙zy et al. (2017) an… view at source ↗
Figure 14
Figure 14. Figure 14: The correlation between the stellar mass M⋆ and the rotational velocity Vrot corresponding to the flat part of the rotation curve for actively star-forming galaxies with specific star formation rates sSFR > 10−10.4 yr−1 at the red￾shift z = 0. The colour bar represents the total synchrotron specific luminosity Lν at 1.4 GHz. Simulated galaxies are shown as circles, while the observational spiral galaxy sa… view at source ↗
Figure 13
Figure 13. Figure 13: The correlation between the star formation rate SFR and the rotational velocity Vrot corresponding to the flat part of the rotation curve for actively star-forming galaxies with specific star formation rates 10−10.4 yr−1 at the redshift z = 0. The colour bar represents the stellar mass M⋆ of the galaxies. Simulated galaxies are shown as circles, while the observational spiral galaxy samples from T16 and T… view at source ↗
Figure 15
Figure 15. Figure 15: The redshift evolution of the correlation between Lν and SFR, similar to [PITH_FULL_IMAGE:figures/full_fig_p024_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The scatter plot of the three-dimensional ve￾locity dispersion as a function of the star formation rate for the observational data from M. R. Krumholz et al. (2018, and references therein) (yellow circles). The blue curve with points represents the median of the scatter. The green dash– dotted line represents the best-fitting median of the data of the form given in equation (1) (used in the Fiducial, LS a… view at source ↗
Figure 17
Figure 17. Figure 17: The bulge-to-total mass ratio (B/T) for dif￾ferent Hubble-type galaxies, using the CALIFA survey data from J. M´endez-Abreu et al. (2021). Elliptical galaxies (E0–E7) are shown as E-types, while lenticular/spiral galax￾ies are grouped as S0 (S0–S0a), Sa (Sa–Sab), Sb (Sb–Sbc), Sc (Sc–Scd), and Sd (Sd–Sdm). Red crosses indicate the me￾dian B/T values for each Hubble type. mation rate of galaxies (M. R. Krum… view at source ↗
Figure 18
Figure 18. Figure 18: The redshift evolution of the specific star formation rate sSFR versus the stellar mass. The blue dashed contours represent the 39%, 68% and 99% confidence levels of the 2D kernel density estimate. Horizontal red dashed lines show the lower threshold sSFR (set at the 68th percentile of the main-sequence population) values used to identify actively star-forming galaxies. Here, the thermal spectral index is… view at source ↗
Figure 19
Figure 19. Figure 19: The top panel shows the redshift evolution of the star formation rate density (SFRD). The solid black line represents the total SFRD of the L16 version of galform (L16) while dashed and dotted lines represent separate con￾tributions from quiescent disc star formation (L16-disk) and starbursts (L16-burst). The red solid line shows the SFRD evolution of A. Traina et al. (2026) (T26). In the bottom panel, th… view at source ↗
Figure 20
Figure 20. Figure 20: Similar to Fig. 5b, but with contribution of large-scale (B) (panel 20a) and small-scale (b) (panel 20b) field only [PITH_FULL_IMAGE:figures/full_fig_p032_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: The redshift evolution of the ratios of the specific luminosities contributed by different terms —- b 2 b⊥ 2 , B 2 b⊥ 2 , b 2B⊥ 2 , and B 2 B⊥ 2 -— to the total synchrotron specific luminosity, plotted as a function of the star formation rate SFR. The dashed red, solid green, dash-dotted yellow, and dashed blue lines indicate the medians of Lbb⊥ /L, LBb⊥ /L, LbB⊥/L, and LBB⊥ /L, respectively. The shaded r… view at source ↗
read the original abstract

Synchrotron radiation dominates the continuum emission of star-forming galaxies in the frequency range from a few $\rm MHz$ to about $30\,\rm{GHz}$. We model the total synchrotron emission of a large population of evolving star-forming galaxies using the semi-analytic galaxy formation model GALFORM combined with the dynamo simulation code MAGNETIZER. Assuming local energy equipartition between cosmic rays and magnetic fields, we calculate the specific synchrotron luminosity $L_{\nu}$ for each simulated galaxy at various frequencies and find strong positive correlations between $L_{\nu}$ and both the star formation rate ($\rm SFR$) and characteristic galaxy rotation speed $V_{\rm rot}$ for redshifts up to $z\simeq 3$. At low redshifts, the turbulent magnetic field is found to dominate in the synchrotron luminosity, but the contribution of the large-scale magnetic field increases with redshift and becomes important for $z\gtrsim 1$. The correlation between $L_{\nu}$ and $\rm SFR$ arises from the tight correlation between the disc gas mass $M_{\rm gas}$ and $\rm SFR$, and the correlation between $L_{\nu}$ and $V_{\rm rot}$ is additionally a consequence of the stellar mass Tully--Fisher relation for main-sequence galaxies. At low redshifts, the model predictions and observational data compiled for this work show remarkable agreement, but a discrepancy arises at higher redshifts, where modelled $\rm SFR$ values are systematically smaller than those previously inferred from observations. These theoretical models will aid the interpretation of next-generation radio surveys with the Square Kilometre Array and other telescopes.

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.

Referee Report

2 major / 1 minor

Summary. The manuscript couples the GALFORM semi-analytic galaxy formation model with the MAGNETIZER dynamo code to compute the total synchrotron luminosity L_ν of a population of evolving star-forming galaxies. Under the explicit assumption of local energy equipartition between cosmic rays and magnetic fields, it reports strong positive correlations between L_ν and both SFR and V_rot up to z ≃ 3. Turbulent fields dominate the luminosity at low z while the large-scale field contribution grows and becomes important for z ≳ 1. The correlations are traced to the M_gas–SFR relation and the stellar-mass Tully–Fisher relation. Model–observation agreement is described as remarkable at low z, but the model systematically underpredicts SFR at higher redshifts.

Significance. If the equipartition assumption remains valid, the work supplies a physically motivated framework for predicting radio continuum emission that can be used to interpret SKA and other next-generation surveys. The separation of turbulent versus large-scale field contributions and the explicit linkage of the correlations to established galaxy scaling relations are clear strengths. The absence of quantitative error bars, independent validation data sets, and tests of the equipartition assumption at z > 1 nevertheless restricts the immediate utility of the reported relations.

major comments (2)
  1. [Abstract and §2] Abstract and §2 (model description): L_ν is obtained solely by imposing local equipartition on the B-field and CR energy densities output by MAGNETIZER. No sensitivity run is shown in which the equipartition ratio is allowed to vary with redshift or with the increasing large-scale-field fraction at z ≳ 1; such a variation would directly rescale the derived L_ν values and therefore alter the slopes and scatter of the L_ν–SFR and L_ν–V_rot relations that constitute the central claim.
  2. [§4] §4 (high-redshift comparison): The text notes that modelled SFR values lie systematically below observational inferences at z > 1. Because L_ν is computed from the same gas and magnetic-field quantities that also set the SFR, any additional systematic shift arising from a redshift-dependent departure from equipartition would compound the existing discrepancy and weaken the assertion that the correlations can be applied to interpret SKA observations at z > 1.
minor comments (1)
  1. [Abstract] Abstract: the phrase 'remarkable agreement' at low redshifts is not accompanied by any quantitative metric (e.g., reduced χ², median offset, or scatter) that would allow the reader to judge the level of agreement.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed report. We address each major comment below, providing our responses and indicating whether revisions will be made.

read point-by-point responses

  1. Referee: [Abstract and §2] Abstract and §2 (model description): L_ν is obtained solely by imposing local equipartition on the B-field and CR energy densities output by MAGNETIZER. No sensitivity run is shown in which the equipartition ratio is allowed to vary with redshift or with the increasing large-scale-field fraction at z ≳ 1; such a variation would directly rescale the derived L_ν values and therefore alter the slopes and scatter of the L_ν–SFR and L_ν–V_rot relations that constitute the central claim.

    Authors: The manuscript explicitly adopts local energy equipartition as a standard and well-motivated assumption for calculating synchrotron luminosity from the magnetic field and cosmic-ray energy densities provided by MAGNETIZER. The reported correlations are derived and presented under this assumption. There is currently no consensus or physically motivated prescription for how the equipartition ratio might vary with redshift or with the relative contribution of the large-scale field; introducing arbitrary variations would therefore add unconstrained parameters without improving the physical interpretation. We have revised Section 2 to state more explicitly that all quantitative results are conditional on the equipartition assumption and have added a brief discussion of this limitation in the conclusions. revision: partial

  2. Referee: [§4] §4 (high-redshift comparison): The text notes that modelled SFR values lie systematically below observational inferences at z > 1. Because L_ν is computed from the same gas and magnetic-field quantities that also set the SFR, any additional systematic shift arising from a redshift-dependent departure from equipartition would compound the existing discrepancy and weaken the assertion that the correlations can be applied to interpret SKA observations at z > 1.

    Authors: The systematic underprediction of SFR at z > 1 is already noted in the manuscript and arises from the underlying GALFORM model. Because L_ν is computed self-consistently from the same gas mass and magnetic-field quantities that determine the SFR within the model, the L_ν–SFR and L_ν–V_rot relations remain internally consistent under the maintained equipartition assumption. We agree that any unmodeled redshift dependence in the equipartition ratio would affect the absolute normalization at high z. We have expanded the discussion in Section 4 to caution that the reported correlations should be applied to SKA data at z ≳ 1 only with this caveat in mind. revision: partial

Circularity Check

0 steps flagged

No significant circularity; correlations are model outputs from external codes under stated assumption

full rationale

The paper runs established external codes (GALFORM, MAGNETIZER) to generate galaxy populations, then computes L_ν from simulated B and CR densities under the explicit local equipartition assumption. The reported L_ν–SFR and L_ν–V_rot correlations are shown to follow directly from the model's pre-existing M_gas–SFR relation and the stellar-mass Tully–Fisher relation; neither correlation is fitted to the target data nor defined in terms of itself. No self-citation is invoked as a uniqueness theorem or load-bearing premise, and no parameter is tuned on a subset of the reported relations and then relabeled a prediction. The high-z discrepancy with observed SFR is noted openly rather than adjusted away. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The model rests on the equipartition assumption and on the internal parameterizations of the two cited simulation codes; no new free parameters are introduced in the abstract itself.

axioms (1)
  • domain assumption local energy equipartition between cosmic rays and magnetic fields
    Invoked to calculate L_ν from the simulated magnetic field and cosmic-ray energy densities.

pith-pipeline@v0.9.1-grok · 5857 in / 1269 out tokens · 24055 ms · 2026-06-28T14:07:57.607175+00:00 · methodology

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