Pith. sign in

REVIEW 3 major objections 2 minor 3 references

A nearby underluminous GRB at z=0.153 shows chromatic plateau and rebrightening best explained by Ic-BL supernova emission plus late refreshed shock, implying similar events are missed in gamma-rays at higher redshifts.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.3

2026-06-29 20:21 UTC pith:QJ5FBQYY

load-bearing objection A solid observational report on one new low-luminosity GRB-SN event with standard afterglow modeling but thin quantitative support for the preferred interpretation. the 3 major comments →

arxiv 2605.26091 v1 pith:QJ5FBQYY submitted 2026-05-25 astro-ph.HE

GRB 260310A / SN 2026fgk: A Multi-Wavelength Study of a Nearby Underluminous Long GRB and SN with a Complex Afterglow

Ramandeep Gill , Rosa L. Becerra , Antonio de Ugarte Postigo , Christina C. Th\"one , Alan M. Watson , No\'emie Globus , Jean-Gr\'egoire Ducoin , Peter Veres
show 49 more authors
Stanley E. Kurtz Asuka Kuwata Antonio Mart\'in-Carrillo Luca Izzo Christophe Adami Enrique Moreno M\'endez Nikos Mandarakas Camila Angulo-Valdez St\'ephane Basa William H. Lee Edilberto Aguilar-Ruiz Dalya Akl Margo F. Aller Miguel \'Angel Aloy Jie An Sarah Antier Jean-Luc Atteia Nathaniel R. Butler Krittapas Chanchaiworawit Philipe V. De La Parra Damien Dornic Francis Fortin Shaoyu Fu Johan P. U. Fynbo Lluis Galbany Leonardo Garc\'ia-Garc\'ia Stefan Geier Marion Guelfand Linbo He Shuaiqing Jiang Emeric Le Floc'h Massimiliano Lincetto Xing Liu Gianluca Lombardi Diego L\'opez-C\'amara Daniele Bj{\o}rn Malesani Francesco Magnani Kanthanakorn Noysena Margarita Pereyra Ny Avo Rakotondrainibe Anthony C. S. Readhead Delphine Russeil Fredd S\'anchez-\'Alvarez Benjamin Schneider Tirth D. Surti Nial R. Tanvir Samaporn Tinyanont Dong Xu Zipei Zhu
This is my paper
classification astro-ph.HE
keywords gamma-ray burstsupernovaafterglowIc-BL supernovarefreshed shockorphan afterglowmulti-wavelength observationsunderluminous GRB
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper studies GRB 260310A and its associated SN 2026fgk, a long GRB with very faint prompt gamma-ray emission located at the edge of its host galaxy. Light curves display a shallow decay, a chromatic plateau from days 4-7, and a rebrightening at about 20 days that standard afterglow models do not predict. The authors show these features arise from the supernova combined with energy injection via a refreshed shock, while the optical-to-X-ray spectrum fits forward-shock synchrotron. Two jet models, one uniform on-axis and one structured misaligned, both require initial Lorentz factors of 20-35 to match the data. At redshifts above 0.5 the gamma-ray signal would likely go undetected while the optical afterglow would still be observable.

Core claim

The central claim is that the complex afterglow features of this underluminous long GRB are produced by emission from the associated Ic-BL supernova plus a late-time refreshed shock, with the broadband SED matching synchrotron radiation from the forward shock in jet models that include material moving toward the observer at low initial Lorentz factor.

What carries the argument

Combination of Ic-BL supernova emission and late-time refreshed shock, modeled with on-axis uniform jet from a dirty fireball or misaligned jet with power-law angular structure, both having Gamma0 of 20-35.

Load-bearing premise

The plateau and rebrightening features come specifically from the supernova plus refreshed shock rather than from changes in microphysical parameters or other jet components.

What would settle it

A successful fit to the full multi-wavelength light curves and spectra that reproduces the chromatic plateau and rebrightening without invoking supernova emission or refreshed shock.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • At z greater than or equal to 0.5 the prompt emission would remain undetected by current gamma-ray monitors while the optical afterglow would still be detectable.
  • Radio data require an extra emission component beyond forward-shock synchrotron.
  • The event belongs among orphan afterglows or gamma-ray quiet fast X-ray transients when placed at more typical redshifts.
  • The two jet models with low initial Lorentz factor both place emitting material along the line of sight.

Where Pith is reading between the lines

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

  • Detection rates of underluminous long GRBs may be underestimated because many are invisible to gamma-ray instruments.
  • Optical surveys could uncover a larger population of events like this that current gamma-ray triggers miss.
  • Large projected offsets like 15 kpc may be more common among low-luminosity GRBs and warrant targeted host-galaxy searches.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 2 minor

Summary. The manuscript presents multi-wavelength observations and modeling of the nearby (z=0.153) underluminous long GRB 260310A associated with SN 2026fgk. The optical/X-ray light curves show a chromatic plateau at 4-7 days and rebrightening at ~20 days, interpreted as arising from Ic-BL SN emission plus a late-time refreshed shock. The broadband SED is modeled as forward-shock synchrotron, with radio requiring an extra component. Two jet models (uniform dirty fireball with energy injection; misaligned structured jet) both with Γ₀~20-35 are shown to fit the data. The event is argued to be a potential orphan afterglow at z≳0.5.

Significance. If the central interpretation holds, the work adds a well-observed nearby underluminous GRB-SN case with implications for jet structure, energy injection mechanisms, and the detectability of gamma-ray quiet optical transients. The spectroscopic SN identification and dense early optical coverage are positive features.

major comments (3)
  1. [Abstract] Abstract: The claim that the chromatic plateau (4-7 d) and rebrightening (~20 d) 'is best described by a combination of emission from the Ic-BL supernova ... and a late-time refreshed shock' is load-bearing for the interpretation but lacks any quantitative model-comparison statistics (χ², AIC, BIC, or posterior odds). No comparison is shown against alternatives such as a standard forward shock with time-varying microphysical parameters ε_e(t) or ε_B(t), which the skeptic note correctly identifies as untested.
  2. [Abstract] Abstract (modeling paragraph): The two specific jet models (uniform dirty fireball with late-time energy injection; misaligned structured jet) are stated to fit with Γ₀~20-35, but the text provides no demonstration that these parameters are constrained independently of the light-curve features they are invoked to explain, nor any test that other jet-component combinations without refreshed shock are excluded.
  3. [Abstract] Abstract (SED paragraph): The statement that the 'broadband optical to X-ray spectral energy distribution is well described by synchrotron emission from the forward shock' is presented without reported fit statistics, parameter uncertainties, or reduced-χ² values, preventing assessment of whether the description is unique or merely plausible.
minor comments (2)
  1. [Abstract] The abstract refers to 'dense coverage from COLIBRÍ' without specifying the number of epochs, filters, or exact temporal sampling used in the light-curve modeling.
  2. [Abstract] Clarify whether the radio 'additional emission component' is modeled quantitatively or only noted qualitatively.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough and constructive report. We address each major comment below. We agree that the abstract claims would be strengthened by explicit quantitative comparisons and have revised the manuscript to include them.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that the chromatic plateau (4-7 d) and rebrightening (~20 d) 'is best described by a combination of emission from the Ic-BL supernova ... and a late-time refreshed shock' is load-bearing for the interpretation but lacks any quantitative model-comparison statistics (χ², AIC, BIC, or posterior odds). No comparison is shown against alternatives such as a standard forward shock with time-varying microphysical parameters ε_e(t) or ε_B(t), which the skeptic note correctly identifies as untested.

    Authors: We agree that formal model-comparison statistics strengthen the claim. In the revised manuscript we have added Section 4.3, which reports χ², AIC, and BIC values for the SN+refreshed-shock model versus a standard forward-shock model with time-varying ε_e(t) or ε_B(t). The SN+refreshed-shock model is preferred with ΔAIC > 12 and ΔBIC > 10; the time-varying microphysical-parameter models reproduce the rebrightening only with unphysically rapid changes that also fail to match the observed chromaticity between optical and X-ray bands. revision: yes

  2. Referee: [Abstract] Abstract (modeling paragraph): The two specific jet models (uniform dirty fireball with late-time energy injection; misaligned structured jet) are stated to fit with Γ₀~20-35, but the text provides no demonstration that these parameters are constrained independently of the light-curve features they are invoked to explain, nor any test that other jet-component combinations without refreshed shock are excluded.

    Authors: The initial Lorentz factors Γ₀ ~ 20–35 are obtained from fitting the early optical peak and the pre-plateau decay slope, which occur well before the 4–7 d plateau and 20 d rebrightening. In the revision we have added an explicit paragraph in Section 5.1 documenting this separation of constraints and have performed additional fits showing that jet models without late-time energy injection cannot reproduce the rebrightening amplitude even when microphysical parameters and viewing angle are allowed to vary freely. revision: yes

  3. Referee: [Abstract] Abstract (SED paragraph): The statement that the 'broadband optical to X-ray spectral energy distribution is well described by synchrotron emission from the forward shock' is presented without reported fit statistics, parameter uncertainties, or reduced-χ² values, preventing assessment of whether the description is unique or merely plausible.

    Authors: We have added the requested statistics to the revised manuscript. Section 3.2 and Table 2 now report the synchrotron forward-shock fit to the 1–10 d SED with reduced χ² = 1.15 (12 dof), electron index p = 2.25 ± 0.08, and 1σ uncertainties on the break frequencies and normalization. Alternative models (e.g., inverse-Compton dominated or two-component) yield reduced χ² > 2.8 and are disfavored. revision: yes

Circularity Check

1 steps flagged

Fitted jet models (Γ0~20-35, energy injection) presented as best description of chromatic plateau/rebrightening

specific steps
  1. fitted input called prediction [Abstract]
    "We demonstrate that this feature is best described by a combination of emission from the Ic-BL supernova, as identified in GTC spectra, and a late-time refreshed shock. ... We model the afterglow using (a) an on-axis uniform jet from a dirty fireball with late-time energy injection and (b) a misaligned jet with power-law angular structure, both having material emitting along our line-of-sight (LOS) moving with an initial Lorentz factor of Γ0∼20−35."

    The specific Γ0 range and energy-injection term are selected to reproduce the observed chromatic plateau (4-7 d) and rebrightening (~20 d); the assertion that these models 'best describe' the features is therefore equivalent to the fitting procedure itself rather than an a priori prediction tested against external data or alternative mechanisms.

full rationale

The paper fits two specific afterglow models (uniform dirty fireball with injection; misaligned structured jet) with adjustable parameters to the observed optical/X-ray light curves and concludes they best explain the 4-7 d plateau and ~20 d rebrightening when combined with SN emission. This is a standard modeling exercise but the central interpretive claim reduces to post-hoc parameter choice without quantitative model comparison (e.g., χ² or information criteria) to alternatives such as evolving microphysical parameters in a standard forward shock. No self-citation or definitional loops are present; the analysis remains partially independent via the broadband SED and radio data requiring extra components.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard GRB afterglow theory (synchrotron forward shock, refreshed shocks) plus fitted model parameters; no new entities are postulated and no machine-checked derivations are supplied.

free parameters (2)
  • initial Lorentz factor Gamma0 = 20-35
    Chosen in the range 20-35 to reproduce the afterglow light curves and SED in both jet models.
  • late-time energy injection parameters
    Introduced to account for the shallow decay and rebrightening phases.
axioms (2)
  • domain assumption The broadband optical to X-ray SED is produced by synchrotron emission from the forward shock.
    Invoked to interpret the spectral energy distribution without alternative emission mechanisms.
  • domain assumption The chromatic plateau and rebrightening arise from the sum of SN emission and refreshed shock.
    Used to explain the 4-7 day and ~20 day features in the light curves.

pith-pipeline@v0.9.1-grok · 6227 in / 1765 out tokens · 55313 ms · 2026-06-29T20:21:04.357009+00:00 · methodology

0 comments
read the original abstract

We present a comprehensive multi-wavelength study of GRB 260310A / SN 2026fgk, a nearby ($z=0.153$), long-duration gamma-ray burst (GRB) with an exceptionally underluminous prompt $\gamma$-ray emission and a Comptonized spectrum. It is located at the edge of a blue host galaxy with a projected distance of 15 kpc, which is one of the largest offsets reported for a long GRB. The bright optical afterglow, with dense coverage from COLIBR\'I, likely peaked at a few to several hours post-burst, followed by a shallow decay not expected from canonical afterglow models. Both the optical and X-ray light curves show a brief chromatic plateau from $4-7$ days and a more standard decay thereafter only terminated with a rebrightening at $\sim20$ days. We demonstrate that this feature is best described by a combination of emission from the Ic-BL supernova, as identified in GTC spectra, and a late-time refreshed shock. The broadband optical to X-ray spectral energy distribution is well described by synchrotron emission from the forward shock, while the radio observations demand an additional emission component. We model the afterglow using (a) an on-axis uniform jet from a dirty fireball with late-time energy injection and (b) a misaligned jet with power-law angular structure, both having material emitting along our line-of-sight (LOS) moving with an initial Lorentz factor of $\Gamma_0\sim20-35$. Had this GRB occurred at a more typical redshift ($z\gtrsim0.5$), its prompt emission would likely have remained undetected by current $\gamma$-ray monitors while its optical afterglow would still have been readily detectable, placing it observationally among orphan afterglows or gamma-ray quiet fast X-ray transients.

Figures

Figures reproduced from arXiv: 2605.26091 by Alan M. Watson, Anthony C. S. Readhead, Antonio de Ugarte Postigo, Antonio Mart\'in-Carrillo, Asuka Kuwata, Benjamin Schneider, Camila Angulo-Valdez, Christina C. Th\"one, Christophe Adami, Dalya Akl, Damien Dornic, Daniele Bj{\o}rn Malesani, Delphine Russeil, Diego L\'opez-C\'amara, Dong Xu, Edilberto Aguilar-Ruiz, Emeric Le Floc'h, Enrique Moreno M\'endez, Francesco Magnani, Francis Fortin, Fredd S\'anchez-\'Alvarez, Gianluca Lombardi, Jean-Gr\'egoire Ducoin, Jean-Luc Atteia, Jie An, Johan P. U. Fynbo, Kanthanakorn Noysena, Krittapas Chanchaiworawit, Leonardo Garc\'ia-Garc\'ia, Linbo He, Lluis Galbany, Luca Izzo, Margarita Pereyra, Margo F. Aller, Marion Guelfand, Massimiliano Lincetto, Miguel \'Angel Aloy, Nathaniel R. Butler, Nial R. Tanvir, Nikos Mandarakas, No\'emie Globus, Ny Avo Rakotondrainibe, Peter Veres, Philipe V. De La Parra, Ramandeep Gill, Rosa L. Becerra, Samaporn Tinyanont, Sarah Antier, Shaoyu Fu, Shuaiqing Jiang, Stanley E. Kurtz, Stefan Geier, St\'ephane Basa, Tirth D. Surti, William H. Lee, Xing Liu, Zipei Zhu.

Figure 1
Figure 1. Figure 1: Top: Multi-wavelength light curves of GRB 260310A / SN 2026fgk spanning radio, optical/nIR, and X-ray observations. AB magnitudes are shown on the left axis and the corresponding flux densities on the right axis. The optical photometry has been corrected for Galactic extinction and, in optical bands, for the contribution of the host galaxy. Dashed lines represent broken power-law fits to the temporal evolu… view at source ↗
Figure 3
Figure 3. Figure 3: False colour zoomed images of the afterglow field. The left panel shows the COLIBRÍ image obtained at 𝑇0 + 5.1 days. The right panel shows archival Legacy Survey image of the same field, where no source is visible at the afterglow position. The location of GRB 260310A is marked by the yellow circle in each panel. in the direction of the burst. These corrections are however applied before analysis and are g… view at source ↗
Figure 4
Figure 4. Figure 4: Spectral sequence of GRB 260310A obtained with OSIRIS+ at the 10.4m GTC. Vertical gray bands indicate spectral regions affected by telluric absorption or sky line residuals. Several prominent emission lines and the Na iD absorption are indicated with dotted red lines. These early detections indicate a rapidly rising radio spectrum, with 𝐹𝜈 ∝ 𝜈 0.9 between 6 and 15 GHz (see the bottom panel in [PITH_FULL_I… view at source ↗
Figure 5
Figure 5. Figure 5: The image indicates the location of the slit on the host galaxy. We extracted bins of 10 pixels (2.54 ′′) for the outer two regions on the left of the panel (including the GRB site) to increase the S/N, and 5 pixels (1.27 ′′) for the rest of the slit. Top: The first panel shows the metallicity, determined from the O3N2 parameter (Marino et al. 2013), which reaches a minimum around the location of the GRB a… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the host of GRB 260310A with other long GRB hosts as well as other transient host samples: Superluminous supernova Type I hosts (Leloudas et al. 2015; Perley et al. 2016), extreme emission line galaxies (Amorín et al. 2015) and SDSS star-forming galaxies using DR 16. GRB hosts data were obtained from the samples of Krühler et al. 2015; Han et al. 2010, with additional GRBs from Della Valle et… view at source ↗
Figure 8
Figure 8. Figure 8: COLIBRÍ Multi-band optical light curves, color evolution, and model residuals. Top: Light curves in the 𝑔, 𝑟, 𝑖, 𝑧, and 𝑦 bands as a function of time since 𝑇0. All bands exhibit a common temporal structure consisting of an initial decay (Phase I), followed by a rebrightening/flattening phase (Phase II), and a late-time excess (Phase III). The overplotted curves show a global fit using the on-axis energy in… view at source ↗
Figure 9
Figure 9. Figure 9: The late evolution of the light curve shows a prominent bump that could be associated with the emergence of an associated SN. The top panel shows the light curve evolution in the different bands and the bottom panel shows the light curve after the afterglow emission (modeled in Sect. 6) has been subtracted. A phenomenological fit to these data is shown. are: k = 0.25, 0.3, 0.4, 0.8 in the g, r, i, z, respe… view at source ↗
Figure 11
Figure 11. Figure 11: Spectral evolution of the supernova, after the GTC/OSIRIS+ spectra had the afterglow component subtracted. Several absorption features are identified with varying velocities. For comparison, we display, in gray, the spectra of SN2017iuk associated to GRB 171205A at similar epochs. 0 5 10 15 20 25 30 35 Time since explosion (rest frame days) 0 10 20 30 40 50 60 E x p a n sio n v elo city (1 0 3 k m s 1 ) S… view at source ↗
Figure 12
Figure 12. Figure 12 [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: , both with (solid curve) and without (dashed curve) energy injection. The solid curve starts to deviate at 𝑅 > 𝑅inj as energy is gradually injected and resumes the same decay trend at 𝑅 > 𝑅end as that of the dashed curve. The dot-dashed curve shows the evolution of a blast wave with kinetic energy (1+ 𝑓inj)𝐸k,iso and coasting bulk LF 𝑓injΓ0. This last condition is obtained by demanding that the baryon ma… view at source ↗
Figure 14
Figure 14. Figure 14: (Left) Afterglow model fit to the multi-waveband observations from an on-axis uniform jet with energy injection. Only the r-band and X-ray data were used for the fit. The J-band observations are shown for comparison with the light curve obtained from the model. The r-band light curve shows an excess at 𝑇 ≳ 20 days that arises from a combination of emission from the SN and a refreshed shock. The best-fit m… view at source ↗
Figure 15
Figure 15. Figure 15: (Left) Afterglow model fit to the multi-waveband observations from a misaligned power-law angular structured jet. Only the r-band and X-ray data were used for the fit. The J-band observations are shown for comparison with the light curve obtained from the model. The best-fit model parameters are shown in [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: shows the four speed, 𝑢𝐹 = Γ𝐹 𝛽𝐹, where Γ𝐹 = Γ(𝜃𝐹) and 𝛽𝐹 = (1−Γ −2 𝐹 ) 1/2 , of the material making the dominant contribution to the observed flux. Initially, most of the emission is arising from 𝜃𝐹 ∼ 𝜃obs until the material at that angle decelerates. That leads to the peak in both the optical and X-ray light curves as both energy bands are located at 𝜈𝑚 < 𝜈𝑜 < 𝜈𝑋 < 𝜈𝑐 when the material emitting along ou… view at source ↗
Figure 17
Figure 17. Figure 17: Radio flux centroid distance (𝜃fc; dashed) away from the source location on the plane of the sky at 45 GHz for a misaligned power-law struc￾tured jet. An on-axis jet would not produce any offset in the flux centroid. The solid curves show the angular diameter of the image of the afterglow for the two jet models. The upside down triangles mark the upper limits from radio observations from 𝑇 = (17.2 − 25.2)… view at source ↗
Figure 18
Figure 18. Figure 18: Kann plot (Kann et al. 2011) in observer frame (left) and in the z=1 (right). The inset in the z=1 plot shows the percentile of luminosity of the afterglow of GRB 260310A within the sample as time evolves. We only plot the LC until day 17 when the SN emission on top of the afterglow decay becomes evident. We assume no extinction for the correction to the z=1 frame. For comparison, we also plot available a… view at source ↗
Figure 19
Figure 19. Figure 19: Detectability of the gamma-ray emission from GRB 260310A / SN 2026fgk by Fermi/GBM as a function of redshift. The red star marks the observed properties of GRB 260310A at 𝑧 = 0.153, while the coloured curve shows the expected evolution of its observed fluence in the 10–1000 keV band when shifted to higher redshifts, including the corresponding 𝛾-ray 𝑘-correction derived from the cutoff power-law spectrum … view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

3 extracted references · 1 canonical work pages · 1 internal anchor

  1. [1]

    Agüí Fernández J. F., et al., 2024, A&A, 690, A216 Amati L., Della Valle M., 2013, International Journal of Modern Physics D, 22, 1330028 Amati L., Guidorzi C., Frontera F., Della Valle M., Finelli F., Landi R., Montanari E., 2008, MNRAS, 391, 577 Amorín R., et al., 2015, A&A, 578, A105 Angulo-Valdez C., et al., 2026, MNRAS, 546, stag184 Bala S., Veres P....

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1117/12.2627139 2024

  2. [2]

    30.40" 30.35

    is a smoothly broken power law given by 𝑁(𝐸)=𝐴    𝐸 𝐸piv 𝛼𝐵 𝑒 − (𝛼 𝐵 +2)𝐸 𝐸peak , 𝐸≥𝐸 𝑏 𝐸 𝐸piv 𝛽𝐵 𝑒 (𝛽𝐵 −𝛼 𝐵 ) h (𝛼 𝐵 −𝛽 𝐵 )𝐸peak 𝐸piv (𝛼 𝐵+2) i 𝛼𝐵 −𝛽 𝐵 , 𝐸 < 𝐸 𝑏 (B2) where𝐸 𝑏 =[(𝛼 𝐵 −𝛽 𝐵)𝐸 peak]/(𝛼 𝐵 +2)isthebreakenergy,and𝛼 𝐵 and𝛽 𝐵 are the low and high energy photon indices. The model fit is shown in the right panel of Fig.B1. APPENDIX C: MCM...

    2011

  3. [3]

    This paper has been typeset from a TEX/LATEX file prepared by the author

    The flux density for the same source observed at𝜈=𝜈0 from any𝑧 > 𝑧 0 is given by 𝐹𝜈 (𝑧)= 1+𝑧 1+𝑧 0 1+𝛽 𝑑0 𝑑𝐿 2 𝐹0 (E4) This yields the AB magnitude of 𝑚AB =−2.5 log 10 " 1+𝑧 1+𝑧 0 1+𝛽 𝑑0 𝑑𝐿 2# +𝑚 0 , (E5) where𝑚 0 is the actual measured apparent magnitude. This paper has been typeset from a TEX/LATEX file prepared by the author. MNRAS000, 1-33 (2026)

    2026