{"id":"ad23c5e9-e3cd-4010-a98c-2012082d2b95","arxiv_id":"2501.19041","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Cosmological simulations tracking cosmic ray electrons from shocks, AGN, and star formation show that shocks dominate the fossil electron budget while galaxy formation alone cannot explain LOFAR's Faraday rotation signal.","lead":"This paper presents new cosmological simulations that track the injection and spread of relativistic electrons from shocks, black hole jets, and star formation across the cosmic web. It finds that shocks inject the most electrons by volume, that galaxy-related sources alone cannot explain recent LOFAR Faraday rotation measurements, and that the combined sources supply enough fossil electrons to seed diffuse radio emission in galaxy clusters.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Shock dominance hinges on the uncalibrated x_inj in Eq. 3: varying x_inj from 3.0 to 4.0 changes the shock CRe injection rate by roughly two orders of magnitude, enough to overturn the claimed hierarchy inside halos.","rationale":"The paper is an ambitious first attempt to track three CRe injection channels and magnetic fields self-consistently in cosmological MHD simulations, and the B4 model reproduces several galaxy observables; the code and data products are a useful resource. The reader's conditional verdict is appropriate. My concern targets the least anchored term in the central shock-dominance claim. While the reader stressed the a posteriori calibration of xi_AGN and xi_SF, those efficiencies are at least tied to radio luminosity functions. The shock term, which is the basis of the headline, is set by Eq. (3) with x_inj = 3.5 and is not calibrated against any shock radio observable in this work; its exponential sensitivity means a plausible shift in x_inj within the PIC-motivated range changes the shock budget by orders of magnitude and can flip the halo hierarchy. The energy-density wording of the abstract is also not directly supported by the number-density figures. A two-point parameter sweep of x_inj on the existing test volume would settle this at modest cost. This does not require changing the verdict, which remains CONDITIONAL; it sharpens the condition.","tokens_in":38702,"tokens_out":9195,"duration_ms":92311,"concrete_test":"Rerun the B4 model (or the smaller 21.25^3 Mpc^3 test volume at identical resolution) with x_inj = 3.0 and x_inj = 4.0, keeping all other parameters fixed, and recompute the per-halo CRe ratios shown in Fig. 20 and the coefficients in Eqs. (5)-(6). If the shock term in Eq. (5) falls below the AGN term at x_inj = 4.0, the headline hierarchy is parameter-sensitive rather than robust. Separately, integrate the ROGER template spectra of Sec. 2.7 over energy to confirm that the number-density dominance in Figs. 19-20 also holds for energy density at the fiducial x_inj = 3.5.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that structure-formation shocks dominate the volume-filling and halo budget of cosmic-ray electrons rests on the DSA injection efficiency in Eq. (3), whose exponential sensitivity to the assumed injection momentum x_inj is not tested in the paper. With x_inj = 3.5 and strong-shock alpha_inj -> 4, Eq. (3) gives xi_e proportional to x_inj^3 exp(-x_inj^2); relative to x_inj = 3.5, x_inj = 4.0 lowers the efficiency by a factor of about 29 and x_inj = 3.0 raises it by a factor of about 16. The shock coefficient in Eq. (5), 5.51e-4, would drop to roughly 1.9e-5 at x_inj = 4.0, comparable to or below the AGN coefficient 4.9e-5, so the conclusion that shocks dominate fossil CRe in halos is not robust to this parameter. The paper calibrates xi_AGN and xi_SF a posteriori to radio luminosity functions, but no equivalent calibration anchors Eq. (3) to a shock-related observable. In addition, the presented support is number-density ratios (e.g. Figs. 19-20), while the abstract claims energy-density dominance; because the injected electrons start at Lorentz factors of only a few to tens, number counts are dominated by the low-energy cutoff and need not track energy density.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents a new suite of ENZO MHD cosmological simulations (42.5 Mpc box, 1024^3 cells) that simultaneously track, at run time, the injection and advection of cosmic-ray electrons (CRe) from three mechanisms: structure-formation shocks, AGN feedback, and star-formation feedback, together with magnetic-field injection from the latter two. A mirror-fluid technique is used to estimate the age of CRe since last injection, and post-processing with pre-tabulated ROGER spectra converts the CRe fields into synchrotron and Faraday-rotation predictions. The sub-grid galaxy-formation models are calibrated against the cosmic star formation history, stellar mass functions, and AGN radio luminosity functions, with run B4 identified as the best overall. The main claims are that shocks dominate the volume-filling and halo budget of fossil CRe, that AGN dominate over star formation as a CRe source, that astrophysical sources alone cannot explain the LOFAR residual Faraday rotation, and that the combined seeding is more than sufficient to fuel large-scale diffuse radio emission.","tokens_in":39086,"tokens_out":5930,"duration_ms":65085,"significance":"If the central claims hold, this would be a valuable step: it is one of the first cosmological simulations to evolve CRe and magnetic fields from multiple astrophysical injection channels at run time, and it introduces a cheap and elegant age-tracing method that could be reused by other groups. The paper also makes a concrete, falsifiable statement about the maximum contribution of galaxy formation to cosmic magnetisation, and it provides a simple fitting formula for the fossil CRe budget in halos. The authors are commendably explicit about many limitations, including the ad hoc nature of several efficiencies and the failure of the star-formation radio luminosity function. However, the headline shock-dominance claim and the quantitative budget formulas are more sensitive to uncalibrated parameters than the text suggests, and the evidence presented is partly in number density rather than energy density.","major_comments":[{"comment":"The claim that shocks dominate the fossil CRe budget is not robust to the injection momentum parameter x_inj in Eq. (3). In the strong-shock limit (alpha_inj -> 4), Eq. (3) gives xi_e proportional to x_inj^3 exp(-x_inj^2), so changing x_inj from 3.5 to 4.0 reduces xi_e by roughly a factor of 30, and changing it to 3.0 increases it by roughly a factor of 16. With x_inj = 4.0, the shock coefficient in Eq. (5) drops from 5.51e-4 to about 2e-5, which is below the AGN coefficient 4.9e-5; the central result that shocks dominate halo CRe would then no longer hold. The paper does not provide a sensitivity scan in x_inj, and no shock-related observable is used to anchor this parameter. Please add such a test, or substantially soften the dominance claim.","section":"§2.4, Eq. (3); §5, Eq. (5)"},{"comment":"The abstract claims that shocks dominate the energy density of fossil relativistic electrons in halos, but the quantitative evidence shown in Figs. 19 and 20 is the ratio of CRe number density to thermal-proton number density. Because the injected electrons start at Lorentz factors of only a few to a few tens and the spectra are steep, the number density can be dominated by the low-energy cutoff while the energy density is dominated by a different population or by another mechanism. The paper does not show an energy-density comparison, and no argument is given that number-density ratios track energy-density ratios across the three injection channels. Please present energy-density ratios, or revise the claim to refer to number density.","section":"Abstract; §3.5, Figs. 19–20"},{"comment":"The star-formation CRe model is calibrated to the high-luminosity end of the radio luminosity function, but Sec. 3.3 states that the resulting luminosity function underpredicts low-power galaxies and overpredicts high-luminosity objects, and that the mismatch is larger than any realistic observational bias. Since the quantitative budget in Eq. (5) includes the star-formation term with xi_SF = 1e-5, and since the paper's conclusion that the combination of mechanisms is sufficient to fuel radio emission depends on the total budget, a component whose calibration demonstrably fails at the population level cannot be treated as a robust prediction. The authors should either remove the SF term from the headline budget, quantify how the SF mismatch propagates into the total, or provide a calibration that reproduces the observed SF radio luminosity function more closely.","section":"§2.6 and §3.3"},{"comment":"The paper's conclusion that galaxy formation alone cannot explain the LOFAR residual Faraday rotation depends on the simulated volume filling factors of astrophysical magnetic fields, yet Sec. 4 explicitly states that the convergence of the volume filling factor of magnetic fields and CRe injected by galaxies has not been assessed. Given that the dynamo and feedback prescriptions are sub-grid and resolution-dependent, the filling factors in Fig. 18 and the resulting RM comparison in Fig. 22 could change with resolution or with the assumed dynamo threshold. Please provide a resolution study (even at lower volume) or explicitly restrict the RM conclusion to the tested resolution regime.","section":"§4 and §3.6"},{"comment":"The normalization of the shock term in the fitting formula appears inconsistent with Eq. (3). For x_inj = 3.5 and strong shocks, Eq. (3) gives xi_e of order 1.3–1.5e-4 depending on Mach number, whereas Eqs. (5)–(6) normalize the shock coefficient to xi_e,M>=5 = 4.6e-4. This factor-of-three discrepancy is not explained; if xi_e,M>=5 is intended as an effective calibrated value that includes a Mach-number distribution or other physics, that should be stated explicitly. As written, the fitting formula mixes a nominally theoretical injection efficiency with a differently normalized coefficient, which makes its predictive content unclear.","section":"§5, Eqs. (5)–(6)"}],"minor_comments":[{"comment":"The citation 'Sarazin e.g. 1999' should read 'Sarazin 1999'.","section":"§2.3, near Eq. (1)"},{"comment":"The phrase 'By an large' should be 'By and large'.","section":"§1"},{"comment":"The in-text reference to 'Figure 3.5' should be 'Figure 23'.","section":"§3.6"},{"comment":"The symbol 'R500 3' in the first paragraph appears to be a formatting artifact; it should read 'R500' or 'R_{500}'.","section":"§3.3"},{"comment":"There are several typographical issues in the reference list, e.g., 'Vog elsberger' should be 'Vogelsberger' and 'Fanaro ff-Riley' should be 'Fanaroff-Riley'.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of A&A and the simulation suite is a useful contribution. The key risk is that the headline shock-dominance claim may not survive a sensitivity scan over x_inj; I would ask the authors to add such a scan and to distinguish number-density from energy-density statements. The RM conclusion also needs a resolution caveat or test. If these points are addressed, the paper could become publishable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper is worth a serious referee but the central quantitative claim has a hole. The new thing is the simultaneous runtime tracking of three CRe injection channels in cosmological MHD, plus the mirror-fluid age tracer. That is real and useful. The authors calibrate a suite of nine runs against observed SFR, stellar mass functions, SMBH scaling relations, and radio luminosity functions, and they are candid about failures (the SF radio LF does not match, see Sec. 3.3). The appendix tests are a plus.\n\nThe soft spots are the ones you flagged. The shock injection efficiency in Eq. 3 depends exponentially on x_inj, and the paper fixes x_inj=3.5 without testing the sensitivity. The stress-test math is right: moving x_inj from 3.5 to 4.0 cuts the shock coefficient in Eq. 5 by ~factor 29, dropping it below the AGN coefficient, so the claimed shock dominance inside halos is not robust. Outside halos, shocks probably still win by default because there are no other sources, but the halo claim is load-bearing and untested. Second, the abstract says 'energy density,' but the presented support is number-density ratios (Figs. 19-20). Low-energy electrons dominate counts; the two can diverge. A referee should ask for an energy-density version of those plots. Third, the B1Mpc=0.37 nG normalization was chosen to match LOFAR, and the C1 run is then 'the best reproduction' of the same data. That is circular as a validation, though the conclusion that astrophysical sources alone fall short is robust because the shortfall is about an order of magnitude. Fourth, the SF radio LF mismatch is admitted; it weakens the SF term in the budget, but that term is small.\n\nOverall: the qualitative hierarchy—shocks volume-filling, AGN second, SF third—is plausible and likely survives. The quantitative formula in Eq. 5 is a useful first-order estimate but should be labeled with the x_inj uncertainty. The paper is honest and technically competent, so yes, send it to peer review. The referee should require a sensitivity run on x_inj and energy-density plots before accepting the headline.","headline":"Ambitious simulation suite with a genuinely new combination of CRe injection mechanisms; the quantitative shock-dominance claim needs a robustness test on x_inj.","tokens_in":39628,"tokens_out":7090,"would_cite":true,"duration_ms":62723,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Shocks, not galaxies, seed most relativistic electrons in the cosmic web; galaxy feedback alone also cannot explain LOFAR's residual Faraday rotation.","keywords":["cosmic ray electrons","cosmic web","cosmological MHD simulations","diffusive shock acceleration","AGN feedback","star formation feedback","Faraday rotation","primordial magnetic fields"],"falsifier":"A targeted survey of residual Faraday rotation from polarised background sources at several redshifts, with the local intervening contribution removed, would decide the claim: the feedback-only models saturate near $0.1$ rad/m$^2$ out to $z\\sim2$, while a primordial field with $B_{1\\,\\mathrm{Mpc}}=0.37$ nG reaches $1$–$3$ rad/m$^2$. A measurement at the primordial level where astrophysical contamination is demonstrably absent would support the paper's conclusion, whereas one at or below the feedback-only level would falsify its claim that galaxy formation alone cannot explain the LOFAR signal.","tokens_in":38495,"feed_emoji":"📡","tokens_out":9656,"duration_ms":88377,"temperature":0.7,"pith_summary":"Using cosmological MHD simulations that inject and advect relativistic electrons from three sources simultaneously, this paper argues that structure-formation shocks, not galaxies, set the fossil electron budget of the cosmic web. Shock-injected electrons are the most volume-filling population and dominate the energy density of fossil relativistic electrons inside halos by $z=0$. The combined seeding by shocks, AGN jets, and star-forming winds is claimed to supply more than enough seed electrons to fuel large-scale radio emission. The paper also claims that even the most extreme feedback models magnetise only a small fraction of the volume, so the residual Faraday rotation recently measured with LOFAR cannot be explained by galaxy formation alone.","feed_headline":"Shocks dominate the universe's fossil electron supply","feed_subtitle":"Cosmological simulations show AGN and star formation lag behind, and galaxy fields can't match LOFAR's Faraday rotation.","key_machinery":"The argument is carried by three run-time injection modules added to a GPU-accelerated cosmological MHD code: an on-the-fly shock finder that computes Mach numbers and injects electrons with a diffusive-shock-acceleration efficiency $\\xi_e(M)$ (with a low-Mach cutoff at $M_{\\mathrm{thr}}=2.3$), an AGN feedback model that assigns black-hole masses from a gas-mass scaling relation and injects electrons at a fixed fraction $\\xi_{\\mathrm{AGN}}=10^{-3}$ of jet thermal density, and a star-formation feedback model injecting electrons at $\\xi_{\\mathrm{SF}}=10^{-5}$. A fourth ingredient is a 'mirror fluid' advected alongside each electron family with artificial exponential decay of timescale $\\tau=0.1$ Gyr, whose ratio to the undecayed fluid recovers the time since last injection in every cell, and a precomputed library of Fokker-Planck electron spectra used to convert age, density, magnetic field, and redshift into synchrotron emission.","core_discovery":"The central claim is that structure-formation shocks, with Mach numbers of order a few, inject cosmic ray electrons everywhere in the cosmic web, and that this mechanism, not AGN or star formation, sets the fossil relativistic electron budget in halos. In the best-calibrated model, the number of shock-injected electrons per thermal proton inside halos is about $5.5\\times10^{-4}$ for massive halos and $6.3\\times10^{-4}$ for small halos at $z=0$, roughly an order of magnitude above the AGN contribution and two orders above star formation. The paper derives an approximate formula (Eqs. 5-6) giving the injected electron budget as a linear combination of the three injection efficiencies. It further claims that all astrophysical seeding combined fills at most a few tens of percent of the volume with magnetic fields above $10^{-15}$ G, and that the residual Faraday rotation observed by LOFAR rises to $1\\text{--}3$ rad/m$^2$ only when a primordial field of $B_{1\\,\\mathrm{Mpc}}=0.37$ nG is included, so galaxy formation alone cannot explain the signal.","pith_inferences":["Because the budget formula is linear in the three efficiencies, a natural test is to plug efficiencies measured from higher-resolution or kinetic-plasma simulations into Eqs. 5-6 and see whether the predicted seed populations shift by less than the model-to-model scatter.","If the fossil reservoir is as large as claimed, faint diffuse radio emission from old shock electrons should be present even in regions with no currently visible shock; existing stacking limits are close to this predicted level.","The same age-tracking machinery could be applied to cross-correlate predicted synchrotron emission with thermal Sunyaev-Zeldovich maps, which would isolate the shock-seeded component from galactic confusion without extra spectral-ageing assumptions."],"forward_implications":["Radio emission from cluster outskirts and filaments should be powered mostly by pre-existing fossil electrons re-energised by weak shocks or turbulence rather than by freshly accelerated thermal electrons.","The total number of relic electrons per proton in a halo is a linear combination of the three injection efficiencies (Eqs. 5-6), so future work only needs to pin down those efficiencies to predict the seed population.","If the LOFAR residual Faraday rotation is real, an astrophysical-only explanation is excluded at the simulated level, and a primordial magnetic field of order $0.37$ nG on megaparsec scales is required.","Deep radio surveys should see a nearly connected, faint synchrotron web from shock-seeded electrons, with the strongest connection when a primordial field supplies the magnetisation."],"supporting_citations":[{"why":"Provides the ENZO code framework that the simulation suite modifies to inject and advect cosmic-ray electrons.","marker":"Bryan et al. 2014"},{"why":"Supplies the on-the-fly shock-finding algorithm and the diffusive-shock-acceleration framework used to inject shock electrons.","marker":"Ryu et al. 2003"},{"why":"Gives the semi-analytical recipe and low-Mach cutoff for electron injection efficiency from shocks used in the runs.","marker":"Kang 2024"},{"why":"Provides the analytical conversion factor used in the sub-grid dynamo model that amplifies magnetic fields in halos.","marker":"Federrath et al. 2014"},{"why":"Introduces the mirror-fluid exponential-decay technique the paper adapts to recover the age of injected electrons in every cell.","marker":"Beckmann et al. 2019"},{"why":"Supplies the gas-mass to black-hole-mass scaling relation that assigns masses to run-time SMBH sites for AGN feedback.","marker":"Gaspari et al. 2019"},{"why":"Provides the observed stellar mass function used to calibrate the star-formation sub-grid model across epochs.","marker":"McLeod et al. 2021"},{"why":"Supplies the observed LOFAR radio luminosity function for star-forming galaxies that fixes the star-formation electron injection fraction.","marker":"Cochrane et al. 2023"},{"why":"Supplies the observed AGN radio luminosity function that calibrates the AGN electron injection fraction.","marker":"Kondapally et al. 2022"},{"why":"Gives the residual Faraday rotation data from LOFAR that the simulations are compared against to rule out astrophysical-only magnetisation.","marker":"Carretti et al. 2024"}],"fun_headline_variants":["Shocks, not AGN or stars, seed most cosmic electrons","Galaxy formation alone can't explain LOFAR rotation","Cosmic shocks dominate fossil electron production","Structure shocks outshine AGN in electron seeding","Faraday rotation demands extra cosmic fields"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire electron budget rests on assumed efficiency fractions for AGN jets and star-forming winds ($\\xi_{\\mathrm{AGN}}=10^{-3}$, $\\xi_{\\mathrm{SF}}=10^{-5}$), which are calibrated after the fact to reproduce observed radio luminosity functions; if real acceleration is much less efficient, the claim that combined seeding is 'more than enough' weakens.","fun_headline_variants_meta":{"raw":{"variants":["Shocks, not AGN or stars, seed most cosmic electrons","Galaxy formation alone can't explain LOFAR rotation","Cosmic shocks dominate fossil electron production","Structure shocks outshine AGN in electron seeding","Faraday rotation demands extra cosmic fields"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00019,"raw_usage":{"total_tokens":1394,"prompt_tokens":1051,"completion_tokens":343,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":667,"completion_tokens_details":{"reasoning_tokens":270}},"tokens_in":667,"tokens_out":343,"duration_ms":3629,"temperature":1.0,"reasoning_tokens":270,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T21:31:25.022584+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A targeted survey of residual Faraday rotation from polarised background sources at several redshifts, with the local intervening contribution removed, would decide the claim: the feedback-only models saturate near $0.1$ rad/m$^2$ out to $z\\sim2$, while a primordial field with $B_{1\\,\\mathrm{Mpc}}=0.37$ nG reaches $1$–$3$ rad/m$^2$. A measurement at the primordial level where astrophysical contamination is demonstrably absent would support the paper's conclusion, whereas one at or below the feedback-only level would falsify its claim that galaxy formation alone cannot explain the LOFAR signal.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the on-the-fly shock-finding algorithm and the diffusive-shock-acceleration framework used to inject shock electrons."},{"cited_title":"J., McLure , R","cited_arxiv_id":null,"evidence_quote":"Provides the observed stellar mass function used to calibrate the star-formation sub-grid model across epochs."}],"review_version":1}