Reionization, UV Luminosity and 21$\,$cm Sensitivity to Primordial Magnetic Fields: Impact of Energy Losses

Abstract: Magnetic fields with field strengths between $10<sup>{-17}\,$G and a few Nanogauss are expected to exist today in the intergalactic medium (IGM). Their origin is unknown, but may be of primordial nature, in which case they would have influenced the thermal and ionization history of the IGM as well as the growth of small-scale matter perturbations. In this work, we revisit constraints on Primordial Magnetic fields (PMFs) by consistently accounting for their energy losses through ambipolar diffusion and decaying turbulences from recombination through the epoch of reionization, which progressively reduces the magnetic field strength over time. We implement these effects in ${\tt HyRec}$ and ${\tt exo21cmFAST}$ to model the interplay between PMFs and astrophysical processes up to reionization. Using a neural-network emulator (${\tt NNERO}$), we perform a MCMC analysis that combines late-time probes of the reionization history and galaxy UV luminosity functions. We find that including PMF energy losses significantly relaxes previous bounds, as the reduced field strength suppresses their imprint on observables. Employing a Fisher matrix analysis, we estimate the sensitivity of the 21$\,$cm signal experiment HERA to the PMFs' imprint on intergalactic medium perturbations and show that 21$\,$cm cosmology could significantly improve on current bounds. Our results highlight the importance of modeling PMF evolution self-consistently with the IGM evolution to extract current bounds and future sensitivities.

• The paper demonstrates that including ambipolar diffusion and decaying turbulence significantly relaxes constraints on primordial magnetic fields during reionization.
• It employs advanced simulations with HyRec and exo21cmFAST to capture PMF effects on the intergalactic medium, dark matter structure, and UV luminosity functions.
• Forecasts indicate that upcoming HERA 21cm measurements may improve PMF sensitivity by one to two orders of magnitude.

Reionization and 21cm Sensitivity to Primordial Magnetic Fields: Accounting for Energy Losses

Overview and Motivation

This work systematically revisits cosmological constraints on primordial magnetic fields (PMFs) by explicitly incorporating PMF energy loss mechanisms—ambipolar diffusion (AD) and decaying turbulence (DT)—during the post-recombination epoch through reionization. The analysis connects PMFs to the evolution of the intergalactic medium (IGM), the growth of small-scale structure, and the resulting impact on reionization, the UV galaxy luminosity function (UV LF), and the $21\,$cm cosmological signal. The principal claims of the paper are that self-consistent modeling of PMF evolution substantially relaxes previous bounds on their properties and that $21\,$cm probes (particularly HERA) will dominate future PMF sensitivity.

Modeling Primordial Magnetic Fields and Their Evolution

Magnetic fields with strengths in the range $10^{-17}$–$10^{-9}\,$G are plausible in the IGM, with their origin either from late-time astrophysical sources (e.g., AGN outflows) or, more fundamentally, from early universe processes such as inflation or cosmic phase transitions. The focus here is on PMFs generated in the early universe, which impact the IGM via two principal mechanisms after recombination:

• Ambipolar Diffusion (AD): Conversion of magnetic energy into heat via relative motion of ions and neutrals.
• Decaying Turbulence (DT): Magnetic turbulence decay sourced by increased plasma mean free path after recombination.

These mechanisms produce redshift-dependent energy loss rates, crucially modifying the time evolution of the PMF power and thus their cosmological imprint. The paper implements these loss terms directly in the HyRec and exo21cmFAST codes, allowing tracking of the evolving PMF amplitude, $\chi_B(z)$, and its impact on the IGM temperature, ionization fraction, and structure growth.

PMF Effects on Structure Formation and the Matter Power Spectrum

The enhancement of small-scale power by PMFs arises through Lorentz-force-induced density perturbations. The paper provides a full treatment of the magnetic growth function and its explicit redshift suppression due to PMF decay:

Figure 1: Matter power spectrum and magnetic growth function as a function of wave number and redshift for varying PMF parameters. The suppression from PMF energy losses compared to naive redshifting is clearly visible.

The matter power spectra show that even a modest reduction in $\chi_B$ (due to energy losses) results in a significant suppression of small-scale enhancements previously attributed to PMFs. The effect on the halo mass function—the abundance of halos per mass interval—is similarly reduced:

Figure 2: The halo mass function is enhanced for increasing PMF normalization or spectral tilt, over a restricted mass range set by magnetic Jeans and Alfvén scales.

This scale-dependent effect directly modulates the abundance of early galaxies, impacting UV LFs and the reionization history.

IGM Thermal/Ionization Evolution and Observational Imprints

Self-consistent coupling of PMF heating (AD and DT) and structure boost modifies the ionization and temperature histories of the IGM. The computation combines the high-redshift HyRec evolution with position- and time-dependent simulations in exo21cmFAST.

Figure 3: Evolution of ionized hydrogen fraction, IGM temperature, PMF amplitude, and heating rates for varying PMF amplitudes and redshifts. The impact of PMF decay is visible, with substantial suppression of $\chi_B$ at low redshift.

A key result is that (for fixed PMF parameters) the increase in optical depth and IGM temperature—critical for CMB and $21\,$cm observables—is significantly reduced relative to analyses neglecting these energy losses.

Cosmological Constraints: Reionization, UV Luminosity Functions, and Degeneracy Structure

Constraints are extracted with a simulation-based emulator (NNERO) trained on exo21cmFAST output, enabling full MCMC sampling of astrophysical and PMF model space.

• Optical Depth to Reionization ($\tau$): The PMF-induced boost of early structure and IGM heating leads to measurable increases in $\tau$ for PMF parameters above certain thresholds.
• UV Luminosity Functions: Enhanced small-scale structure formation increases the number of faint galaxies, with data at $21\,$0 from HST placing additional constraints.

Figure 4: $21\,$1 CL exclusion regions for PMF normalization as a function of spectral index, comparing Planck-$21\,$2, UV LF, and combined likelihoods. The combined constraint is dominated by structure formation enhancement, closely tracing contours of constant Lorentz force.

A central result is that, once PMF decay is included, exclusion regions in the $21\,$3–$21\,$4 plane are shifted upward by roughly an order of magnitude compared to those derived with purely redshifting ($21\,$5 scaling) PMFs, and detailed degeneracies with star-formation efficiency and X-ray luminosity remain critical.

Figure 5: Corner plot showing joint posteriors for main astrophysical and PMF parameters from combined likelihoods. The key degeneracies are in star formation efficiency and UV escape fraction, with no strong correlation to PMF amplitude.

21cm Forecasts and Fisher Analysis for HERA

The $21\,$6cm power spectrum from Cosmic Dawn and reionization is highly sensitive to IGM heating. The paper investigates the forecasted reach of HERA through Fisher matrix analysis, focusing on the suppression of the $21\,$7cm signal’s absorption trough (due to early heating from PMFs).

Figure 6: $21\,$8cm power and global signal as a function of redshift for various PMF amplitudes. PMF heating suppresses the absorption trough and power spectrum peak at $21\,$9.

Projected HERA sensitivity offers improvements of $10^{-17}$0–$10^{-17}$1 orders of magnitude over current cosmological probes:

Figure 7: Sensitivity forecasts for PMF amplitude from HERA, illustrating dependence on astrophysical X-ray luminosity.

The strongest degeneracy is between PMF heating and X-ray heating from star formation; for low $10^{-17}$2 (astrophysical X-ray amplitude), HERA is limited nearly exclusively by its experimental noise, while high $10^{-17}$3 scenarios show degraded PMF sensitivity. The $10^{-17}$4cm constraints are not very sensitive to structure-growth enhancement below current bounds, as the relevant minihalos have masses below the star-formation threshold in the present modeling.

Implications and Outlook

The explicit inclusion of AD and DT energy losses dramatically alters the derived constraints on PMFs, resolving the long-standing discrepancy between naive estimates and realistic evolution of PMFs through the relevant epochs. The demonstrated relaxation of bounds closes the gap between cosmological and astrophysical limits and shifts the focus of future searches toward low-$10^{-17}$5, low–$10^{-17}$6 parameter space, best addressed by $10^{-17}$7cm observations.

The analysis highlights the importance of astrophysical degeneracies—notably with X-ray heating—in future CMB and $10^{-17}$8cm analyses. Systematic inclusion of forthcoming galaxy luminosity function data (e.g., from JWST) and more sophisticated modeling of minihalo populations should further refine these constraints.

Conclusion

This study presents the most sophisticated treatment to date of PMF imprint on reionization, galaxy luminosity, and $10^{-17}$9cm cosmology. The authors find that including realistic PMF energy loss mechanisms significantly loosens previous cosmological PMF limits. The combined use of $10^{-9}\,$0cm power spectra and galaxy UV LF data, alongside improved simulation and emulation pipelines, demonstrates that future HERA measurements will supersede existing constraints by up to two orders of magnitude, contingent on improved knowledge of astrophysical X-ray processes. These results establish $10^{-9}\,$1cm cosmology as an essential probe of magnetic fields from the early universe (2604.22703).