Two domains of extended Lyman-alpha emission around galaxies: from local radiation to environmental regulation

Abstract: We examine the relation between extended Ly$α$ halos around high-redshift galaxies and the main factors responsible for driving the emission in such halos, in particular at distances around and beyond one virial radius $r_\mathrm{vir}$. To reach the required surface brightness sensitivity we take advantage of the MUSE eXtremely Deep Field (MXDF) survey, allowing us to probe levels as faint as $\sim 10<sup>{-20}$ erg cm$<sup>{-2}$ s$<sup>{-1}$ arcsec$<sup>{-2}$ in individual Ly$α$ halos. Our sample consists of the 21 apparently core- and halo-brightest (yet intrinsically low luminosity $\log_{10}$L$<em>{\mathrm{Ly}α} &lt; 42.3$ erg s$<sup>{-1}$) Ly$α$ emitters (LAEs) in the MXDF at $3<z<4$, with typical virial radii around 20 kpc. We measure their radial surface brightness profiles out to 50 kpc (more than $2r</em>{\mathrm{vir}}$) and investigate the correlations between surface brightness and internal (star formation rates of the host galaxies, SFR) or external influences (environmental density, $δ+1$). We find a clear break in these correlations at radii around or just below $1r_{\mathrm{vir}}$. Below this break the emission correlates tightly with SFR (as expected) and not at all with $δ+1$. Beyond $\sim 1r_\mathrm{vir}$(20 kpc) we observe the opposite trend with no dependence on SFR, but an emerging correlation with $δ+1$. We compare our measurements with the expected integrated surface brightness from ultrafaint, individually undetected LAEs and find that the latter is insufficient to drive the observed correlation. We conclude that Ly$α$ emission from the outer halos is regulated by the surrounding environment, but originates mostly from diffuse gas rather than discrete sources.

• The paper shows that individual Lyα halos around 21 galaxies at redshift 3–4 change behavior near 15–20 kpc: inner emission closely tracks host star formation, while outer emission tracks environmental density.
• Deep MUSE measurements find that undetected neighboring emitters generally cannot explain the observed surface brightness within 50 kpc, and UV-background fluorescence or nearby AGN also fail as common dominant sources.
• The results support a two-domain model in which diffuse cool gas beyond the virial radius may be powered by cold accretion, with spatially resolved Lyα line profiles identified as the key test of inflow versus outflow.

Overview and motivation

Extended Ly$\alpha$ emission (Ly$\alpha$ halos, LAHs) is detected around most high-redshift star-forming galaxies, but the origin of this emission at large galactocentric distances remains contested. A recurring hypothesis holds that the apparently diffuse emission beyond tens of kpc is in fact a superposition of contributions from faint, individually undetected neighboring Ly$\alpha$ emitters (LAEs) — the "two-halo term" — rather than genuine circumgalactic medium (CGM) gas. Testing this idea requires surface-brightness sensitivity at the $\sim10^{-20}$ erg cm$^{-2}$ s$^{-1}$ arcsec$^{-2}$ level and object-by-object measurements, since stacking erases correlations between observables. This paper by Kozlova et al. exploits the 141-hour MUSE eXtremely Deep Field (MXDF) on the Hubble Ultra-Deep Field to do exactly that: measuring individual radial surface brightness profiles out to 50 proper kpc for a small, exceptionally well-characterized sample of low-luminosity LAEs at $3SFR) and external ones (environmental overdensity $\delta+1$).

The central result is a clean regime change near one virial radius ($r_\mathrm{vir}\simeq20$ kpc): inside it, Ly$\alpha$0 surface brightness correlates tightly with SFR and not at all with environment; outside it, the SFR correlation vanishes entirely while an environmental correlation emerges.

Data, sample selection, and modeling

The sample comprises 21 LAEs drawn from the AMUSED catalog of the MXDF, restricted to $\alpha$1, secure redshifts, $\alpha$2 h exposure coverage, and continuum-subtracted pseudo-narrowband (NB) images fully contained in the deep footprint. Two selection channels were used:

• Core-bright (16 objects): central Ly$\alpha$3 S/N within 1 Kron radius exceeding 30, irrespective of halo properties; representative of the general LAE population.
• Halo-bright (9 objects, 4 overlapping): significant detection ($\alpha$4) in the 15–50 kpc annulus; deliberately not representative, but informative about outer halos.

Notably, despite being the brightest LAEs in an ultradeep dataset, most objects have $\alpha$5 erg s$\alpha$6 — intrinsically fainter than samples in most previous stacking studies. The two selection quantities are essentially uncorrelated: bright cores do not imply extended halos or vice versa. Special cases handled individually include ID 8537, which shows a central Ly$\alpha$7 depression with a clumpy ring-shaped halo, and ID 7586/8469, a same-redshift pair likely sharing one halo.

Each LAE was modeled as the sum of an elongated exponential disk (structural parameters fixed to those of its HST F775W continuum counterpart) plus a circular exponential halo component using galfit. Radial SB profiles were extracted in azimuthally averaged annuli from 0 to 50 kpc, reaching more than $\alpha$8 for typical virial radii of $\alpha$920–30 kpc estimated via three independent methods (stellar-mass scaling, clustering-inferred halo masses, and size–halo scaling), all converging on $\alpha$0 kpc.

Profile morphology and comparison with stacking

The halo components are well described by single exponentials in nearly all objects, with large dispersion in scale lengths (from $\alpha$11 kpc to $\alpha$2 kpc). Only four halo-bright objects (IDs 2726, 4842, 400, 8284) show flattening beyond 15–20 kpc, and in each case this traces directly to secondary Ly$\alpha$3 peaks from companions or complex structures — not to a smooth transition to a different profile family. The median-stacked profile of the core-bright subsample agrees within errors with the Wisotzki et al. (2018) stacked profile of $\alpha$4100 faint MUSE LAEs, confirming that the small sample behaves like the broader population; the halo-bright stack sits substantially higher at large radii by construction.

The key implication is that individual, ultradeep data reveal a diversity of halo sizes and profile shapes invisible in stacks, and that apparent profile flattening in individual systems is often attributable to discrete neighbors rather than intrinsic CGM structure.

Discrete neighbors versus diffuse gas

Using the formalism of Herrero-Alonso et al. (2023) with an updated Ly$\alpha$5 luminosity function (Schechter faint-end slope $\alpha$6 from Tornotti et al. 2025), the authors compute, per object, the integrated surface brightness $\alpha$7 expected from undetected neighbors below the MXDF selection function, including HOD-based clustering boosts ($\alpha$8 averaged over the relevant luminosity range). The comparison shows that measured surface brightness exceeds $\alpha$9 by a large factor at essentially all radii where emission is significantly detected; only in the outermost bin (37–50 kpc) do individual measurements become consistent with the prediction, and even there the error bars are large.

This is a strong quantitative statement against the two-halo-term interpretation as the dominant explanation for outer-halo emission within 50 kpc. The main caveat the authors concede is the still-poorly constrained faint-end slope of the Ly$\sim10^{-20}$0 LF: adopting a steeper value such as $\sim10^{-20}$1 would raise the predicted neighbor contribution by up to a factor $\sim10^{-20}$2, though they argue recent large LAE samples favor shallow slopes.

The environmental density correlation

Environmental density $\sim10^{-20}$3 was assigned via kernel-density estimation over the redshift distribution of the full AMUSED catalog, exploiting the pencil-beam geometry of MXDF/MOSAIC where structure manifests primarily along the line of sight. Correlating SB against $\sim10^{-20}$4 across six radial bins yields the paper's most striking result:

• For $\sim10^{-20}$5 kpc there is no positive correlation (a weak anti-correlation at $\sim10^{-20}$6 kpc is not statistically significant).
• For all four bins with $\sim10^{-20}$7 kpc, a positive correlation appears, formally significant at $\sim10^{-20}$8 confidence in the 15–20 kpc annulus, with closely similar trends across all four bins despite differing SB levels.

Taken together, the similarity of the relation across the outer bins argues for a common physical driver of outer-halo emission tied to environment. Consistent with this picture, neither the fitted halo scale lengths nor halo flux fractions correlate with overdensity — these parameters are set entirely by the inner halo.

The SFR correlation and its breakdown

Correlating SB with Prospector-based SFRs (100 Myr averages; Magphys gives consistent results) reveals the mirror-image behavior:

• A highly significant positive correlation exists from the center out to $\sim10^{-20}$920 kpc — notably holding even at 10–15 kpc, several exponential halo scale lengths and 20–40 stellar scale lengths from the stars themselves.
• Beyond 20 kpc the correlation disappears entirely.

Because the y-axis uses directly measured mean surface brightness rather than total luminosity, hidden distance-driven correlations are excluded. The joint pattern — SFR-tracked emission inside %%%%4$\alpha$4%%%%1, environment-tracked emission outside — constitutes the paper's core evidence for a physical transition rather than a gradual blending. The authors locate the turnover robustly at 15–20 kpc, close to $^{-2}$2, and confirm robustness against alternative radial binnings and against analyzing the core-bright subsample alone.

Powering mechanisms for the outer halo

Three candidate power sources for the outer emission were evaluated quantitatively:

• UV background fluorescence: following Cantalupo et al. (2005) and Gallego et al. (2021) with the Puchwein et al. (2019) UVB model, the maximal predicted SB (covering fraction $^{-2}$3) is of order $^{-2}$4–$^{-2}$5 scaled units. Several halo-bright objects at 27–37 kpc exceed this upper limit, ruling out UVB fluorescence as their dominant mechanism at those radii; at 37–50 kpc the data cannot decisively exclude it, but fluorescence also fails to explain the environmental correlation.
• Locally boosted radiation field from LAE overdensities: no evidence found; the SB–density trend does not strengthen at the largest radii where boosting should be most prominent.
• Nearby AGN: four objects lie within proximity zones of two known type-2 AGN/QSOs, with generous (likely overestimated) photoionization-rate enhancements of factors $^{-2}$62–10. None shows systematically enhanced outer halos except possibly ID 8284, whose asymmetric halo has a likely subthreshold companion and is therefore an ambiguous case. Undetected dusty star-forming galaxies are dismissed as too rare to provide a common explanation.

Discussion: two domains and the cooling-radiation hypothesis

The synthesis is that inner and outer LAHs constitute two physically distinct domains separated near $^{-2}$7. Inside it, emission is powered by massive stars — either recombination radiation scattered outward through CGM neutral gas or in-situ recombination from leaking LyC photons — with star-formation-driven outflows shaping the gas independently of environment. Outside it, the emission responds to environmental richness but not to the host's recent star formation, implying diffuse cool gas extending beyond the virial radius rather than discrete sources: richer environments harbor larger cool-gas reservoirs capable of shining in Ly$^{-2}$8.

For the powering mechanism of this diffuse outer emission, the authors advance cold accretion flows (Ly$^{-2}$9 cooling radiation) as the leading candidate: inflow rates scale with environmental density but not with central SFR, naturally reproducing the observed reversal of correlations. Fossil radiation from past star formation episodes is ruled out because recombination timescales ($^{-1}$0 yr) are far shorter than the 100 Myr SFR averaging window. This interpretation remains a hypothesis the present data cannot test directly.

Limitations and open questions

Several limitations bear directly on the strength of the conclusions. The sample is small (21 objects) and heterogeneous, mixing a representative core-bright subset with a deliberately non-representative halo-bright subset; the environmental correlation is individually significant only in one radial bin, relying on the mutual similarity of four bins for statistical weight. Virial radii rest on global scaling relations with substantial uncertainty. The exclusion of the two-halo term depends on the assumed Ly$^{-1}$1 LF faint-end slope; a steeper slope would partially rehabilitate the neighbor contribution, particularly at the largest radii where measurements approach the noise floor. UVB fluorescence can be constrained only weakly at 37–50 kpc given current sensitivities.

The clearest open question posed by the paper is empirical: what powers the environmentally regulated outer-halo emission, if neither discrete neighbors nor UVB/AGN fluorescence suffice? The authors identify radially resolved Ly$^{-1}$2 spectral line profiles as the discriminating observable — outflow-dominated inner emission should be redshifted relative to systemic, whereas inflow-dominated outer emission should show blueshifted peaks, consistent with hints from prior stacking work — and flag this as the natural next step.

Conclusion

By pushing individual Ly$^{-1}$3 halo measurements beyond one virial radius for the first time at $^{-1}$4, this study establishes that circumgalactic Ly$^{-1}$5 emission divides into two regimes at $^{-1}$6 kpc: an internally powered domain tracking host SFR and insensitive to environment, and an externally regulated domain tracking environmental density while decoupled from star formation. The integrated light of undetected faint LAEs and UVB-related fluorescence are both quantitatively insufficient to explain the outer emission, pointing instead toward diffuse cool gas — plausibly energized by cold accretion — as the reservoir responsible. The proposed spectroscopic test of this interpretation through radial line-profile evolution remains the outstanding challenge.