UV spectra of little red dots: Broad-line N/C, gas recycling and black hole masses

Introduction

A candidate population of supermassive black holes embedded in dense gas, the so-called ‘Little Red Dots’ (LRDs; [55, 30, 42]), is characterised, among other properties, by their V-shaped spectra with blue ultraviolet (UV) and red optical colours. The inflection near the Balmer break wavelength ([73]), in some cases more prominent than possible with stellar populations ([19, 60]), is likely due to UV absorption by enshrouding gas ([33, 71, 76, 56]). A population of ‘little blue dots’ (LBDs) has also been discovered with properties similar to LRDs (e.g. [71, 25, 56] (Brazinni et al. 2026)), and has been interpreted as LRDs with lower column densities ([75, 53]). We therefore include these objects under the general term LRD unless otherwise specified.

The UV light from LRDs is sometimes extended, indicating a significant host galaxy contribution at these wavelengths (e.g. [69, 16, 24, 34] (Sun et al. 2026)). Several properties, however, require that some UV emission from the LRD phenomenon itself must escape: LRD UV emission is typically redder than star-forming galaxies at the same redshifts and the observed damped Lyα downturn is correlated with the strength of the Balmer break ([2]) – the UV light is therefore tied to the nuclear gas structure that produces the break, indicating an origin near the gas-enshrouded nucleus rather than in the host; furthermore, while the population as a whole seems unusually deficient in classical high-ionisation AGN UV lines ([81, 86] (Lambrides et al. 2026)), moderately high-ionisation lines have nevertheless been detected in deep spectra, e.g. N IV, C IV and He II, demonstrating that photons with energies above $\sim50$ eV are present in at least some LRDs ([1, 81, 6, 79]); at a population level, the Lyα luminosity is comparable to similar redshift star-forming galaxies (Ji et al. 2026c), but broad Lyα lines have been detected in a small number of individual objects ([80, 39, 58] (Ji et al. 2026b)).

Self-consistent radiative transfer modelling with the Sirocco code has demonstrated that AGN emission mediated through dense gas flows around a supermassive BH could reproduce the dearth of X-ray emission, the UV through NIR SED, the ensemble of emission and absorption lines, as well as unify the diverse populations observed ([76 d]). In the UV, such modelling has predicted weak broad emission lines ([75, 53, 38]) and rich absorption lines from metals in the enshrouding gas (see Figure 1). Now deep rest-UV grating spectroscopy from the JWST SPURS program of four LRDs at $z = 6.7$–$7.2$ and $M_{\mathrm{UV}} < -20$ (GO-9214, PIs Mason & Stark, Chen et al. 2026) has provided stringent constraints on metal absorption features ([79, 43]). All four LRDs, labelled GN-2, GN-29, GN-2004 in GOODS-N and CEERS-7902 in EGS, show nitrogen-enhanced narrow-line gas, are UV-bright $M_{\mathrm{UV}} = -20.4$ to $-21.1$ and span the blue end of the LRD colour distribution ($\beta_{\mathrm{opt}} = 0.06$–$0.48$ [79]). Notably, such nitrogen-rich gas, a hallmark of a growing class of high-redshift N-emitters ([9, 72, 83]), links the dense nuclear environments of LRDs to the sites of hydrogen-burnt material (e.g. see discussion in Torralba et al. [84]).

In this paper, we revisit these Sirocco models to expand on the detailed constraints permitted by the absorbers and the emission features. In the context of the SPURS LRDs, this allows us to i) measure the nitrogen overabundance of the broad-line gas proper and ii) probe the radial velocity law of the gas flow.

Methods

We employ Sirocco ([50, 57]) to model LRDs with self-consistent radiative transfer and adopt the axisymmetric inflow/outflow gas-cocooned AGN models described in previous papers (i.e., Sneppen et al. [74], see also [53, 38]) and detailed in App. B. These papers employ a standard Sirocco line list, where for instance the resonance doublet C iv $\lambda\lambda1548,1551$, like all metal lines, is treated as a collisionally excited two-level atom in the Sobolev approximation with resonance scattering and self-absorption redistributing photons. This line list contains no UV semi-forbidden lines other than C iii] $\lambda\lambda1907,1909$. We therefore expanded the line-list (e.g. N ii] $\lambda2143$, N iii] $\lambda1750$, N iv] $\lambda1486$, O iii] $\lambda\lambda1661,1666$, O iv] $\lambda1401$, O v] $\lambda1218$, C ii] $\lambda2326$) using ‘simple-atom’ transitions with radiative rates and collision strengths from CHIANTI v10.1 ([22, 20]). This treatment captures their emissivity and its collisional quenching. We assume a solar relative abundance pattern with $Z = 0.1Z_{\odot}$ ([63]), but explore N/C variations, motivated by growing evidence for nitrogen enhancement in at least some LRDs ([45, 58, 65, 79, 84]).

For each relevant ion and line in Sirocco spectra, we fit Gaussian absorption lines to determine the line centroids, as done in Tang et al. [79]. The cocoons in our models are observed to be ionisation stratified, which means that the velocities of the absorption lines of the different metal ions effectively probe the radial kinematics of the gas. We adopt a ballistic radial velocity-law, $v_R(r)^2 = v_R(\infty)^2 + 2GM_{\mathrm{eff}}/r$, characterised by a wind driven near the escape velocity (i.e. $v(r) \gg v(\infty)$) of an effective potential $GM_{\mathrm{eff}}/r$, reminiscent of radiation pressure-dependent winds proposed for LRDs ([38]). We favour this model as it is i) theoretically motivated by the dynamics of such gas and ii) explains the observed ordering of the absorbing ions in some LRDs. The observed absorption ordering constrains the ionisation state as a function of velocity not radius, so an accelerating wind with ionisation parameter rising outward would produce a similar trend. However, low-ionisation troughs and Balmer breaks imposed on the spectrum require neutral gas outside the continuum-forming region, favouring the solution where ionisation state declines as a function of radius outwards.

Here we use the self-consistently solved ionisation structure in Sirocco to extract the $N_{\mathrm{H\,I}}$ and gauge the cocoon’s own potential imprint on the damping wing. Specifically, we add the wing in post-processing where the column is integrated along the radial ray nearest the sightline, $N_{\mathrm{H\,I}} = \sum X_{\mathrm{H\,I}} n_{\mathrm{H}}\,\mathrm{d}r$. The optical depth is a sum of Voigt profiles for Ly$\alpha$–Ly10 ([59]), and is applied with partial covering, $F_{\mathrm{model}} = f_{\mathrm{cov}}e^{-\tau} + (1-f_{\mathrm{cov}})$. The treatment of the neutral column as a slab is an approximation motivated by an interpretation of the damped Ly$\alpha$ agnostic to whether the damping wing arises from the cocoon reservoir itself or from a foreground (galactic) screen. The hydrogen two-photon continuum, which can mimic a downturn blueward of 1400 Å ([10]), is not computed by Sirocco’s $n$-resolved hydrogen atom. Regardless, the observed spectra show a Ly$\alpha$ trough rather than the gradual two-photon turnover ([79]). We note that the Sobolev approximation used in Sirocco makes the emergent Ly$\alpha$ line-shape potentially unreliable, which requires dedicated Ly$\alpha$ Monte Carlo treatment, although it is still possible that electron-scattering dominates line-broadening in the ionised medium for very low neutral fractions.

A key assumption throughout this Sirocco modelling is that the gas-enshrouded AGN produces the observed UV-features of absorption and broad emission. For the interpretation of differential absorber kinematics, it further assumes the black hole dominates the gravitational potential within the absorbing region. Alternate frameworks, such as offset between high and low ions for star-forming galaxies with multiphase winds (Keerthi Vasan G. et al. [40]; Li et al. 2026b) or broad N iv] potentially from the winds of very massive stars (Chen et al. 2026), are outside the purview of these models (for a detailed discussion of a stellar UV see Tang et al. [79]). We emphasise that the ensemble of UV absorption and emission probes discussed here was predicted for the gas-enshrouded AGN phase from models constrained by the optical spectra (Sneppen et al. [76]), not features fitted to the SPURS data.

Results

Figure 1 shows the spectrum of a model published previously (Sneppen et al. [75]), which reproduces typical optical features of LRD-like objects (e.g. Balmer broad line-width and line-absorption). Here we focus on the UV part, but generally emphasise that the modest metallicity at $Z = 0.1 Z_{\odot}$ is sufficient to produce both the observed metal features and hydrogen lines. Next we will address in turn the model predictions and the observational comparison of i) broad metal emission and ii) narrow metal absorption.

Broad emission features – N/C overabundance

Several broad UV emission features of similar width, modest intensity and at times with significant self-absorption are produced in the models (Sneppen et al. [75]). By including electron and resonant scattering effects (e.g. as likely relevant for C iv; Lim et al. [49]; Li et al. 2026a), Sirocco allows us to infer constraints on elemental abundance ratios of the broad-line emitting gas. Tang et al. [79] reported broad components of N iv] $\lambda1486$, C iv $\lambda1549$, N iii] $\lambda1750$ and C iii] $\lambda1909$ in GN-2, while our independent fits agree in flux ratios within $1\sigma$ and additionally give a $2\sigma$ upper limit on broad O iii] $\lambda1666$ (see App. A).

In GN-2, the broad flux ratio N iv] $\lambda1486$/C iv $\lambda1549$ is around eight times the expectation from solar N/C (at $T_{\mathrm{e}} = 15\,000$ K, low density $n_{\mathrm{e}} < 10^9\ \mathrm{cm}^{-3}$, see App. A). This ratio measures N/C directly, because both ions are created at $\approx47.5$ eV and in our Sirocco models occupy similar gas with emission-weighted ionic fractions $x(\mathrm{N\,IV})/x(\mathrm{C\,IV}) = 0.8$–$1.0$.² As C iv is a permitted line, only the nitrogen line is collisionally quenched with a critical density n_{\mathrm{crit}}(\mathrm{N,IV})=10^{10.2}\ \mathrm{cm}^{-3}. The N/C is thus unambiguously super-solar and can only rise with density (N/C > 6$(N/C)$_{\odot}$at$2\sigma$for any$n_{\mathrm{e}}$, see Figure 2 left panel).

The broad N iii] $\lambda1750$/C iii] $\lambda1909$ ratio provides a complementary N/C at about 15–30 times the solar expectation (at $T_{\mathrm{e}} = 15\,000$ K and $n_{\mathrm{e}} < 10^9\ \mathrm{cm}^{-3}$). This is a lower limit with $x(\mathrm{N\,III})/x(\mathrm{C\,III})$ less than or equal to $1$ across the N iii]-C iii] ionisation zone (29.6–47.5 eV) enclosed within the C iii zone (24.4–47.9 eV). This ratio moves in the opposite direction with increasing $n_{\mathrm{e}}$, as the inferred N/C first decreases due to the critical density of the denominator, $n_{\mathrm{crit}}(\mathrm{C\,III})=10^{9.8}\ \mathrm{cm}^{-3}$, and then saturates when both lines are quenched beyond $n_{\mathrm{crit}}(\mathrm{N\,III})=10^{10.5}\ \mathrm{cm}^{-3}$. The two line-ratios are reconciled only if N/C = $12^{+3}_{-2}$(N/C)$_{\odot}$ and $n_{\mathrm{e}} \sim $10^{9.3}$–$10^{10}\ \mathrm{cm}^{-3}$ from atomic data arguments alone (see Figure 2, left panel). Although each ionisation pair is co-spatial, the N iv] zone is denser than the N iii] zone in Sirocco models. If both share one N/C, this ordering can only raise the inferred N/C up to 20 (N/C)$_\odot$ and keeps the N iv] zone at $n_e \sim10^{9.8}$–$10^{10.3}\ \mathrm{cm}^{-3}$. The density is bounded from above at $n_e \lesssim2 \times10^{10}\ \mathrm{cm}^{-3}$ due to the broad-line N iv] detection. This broad-line $n_e$ is consistent with the lower $n_e$-limit of the ‘narrow-line’ gas ($> 10^6\ \mathrm{cm}^{-3}$ at $3\sigma$ from C iii]/[C iii], [79]), which could be the unscattered component of the same broad-line gas. The constraint is also consistent with our fiducial Sirocco model density, but does not permit very strong clumping in the spatial scales modelled. In particular, given i) the upper limit on $n_e$, ii) the required columns for LRDs (e.g. $N_e \sim10^{25}\ \mathrm{cm}^{-2}$ in [75]) and iii) the implied cocoon spatial scales, the volume filling-factor is $\gtrsim0.05\ (N_e/10^{25}\ \mathrm{cm}^{-2})(R/10^{16}\ \mathrm{cm})^{-1}$. This clumping is within our space of models with clumping factors up to $\sim100$ explored in [76], but disfavours the most extreme clumped scenarios.

Broad-line gas N/O provides a complementary albeit weaker constraint, but is nonetheless interesting as the intermediate processing from hydrogen burning can either keep its oxygen (the CN cycle) or have burnt it to nitrogen as well (the full CNO cycle). In the Sirocco models, a broad oxygen line O iii]$\lambda$1666 is produced when there is both i) solar N/O and ii) a large N iv] flux as observed. O iii (35.1–54.9 eV) overlaps mostly with the gas of N iv, with the majority of O iii] emission coming from the denser N iv zone of the Sirocco models, while the O iii level itself is less density-quenched, with a critical density $n_{\mathrm{crit}}(\mathrm{O\ iii}]) = 10^{10.7}\ \mathrm{cm}^{-3}$, higher than the nitrogen lines. The observed broad N iv] and N iii] lines and the undetected broad O iii]$\lambda$1666 (with $< 6 \times10^{-19}\ \mathrm{erg\ s}^{-1}\mathrm{cm}^{-2}$ at $2\sigma$, see Fig. A.1), together imply N/O $\gtrsim0.7$ (N/O $\gtrsim5$(N/O)$_\odot$), implying highly super-solar N/O as well as highly super-solar N/C.

The GN-2 cocoon is thus likely as nitrogen overabundant as the narrow-line gas [79], as well as nitrogen-loud quasars [4, 54], and the population of high-redshift N-emitters (e.g. [9, 72, 83, 82, 61, 8, 70]), see Figure 2, middle panel. It is unlikely to be a coincidence of a small sample that all four SPURS LRDs show nitrogen emission (measured in [79]), whereas only 3 of 38 high-redshift galaxies with comparably deep rest-UV spectra show N iv] [82], which corresponds to a chance probability of $3 \times10^{-4}$ or $3.4\sigma$ significance. Indeed, Tang et al. [79] detect N iv] or N iii] in 12 of 18 LRDs with sufficiently deep archival spectra. Such nitrogen-rich conditions, now determined to be present specifically in the broad-line gas for the first time, make a direct link between the LRD engines, formation-channel or environments [9, 15, 79, 43] and the nitrogen producers (e.g. Wolf-Rayet stars [41], very massive stars (VMS, [17, 85]) or as of yet unobserved supermassive stars (SMS, [21, 12]). Tidal disruption events, a proposed LRD mechanism [5] and a known nitrogen-rich source (e.g., [88]), are not considered here because this source would require a regular ($\sim$ yearly) disruptions to supply the cocoon and ii) tidal forces act only on scales several orders of magnitude below the cocoon. These constraints suggest the dense gas shares or possibly even produces, the nitrogen-rich reservoir of the region producing the narrow lines. It is worth emphasising again that the narrow lines where the N-excess is measured are fairly high-ionisation and appear to come from very high-density regions ($\gtrsim10^6\ \mathrm{cm}^{-3}$, see Fig. 8 in Tang et al. [79]), despite the fact that they are relatively narrow, so they are quite likely not to come from the host galaxy generally, but rather from the LRD cocoon or possible from some special region(s) in the host. It remains to be shown whether the lower density, lower ionisation regions of the bulk of the host galaxy also show the same N-excess. We emphasise that in general, such broad high-ionisation components are predicted by Sirocco, for the lowest-column density objects, where the least gas reprocessing leaves the bluest LRD [76, 56, 53]. The bluest SPURS LRD, GN-2, is exactly the LRD subclass where prominent UV broad lines are expected in Sirocco models.

The CNO-processed fraction, the nitrogen budget, and the requirement to recycle the gas

The observed N/C = $12^{+3}_{-2}$ (N/C)$_\odot$ lies far above ordinary enrichment [62] and far below the hydrogen burning equilibrium ($\gtrsim100$ (N/C)$_\odot$), see [3], so this requires a mixture of processed and unprocessed material. The carbon share probes the processed fraction directly. CNO burning converts the polluters’ own initial carbon and oxygen into nitrogen while conserving C+N+O [12, 32]. Figure 2 (right panel), which mixes solar-scaled gas with ash at hydrogen-burning equilibrium, illustrates that the observed N/C implies $f \approx50\%$ has passed through the CNO cycle, or $f \approx70\%$ if only the CN cycle is considered. The absence of broad O iii]$\lambda$1666 and the high implied N/O ratio favour the former (App. A). In every other respect $f$ is a lower limit. Wolf-Rayet winds can add helium-burning carbon [12], which would only lower N/C at fixed $f$. Metal-poor unprocessed gas starts with a lower N/C than the solar-scaled ratios adopted here, so that the observed ratio would require more processing. Ash that has not reached equilibrium would require more still. We emphasise these abundance ratios are largely independent of metallicity. From these extreme processed fractions, the limited UV luminosity, and the rapid turnover rate of the cocoon gas, we can infer whether the cocoon gas must be recycled, rather than purely fed-in and ejected, as follows.

In high-$z$ N-emitters the N-rich line-emitting gas may be only a small fraction of the ISM (e.g. [52]), but here the short depletion time of the broad-line gas means that we can infer the rate at which this small mass is turned over. The mass of CNO-processed material, so-called hydrogen burning ‘ash’, is just $M_{\mathrm{ash}} = fM_{\mathrm{gas}}$, with a correction factor for the relative metallicity of the cocoon compared to the stars contributing the ash, so $M_{\mathrm{ash}} = fM_{\mathrm{gas}}(Z_{\mathrm{cocoon}}/Z_*)$ where $Z_*$ is the original metallicity of the polluting stars and by extension of their ash. Since it is very likely that the gas that formed the stars and the nuclear gas share a common origin, $Z_{\mathrm{cocoon}} \simeq Z_*$ unless the nucleus was since diluted by pristine inflow. The many metal features observed in LRDs show it is not pristine and support adopting similar enrichment as the preceding stars. The mass of the instantaneously observed line-emitting cocoon is modest and thus the N-enhanced ash is also modest, $M_{\mathrm{ash}} \sim10^2 M_\odot$ for the inferred values above. For a yield of ash per unit stellar mass formed of $\eta_{\mathrm{CN}} = 0.01$, i.e., the mass of hydrogen-burning processed gas returned by a full stellar population, for which the massive stars dominate [12, 32], this requires only $\sim10^4 M_\odot$ of pre-supernova stars to supply the instantaneous cocoon. But at the observed outflow speeds of a few hundred km/s, this gas is being replaced on $R/v \sim100$ yr timescale in order to be observed [76]. Sustaining observable N-enrichment on timescales, $t_N$, would require $M_\star= f \dot{M} t_N (Z_{\mathrm{cocoon}}/Z_\star)/\eta_{\mathrm{CN}}$, where $\dot{M}$ is the mass flux leaving the N-rich region. The active LRD phase is not measured directly, but likely of order $\sim10$ Myr given how common the LRD phenomenon is [78], while the characteristic outflows from Sirocco carry masses of $\dot{M}_{\mathrm{wind}} \simeq O(1\,M_\odot\,\mathrm{yr}^{-1})$ in [76]. If the wind escapes, $M_{\star,\mathrm{esc}}(\eta_{\mathrm{CN}}/0.01) \sim10^9\,M_\odot\,(\dot{M}_{\mathrm{wind}}/M_\odot\,\mathrm{yr}^{-1})$ of stars are needed within the central parsecs. If, however, the gas is recycled, the requisite mass budget is no longer the integral of the wind’s mass-loss rate, but now only needs to match the much smaller accreted stream, $\dot{M}_{\mathrm{BH}} \propto\Gamma L_{\mathrm{Edd}}$ and $M_{\star,\mathrm{rec}}(\eta_{\mathrm{CN}}/0.01) \sim10^7\,M_\odot\,(\Gamma M_{\mathrm{BH}}/10^6\,M_\odot)$. A partial escape fraction, $f_{\mathrm{esc}}$, lies somewhere between the two extremes:

For standard stellar populations, the observed UV luminosity ($M_{\mathrm{UV}}=-20.7$ for GN-2, [79, 43]) sets an independent upper limit on the stellar mass, which is most stringent for the young population implied by the supernova-free abundance pattern. For a Kroupa [44] IMF and a $\lesssim3$ Myr stellar burst without dust, Bagpipes [11] gives $\lesssim10^8\,M_\odot$ (see Figure 3). The limit is insensitive to the star-formation history, because i) continuous star formation over $t_N$ gives the same $M_{\mathrm{UV}}$ per unit mass as the 1 Myr old burst and ii) any population old enough to relax it has passed through its supernovae. This limit is conservative in two other respects. First, the prominent absorption (with a different pattern from star-forming galaxies at similar redshifts, [43]) and the Sirocco modelling here favour a sub-dominant stellar contribution to the UV (however, see discussion in Tang et al. [79]). Second, stars beyond the central parsecs contribute to $M_{\mathrm{UV}}$ without feeding the black hole. Even so, this stellar mass upper bound disfavors a fully escaping wind and instead suggests $f_{\mathrm{esc}}\lesssim0.2$ (see Figure 3). Polluters with a far higher yield per unit mass, $\eta_{\mathrm{CN}}\gtrsim0.5$, could provide the same escaping wind cold be fed by tens of supermassive stars of $\sim10^5\,M_\odot$ [26] or by $\gtrsim10^5$ very massive stars (e.g. between 100–300 $M_\odot$ and $Z\lesssim0.2Z_\odot$ with $\eta_{\mathrm{CN}}\lesssim0.5$ per unit VMS mass, [32]). Gas recycling with the pathway-agnostic Eq. 1 can lower these requirements by more than an order-of-magnitude for $f_{\mathrm{esc}}\lesssim0.1$. We now turn to an independent argument for gas recycling from absorber kinematics.

Metal absorption – a ballistic velocity law

Several, often saturated, narrow absorption features are produced by the metal ions in the enshrouding gas in Sirocco models. Because the ionisation states are radially stratified, a velocity field that changes with radius gives a systematic difference in their line velocity centroids (see Figure 4). In the models, the velocity gradient of these lines with increasing ionisation state is i) positive for a decelerating flow, indicating a gas outflow coasting in the SMBH gravitational potential or ii) negative for an accelerating flow such as from a radiatively-driven flow. The observations of GN-2 and CEERS-7902 show the former with fast C IV and slow Al II (for the saturated Mg II, see App. A). Sirocco reproduces this ordering with a ballistic law in which gas coasts near the local escape speed with an effective gravity $M_{\mathrm{eff}}\sim10^5\,M_\odot$ (see Figure 5). The effective mass is not the black-hole mass but the residual of gravity and radiation pressure, $M_{\mathrm{eff}}=M_{\mathrm{BH}}(1-\Gamma)$, with $\Gamma$ being the ratio of the forces. By definition $\Gamma\sim1$ close to the Eddington accretion limit and indeed is in the Sirocco model in Figure 5, when its own radiation field is used to compute the radiation force. For the model in Figure 5 with a representative LRD luminosity $L=10^{44}\,\mathrm{erg\,s^{-1}}$ this requires $M_{\rm BH}\simeq(1\mathord{-}2)\times10^{6}\,M_{\odot}$. For comparison, an over-massive SMBH ($\sim10^{8}\,M_{\odot}$, $\Gamma\sim0.01$), by definition very sub-Eddington at these luminosities, would decelerate the flow immediately, whereas a low-mass black hole (e.g. $\sim10^{4}\,M_{\odot}$, $\Gamma\sim100$) would not decelerate the flow at all and be dominated by the radiation field (see Figure 6). Within the Sirocco framework, the proposed black hole mass estimate is uncertain to the same level as the bolometric luminosity and is thus likely robust to $\lesssim1$ dex (see App. B). This SMBH mass estimate is significantly below broad line virial estimates for LRDs (e.g. Maiolino et al. [51]; D’Eugenio et al. [23]), but is comparable to virial relation estimates when corrected for electron-scattering broadened lines (e.g. Rusakov et al. [71]; Sneppen et al. [76]), and well above the $10^{4\mathord{-}5}\,M_{\odot}$ that Sun et al. 2026 infer when treating the blackbody radius of the continuum as a physical pseudo-photosphere.

The ballistic model suggests the gas is launched close to the local escape speed and thus could remain bound. Such material turns around on a $t=r/v\sim100$ yr timescale, which is the same timescale on which the line-emitting cocoon is replaced (Sneppen et al. [76]). It is thus likely the nitrogen-rich gas is not lost but cycles through the cocoon, which is what Eq. (1) assumes, and the comparable inflow and outflow mass fluxes required by the symmetric electron-scattering wings (Sneppen et al. [76]) are the natural signature of such a fountain (see also Kaaz et al. [38]). We already require, based on line-shape arguments and the absorber velocities, that simultaneous inflows of accretion and outflows caused by feedback are present

(Sneppen et al. [76]), suggesting that these absorber kinematics are directional. Objects with faster outflows with lower column density will likely preferentially show up in the blue part of the colour-space of gas-enshrouded AGN (e.g. Fig. 10 in Mascia et al. [53]). The clearest absorber ordering is seen in the bluest of the LRDs, GN-2 ($\beta_{\rm opt}\sim0.1$, $\beta_{\rm FUV}\sim-2.4$; Tang et al. [79]), whereas the comparatively redder GN-29 ($\beta_{\rm opt}\sim0.4$, $\beta_{\rm FUV}\sim-1.4$; Tang et al. [79]), shows every absorber near systematic and has no velocity gradient, as expected for a sight-line not probing the unbound wind. With only four objects this is suggestive, but requires a larger sample spanning the LRD colour sequence.

Abundance inferences from UV lines

The spatial stratification of different ions also makes it difficult to assess the intrinsic abundance ratio of elements. For example, fitting and interpreting the Al III absorption line in the model, [Al/Fe] or [Al/Mg] seems 1–2 orders of magnitude supersolar, even though the input metal abundance follows a solar composition (see Fig. B.1). The recovered ratios become decoupled from the underlying abundances for two reasons. First, higher ionisation is reached deeper within the gas cocoon and thus in a higher density region. Second, the model troughs are often saturated but partially refilled by the diffuse emission from the cocoon itself. Similarly, abundances expressed relative to the neutral gas column from damped Ly$\alpha$ also require this warm and cold stratification to be modelled. In these Sirocco models only the outer cocoon is neutral, so $N_{\rm HII}\ll N_{\rm H}$, while Figure 7 illustrates the damping wing from an enshrouding cocoon at $10^{16\mathord{-}10^{19}\,\mathrm{cm}}$, which is largely neutral beyond $\gtrsim10^{18}\,\mathrm{cm}$ and with $\log(N_{\rm HI}/\mathrm{cm}^{-2})\simeq22.7$. For such a column the UV is barely reddened, requiring only $A_V = 0.5$–$0.9$ for a Calzetti et al. [7] attenuation law to match the UV-slope from Sirocco model in Figure 7, so the neutral gas has $N_{\mathrm{H,I}}/A_V = 5^{+4}_{-2} \times10^{22}$ cm$^{-2}$ mag$^{-1}$, 10–30 times the Galactic value (Watson [87]). Such a low dust-to-neutral-gas ratio is an expected consequence of LRDs being in low metallicity systems at $\sim0.1 Z_\odot$ (Nikopoulos et al. [63]; Tang et al. [79]), and the possibly linear (Heintz et al. [31]; Hamanowicz et al. [29]) or super-linear decline seen in local low-metallicity dwarfs (Rémy-Ruyer et al. [68]).

Conclusions

Deep rest-UV spectroscopy from SPURS resolves the stratified metal absorbers and weak broad emission lines anticipated by the Sirocco cocooned-AGN models. Interpreted within the radiative transfer framework, the data yields the following constraints.

1. The broad N iii]/C iii] and N iv]/C iv ratios of GN-2 indicate N/C = $12^{+3}_{-2}$(N/C)$_\odot$ in the broad-line gas, matching its narrow-line values for the same lines and placing the LRD proper among the high-redshift N-emitters. About half or more of CNO nuclei have been through hydrogen burning. Given the short depletion times of the broad-line proper, this provides a progenitor-independent limit for the preceding stellar enrichment. An escaping wind and a sustained nitrogen-rich phase ($t_N \sim10$ Myr) are not compatible with the $M_{\mathrm{UV}}$ stellar-mass limit.

2. The high ratio of N iv]/C iv puts an upper bound on the emitting region’s electron density, $n_e < 2 \times10^{10}$ cm$^{-3}$, which disfavours models with large clumping factors (e.g., by factors $\gtrsim20$).

3. Absorption line velocities are ordered by ionisation potential (e.g. fast C iv and slow Al ii in GN-2 and CEERS-7902) indicating a velocity law that decreases outward in the models. A ballistic flow coasting near the escape speed reproduces this ordering, and implies $M_{\mathrm{BH}} \simeq10^{6-7}M_\odot$ and near-Eddington accretion.

4. Apparent optical-depth abundances do not reflect the input abundance of the Sirocco models due to spatial stratification and refilled saturated line troughs. A cocoon with solar abundances and saturated lines naturally reproduces Al-rich, Mg-poor absorption pattern reported for LRDs (see Kokorev et al. [43], and Appendix A).

Recycled gas is favoured by diagnostics in both emission (the nitrogen budget) and absorption (marginally bound, decelerating flow). Thus, the LRD cocoon may be a partially failed wind, where feedback at near-Eddington luminosity lifts hydrogen-burnt gas, which falls back and is re-accreted. Deep rest-UV spectroscopy of LRDs is still limited to a handful of objects. The far-reaching conclusions that can be drawn in this regime and exemplified here suggest that significantly larger UV observational samples will be important to understand the LRD phenomenon.

Acknowledgements. We would like to thank Charlotte Mason for insightful comments and suggestions on the manuscript. AS, DW are funded in part by the European Union (ERC, HEAVYMETAL, 101071865). Views and opinions expressed are, however, those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. AS and KEH acknowledge support from Independent Research Fund Denmark (DFF) under grant 6219-00033B and 5251-00009B, respectively. The Cosmic Dawn Center (DAWN) is funded by the Danish National Research Foundation under grant DNRF140. JHM acknowledges funding from a Royal Society University Research Fellowship (URFR1221062).

![N IV] λ1486, C IV λ1549, O III] λ1666, N III] λ1750 and C III] λ1909 emission-line fits](media/figA.1.png) bbox=0.10,0.07,0.93,0.30

Abundances

Figure 2 shows the N/C implied by the broad emission components N III]/C III] and N IV]/C IV ratios of GN-2 [79]. Similar $n_{\mathrm{e}}$ and N/C constraints follow from our independent fits (see Fig. A.1), which give broad-line ratios N IV]/C IV $= 0.52 \pm0.14$ and N III]/C III] $= 1.08^{+0.25}_{-0.20}$, against $0.48 \pm0.09$ and $1.36 \pm0.47$ from Tang et al. [79] and $0.058$ and $0.064$ for solar expectation at $T_{\mathrm{e}} = 1.5 \times10^{4}\ \mathrm{K}$ and low density ($n_{\mathrm{e}} \lesssim10^{9}\ \mathrm{cm}^{-3}$). The key assumption behind these constraints is that the ionic fractions of each pair are similar, $x(\mathrm{N\ III}) \approx x(\mathrm{C\ III})$ and $x(\mathrm{N\ IV}) \approx x(\mathrm{C\ IV})$, as motivated from their nearly coincident ionisation potentials. That the broad components arise in similar gas is supported by the Sirocco models, where $x(\mathrm{N\ IV})/x(\mathrm{C\ IV}) = 0.8$–$1$, while $x(\mathrm{N\ III})/x(\mathrm{C\ III}) = 0.5$–$0.8$ because C III extends to lower ionisation than N III. If we adopt these Sirocco ionic ratios, the joint constraint rises on N/C to $\approx13$–$19\ (\mathrm{N/C})_{\odot}$ at $n_{\mathrm{e}} \approx10^{10}\ \mathrm{cm}^{-3}$, so assuming equal ionic fractions is conservative. The computation is evaluated at $T_{\mathrm{e}} = 1.5 \times10^{4}\ \mathrm{K}$, but similar constraints are found for other assumed $T_{\mathrm{e}} = 10\,000$–$30\,000\ \mathrm{K}$, whereas the N/C confidence intervals are dominated by the observed broad-line ratio uncertainty. At $T_{\mathrm{e}} \gtrsim30\,000\ \mathrm{K}$, $n_{\mathrm{e}}$ is no longer constrained from below, but N/C abundance and the upper bound on $n_{\mathrm{e}}$ is a robust feature. Regardless, this is beyond the regime suggested by the Sirocco models for the broad-line emitting gas for these ions. Similarly, we explore the sensitivity diagnostics of N IV]/O III]. In the Sirocco models $\sim80\%$ of O III] arises in the N IV] zone. Notably, if photons capable of ionising to O IV ($\gtrsim54.9\ \mathrm{eV}$) dominated N IV formation, prominent broad recombination lines from He III ($\gtrsim54.4\ \mathrm{eV}$) would follow, but these recombination lines are weak. For the mixtures that reproduce N/C, CN ash predicts $7$–$15 \times10^{-19}\ \mathrm{erg\ cm}^{-2}\mathrm{s}^{-1}$ (N/O $= 4\ (\mathrm{N/O})_{\odot}$) and CNO ash $1$–$5 \times10^{-19}$ ($13\ (\mathrm{N/O})_{\odot}$). The Figure 1 model recomputed with N/O $= 5\ (\mathrm{N/O})_{\odot}$ gives $6$–$10 \times10^{-19}$ once scaled to the observed N IV]. The bound N/O $\gtrsim5\ (\mathrm{N/O})_{\odot}$ spans these uncertainties in ionisation correction, $n_{\mathrm{e}} = 1$–$2 \times10^{9}\ \mathrm{cm}^{-3}$ and $T_{\mathrm{e}} = 1$–$3 \times10^{4}\ \mathrm{K}$.

To test how reliably elemental abundances can be read from the absorption lines, we applied the apparent-optical-depth recipe of Kokorev et al. [43] to the emergent Sirocco spectra, smoothed to NIRSpec resolution. Columns of Mg II, Fe II, Si II, Si IV, Al II and Al III are converted to [Mg/Fe], [Si/Fe] and [Al/Fe] with their ionisation corrections. All models have solar abundance ratios for these elements, while having different column densities and by extension differing degrees of absorption line saturation. This apparent-optical-depth recipe applied to the Sirocco models returns over-abundant aluminium and often, but not ubiquitously, under-abundant magnesium, close to the values measured in LRDs (see Fig. B.1). This is largely due to two effects. First, Al III occupies a deeper and larger column than the low ions, which are confined to the outer ionisation front, so corrections should generally consider and account for stratified gas. Second, the troughs are saturated against the central source but partially refilled by emission from the cocoon itself (Fig. B.2).

Because the absorbers are typically saturated, the fitted centroids trace the velocity extent of each ion rather than its column-weighted velocity. Additionally, the trough infilling by emission from greater radii could shift the measured centroids further. However, the comparison uses the same fitting recipe on observations and the emergent model spectra, so these biases likely cancel to first order. For instance, Sirocco Mg II shares the gas and mean velocity of the other low ions, yet when the emergent spectrum is fitted the Mg II absorber comes out 70 km s$^{-1}$ bluer than the others, because the large oscillator strength of Mg II λ2796 keeps it saturated into the fast tail of the flow. The SPURS LRDs show a Mg II offset of similar size and sign, $100 \pm40\ \mathrm{km\ s}^{-1}$ [79], which the models thus reproduce without any kinematic difference between the ions. Thus, we stress the ionisation ordering should be read as an ordering of velocity extents, which depend on line strength as well as on kinematics.

Sensitivity to black hole masses in the Sirocco models

The fiducial models are defined by a $L = 10^{44}\ \mathrm{erg\ s}^{-1}$ blackbody with $3 \times10^{4}\ \mathrm{K}$ irradiating a cocoon initialised at a radius $10^{16}\ \mathrm{cm}$ and $\tau_{\mathrm{es}}$ of a few. Figure 1 employs a spherical cocoon with gas expanding radially at $100$–$1000\ \mathrm{km\ s}^{-1}$ (see Sneppen et al. [75]) and Figure 4, Figure 5 and Figure 7 use an axisymmetric cocoon with a ballistic outflow decelerating from $600$ to $90\ \mathrm{km\ s}^{-1}$. Currently, a formal parameter search is computationally prohibitive, so we use these examples to illustrate the generic UV constraints (e.g. absorber centroids for velocity-structures) or to elucidate atomic data arguments (e.g. emission strengths for N/C). In earlier models, we were agnostic to the velocity-law, as choosing between stellar, homologous or marginally unbound winds did not strongly affect the emergent spectral continuum and the H and He absorbers only probed the characteristic line-of-sight velocity (Sneppen et al. [76]; Kaaz et al. [38]). Parameter exploration is detailed in Sneppen et al. [76] and the presented specific model spectra are typical of this part of the simulation grid, rather than extreme cases.

To gauge absorber kinematics constraints on the black hole mass, we rescaled all radii of the fiducial Sirocco model by a factor $s = 0.1$–$10$ at fixed luminosity, lowering the density inside the clumps by $s^{-2}$ (to keep the ionisation similar) and raising their volume filling factor by $s^{2}$ (to keep the column density fixed). The models thereby still obey the same observational constraints, keeping the absorber ladder preserved and reproducing a similar UV spectrum. The effective masses $M_{\rm BH}(1-\Gamma)$ differ by two orders of magnitude, but the inferred black hole mass nevertheless varies only by a factor of few (see Figure 6). That is because i) the deceleration measures only the difference between gravity and radiation force, $M_{\rm BH}(1-\Gamma)$ and ii) the luminosity constrains $M_{\rm BH}$. The Sirocco inferred black hole mass is constrained by this intersection. Within the model framework, we are not strongly sensitive to the scale of the cocoon as radiation force and gravity both decrease proportionally with distance, while the exact geometrical structure does not affect the black hole gravitational potential. Within this model-space the dominant uncertainty becomes the intrinsic luminosity, which, with uncertainty at the factor of a few level, linearly propagates into the uncertainty in $M_{\rm BH}$. The mass thus relies on being able to infer the bolometric luminosity (e.g. Greene et al. [28]). This is only strongly biased if dust dominates the reddening of the SED (instead of intrinsically red gas emission) and most of the energy is emitted through dust, in tension with most infrared observations (Pérez-González et al. [66]). Other interpretations of the deceleration could significantly bias the gravitational mass, so are also worth defining and testing against the data. For instance, a wind ploughing into dense ambient gas would slow in a momentum-conserving shell. Here the deceleration would be set by the ambient density rather than by gravity. It is not clear, however, how shocks would produce the ordered velocities of different ions, because the ambient medium would be both the reprocessing and the absorbing gas, with no clear velocity structure on its own.

For Figure 6, we include the comparison mass inferred from H$\alpha$ in G395M using local relations (Greene & Ho [27]) and using these relations when correcting for electron-scattering (Rusakov et al. [71]). The latter includes a broad Gaussian Doppler core, exponentially scattered wings and a Gaussian absorber, with the narrow lines set by the unresolved [O iii] $\lambda$5008. The core broad FWHM is 300–400 km s$^{-1}$, embedded within exponential wings which carry 70–80% of the broad flux at $\tau_{\rm e} \approx1.1$–1.5. Using standard local relations (Reines & Volonteri [67]), the core gives $\log(M_{\rm BH}/M_\odot) = 6.4 \pm0.2$, versus 8.0 for a single broad Gaussian and 7.8 for two-Gaussian parametrization (both for a narrow line with free centroid). GN-2 is a fairly bright LRD with a H$\alpha$ luminosity ×7 and ×10 brighter than the median source in Sneppen et al. [76] and de Graaff et al. [18], respectively. Thus, each estimator gives a value somewhat more massive compared to a typical LRD object.