Can LISA See Inside the Little Red Dots?

abstract · abstract

The Little Red Dots (LRDs) are compact, broad-line sources that appear to contain accreting black holes (BHs) embedded in dense gas. Proposed models for their central environments (including quasi-stars, radiative BH envelopes and super-Eddington accretion discs) predict gas densities at the radii probed by an extreme-mass-ratio inspiral that differ by many orders of magnitude. We compute the inspiral of a $10$--$30\Msun$ BH for a range of LRD interior models, including environmental effects from the gas, and test with a mismatch criterion whether the resulting waveforms can be distinguished from vacuum and from one another. Dense interiors (Bondi-like free-fall cavities and radiative envelopes) produce measurable deviations from vacuum in essentially every detectable event. Convective quasi-star interiors are measurable for $\MBH\lesssim10^5\Msun$ and $z\lesssim0.6$, while a co-rotating disc leaves no measurable imprint. In favorable cases the models are also mutually distinguishable. None of the 14 JWST LRDs at $z>3.9$ would be detectable with a $10\Msun$ companion, but 30 of 31 LRDs at $z<0.9$ would be if their black holes are $\sim100$ times less massive than their virial estimates, and in many of them the interior's imprint would be measurable. Across the LRD population to $z=6$, a 4-yr LISA mission would yield $0.08$--$0.8$ detectable events for $10^5\Msun$ hosts and $10\Msun$ companions ($1.5$--$15$ for $30\Msun$) if LRD nuclei host inspirals at the rate of ordinary galactic nuclei. In dense clusters, where captures are plunges, this falls to $\lesssim10^{-4}$.

S7: VII Conclusions / block 1 · html

A LISA EMRI can in principle distinguish the proposed LRD interiors. Dense interiors—a Bondi-like free-fall cavity or a radiative envelope—are resolvable in any detected, perturbative event, while a quasi-star with a convective interior is resolvable with a 10 ​ M ⊙ 10\,M_{\odot} companion only for M BH ≲ 10 5 ​ M ⊙ M_{\rm BH}\lesssim 10^{5}\,M_{\odot} at z ≲ 0.6 z\lesssim 0.6 ; a disc, on the other hand, is not resolvable through its enclosed mass. The JWST LRDs are beyond reach with a 10 ​ M ⊙ 10\,M_{\odot} companion, but at the scattering-corrected masses the local ones lie within the horizon. The limitation is the event rate: the known local objects yield ≲ 10 − 4 \lesssim 10^{-4} inspirals in four years, while the full population to z = 6 z=6 gives 0.08 0.08 – 0.8 0.8 ( m = 10 ​ M ⊙ m=10\,M_{\odot} ) or 1.5 1.5 – 15 15 ( m = 30 ​ M ⊙ m=30\,M_{\odot} ) events for M BH = 10 5 ​ M ⊙ M_{\rm BH}=10^{5}\,M_{\odot} hosts if LRD nuclei host inspirals at the ordinary-nucleus rate.

S7: VII Conclusions / block 1 · html

A single such event would be valuable well beyond these models. On its own, the waveform measures the redshifted BH and companion masses with high precision, the BH spin, the luminosity distance and an approximate sky position, and, if the gas imprint is resolvable, the gas density and its slope within a few tens of Schwarzschild radii. Combined with electromagnetic observations, the distance and sky position can identify the host, whose spectroscopic redshift yields the source-frame mass. Comparing that mass with the virial estimate would test directly whether the broad lines are virial or broadened by electron scattering, and, together with the observed luminosity, may further provide an indication on the quasi-star stage, M BH / M ∗ M_{\rm BH}/M_{*} . The GW-inferred density close to the BH and the dense gas inferred from Balmer absorption further out would together constrain the gas distribution over several orders of magnitude in radius, a region inaccessible to either messenger alone.

S7: VII Conclusions / block 1 · html

These estimates carry several uncertainties. Astrophysically, the LRD BH mass function, the companion masses and, above all, the per-nucleus inspiral rate are poorly known, and the latter spans five orders of magnitude between ordinary and dense-cluster nuclei. On the modelling side, we assume circular orbits and gas at rest, include only the enclosed mass for the disc, and fit only the coalescence time and phase, so our resolvability estimates are optimistic; each interior model also carries its own caveats (Sec. II ). Within these limits, LISA has the potential to probe the interiors of LRDs if they are dense and host multi-year inspirals at ordinary galactic-nucleus rates, preferably with companions of a few tens of solar masses.

S2.SS0.SSS0.Px1: Quasi-star (QS) / block 1 · html

The convective efficiency η \eta is poorly constrained, while convective eddies moving at a sizeable fraction of the orbital speed make the gas-at-rest drag prescription approximate; together, these effects make the drag uncertain by a factor of several. Our quasi-star results should therefore be regarded as upper limits.

S1: I Introduction / block 1 · html

The large differences in gas density predicted by these central-environment models therefore offer a potential way to distinguish them with LISA EMRIs. This Letter investigates whether an EMRI in an LRD can discriminate among the broad classes of models described in Sec. II . The methods used to compute dephasing during an inspiral are detailed in Sec. III , while results are presented in Secs. IV – VI . We adopt a flat Λ \Lambda CDM cosmology with H 0 ≃ 67.7 H_{0}\simeq 67.7 km s -1 Mpc -1 and Ω m ≃ 0.31 \Omega_{m}\simeq 0.31 .

S2.SS0.SSS0.Px1: Quasi-star (QS) / block 1 · html

with η = 0.1 \eta=0.1 . The sound speed, c s 2 = 8 ​ G ​ M BH / 9 ​ r c_{s}^{2}=8GM_{\rm BH}/9r , makes the companion’s orbit transonic, v / c s ≃ 1.06 v/c_{s}\simeq 1.06 . In the evolutionary models of Hassan et al. [14] , which reach M BH / M ∗ = 0.33 M_{\rm BH}/M_{*}=0.33 , approximately 70 % 70\% of the lifetime is spent at M BH / M ∗ = 0.1 − 0.33 M_{\rm BH}/M_{*}={0.1-0.33} . In an exploratory model with eruptive winds, however, the envelope is consumed early and the bright phase is concentrated at M BH / M ∗ ≲ 0.02 M_{\rm BH}/M_{*}\lesssim 0.02 . We therefore take M BH / M ∗ = 0.1 M_{\rm BH}/M_{*}=0.1 , typical of the no-wind evolution, as the fiducial value, and bracket it with the gas-rich early stage, M BH / M ∗ = 0.01 M_{\rm BH}/M_{*}=0.01 (envelope M ∗ = 100 ​ M BH M_{*}=100\,M_{\rm BH} ), and the gas-poor late stage, M BH / M ∗ = 0.33 M_{\rm BH}/M_{*}=0.33 (envelope M ∗ = 3 ​ M BH M_{*}=3\,M_{\rm BH} ), the latest stage evolved by Hassan et al.

article / block 1 · html

The Little Red Dots (LRDs) are compact, broad-line sources that appear to contain accreting black holes (BHs) embedded in dense gas. Proposed models for their central environments (including quasi-stars, radiative BH envelopes and super-Eddington accretion discs) predict gas densities at the radii probed by an extreme-mass-ratio inspiral that differ by many orders of magnitude. We compute the inspiral of a 10 10 – 30 ​ M ⊙ 30M_{\odot} BH for a range of LRD interior models, including environmental effects from the gas, and test with a mismatch criterion whether the resulting waveforms can be distinguished from vacuum and from one another. Dense interiors (Bondi-like free-fall cavities and radiative envelopes) produce measurable deviations from vacuum in essentially every detectable event. Convective quasi-star interiors are measurable for M BH ≲ 10 5 ​ M ⊙ M_{\rm BH}\lesssim 10^{5}M_{\odot} and z ≲ 0.6 z\lesssim 0.6 , while a co-rotating disc leaves no measurable imprint. In favorable cases the models are also mutually distinguishable. None of the 14 JWST LRDs at z > 3.9 z>3.9 would be detectable with a 10 ​ M ⊙ 10M_{\odot} companion, but 30 of 31 LRDs at z < 0.9 z<0.9 would be if their black holes are ∼ 100 \sim 100 times less massive than their virial estimates, and in many of them the interior’s imprint would be measurable. Across the LRD population to z = 6 z=6 , a 4-yr LISA mission would yield 0.08 0.08 – 0.8 0.8 detectable events for 10 5 ​ M ⊙ 10^{5}M_{\odot} hosts and 10 ​ M ⊙ 10M_{\odot} companions ( 1.5 1.5 – 15 15 for 30 ​ M ⊙ 30M_{\odot} ) if LRD nuclei host inspirals at the rate of ordinary galactic nuclei. In dense clusters, where captures are plunges, this falls to ≲ 10 − 4 \lesssim 10^{-4} .

S1: I Introduction / block 1 · html

JWST has revealed a population of compact, red sources with broad Balmer lines at z ∼ 4 z\sim 4 – 9 9 , known as the “Little Red Dots” (LRDs) [ 34 , 13 , 23 , 21 ] . Their spectra combine a blue UV continuum with a red optical continuum, show little hot dust [ 43 ] and weak X-ray emission [ 32 ] , and often exhibit strong Balmer breaks and absorption features that require very dense gas close to the nucleus [ 11 , 35 ] . Their comoving density at z ≳ 4 z\gtrsim 4 is ∼ 10 − 5 \sim 10^{-5} – 10 − 4 10^{-4} cMpc -3 [ 23 , 21 ] , and analogous sources have now been identified down to z ≃ 0.1 z\simeq 0.1 [ 26 , 27 , 37 , 12 ] .

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As an extreme dense case we take the profile of gas falling freely onto the BH inside its Bondi-like radius R i R_{i} , ρ B = ρ i ( r / R i ) − 3 / 2 \rho_{\rm B}=\rho_{i}(r/R_{i})^{-3/2} . We anchor it at the boundary values of Hassan et al. [14] , R i = 1.2 × 10 15 R_{i}=1.2\times 10^{15} cm and ρ i = 4.5 × 10 − 10 \rho_{i}=4.5\times 10^{-10} g cm -3 for M BH / M ∗ = 0.10 M_{\rm BH}/M_{*}=0.10 and M ∗ = 10 5 ​ M ⊙ M_{*}=10^{5}\,M_{\odot} , rescaled as R i ∝ M ∗ 1 / 2 R_{i}\propto M_{*}^{1/2} and ρ i ∝ M ∗ − 1 / 2 \rho_{i}\propto M_{*}^{-1/2} , with an adiabatic sound speed. At 1 1 – 3 ​ r ISCO 3\,r_{\rm ISCO} ( r ISCO = 6 ​ G ​ M BH / c 2 r_{\rm ISCO}=6GM_{\rm BH}/c^{2} ) it is 10 4 10^{4} – 10 5 10^{5} times denser than the quasi-star model from Eq. ( 1 ). Notice that it is not a self-consistent interior: gas with this profile falls in at nearly the free-fall speed, comparable to the orbital speed, and at these densities would empty the cavity within decades. Treating it as at rest therefore overestimates the drag.

S5: V Discussion / block 1 · html

The picture of LRDs as quasi-stars carries with it an evolutionary sequence that includes stages prior to and following the phenomena we have focused on in this paper. We have illustrated this sequence schematically in Fig. 1 . The SMS stage should last only ∼ 2 − 5 % \sim 2-5\% of a late-stage quasi-star lifetime and should thus be rarest on the sky. They should also be ∼ 10 − 100 \sim 10-100 times less luminous on average, i.e. L ∼ 10 42 − 10 43 L\sim 10^{42}-10^{43} erg s -1 , with color temperatures ranging from ∼ 5000 \sim 5000 K at lower masses to ∼ 10 4 \sim 10^{4} K as masses approach 10 5 ​ M ⊙ 10^{5}M_{\odot} [ 17 ] . Early-stage quasi-stars should be more common than SMSs ( ∼ 10 % \sim 10\% compared to late-stage quasi-stars) and — at constant envelope mass — should evolve from hotter (several × 10 4 \times 10^{4} K) to cooler color temperatures as the BH grows inside [ 11 ] . However, this evolution could be obscured by the diversity of quasi-star masses and mass ratios. Efforts should be made to find the immediate precursors to LRDs. Little is known about the fate of a quasi-star once the BH swallows most or all of the envelope, e.g., whether the residual gas disperses or is able to settle into a steady state with a much lower envelope mass if matter continues to be supplied from the environment at a sufficient rate [ 32 , 12 , 21 , e.g., resembling one of the stand-alone models as in] . Alternatively, if stripped of their envelopes these immediate post-quasi-stars could be the first proper AGNs in the universe — examples of which may have already been discovered [ 9 , 34 , e.g.] .

S2: II Late-stage quasi-stars / block 1 · html

implying Δ r / R ∗ ≈ 0.2 A 23 − 2 / 15 β − 1 14 / 75 M 6 17 / 150 \Delta r/R_{*}\approx 0.2A_{23}^{-2/15}\beta_{-1}^{14/75}M_{6}^{17/150} . A numerical solution assuming fiducial parameters M 6 = β − 1 = 1 M_{6}=\beta_{-1}=1 and calculating n e / n n_{e}/n self-consistently gives nearly identical results, which is not surprising since the ionization fraction is 0.96.

S5: V Summary / block 1 · html

Similar to the luminosity ratio, the ratio of BH mass to nuclear stellar mass at the end of LRD phase also converges to a narrow range at each redshift, with M BH / M ⋆ , nuc ≃ 0.1 M_{\rm BH}/M_{\star,\rm nuc}\simeq 0.1 for 5 < z < 10 5<z<10 . Toward lower redshifts ( z < 1 z<1 ), the ratio shifts increasingly toward stellar dominance and eventually approaches the local value of ∼ 0.1 % \sim 0.1\% [ 82 , 132 , 44 , e.g.,] .

S2.SS1: II.1 Rapidly accreting envelope onto a BH / block 1 · html

To maintain a radiation-dominated convective envelope against disruption by AGN feedback, the mass inflow rate from the parent halo must far exceed the Eddington rate (see discussion in Section III.2 ), defined as M ˙ Edd ≡ L Edd / ( η rad ​ c 2 ) \dot{M}_{\rm Edd}\equiv L_{\rm Edd}/(\eta_{\rm rad}c^{2}) with a 10% radiative efficiency η rad = 0.1 \eta_{\rm rad}=0.1 . Such high inflow rates are plausible in protogalactic nuclei hosted by massive dark matter halos with masses of M h M_{\rm h} , in which the baryonic accretion rate with a cosmic baryon fraction of f b = 0.16 f_{\rm b}=0.16 , can reach

abstract / block 1 · abstract

As an unprecedented large population in the early universe, the JWST-discovered little red dots (LRDs) have garnered much attention for formation of massive black holes and galaxies, but their nature remains a mystery. The LRDs appearing as ``Chimeras" like both active galactic nuclei (AGNs) and galaxies have stimulated renewed interest in the roadmap of central massive black hole (cMBH) formation in AGNs. In this paper, we suggest that the LRDs contain $M_{\bullet}\lesssim 10^6\,M_{\odot}$ cMBHs as demonstrated by the Sołtan argument and there is a large population of stellar-mass black holes (sMBHs with total mass of $\mathscr{M}_{m_{\bullet}}$) embedded inside cMBH accretion disks (cMBH-disk) as motivated by anomalous reverberations of broad H$β$ line in local AGNs. This embryo structure of LRDs ($M_{\bullet}<\mathscr{M}_{m_{\bullet}}$) is formed as a consequence of gravitational collapse of primordial clouds. In this Chimera, accretion onto sMBHs powers the rest-frame optical continuum of the LRDs but the UV continuum is jointly contributed by slim parts of the cMBH-disks and nuclear starbursts in the core of collapsing clouds governing the appearance of the observed V-shaped spectral energy distributions (SEDs). Outflowing clumped-envelopes are unavoidably formed by radiation pressure leading to absorption features of the Balmer lines. The present model works very well for LRDs' SEDs and avoids the issues of overly massive cMBHs. Evolution of LRDs is briefly discussed including gravitational waves.

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In conclusion, when the outflow reaches observable regions, various tensions will likely arise, suggesting that outflows are a “no-go.” These feedback problems arise mainly because the BH mass is unusually large compared to the galaxy mass (see Figure 1 ). In other words, this is a common issue in models with overmassive BHs ( Inayoshi et al., 2022 ; Hu et al., 2022b ) . Note that simply reducing the BH mass while keeping the luminosity fixed does not solve the issue, as it only increases the super-Eddington ratio m ˙ \dot{m} (and in fact makes things even worse by increasing ξ \xi ).

S3: 3 AGN BH envelope / block 1 · html

A BH envelope could also form in direct-collapse models. As a result of the collapse of a supermassive star, a seed BH may form at the centre of a gaseous envelope. This scenario has been discussed in the context of quasi-stars ( Begelman et al., 2006 ; Begelman et al., 2008 ) .

S6: VI Conclusion / block 1 · html

Two of our sources show water absorption in their spectra, which necessitates a two-component fit to their data. The hot and cold components of WIDE-EGS-2974 share a ϕ \phi value, fully consistent with our ϕ \phi -conservation test, implying that its water forms at the top of an extended atmosphere. UNCOVER-A2744-20698 instead has a cold-component that is 2 2 dex denser than its hot-component, which we interpret as material in a dense cloud.

S4.SS4: IV.4 The Population in the Photospheric Plane / block 1 · html

We also note that these results are sensitive to the priors that we impose on our host galaxies. On average, our host galaxies are slightly more massive than what Sun et al. [115] derive by ∼ 0.6 \sim 0.6 dex. When we refit each galaxy with a host that forms all of its stars within the last 30 Myr, we find no population-level change to our reported ϕ \phi values within their quoted uncertainties. However, compared to our fiducial host masses, our refit galaxies end up being less massive by ∼ 0.65 \sim 0.65 dex on average, aligning us with the population average of Sun et al. [115] . These young-host refits move individual PRISM ϕ \phi values by ∼ 0.16 \sim 0.16 dex on median, while the DESI values move by ∼ 0.32 \sim 0.32 dex, and we propagate these shifts into all of our figures which changes none of our results. Even with conservative uncertainties, almost all of our fitted LRDs are still consistent with being super-Eddington (Figure 6 ), and almost every quasi-star–host galaxy pair sits well below the Reines and Volonteri [105] limit (see Figure 5 ).

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Figure 9 : Cumulative black hole spin distribution predicted by the combined MCMC analysis based on X-ray and broad-line emission. Red and blue curves show the results for the high-mass and low-mass solutions, respectively. Assuming the high BH mass solution, the analysed population would systematically require low spin values, with a < 0.2 a<0.2 for ≈ 50 % \approx 50\% of sources, in order to remain consistent with the X-ray non-detections.

S4: 4 Discussion and Conclusions / block 1 · html

In addition, it is important to stress that LRDs represent only ∼ 10 − 30 % \sim 10-30\% of the broad-line AGN population detected at high redshift. Consequently, the vast majority of sources still exhibit a complete lack of X-ray detection, without clear indications of dense gas along the line of sight. If, as recently suggested by Brazzini et al. (2026) , LRDs and the broader population of Little Blue Dots are powered by the same central engines and differ primarily in geometry and/or in the evolutionary stage of their surrounding environments, this would imply that both populations are intrinsically X-ray weak. In this framework, the presence of dense gas in the minority of sources displaying a steep red optical continuum would further enhance their apparent X-ray weakness.

S1: 1 Introduction / block 1 · html

The origin of the rest-optical continuum emission is perhaps most contentious. If dominated by the emission from a (strongly) dust-attenuated AGN, the implied host galaxy mass is small, resulting in a black hole to host mass ratio that lies far above well-established scaling relations in the local Universe ( Maiolino et al., 2024 ; Pacucci et al., 2023 ; Furtak et al., 2024 , e.g.) , although this may in part be driven by uncertainties in the black hole and galaxy masses as well as selection effects ( Li et al., 2024 ; Lupi et al., 2024 ; Wang et al., 2024b , e.g.) . If confirmed, such a large population of overmassive black holes may have important implications for the seed masses and growth mechanisms of early black holes ( Kokorev et al., 2023 ; Bogdán et al., 2024 ; Goulding et al., 2023 , e.g.) , and would be in tension with current cosmological hydrodynamical simulations ( Habouzit, 2025 ; Matthee et al., 2024b , e.g.) . Intriguingly, however, the transition in the v-shaped SED from blue to red has been shown to occur at the Balmer limit for ∼ 50 % \sim 50\% of LRDs ( Setton et al., 2024 ) , and some LRDs show Balmer breaks that are as strong as those observed in high-redshift post-starburst galaxies ( Labbe et al., 2024 ; Wang et al., 2024b ; Ma et al., 2024 , e.g.) . At face value, it therefore appears reasonable to interpret the rest-optical as being dominated by emission from an evolved stellar population in a host galaxy instead of by an AGN.

S7: 7 Conclusions / block 1 · html

The SED is characterised by a Balmer break that exceeds the break strengths of z > 3 z>3 massive quiescent galaxies and LRDs published thus far by a factor 2. Together with a (weak) blue UV slope, this gives rise to the ‘v-shape’ typically observed in LRDs. The PRISM spectrum (extending to rest 1.2 ​ μ ​ m 1.2\,\rm\mu m ) and MIRI photometry (rest ∼ 2 − 4 ​ μ ​ m \sim 2-4\,\rm\mu m ) reveal a blue SED in the near- and mid-IR, indicating there is no evidence of hot dust emission at least to rest ≲ 4 ​ μ ​ m \lesssim 4\,\rm\mu m .

S5.SS6: V.6 Summary / block 1 · html

Figure 1 is an infographic that summarizes the salient features of our model, which we list here:

S5.SS6: V.6 Summary / block 1 · html

The slow outflows of LRDs pose an energy-budget problem for super-Eddington accretion models that requires an off-axis line of sight (Sec. II , Fig. 1 - 2 ). LRDs show slow, ∼ 100 − 300 ​ km ​ s − 1 \sim 100-300\,{\rm km\,s^{-1}} outflows, yet a super-Eddington torus must shed most of its viscously generated energy into far faster winds, ≳ 10 3 − 10 4 ​ km ​ s − 1 \gtrsim 10^{3}-10^{4}\,{\rm km\,s^{-1}} . Since we observe slow gas, the fast wind must escape near the poles where it is collimated into funnels, while we view the system off-axis.