Little Red Dots with Broad H$β$ Lines Reveal the Black Hole Mass Function at 7<z<9.5

abstract · abstract

We present a systematic search for broad H$β$ emission at $7<z<9.5$ in 21,770 JWST/NIRSpec PRISM spectra drawn from four blank fields and six lensing clusters with photometry spanning 1942 arcmin$^2$. We find a sample of 20 sources with statistically significant broad-H$β$ emission, including 13 new sources. Our entire sample has colors and morphologies consistent with little red dots (LRDs), compared to only 37\% of broad-line emitters at $3.5<z<6$. Interpreting the broad-lines as indicators of Broad-line Active Galactic Nuclei (BLAGN), we infer black hole masses of $4.2\times10^{6}-2.1\times10^{8}$\,$M_{\odot}$. We calculate completeness corrections and construct the black hole mass function at $z\sim8$. The normalization of the black hole mass function rises by $\approx1.0$~dex from $z\sim8-5$, consistent with average black hole growth at $f_{\textrm{Edd}}\approx0.1$. Comparing with cosmological simulations, the $z\sim8$ black hole mass function requires heavy ($10^5$\,$M_{\odot}$) seeds or super-Eddington accretion onto light or intermediate mass seeds to match its normalization. Finally, we infer bolometric luminosities for the sample and construct a bolometric luminosity function. We integrate over this luminosity function to derive a black hole accretion density (BHAD) of $4.8^{+5.8}_{-2.6}\times10^{-7}~M_{\odot}~\textrm{yr}^{-1}~\textrm{Mpc}^{-3}$, showing broad agreement with previous photometric work, but disagreement with previous X-ray models, reinforcing the idea that BLAGN are more common in the early universe than previously expected.

S5.SS2: V.2 The Bolometric Luminosity Function and Black Hole Accretion Density / block 1 · html

Figure 6: Left panel: The L bol L_{\textrm{bol}} luminosity function for the full z ∼ 8 z\sim 8 H β \beta -emitter sample computed using the [ 66 ] L bol / L 5100 L_{\textrm{bol}}/L_{5100} correction, as well as recent literature results from LRDs. This luminosity function falls off rapidly at L bol ∼ 10 45 L_{\textrm{bol}}\sim 10^{45} erg s -1 and appears to extend in a power-law-like manner to lower luminosities (omitting the lowest luminosity highly incomplete data point). The red curve and shaded region shows the median and 68% confidence interval Schechter function fit to the most luminous three data points from this work. Right panel: The BHAD as a function of redshift. We also overplot the cosmic star-formation rate density from [ 67 ] re-normalized by a factor of 3000 to match the BHAD at z ∼ 3 z\sim 3 as a point of reference. Our detected BLAGN sample produces a result that broadly agrees with a photometric LRD sample from [ 140 ] . This sample was initially introduced in [ 3 ] using non-LRD specific assumptions and was reprocessed with LRD-specific corrections by [ 140 ] . We find good agreement with the BHAD derived from the M H , L = 10 8 ​ M ⊙ M_{H,L}=10^{8}M_{\odot} models of [ 79 ] , a simulation in which BHs are seeded and grow within atomic cooling halos. We note that our data are likely a lower limit on the true BHAD, as they do not account for obscured, non-broad-line AGN.

S6.SS1: VI.1 LRDs and the Black Hole Mass Function / block 1 · html

Let us then consider a different treatment for the LRDs. Instead of excluding them entirely, let us assume that LRDs do indeed host AGN, but their observed broad-lines do not reliably trace BLR kinematics, resulting in black hole masses that are overestimated by a factor of ten [ 127 , e.g.] . This rescaling, when averaged across the completeness weighted sample, is equivalent to computing M BH M_{\textrm{BH}} for the sample using bolometric luminosities (using the formalism of Greene et al. 66 , see § V.2 ), and assuming a 10% radiative efficiency and f Edd = 0.8 f_{\textrm{Edd}}=0.8 . For reference, assuming f Edd = 0.5 f_{\textrm{Edd}}=0.5 , as in [ 140 ] , would instead reduce our completeness weighted M BH M_{\textrm{BH}} to 16% of our fiducial masses, and shift our black hole mass function lighter (to the left) by 0.8 dex.

S6.SS1: VI.1 LRDs and the Black Hole Mass Function / block 1 · html

We explore the factor of ten reduction in M BH M_{\textrm{BH}} in Figure 8 (right panel). Here, at z ∼ 5 z\sim 5 , the LRDs contribute less than 10% of the number density of BLAGN at all masses, making their contributions nearly negligible. As a result, the z ∼ z\sim 5 black hole mass function’s normalization falls by ∼ 0.3 \sim 0.3 dex at the heavy end, and is nearly unchanged at the light end. Due to the 100% fraction of LRDs at z ∼ 8 z\sim 8 , applying a factor-of-ten mass adjustment drastically alters the black hole mass function, reducing its normalization by 0.5 dex.

S6.SS2: VI.2 Comparison with Empirical and Theoretical Models / block 1 · html

The results of [ 81 ] —which are based on a semi-analytic model with black hole seeding and growth implementations—further drive a need for heavy seeds, as while their sub-Eddington heavy seed model offers a good match to the observed black hole mass function, even their super-Eddington light seed model fails to match the observed black hole mass function’s mass range or normalization. As in the [ 98 ] models, adopting the reduced 10%-LRD masses would permit lighter seeds with less extreme super-Eddington accretion.

S7: VII Summary / block 1 · html

We measure the UV luminosity function for the BLAGN sample, and—as at z ∼ 5 z\sim 5 —find a ∼ 1 − 2 \sim 1-2 dex excess in the UV luminosity function normalization for AGN when compared to pre- JWST studies.

S1: I Introduction / block 1 · html

As a result of this high brightness and characteristic broad emission lines, BLAGN are straightforward to identify in spectroscopy, even at high redshifts. The limiting factor in identification with increasing redshift is spectral wavelength coverage, as the typically brightest emission line from BLAGN, H α \alpha , enters the near-infrared at z ∼ 1 z\sim 1 . Prior to the launch of the James Webb Space Telescope [ 60 , 59 , JWST ;] , the detection of BLAGN at z > 3 z>3 was limited to only the brightest (and thus most massive ≳ 10 8 ​ M ⊙ \gtrsim 10^{8}M_{\odot} ) sources (typically quasars) using rest-UV emission features such as N v , C iv , or Mg ii [ 82 , 144 , e.g.] . With the advent of JWST and its unprecedented sensitivity to the near- and mid-infrared, the population of known BLAGN at 3 < z < 7 3<z<7 (via H α \alpha observed at up to 5.3 μ \mu m) has rapidly expanded to both fainter luminosities and lower masses [ 90 , 68 , 89 , 134 , 85 , e.g.] .

S4.SS1: IV.1 Black Hole Masses / block 1 · html

For LRDs, these uncertainties are even greater, as multiple models suggest that the broad-lines observed in LRDs do not probe the broad-line region directly, and instead are the result of scattering within a dense medium [ 127 , e.g.] . [ 66 ] have also proposed that standard bolometric corrections may be inappropriate for LRDs, casting further doubt upon the accuracy and applicability of virial relations—which also depend on line luminosity—to LRDs. However, a recent study [ 86 ] has shown that for one lensed, multiply imaged LRD, the virial relations of [ 126 ] are well matched to a black hole mass derived from spectroastrometry. Given the unsettled nature of this debate, we fall back to the traditional approach and use the virial relation presented in Equation 10 from [ 64 ] , reproduced here as Equation 1 , where L H ​ β L_{{\rm H}\beta} and FWHM H ​ β \textrm{FWHM}_{{\rm H}\beta} are the luminosity and FWHM of the broad component of H β \beta , respectively.

S4.SS3.SSS1: IV.3.1 Line Detection Completeness / block 1 · html

Figure 3: Line Detection completeness fraction as a function of black hole mass for different exposure times. As expected, longer exposure times result in higher completeness due to increased sensitivity to lower broad-line fluxes. The majority of the sample is selected from relatively shallow ( ≲ 2 \lesssim 2 hours) data, suggesting that much higher completeness and larger samples of BLAGN may be found in future deeper observations.

S7: VII Summary / block 1 · html

In this work we present the results of a systematic search for broad-H β \beta lines at z > 7 z>7 in JWST NIRSpec PRISM spectra. We summarize our main results below.

S4.SS3: IV.3 M BH − M ∗ M_{\rm BH}-M_{*} relation / block 1 · html

One source has a modest M BH / M ∗ ∼ 0.1 % M_{\rm BH}/M_{*}\sim 0.1\% . This value is considerably lower and aligns more closely with the relation observed in the local universe [ 65 , ∼ 0.5 % \sim 0.5\% ; ] . This result corroborates recent discoveries of low-luminosity AGNs in massive galaxies that also follow the local trend [ 69 ] . Four sources (ID 11026, ID 46938, ID 12248, and ID 39803) have a significantly higher BH-to-stellar mass ratio of M BH / M ∗ ≥ 2 % M_{\rm BH}/M_{*}\geq 2\% , which are consistent with faint AGNs identified in previous studies [ 47 , 80 , e.g., ] .

A2: Appendix B All fitting results / block 1 · html

Figure B.2: Fitting results. Similar to that shown in Figure B.1 .

S6: VI Summary / block 1 · html

Using JWST /NIRSpec PRISM spectroscopy from the CAPERS program, we identify the highest redshift ( z = 9.288 z=9.288 ) BLAGN yet discovered—CAPERS-LRD-z9—based on a strong detection of broad (FWHM= 3525 ± 589 3525\pm 589 km s -1 ) H β \beta emission.

S6: VI Summary / block 1 · html

From our canonical black hole mass, we calculate a black hole mass to stellar mass ratio M BH / M ∗ > 4.5 % M_{\textrm{BH}}/M_{*}>4.5\% for CAPERS-LRD-z9. However, we recognize our estimates of both M BH M_{\textrm{BH}} and M ∗ M_{*} are subject to large systematic uncertainties. Based on our systematic bounds of M BH M_{\textrm{BH}} , the lower limit on M BH / M ∗ M_{\textrm{BH}}/M_{*} ranges from > > 46% to as low as > > 0.5%. Even our absolute lowest bound presents a significant deviation from the “typical” M BH / M ∗ ∼ 0.1 % M_{\textrm{BH}}/M_{*}\sim 0.1\% value exhibited by local quasars.

S5.SS6: V.6 The M BH / M ★ \mathrm{M}_{\mathrm{BH}}/\mathrm{M}_{\bigstar} relation for LRD subtypes / block 1 · html

Figure 15: Comparison of the BH and stellar masses for our stacks are shown with filled hexagons in colors, each one representing a different LRD subtype. Open hexagons show results if we consider that 50% of the bolometric luminosity of the LRD core is linked to stellar emission (see text for details). Open hexagons show results for our stacks using a calibration based on BH masses from single-epoch Balmer line data. We also show with a shaded area the z = 0 z=0 AGN in Reines and Volonteri [186] , and with brown lines the relationships found by Greene et al. [84] for all (continuous line), early-type (dotted), and late-type (dash-dot) z = 0 z=0 galaxies. The dots in black and gray depict the AGN in Jones et al. [110] , LRDs and non-LRDs, respectively. The squares are the AGN in Rusakov et al. [193] . The open triangles depict the AGN in Ma et al. [144] . Dashed oblique lines mark specific BH-to-stellar mass ratios.

S6.SS2: VI.2 Do LRDs host overmassive SMBHs? / block 1 · html

We remark several points about this comparison. First, we are comparing total stellar masses for galaxies with BH masses. If LRDs probe the early formation of bulges, we should compare with results in, e.g., Kormendy and Ho [121] , which obtain larger BH-to-stellar mass ratios (as high as 0.7%). These ratios would be more consistent with our measurements for LRDs, especially if the LRD core is not completely dominated by an AGN but has some stellar contribution (cf. open hexagons in Figure 15 ).

S7: VII Summary / block 1 · html

The fraction of broad-line AGNs (BLAGNs) satisfying the LRD photometric selection is high, ranging from ∼ \sim 58–92% across different fields. This fraction increases with a more inclusive selection that extends to bluer optical slopes.

S7: VII Summary / block 1 · html

Among photometric LRDs with NIRSpec grating spectra at 3.5 < z < 6.8 3.5<z<6.8 , ∼ \sim 50–70% exhibit broad emission lines. These represent lower limits, as nearly all show clear emission lines, and the identification of broad components is limited by depth and sensitivity.

S5.SS3: V.3 Strong High-ionization Emission and the Continuum State of the Host / block 1 · html

A second unexpected result of this work is the connection between the relative strength of [Ne V] and the continuum properties of the host. The strong [Ne V]/[Ne III] sources do not differ significantly in M UV M_{\rm UV} from the sensitivity-qualified lower-ratio comparison sample. They do, however, have redder UV slopes and stronger measured Balmer breaks. In the redshift-matched comparison, the differences are Δ ​ β = 0.63 \Delta\beta=0.63 and Δ ​ log 10 ⁡ ( B Balmer ) = 0.183 \Delta\log_{10}(B_{\rm Balmer})=0.183 dex, corresponding to a Balmer break approximately 1.5 times stronger on average. The association is therefore with continuum shape rather than simply with UV luminosity.

S6: VI Conclusions / block 1 · html

[Ne V] selection overlaps only partly with other AGN diagnostics. Among SHINE-[NeV] galaxies securely classifiable in S2–VO87, 67% lie above the Kewley et al. [62] maximal-starburst relation, whereas only 14% lie above the more conservative high-redshift boundary of Scholtz et al. [110] . However, 32% of galaxies with constraining [Ne V] nondetections also lie above the Kewley relation, showing that this region is not specific to [Ne V] emitters. Five of the 25 SHINE-[NeV] galaxies have adopted broad-line classifications; for the remainder, broad emission is either not required in the assessable spectra or cannot be determined from the available data. Broad-line, narrow-line, and [Ne V] selection therefore provide complementary views of the high-redshift AGN population. Stellar masses are available for 20 sources and span approximately log ⁡ ( M ∗ / M ⊙ ) ∼ 7.4 \log(M_{\ast}/M_{\odot})\sim 7.4 –11, including one exceptionally low-mass source at log ⁡ ( M ∗ / M ⊙ ) ∼ 7.4 \log(M_{\ast}/M_{\odot})\sim 7.4 . Luminous very-high-ionization emission can therefore occur in low-mass hosts, although low stellar mass alone does not imply the presence of an intermediate-mass black hole.

S6: VI Conclusions / block 1 · html

Our photometric catalog is cross-matched with the DJA v4.4 spectroscopic catalog, finding 673 673 unmasked “grade 3” NIRSpec PRISM spectra at z spec > 6.5 z_{\rm spec}>6.5 , of which 566 566 are unmasked, and perform the most comprehensive completeness/contamination analysis at z > 6.5 z>6.5 with JWST spectra to date. A photometric–spectroscopic redshift comparison is performed for 4 4 EPOCHS-DR2 selected samples produced from EaZy-py SED fits using the “fsps_larson”, “fsps_jades”, “sfhz”, and “sfh_blue_agn” templates; we find that the latter produces the tightest σ NMAD = 0.017 \sigma_{\rm NMAD}=0.017 , fewest extreme outliers, η = 4.3 % \eta=4.3\% , and smallest median redshift offset, ⟨ Δ ​ z ⟩ = − 0.022 \langle\Delta z\rangle=-0.022 . 293 293 NIRSpec/PRISM spectra are successfully selected ( 52 % 52\% ) with this fiducial “sfh_blue_agn” template set, including 14 / 22 14/22 z spec > 10 z_{\rm spec}>10 objects from the literature. We find that the lowest redshift bin, 6.5 < z < 7.5 6.5<z<7.5 , has the smallest selection success rate ( 47 % 47\% ), predominantly caused by the SNR red ​ Ly ​ α > { 5.0 , 5.0 } \mathrm{SNR}_{\rm red\,Ly\alpha}>\{5.0,5.0\} (#2) and Δ ​ χ low − z 2 > 4 \Delta\chi^{2}_{\rm low-z}>4 (#5) criteria, which remove 34 % 34\% and 17 % 17\% real high- z z sources respectively.

S6: VI Conclusions / block 1 · html

We provide a “gold” sample of 45 45 10.5 < z phot < 13.5 10.5<z_{\rm phot}<13.5 and 17 17 13.5 < z phot < 16.5 13.5<z_{\rm phot}<16.5 candidates with an increased SNR red ​ Ly ​ α \rm SNR_{\rm red\,Ly\alpha} threshold, 38 38 and 15 15 of which have no associated NIRSpec spectra. The 13.5 < z < 16.5 13.5<z<16.5 sample shows widely varied galaxy sizes and UV colors, a number of which are extended beyond r c > 1 ​ pkpc r_{\rm c}>1\,\rm pkpc . Even after accounting for 60 − 75 % 60-75\% of the ultra-high redshift sample expected to be strong emission line or quiescent galaxy interlopers, we expect 5 − 7 5-7 of these to be real, in mild tension with number density estimates from McLeod et al. [180] and Weibel et al. [254] . Two robust β UV < − 3 \beta_{\rm UV}<-3 sources with Ly α \alpha break colors > 1.6 ​ mag >1.6\,\rm mag and ≳ 3 ​ σ \gtrsim 3\sigma F335M and F410M detections, which merit spectroscopic follow-up, and may somewhat relieve this tension.

S5: V Conclusions / block 1 · html

We report the discovery of MoM-BL-z10, the highest-redshift broad-line AGN currently known at z = 9.98 z=9.98 , identified through our systematic search for broad-line AGNs at 6 < z < 10 6<z<10 using archival JWST/NIRSpec PRISM spectra. A full description of the survey will be presented in X. Cai et al. (in preparation). Our main conclusions are as follows:

S5: V Conclusions / block 1 · html

MoM-BL-z10 at z = 9.98 z=9.98 is the highest-redshift object in our broad-line AGN sample, selected solely on the basis of NIRSpec/PRISM spectroscopy of 1,247 objects at 6.0 ≤ z ≤ 10.3 6.0\leq z\leq 10.3 without photometric pre-selection. The H β \beta emission-line profile of MoM-BL-z10 is well reproduced by a model consisting of narrow and broad Gaussian components, with the narrow component constrained by the [O iii ] λ ​ 4960 \lambda 4960 line profile. The BIC favors this model over a narrow-line-only model with Δ ​ BIC = − 15.55 \Delta{\rm BIC}=-15.55 . The broad H β \beta component is detected at S/N = 3.87 =3.87 , with FWHM = 3480 − 950 + 2040 \mathrm{FWHM}=3480^{+2040}_{-950} km s -1 .

S3.SS2: III.2 NIRSpec/MSA Spectrum Fitting / block 1 · html

For each source, we compare the best-fit results of the narrow H α \alpha and the broad H α \alpha models, and identify broad H α \alpha emitters using the following criteria: (1) the broad H α \alpha model has a lower Bayesian Information Criterion (BIC) than the narrow H α \alpha model; (2) the broad H α \alpha model has a lower reduced chi-square χ ν 2 \chi_{\nu}^{2} than the narrow H α \alpha model; and (3) the integrated S/N of the best-fit broad H α \alpha component is greater than 5. Using these three criteria, we identify four broad H α \alpha emitters at z < 6.4 z<6.4 , among 49 line-emitting galaxies observed by NIRSpec/MSA. The corresponding broad-line AGN fraction is ( 8 ± 4 ) % (8\pm 4)\% , similar to the broad-line AGN fraction measured from NIRSpec data [ 44 ] , significantly higher than the broad-line AGN fraction of 1 % − 2 % 1\%-2\% measured from NIRCam/WFSS data [ 72 , 106 , 64 ] , highlighting the NIRspec’s higher sensitivity in recovering the broad emission lines than NIRCam/WFSS. Figure 2 shows the NIRSpec spectrum of AGN candidates. The FWHM of the broad H α \alpha components derived from the best-fit model ranges from ( 1000 ± 498 ) ​ km ​ s − 1 (1000\pm 498)~{\rm km\;\!s^{-1}} to ( 2790 ± 752 ) ​ km ​ s − 1 (2790\pm 752)~{\rm km\;\!s^{-1}} , and none of these four AGN candidates have broad H β \beta emission lines.

S7: VII Summary / block 1 · html

The observed IGM-galaxy cross-correlation function is consistent with the THESAN IGM-galaxy cross-correlation function at z ∼ 6 z\sim 6 with an average IGM neutral fraction of 5 % − 7 % 5\%-7\% and an average ionizing photon escape fraction of 6 % 6\% .