A dynamical measure of the black hole mass in a quasar 11 billion years ago

Abstract

Tight relationships exist in the local Universe between the central stellar properties of galaxies and the mass of their supermassive black hole (SMBH)^1-3. These suggest that galaxies and black holes co-evolve, with the main regulation mechanism being energetic feedback from accretion onto the black hole during its quasar phase^4-6. A crucial question is how the relationship between black holes and galaxies evolves with time; a key epoch to examine this relationship is at the peaks of star formation and black hole growth 8-12 billion years ago (redshifts 1-3)⁷. Here we report a dynamical measurement of the mass of the black hole in a luminous quasar at a redshift of 2, with a look back in time of 11 billion years, by spatially resolving the broad-line region (BLR). We detect a 40-μas (0.31-pc) spatial offset between the red and blue photocentres of the Hα line that traces the velocity gradient of a rotating BLR. The flux and differential phase spectra are well reproduced by a thick, moderately inclined disk of gas clouds within the sphere of influence of a central black hole with a mass of 3.2 × 10⁸ solar masses. Molecular gas data reveal a dynamical mass for the host galaxy of 6 × 10¹¹ solar masses, which indicates an undermassive black hole accreting at a super-Eddington rate. This suggests a host galaxy that grew faster than the SMBH, indicating a delay between galaxy and black hole formation for some systems.

Fig. 1. Main BLR observational and modelling results.

a, Observed GRAVITY+ Hα total flux line profile averaged over the four Unit Telescopes and normalized to the continuum (black points) with 1σ error bars. The red curve and shaded region indicate the line profile for our best-fit BLR model and 68th percentile confidence region, respectively. b, Differential phase curve across the Hα line averaged over three baselines (blue points) with 1σ uncertainties. The red curve and shaded region also show the differential phase for our best-fit BLR model and 68th percentile confidence region, respectively. The distinct S-shape signal is expected for a velocity gradient. c, Model-independent photocentres for the central ten wavelength channels (small coloured points). The colour of the points represents the line-of-sight velocity and the grey ellipses show the 68th percentile confidence region. The larger blue and red points with ellipses show the average blueshifted and redshifted photocentres with their 68th percentile confidence regions. d, On-sky cloud representation of our best-fit BLR model showing an inclined, rotating, thick disk. As in c, the colour represents line-of-sight velocity. Source data

Fig. 2. BLR radius–luminosity relation.

Empirical correlation between BLR radius and AGN luminosity (as measured by the luminosity at 5,100 ångström). Grey points are reverberation-mapping measurements from ref. . Moderate luminosity, local AGN measured by GRAVITY (red squares)^– confirm the reverberation-mapping-based relation (ref. ; dashed line). High-luminosity quasars, including J0920 (red star), indicate a potential deviation from the relation towards smaller radii. All error bars represent 1σ uncertainties. Source data

Fig. 3. Black hole and host galaxy relation.

The location of J0920 in the SMBH mass–stellar mass plane (red star) compared with previously measured z ≈ 2 AGN from ref.  (grey points) and the WISSH survey (yellow squares). We split the figure into two panels based on the bolometric luminosity of the comparison sample with a cut at L_Bol = 10⁴⁷ erg s⁻¹. Effectively, this places all of the quasars from ref.  in the left panel with lower luminosities and all of the WISSH quasars in the right panel with high luminosities. Although J0920 has L_Bol > 10⁴⁷ erg s⁻¹, we still plot it in both panels for comparison. GRAVITY+ provides a greatly improved constraint on the SMBH mass. J0920 clearly lies well below the high-luminosity WISSH quasars and within the population of the ref.  sample, showing the unique nature of J0920. Compared with recent local scaling relations, J0920 is off the early-type galaxy relation (red line) and near the late-type galaxy relation (blue line). Given the SMBH accretion rate of J0920, it should shift directly up towards the early-type relation (blue arrow in right panel) and indicates that it is in a state of rapid SMBH growth at present. All error bars represent 1σ uncertainties. Source data

Extended Data Fig. 1. Individual baseline differential phase spectra.

Average differential phase spectra for each baseline in the 2.16–2.20-μm region (coloured points with 1σ error bars), together with the total flux spectrum (grey line) and best-fit BLR model (black line) with 68th percentile confidence region (shaded region).

Extended Data Fig. 2. Corner plot of the 2D and 1D posterior distributions for the BLR fit.

We plot the 2D joint and 1D marginalized posterior distribution for each parameter of the BLR model used to fit the differential phase and flux spectra. Blue shaded contours represent the 1σ, 2σ and 3σ regions and the orange crosses are the median values that are also reported in Extended Data Table 1. The dotted lines in the 1D posteriors indicate the 16th and 84th percentiles. The orange lines are again the median value. The dashed grey lines show a sampling of the priors used in the fitting, which are listed in Extended Data Table 1.

Extended Data Fig. 3. APO/TripleSpec observed H+K spectrum and spectral decomposition.

The top panel shows our flux-calibrated APO/TripleSpec spectrum (black line), together with our best-fit model (red line). The model consists of the following components: fourth-order polynomial for the continuum (blue line), Fe II template (orange line), Hβ Gaussian emission line (green line), [O III] Gaussian emission lines (brown lines) and two Hα Gaussian components (purple lines). The best fit matches the data very well with relative residuals (lower panel) below 20%. The data and residuals are smoothed by a Gaussian kernel with the standard deviation of three channels for clarity of display, whereas the fitting is conducted with the originally reduced data.

Extended Data Fig. 4. Comparison between C IV and Hα line profiles.

We compare the continuum-normalized line profiles of C IV from the LAMOST quasar survey (orange) to both of our Hα line profiles from GRAVITY (purple) and APO/TripleSpec (blue). Wavelengths were converted to velocities using the measured redshift of Hα (z = 2.325). C IV shows both a systematic blueshift of about 7,000 km s⁻¹ and increased linewidth compared with Hα, along with a heavy skew to blueshifted velocities. C IV therefore is probably dominated by outflowing gas and not the virial motion of the BLR.

Extended Data Fig. 5. NOEMA CO (3-2) data and analysis.

a, Moment 0 map of J0920 using the channels spanning −700 to 700 km s⁻¹ around the expected location of the CO (3-2) line. The contours are (−1, 1, 2, 4, 8, 16) times the root-mean-square noise level, with the −1σ level in the dashed line. The synthesized beam (4.7″ × 3.2″) is shown in the lower-left corner. b, Average real part of the visibilities as a function of baseline length (black points) showing decreasing visibility with increasing baseline with 1σ error bars. This indicates that J0920 is extended even with the relatively large beam size. The red line is a fit using an elliptical exponential disk model in which we find an effective radius of 8.23 kpc. c, Integrated spectrum within the 1σ contour shown in panel a showing the detection of the CO (3-2) line. We fit the line with a single Gaussian (red line), finding a FWHM of 432 ± 42 km s⁻¹ and use this with the effective radius determined in panel b to estimate the dynamical mass of J0920 and place it on the SMBH–galaxy scaling relation (see main text).