For this study we targeted the fast-rotating early-type galaxy (ETG) NGC 4526. This object has a stellar velocity dispersion within one effective radius9 σ e = 222 km s–1. This galaxy has not had its black-hole mass measured by any other technique so far but, given that most galaxies with bulges seem to have a black hole2,5, from the σ–M BH relation10 we can estimate . The sphere of influence (SOI) of a supermassive black hole (SMBH) would thus be r SOI = GM BH /σ2 ≈ 20 pc or 0.25″ at the 16.4 Mpc distance of NGC 4526 (derived from surface-brightness fluctuations11). NGC 4526 also has a large molecular gas reservoir (total molecular hydrogen mass (ref. 12)), previously mapped at low spatial resolution13 (∼4″). The molecular gas co-rotates with the stars14, and Hubble Space Telescope images show that it is coincident with regular dust lanes extending up to the galaxy centre, strongly suggesting that molecular gas with regular kinematics exists around the SMBH (ref. 7).

NGC 4526 was observed in the CO(2–1) line (230 GHz) using the Combined Array for Research in Millimetre Astronomy (CARMA) in A, B and C configurations15. The data were reduced in the standard manner16,17, and more details are presented in Fig. 1. The spatial resolution achieved along the kinematic axis of the galaxy is 0.25″ (20 pc), equal to the predicted SMBH SOI. The gas in this source seems to be distributed in a central component, and in an inner ring with spiral spurs that lead outwards to another ring at larger radii. A detailed analysis of the molecular gas morphology will be conducted in the future. We note, however, that the gas structures lie in the plane of the galaxy and seem to be regularly rotating; they are therefore likely to be dynamically cold and a good tracer of the potential18

Figure 1: NGC 4526 kinematic models and data. a–c, Model PVDs (black contours), overlaid on the observed CO(2–1) PVD (greyscale). This PVD was created from our CO(2–1) observations of NGC 4526 from CARMA. The synthesized beam size achieved in these observations was 0.27″ × 0.17″, and the velocity channel width was 10 km s–1. The final fully reduced and calibrated data cube had a root-mean-square noise of 2.88 mJy per beam. The PVD was created by rotating the data cube to align the kinematic major axis of the molecular gas with the x axis, and then summing over one beam width around the axis in the y direction. The spatial resolution achieved in the PVD was 0.25″ (20 pc), equal to the predicted SMBH SOI. Our results do not depend on the method used to extract the PVD. Shown are the best model with no SMBH (a), the overall best-fit model (b) and a model with an overweight SMBH (c). The model M BH and M/L I are indicated in the top left corner of each panel, and an inset of the central ±1.15″ is shown in the bottom right corner. d–f, Black points show the trace extracted from the respective observed PVD, and associated standard errors. The grey line shows the trace extracted from the models, and the grey crosses denote the value of the trace at the same radius as the observed points. g–i, Residuals between the model and data at each position (ΔV = data minus model; km s–1). The error bars in d–f and g–i correspond to the formal uncertainties in fitting the trace (see section 1.2 in Supplementary Information), added in quadrature with two factors of 5 km s–1 (to account for the finite velocity channel width in both the data and model). Full size image Download PowerPoint slide

We created a grid of simulations of NGC 4526 spanning a range of SMBH masses (no SMBH, M BH = 3 × 106, and then from to in linear steps) and I-band mass-to-light ratios ( in linear steps). For full details of these simulations see section 1.1 in Supplementary Information. We fix the inclination of the gas disk19 (i = 79°) and use an axisymmetric mass model of NGC 4526 (ref. 9) (carefully fitted to avoid contamination due to dust; see section 1.1.2 in Supplementary Information) to derive the circular-velocity curve expected from the luminous matter alone. The presence of a SMBH in NGC 4526 manifests itself as an inner Keplerian rise of the rotation curve (above that expected from luminous matter only). On larger angular scales such fast-rising rotation curves have been observed and have been used to infer the masses of central star clusters and bulges20. We fitted these models to our observed data to determine whether such an excess due to a central dark mass is detectable in NGC 4526.

Figure 1a–c shows three different simulated position–velocity diagrams (PVDs) overlaid on the observed PVD of NGC 4526, with ±1.15″ insets. Figure 1a shows the best model with no SMBH, with a clear excess of high-velocity molecular gas at the centre. Figure 1b shows our overall best-fit model, clearly better reproducing the observed PVD at all radii, with and . Figure 1c shows a model with a much larger SMBH, clearly incompatible with our data. Figure 1d–f shows the trace extracted from each observed PVD (as described in Supplementary Information), and the associated errors. The grey line shows the trace extracted from the models in the same way (with points denoting the values at the same radius as the observed points). The residuals between the data and the model at each position (ΔV = data minus model) are shown in Fig. 1g–i. Clearly the best-fit model produces a significantly better fit to the data.

Figure 2 shows the χ2 contours of our fits (conducted as described in Supplementary Information) as a function of M BH and M/L I . A clear global minimum is present at the best-fit values, with a minimum reduced χ2 of 1.27. We define uncertainties for each of our fitted parameters from likelihood functions of each parameter (marginalized over the other) by finding the region containing, respectively, 68% and 99% of the probability. Our final best-fit values are with (68% confidence level), and with (99% confidence level). These values are fully consistent within the 3σ uncertainties with the reported σ e –M BH relation10. Our formal uncertainties (0.14 dex and 0.5 dex at 1σ and 3σ, respectively) are also similar (and in many cases smaller) than the average uncertainties reported by other authors. For instance the mean 1σ error reported when using dynamical stellar and ionized gas techniques is ∼0.6 dex (ref. 10) (however, the rather different systematic errors involved make direct comparison difficult).

Figure 2: NGC 4526 SMBH mass uncertainties. contours of our fits to the CO(2–1) PVD, as a function of the two free parameters M BH and M/L I . The model grid is shown with black dots and the overall best-fit model by a white star. The solid shaded contours with black lines correspond to the 1σ–3σ levels with one degree of freedom (Δχ2 = 1, 4, 9) with good models in the darkest areas. The 4σ and 5σ levels (Δχ2 = 16, 25) are shown by dashed grey lines. Full size image Download PowerPoint slide

The χ2 contours show the usual degeneracy between SMBH mass and mass-to-light ratio found in other studies. To fit the data without a SMBH, a negative M/L gradient would be necessary, with older stellar populations dominating in the inner parts (high M/L) and young stars at large radii (low M/L). Although the real M/L is unlikely to be exactly constant, this is opposite to the trend reported by reddening free-stellar-population studies21 and that expected from the presence of molecular gas and star formation in the central regions22.

The ability to determine a black-hole mass accurately by using molecular gas can be affected by many of the same issues that affect measurements of ionized gas. Turbulent motions are in general small in molecular gas, but they could conceivably increase around a black hole. Similarly, if the inner gas were to be misaligned from the stellar body, our mass estimate would be systematically affected in a way that is degenerate with a change in M/L. In this galaxy, however, we find no evidence that the velocity dispersion increases in the inner regions (as described in section 1.1.1 in Supplementary Information), and constrain the inner gas to be aligned with the stellar body within <3°. Such a misalignment could change velocities by an insignificant amount (∼3 km s−1; see section 1.1.2 in Supplementary Information). The presence of dust could also cause mass models to underestimate the contribution of luminous matter to the potential. We again believe this should not introduce significant errors in this object, because of our careful treatment of dust in the mass model (see section 1.1.2 in Supplementary Information). Future studies with this technique should choose their targets to minimize the impact of such effects, but they can also include warps and turbulent motions in their gas disk models23 and use near-infrared photometry as done in previous studies of dusty objects23.

The use of molecular gas as a kinematic tracer holds great promise to increase the total number of SMBH mass measurements in galaxies of all types where CO is detected. Angular resolutions of up to 0.15″ can be achieved with current millimetre-wavelength interferometers, allowing one, for instance, to resolve the SOI of a SMBH in a galaxy with σ e = 200 km s–1 only out to about 30 Mpc. The next generation of millimetre-wavelength interferometers will have an angular resolution that is more than an order of magnitude greater (for example, ∼6 mas at 690 GHz with ALMA), as well as greatly increased sensitivity. In less than 5 h of integration time with ALMA one could achieve the same sensitivity and linear resolution as the observations presented here, in a galaxy 75 Mpc away. Galaxies of lower mass (with smaller SMBHs) will also become accessible. For instance, the SOI of a Milky-Way-like SMBH24 ( , σ e = 105 km s–1) will be resolved up to ∼50 Mpc.