Here we discuss the details of our data, the kinematics and the modelling of the light profile. We then provide details on the dynamical modelling and discuss alternatives to a supermassive black hole. The Supplementary Information has additional information on our calculation of the number of black holes in UCDs compared to galaxies and details on our simulations showing that M60-UCD1 is consistent with being a galaxy tidally stripped by M60.

Gemini/NIFS data

The kinematic data presented here are derived from integral field spectroscopic observations of M60-UCD1 taken on 20 February, 18 May and 19 May 2014 using Gemini/NIFS31 using the Altair laser guide star adaptive optics with an open loop focus model. Gemini/NIFS provides infrared spectroscopy in 0.1′′ × 0.04′′ pixels over a 3″ field of view; our observations were taken in the K band at wavelengths of 2.0–2.4 µm.

The final data cube was made from a total of nine 900-s on-source exposures with good image quality (four taken on 20 February, four on 18 May and one on 19 May). Data were taken in the order: object–sky–object. The sky frames were taken with small ∼10″ offsets from the source at similar galactocentric radii within M60. Large diagonal ∼1″ dithers made between the two neighbouring object exposures ensure that the same sky pixels were not used even when the data are binned, thus improving our signal-to-noise ratio.

The Gemini/NIFS data were reduced similarly to in our previous work with NIFS32. Each individual data cube was corrected using an A0V telluric star (HIP 58616) at similar air mass. However, owing to an error, no telluric star was observed on 20 February so the telluric from 18 May was used to correct that exposure as well; below we test any effects this may have on our kinematic data and show that they are minimal. The Gemini NIFS pipeline was modified to enable proper error propagation and additional codes written in the Interactive Data Language were used to combine the final data cube including an improved outlier rejection algorithm that uses neighbouring pixels to help determine bad pixels. Each dithered data cube was shifted and combined to yield a final data cube with 0.05′′ × 0.05′′ spatial pixels; a velocity offset to compensate for the differing barycentric corrections was applied to the February cubes. The final signal-to-noise ratio in the central pixels is ∼60 per resolution element at λ = 2,350 nm.

The instrumental dispersion of NIFS varies by ∼20% across the field of view. To determine the instrumental dispersion of each spatial pixel, the sky frame exposures were dithered and combined identically to the science images. Using this sky data cube, we fitted isolated OH sky lines in each spatial pixel using double Gaussian fits to derive the instrumental dispersion; the median FWHM was 0.421 nm.

The point spread function (PSF) was derived using an image from the Hubble Space Telescope’s Advanced Camera for Survey Wide Field Channel (Program ID: 12369). This image was convolved to match the continuum emission in the NIFS data cube. We used a Lucy–Richardson deconvolved version of the Hubble Space Telescope image in the F475W filter; the available F850LP filter image is closer in wavelength, but has a significantly more complicated and less well modelled PSF. The deconvolved F475W image was then fitted to our NIFS image using the MPFIT2DFUN code (http://physics.wisc.edu/~craigm/idl/fitting.html). A double Gaussian model was required to obtain a good fit to the PSF; the inner component has a FWHM of 0.155′′ and contains 55% of the light while the outer component has a FWHM of 0.62′′ and contains 45% of the light. The residuals to the fit have a standard deviation of just 6% out to a radius of 1′′. This PSF was assumed for the kinematics in all dynamical models.

Deriving the kinematics

The kinematics were determined by fitting the CO bandhead region (2.295–2.395 µm) to stellar templates33 using the penalized pixel-fitting algorithm PPXF34. We fitted the radial velocity V, dispersion σ, skewness h 3 and kurtosis h 4 to the data. Before fitting, the data were binned together using Voronoi binning35 to achieve signal-to-noise ratios of >35 per resolution element in each bin. The Voronoi bins at large radii were predominantly radial in shape, and thus beyond 0.5′′ we binned spectra using elliptical sections with an axial ratio of 0.85 on the basis of the observed ellipticity at these radii in the Hubble Space Telescope images. These outer bins have signal-to-noise ratios between 24 and 42 per resolution element. An example of kinematic fits in a high dispersion central pixel and low dispersion outer bin are shown in Extended Data Fig. 1. To determine errors on the derived kinematics in each bin, Monte Carlo estimates were performed by adding Gaussian random noise to each spectral pixel in each bin, refitting the kinematics and then taking the standard deviation of the resulting data. The central velocity of M60-UCD1 is found to be 1,294 ± 5 km s−1, while the integrated dispersion at r < 0.75′′ is found to be 69 ± 1 km s−1. Both values are consistent with the integrated optical spectroscopy measurements5. The kinematic maps in all four velocity moments are shown in Extended Data Fig. 2.

The robustness of the kinematic measurements and their errors was tested by comparing the data taken on 20 February with the data taken in May. The four February and five May cubes were combined into separate final cubes. Spectra were then extracted in the same bins as used for the full data set. We compared the velocity and dispersion differences between the cubes to the differences expected from the errors and found that these were consistent. More explicitly, we found that the distribution of had a standard deviation between 0.9 and 1.1 for both velocity and dispersion measurements; the bias between the two measurements was less than the typical errors on the measurements. We also tested for template mismatch using PHOENIX model spectra36 and find consistent kinematic results within the errors. Thus we conclude that (1) our kinematic measurements are robust and (2) our kinematics errors are correctly estimated.

Multi-Gaussian expansion model of M60-UCD1

Archival Hubble Space Telescope data in the F475W (g) filter (Program ID: 12369) provide the cleanest measurement of the light distribution of M60-UCD1. We first fitted the data to a PSF-convolved two-component Sérsic profile using methods and profiles similar to previous fits of M60-UCD15. To enable the fitting of axisymmetric models (see below), we forced the outer nearly circular component (with axial ratio b/a ≈ 0.95) to be exactly circular to ensure that the model had no isophotal twist caused by a misalignment of the inner and outer component. Enforcing circularity in the outer component had a negligible effect on the quality of fit compared to the previous best-fitting model5. Our best-fitting axisymmetric model has an outer Sérsic component (circular) with surface brightness µ e = 20.09, effective radius r e = 0.″600, Sérsic n = 1.20 and integrated magnitude g = 18.43, and an inner Sérsic component with position angle PA = −49.45, b/a = 0.749, µ e = 17.322, r e = 0.175′′, n = 3.31 and g = 18.14. We generated a multi-Gaussian expansion37,38 of this profile for use in our dynamical models. The multi-Gaussian expansion values are shown in Extended Data Table 1.

We note that data in the F850LP filter of M60-UCD1 is also available, but due to the lack of a red cutoff on the filter the PSF is asymmetric, temperature dependent, and difficult to characterize. The one downside of using the F475W filter is that it is at a significantly different wavelength than the kinematic measurements. However, there is no evidence for any colour variation within the object; the inner and outer morphological components have consistent colours within 0.01 mag (filter magnitudes F475W minus F850LP = 1.56 and 1.57 for the inner and outer components respectively). The radial profile of deconvolved F475W and F850LP images is flat; any colour differences are ≲0.03 mag. Thus there is no evidence for any stellar population differences within the object.

Dynamical modelling

The most common method for measuring dynamical black hole masses is Schwarzschild orbit-superposition modelling7 of the stellar kinematics. Here we use a triaxial Schwarzschild code described in detail in ref. 8. To briefly summarize the method, the dynamical models are made in three steps. First, a three-dimensional luminous mass model of the stars is made by de-projecting the two-dimensional light model from the Hubble Space Telescope image. This is done with the multi-Gaussian expansion from the previous section, which is deprojected to construct a three-dimensional mass distribution for the stars, assuming a constant mass-to-light ratio and a viewing angle. Second, the gravitational potential is inferred from the combination of the stellar mass and the black hole mass. In a triaxial potential, the orbits conserve three integral of motions that can be sampled by launching orbits orthogonally from the x–z plane. A full set of representative orbits are integrated numerically, while keeping track of the paths and orbital velocities of each orbit. The orbit library we used for M60-UCD1 consists of 7,776 orbits. Third, we model the galaxy by assigning each orbit an amount of light, simultaneously fitting both the total light distribution and the NIFS stellar kinematics (Extended Data Fig. 2) including the effects of the PSF given above. Each of these steps is then repeated with different viewing angles and potentials to find the best-fitting mass distribution and confidence intervals. The recovery of the internal dynamical structure (distribution function), intrinsic shape, and black hole mass using this code are validated in a series of papers9,39,40. The orbit-based models are fully self-consistent and allow for all physically possible anisotropies; the models make no a priori assumptions about the orbital configuration.

For modelling M60-UCD1, we adopted a (nearly) oblate geometry with an intermediate axis ratio of b/a = 0.99. In total there are three free parameters: the stellar M/L, the black hole mass, and the viewing angle. A total of 62 different stellar M/L ratios, sampled in linear steps, and 22 black hole masses, sampled in logarithmic steps, were modelled at four inclinations between 41 and 85 degrees to sample the intrinsic flattening of the shortest to longest axis, c/a, between 0.13 and 0.73. The individual grid points sampled are shown in Fig. 3. We note that the observed rotation does not appear to rotate cleanly around the short axis, as the zero-velocity curve appears to twist at 0.3′′. This may suggest that the object is mildly triaxial, but this has minimal impact on our determination of the black hole mass and stellar M/L. More significant is the increasing roundness of M60-UCD1 at large radii, which is fitted by our modelling.

The NIFS kinematics is used by the model to constrain the total mass distribution. The confidence contours shown in Fig. 3 of the main paper are marginalized over inclination and are based on fits to point symmetrized kinematic data9. Error bars are determined for the remaining two degrees of freedom, with Δχ2 = 2.30, 6.18 and 11.83 corresponding to 1σ, 2σ and 3σ. The best-fitting constant M/L model with no black hole has Δχ2 = 20.0, and thus is excluded at more than 4σ. The reduced χ2 of the best-fitting model to the unsymmetrized data are 0.96 for 280 observables and three parameters. The best-fitting inclination is only constrained to be >50°. Such a weak constraint on the viewing angle is usual for dynamical models40. There is no dust disk present in this object that can help to constrain the inclination. We note that the maximum M/L ratio expected for an old stellar population with solar metallicity and a canonical initial mass function is ∼4.1 in the V band and ∼5.1 in the g band2. This value is somewhat higher than the best-fitting M/L g ≈ 3.6, but is allowed at ∼2σ (see Fig. 3).

The ability to detect a black hole with a given set of observations is often quantified by calculating the sphere of influence of the black hole. While the sphere of influence is normally calculated based on the dispersion of the object, the large black hole mass fraction in M60-UCD1 makes the enclosed mass definition of the gravitational sphere of influence M star (r < r infl ) = 2M bh more comparable to previous r infl measurements41. Using this definition, we find r infl = 0.27′′. Following the convention presented in a recent review of black hole masses10, we obtain r infl /σ* ≈ 4, where σ* is the resolution of our PSF core. We have many independent measurements of the kinematics within this radius.

The dynamics show that this object has a multi-component structure. In the phase space there are several components visible (Extended Data Fig. 3). Roughly 70% of the stars are on co-rotating orbits, but the remainder are evenly split between counter-rotating and non-rotating, radial, orbits. This indicates that this object was not formed in a single formation event. The co-rotating orbits dominate at smaller radii, while at larger radii both co-rotating and non-rotating orbits are seen. This corresponds well to the two-component structure fit to the integrated light where we find an inner component with an axial ratio b/a = 0.75 and an outer component that is nearly round5. The anisotropy is nearly isotropic and does not significantly vary as function of radius. On the other hand (where R and z are cylindrical coordinates) gradually decreases outwards from 0 to smaller than −1 and is thus strongly negative. The anisotropy profiles and orbit types are shown in Extended Data Fig. 4. As expected in an (nearly) oblate system the orbits are dominated by short-axis tubes, apart from the region near the black hole where the radial orbits take over.

One of the most critical assumptions we make in these best-fitting models is the assumption of a constant M/L. This is a well justified simplification for M60-UCD1. As discussed above, there is no evidence for any radial colour variation, suggesting a stellar population with a constant age. Furthermore, the formal age estimate from spectral synthesis measurements of integrated optical spectra is 14.5 ± 0.5 billion years (Gyr) (ref. 5), leaving little room for any contribution from young populations with significant M/L differences. Radial variations in the initial mass function that would leave the colour unchanged are not excluded a priori but are highly unlikely, as discussed below.

To test our modelling, we also ran Jeans models using the JAM code42. These models have been shown in the past to give consistent results in comparisons with Schwarzschild models43. However, we also note that the JAM models enforce a simpler and not necessarily physical orbital structure, including a constant anisotropy aligned with cylindrical coordinates. Furthermore, the Jeans models do not fit the full line-of-sight velocity distribution, as the Schwarzschild models do. JAM models were run over a grid of black hole mass, M/L g , anisotropy β, and inclination i. Fitting only the second moments (the root-mean-square velocity ), we obtain a best-fitting stellar dynamical M/L g = 2.3 ± 0.9 and marginalizing over the other two parameters. The 1σ error bars given here were calculated assuming Δχ2 < 2.30 to give comparable error bars to the Schwarzschild models. The fit is relatively insensitive to the other two parameters, with β z varying between −1 and 0 and i between 50° and 90°. These models are fully consistent with the Schwarzschild models fits. A JAM model with zero black hole mass is strongly excluded in the data with Δχ2 > 46 and a best-fitting stellar dynamical M/L g ≈ 6.5.

We also use the Jeans modelling to investigate fully isotropic models. Isotropy is observed in the central parsec of the Milky Way44, the only galaxy nucleus where three-dimensional velocities for individual stars have been measured. Furthermore, isotropy has been assumed in the modelling of possible black holes in UCDs2. Interestingly, the V RMS data of M60-UCD1 is also fully consistent with an isotropic model with a (within the 1σ contour). This is consistent with the Schwarzschild models, which find that the system is close to isotropic with β ≈ 0.0. The best-fitting isotropic Jeans model has a black hole mass of and M/L g = 2.8 ± 0.7.

Dark matter and alternatives to a black hole

We now discuss the possible dark matter content of M60-UCD1 and consider whether an alternative scenario could explain the kinematics of M60-UCD1 without a supermassive black hole.

Dark matter is not expected to make a significant contribution to the kinematics of M60-UCD1. This is due to the extremely high stellar density; dissipationless dark matter cannot achieve anywhere close to the same central densities as baryonic matter. This is shown clearly in previous work matching dark matter halos to galaxies45. For realistic dark matter halo profiles, even a halo would have only within the central 100 pc, while a halo would be required to have just within M60-UCD1’s effective radius; thus even such a massive halo (about three orders of magnitude more massive than would be expected for a galaxy with a stellar mass of about ) would contribute only around 1% to M60-UCD1’s mass. More importantly, a dark matter halo would contribute an extended distribution of mass and fail to produce the central rise in the velocity dispersion. We note that the one previous resolved measurement of UCD kinematics3 found no evidence for dark matter in a significantly more extended UCD. Including dark matter in our dynamical models would slightly decrease the stellar M/L, which in turn would further increase the inferred black hole mass in this object.

An alternative to a massive black hole could be a centrally enhanced M/L. To test this scenario we constructed dynamical models without a black hole, but with a radial M/L gradient increasing towards the centre. We found that the models with an M/L slope of −0.44 ± 0.16 in log(radius) can yield a good fit, with a Δχ2 difference of 3 from the best-fitting constant M/L + black hole model. This indicates that a model without a black hole and with a M/L gradient is allowed at 2σ. However, in addition to providing a slightly worse formal fit to the data, the M/L gradient model is also less physically plausible than the presence of a supermassive black hole. The log(r) dependence means that the centre has a very large M/L. This is shown clearly in Extended Data Fig. 5. Within our central resolution element (r ≈ 5 pc), the M/L g in this model is ∼12 compared to a value of ∼2 at 100 pc. The model is thus replacing the black hole mass with stellar mass near the centre in order to match the kinematic data.

This dramatic M/L gradient cannot be due to stellar age variations, given M60-UCD1’s uniform colour. The M/L at r < 5 pc is a factor of more than 2 above that expected for an old stellar population with a canonical initial mass function (see above) and thus would require that more than half of the approximately inside that radius be in low-mass stars or stellar remnants that produce little light4,46. We note that dynamical mass segregation is not expected to occur in M60-UCD1, because the half-mass relaxation time is about 350 Gyr and remains more than 10 Gyr at smaller radii41,47. Thus the only way to explain the M/L gradient would be to have extreme radial variations in the initial mass function. Assuming a change in the high-mass end of the initial mass function (and thus an increase in stellar remnants), the required upper initial mass function slope α (where the slope of the stellar mass function is specified as dN/dM ∝ M−α) is between 0 and 1.4 at the centre, as opposed to the canonical 2.35 (ref. 48). We consider this possibility very unlikely.