The relatively small number of stars (around 40) currently known to orbit the black hole at the centre of the Milky Way limits the statistical analysis that can be done of this region of space. The current limitation comes from stellar crowding: while the brighter stars can be seen, stars fainter than magnitude of around 18 are hidden in the stray light of the surrounding brighter ones. MICADO will overcome this limitation. By reaching fainter magnitudes and higher precision positions than possible with 8-metre-class telescopes, the number of stellar orbits will increase into the hundreds, and the radial distance out to which one can detect orbits via accelerations will be increased. This means that, with MICADO, astronomers will be able to measure statistical quantities related to the orbits of stars close to black hole, including the eccentricity distribution and the distribution of specific angular momentum vectors. This will provide clues on how the stars formed and how they can reside where we find them today.  

The spin of a black hole is one of its key properties and measuring it would be a crucial test of General Relativity. The value of this parameter affects the orbits of stars and gas very close to the black hole. However, measuring the spin of Sagittarius A* from stellar orbits via astrometry is a very tough problem since it is not clear whether a suitable star (with a short enough orbital period and high enough eccentricity) exists. ELT is likely to reveal stars closer to Sagittarius A* than any found to date, moving so fast that we can detect the effects of general relativity on their orbits. If a star on the same type of orbit as S2, but with 10 times smaller semi-major axis can be followed at a radial velocity accuracy of < 10 km/s the data start getting sensitive to spin.

Discovering more stars orbiting close to Sagittarius A* will enable astronomers to better estimate the mass contained in the Galactic Centre, as well as to determine the Initial Mass Function (IMF) that describes the initial distribution of masses for a group of stars. This will enable astronomers to test the emerging evidence that the IMF close to Sagittarius A* is much flatter (i.e., it includes more massive stars) than in the Galactic Disc, indicating a different mode of star formation. 

Further, with MICADO, we expect to get more mass measurements referring to a range of radii, mapping out the radial mass distribution. While it is clear that the gravitational potential is dominated by Sagittarius A*, theory predicts that there should be a population of stellar remnants which have sunk in the nuclear cluster due to dynamical friction. Detecting this population would test our fundamental understanding of the evolution of dense stellar systems. 

In addition, with a much larger number of stars being monitored, we increase the chances of detecting a stellar flyby. We might witness how one or more of the stars experience a "kick" along its path, from which one can estimate the mass of the perturber.

Most of the objects seen at the Galactic Centre are stars. However, a few gaseous objects have been discovered, and their nature is the subject of current research. MICADO will be able to make more detailed spectra of gaseous objects around Sagittarius A* to determine whether they are all of the same type, whether some or all contain a central star, what orbits they follow and how they formed.

One outstanding mystery is whether the gas that falls into the centre of the Milky Way forms stars near the massive black hole or whether it is accreted directly onto the massive black hole. Answering this question would help us find out if star formation at the centre of the Milky Way is related to the activity of Sagittarius A*. Observations of a group of young stars in the Galactic Centre have yielded the remarkable result that episodic star formation deep in the sphere of influence of the massive black hole appears to be efficient and has a top-heavy (i.e., with more massive stars than normally found) mass function. A better quantitative determination of the processes involved in stellar formation in this extreme environment, a precise determination of the resulting stellar mass function and density profile, and the exploration of the connection between the rates of star formation and black hole accretion are critical for understanding the cosmological co-evolution of galaxies and massive black holes. 

Sagittarius A* is the prototype of the very common class of radiatively inefficient accretion sources. Detailed multi-wavelength observations of the black hole have shed light on the complex physics underlying the inefficient accretion process that appears to dominate at relatively low accretion rates and is guiding current theoretical work. The fact that infrared emission from Sagittarius A* is sporadic and faint and at a very confused location makes further substantial observational progress difficult without instrumental advances.

They could plausibly form from the first ultra-massive stars, or via the same unknown mechanism that forms supermassive black holes. Their existence in the local Universe cannot unambiguously be proven with current observational facilities. To date, only a few detections at the centres of dwarf galaxies and massive star clusters have been reported. Their existence has been inferred either from X-ray and radio emission that is believed to originate from matter falling onto a black hole, or from the disturbance in the motions of stars and gas at the centre of these objects. 

In the search for possible intermediate mass black holes, the MICADO instrument on the ELT will allow astronomers to make dynamical measurements of prominent young star clusters, such as massive globular clusters. The unambiguous detection of an intermediate mass black hole in such a cluster has far-reaching consequences for black hole formation during the early Universe. 

With HARMONI, astronomers will carry out deep kinematical studies of stellar populations to trace the gravitational potential at the centre of the cluster, to disentangle the effects of mass segregation from that of an intermediate mass black hole. This will allow us to obtain a census of black hole masses to constrain the formation mechanism of intermediate mass black holes and their relation to supermassive and stellar-mass black holes. It will also lead to more accurate predictions for gravitational-wave experiments.  

Testing whether intermediate mass black holes exist and understanding their demographics is also an essential part of understanding the formation and co-evolution of galaxies and active galactic nuclei, and more generally, the overall formation of cosmic structure. The fundamental idea in detecting intermediate-mass black holes in nuclear star clusters and galactic globular clusters is the same: use stellar kinematics to look for evidence of a dark, central concentration of mass over and above what one would expect from dynamical mass-segregation processes. In nearby globular clusters, in particular, we expect that around one star exists per central spaxel, meaning we could measure radial velocities of individual stars.  

Detailed simulations show that detection of an intermediate mass black hole within a faint nuclear star clusters requires: (a) spectral resolution ≥ 10,000; (b) a point spread function with a FWHM < 14 mas (K band: 2.0–2.3 μm) and < 8 mas (I band: 0.8–1.0 μm). These last constraints require diffraction-limited performance, that is a spaxel scale of 4 mas. These two bands provide the best possible prior constraint on the stellar mass distribution in the galaxy (K band) and achieve the best possible spatial resolution for kinematics (I band).  

This goal requires systematic surveys that sample black holes with a large range of masses across cosmic time. The fundamental limiting factor so far has been the spatial resolution of current imaging and spectroscopic instrumentation. The best measurements of supermassive black hole masses have so far been obtained either through measuring the orbits of stars around the black hole in our own Milky Way or from the measurements of stimulated microwave emission (masers), but these methods are limited to only a few galaxies. While larger numbers and volumes can in principle be reached through secondary techniques, these need to be calibrated against measurements that rely on first principles for their mass estimates, namely dynamical measurements. Although they are challenging to obtain observationally, and to treat numerically, data on stellar motions are the easiest to interpret physically and are regarded as the highest confidence mass determinations beyond maser measurements. 

The size of the spatial region where black holes directly influence the motions of stars and gas through their gravity is called the sphere of influence. To study this region of space and obtain accurate measurements of the motions of stars and gas within it, a telescope must be able to at least marginally resolve the radius of influence. The upcoming Enhanced Resolution Imager and Spectrograph (ERIS) on ESO’s Very Large Telescope will provide the highest available spatial resolution (~50 mas) in today’s telescopes, but even this is too low to probe the sphere of influence of a typical supermassive black hole beyond about 100 Mpc, and the most massive black holes, with billions of solar masses, are detectable only out to around 200 Mpc. In the closest galaxies, black holes that don’t significantly affect their surroundings, can only be detected if their masses are about one million solar masses or higher. This means that, at present, astronomers can only do direct stellar dynamical measurements for around 100 objects. Therefore, the redshift evolution of black hole scaling relations as measured by dynamical means are entirely hidden to us and, thus, any study of a possible correlation with the environment is currently impossible. The ELT will be able to detect black holes with about one million solar masses at distances up to about 30 Mpc. Heavier black holes, with masses of around one billion solar masses, will be detected up to distances of about 1 Gpc (redshift of about 0.3).  

The James Webb Space Telescope (JWST) will improve on the flux sensitivity of current black hole surveys but it will not significantly improve upon the spatial resolution. In contrast, the ELT MICADO instrument will reach a much higher spatial resolution (a few mas compared to a few tenths of mas on JWST), and consequently, the observable volume will increase by a factor of more than 300 compared to what is possible today. MICADO will be able to determine black hole masses down to around a million times the mass of the Sun and out to redshifts of 3 (for much larger masses). This will increase the number of direct measurements of black hole mass that we can currently do by tracking stellar movements from a few hundred to several tens of thousands. The cores of the highest mass black holes will be resolvable at virtually all redshifts and, ultimately, their observability will be limited only by the dimming of their surface brightness.

Complementary to this imaging, the ELT’s HARMONI instrument will estimate the masses of black holes in active galactic nuclei using spectroscopy. Moreover, by subtracting the nuclear contribution, HARMONI observations offer the prospect of unveiling the properties of the black hole’s host galaxy, for example the bulge mass and stellar velocity dispersion. Detailed simulations of a host galaxy and the quasar at its centre at a redshift of 1.5 carried out by the HARMONI consortium enabled the simultaneous observation of emission and absorption lines to estimate the properties of the quasar and the host galaxy. These results indicate that HARMONI can be used to unveil the co-evolution of galaxies and their central black holes. 

Lower mass black holes — those with less than 100,000 times the mass of the Sun — are particularly tricky to study, and many are beyond the reach of the first generation of ELT instruments. A technique called spectro-astrometry makes it possible to measure gas rotational velocities on scales down to a tenth of the spatial resolution of the instrument. Working with this technique at the diffraction limit of the ELT, second-generation instrument ANDES will be able to detect smaller and more distant black holes, with masses down to 10,000 times the mass of the Sun up to a distance of about 20 Mpc (e.g., in the Virgo Cluster).