In recent years, the discovery of massive quasars at $z\sim7$ has provided a striking challenge to our understanding of the origin and growth of supermassive black holes in the early Universe. Mounting observational and theoretical evidence indicates the viability of massive seeds, formed by the collapse of supermassive stars, as a progenitor model for such early, massive accreting black holes. Although considerable progress has been made in our theoretical understanding, many questions remain regarding how (and how often) such objects may form, how they live and die, and how next generation observatories may yield new insight into the origin of these primordial titans. This review focusses on our present understanding of this remarkable formation scenario, based on the discussions held at the Monash Prato Centre from November 20 to 24, 2017, during the workshop ‘Titans of the Early Universe: The Origin of the First Supermassive Black Holes’.

The formation of stars is a “social” process. It leads to the assembly of young stars at various length-scales into structures of diverse degrees of self-binding, from gravitationally-bound star clusters to unbound stellar associations, and beyond (e.g., Elmegreen 2000). These different young stellar systems are, however, not independent to each other. In nearby star-forming regions compact clusters appear at few 1-pc scales as the nested centers of star formation within loose stellar aggregations of few 10-pc sizes (e.g., Schmeja et al. 2009). Resolved populations across whole galaxies show that these structures are themselves components of larger stellar complexes with typical sizes of few 100-pc, and this structural behavior seems to extend to kpc scales in galactic super-structures and spiral arms (e.g., Gouliermis et al. 2015). From the stellar clustering point-of-view, star formation behaves as a scale-free process, expressed by power-laws in size distributions and correlation functions (e.g., Elmegreen et al. 2014). The origins of the self-similar stellar structural morphology, the scales where it changes behavior, and how these scales are determined, are fundamental questions to our understanding of star formation.

The first galaxies form due to gravitational collapse of primordial halos. During this collapse, weak magnetic seed fields get amplified exponentially by the small-scale dynamo - a process converting kinetic energy from turbulence into magnetic energy. We use the Kazantsev theory, which describes the small-scale dynamo analytically, to study magnetic field amplification for different turbulent velocity correlation functions. For incompressible turbulence (Kolmogorov turbulence), we find that the growth rate is proportional to the square root of the hydrodynamic Reynolds number, Re1/2. In the case of highly compressible turbulence (Burgers turbulence) the growth rate increases proportional to Re1/3. With a detailed chemical network we are able to follow the chemical evolution and determine the kinetic and magnetic viscosities (due to Ohmic and ambipolar diffusion) during the collapse of the halo. This way, we can calculate the growth rate of the small-scale dynamo quantitatively and predict the evolution of the small-scale magnetic field. As the magnetic energy is transported to larger scales on the local eddy-timescale, we obtain an estimate for the magnetic field on the Jeans scale. Even there, we find that equipartition with the kinetic energy is reached on small timescales. Dynamically relevant field structures can thus be expected already during the formation of the first objects in the Universe.

We present a systematic study of the influence of different forcing types on the statistical properties of supersonic, isothermal turbulence in both the Lagrangian and Eulerian frameworks. We analyse a series of high-resolution, hydrodynamical grid simulations with Lagrangian tracer particles and examine the effects of solenoidal (divergence-free) and compressive (curl-free) forcing on structure functions, their scaling exponents, and the probability density functions of the gas density and velocity increments. Compressively driven simulations show significantly larger density contrast, more intermittent behaviour, and larger fractal dimension of the most dissipative structures at the same root mean square Mach number. We show that the absolute values of Lagrangian and Eulerian structure functions of all orders in the integral range are only a function of the root mean square Mach number, but independent of the forcing. With the assumption of a Gaussian distribution for the probability density function of the velocity increments for large scales, we derive a model that describes this behaviour.

We implemented sink particles in the Adaptive Mesh Refinement (AMR) code FLASH to model the gravitational collapse and accretion in turbulent molecular clouds and cores. Sink particles are frequently used to measure properties of star formation in numerical simulations, such as the star formation rate and efficiency, and the mass distribution of stars. We show that only using a density threshold for sink particle creation is insufficient in case of supersonic flows, because the density can exceed the threshold in strong shocks that do not necessarily lead to local collapse. Additional physical collapse indicators have to be considered. We apply our AMR sink particle module to the formation of a star cluster, and compare it to a Smoothed Particle Hydrodynamics (SPH) code with sink particles. Our comparison shows encouraging agreement of gas and sink particle properties between the AMR and SPH code.

Massive stars influence the surrounding universe far out of proportion to their numbers through ionizing radiation, supernova explosions, and heavy element production. Their formation requires the collapse of massive interstellar gas clouds with very high accretion rates. We discuss results from the first three-dimensional simulations of the gravitational collapse of a massive, rotating molecular cloud core that include heating by both non-ionizing and ionizing radiation. Local gravitational instabilities in the accretion flow lead to the build-up of a small cluster of stars. These lower-mass companions subsequently compete with the high-mass star for the same common gas reservoir and limit its overall mass growth. This process is called fragmentation-induced starvation, and explains why massive stars are usually found as members of high-order stellar systems. These simulations also show that the H ii regions forming around massive stars are initially trapped by the infalling gas, but soon begin to fluctuate rapidly. Over time, the same ultracompact H ii region can expand anisotropically, contract again, and take on any of the observed morphological classes. The total lifetime of H ii regions is given by the global accretion timescale, rather than their short internal sound-crossing time. This solves the so-called lifetime problem of ultracompact H ii region. We conclude that the the most significant differences between the formation of low-mass and high-mass stars are all explained as the result of rapid accretion within a dense, gravitationally unstable flow.

We show that ALMA is the first telescope that can probe the (dust) obscured central region of quasars at z > 5 with a maximum resolution of ~ 30 pc employing the 18 km baseline.

The formation of the first stars out of metal-free gas appears to result in stars at least an order of magnitude more massive than in the present-day case. We here consider what controls the transition from a primordial to a modern initial mass function. We study the influence of low levels of metal enrichment and different initial conditions on the cooling and collapse of initially ionized gas in small protogalactic halos using three-dimensional, smoothed particle hydrodynamics simulations. We argue that fragmentation at moderate density depends on the initial conditions for star formation more than on the metal abundances present.

We show that ALMA is the first telescope that can probe the dust-obscured central region of quasars at z > 5 with a maximum resolution of ~ 30 pc employing the 18 km baseline.

We explore the possibility of detecting the first quasars with ALMA (Schleicher, Spaans, & Klessen 2009). For this purpose, we adopt the Seyfert 2 galaxy NGC 1068 as a reference system and calculate the expected fluxes if this galaxy were placed at high redshift. This choice is motivated by the detailed observations available for this system and the absence of any indication for an evolution in metallicity in high-redshift quasars. It is a conservative choice due to the moderate column densities in NGC 1068, leading to moderate fluxes.

We present results of hydrodynamic simulations of star formation triggered by cloud-cloud collisions. During the early stages of star formation, low-mass objects form by gravitational instabilities in protostellar discs. A number of these low-mass objects are in the sub-stellar mass range, including a few objects of planetary mass. The disc instabilities that lead to the formation of low-mass objects in our simulations are the product of disc-disc interactions and/or interactions between the discs and their surrounding gas.

We discuss results from numerical simulations of star cluster formation in the turbulent interstellar medium (ISM). The thermodynamic behavior of the star-forming gas plays a crucial role in fragmentation and determines the stellar mass function as well as the dynamic properties of the nascent stellar cluster. This holds for star formation in molecular clouds in the solar neighborhood as well as for the formation of the very first stars in the early universe. The thermodynamic state of the ISM is a result of the balance between heating and cooling processes, which in turn are determined by atomic and molecular physics and by chemical abundances. Features in the effective equation of state of the gas, such as a transition from a cooling to a heating regime, define a characteristic mass scale for fragmentation and so set the peak of the initial mass function of stars (IMF). As it is based on fundamental physical quantities and constants, this is an attractive approach to explain the apparent universality of the IMF in the solar neighborhood as well as the transition from purely primordial high-mass star formation to the more normal low-mass mode observed today.

We present numerical experiments that demonstrate that the nonlinear development of the Toomre instability in disks of isothermal gas, stars, and dark matter reproduces the observed Schmidt Law for star formation. The rate of gas collapse depends exponentially on the (minimum) value of the Toomre parameter in the disk. We demonstrate that spurious fragmentation occurs in the absence of sufficient resolution in our SPH model. Our models also reproduce observed star formation thresholds in disk galaxies. We finally briefly discuss the application of our models to the study of globular cluster formation in merging galaxies.

In cold dark matter cosmological models, the first stars to form are believed to do so within small protogalaxies. We study the influence of low levels of metal enrichment on the cooling and collapse of ionized gas in these protogalactic halos using three-dimensional, smoothed particle hydrodynamics simulations.

Stars form by gravoturbulent fragmentation of interstellar gas clouds. The supersonic turbulence ubiquitously observed in Galactic molecular gas generates strong density fluctuations with gravity taking over in the densest and most massive regions. Collapse sets in to build up stars and star clusters.

Turbulence plays a dual role. On global scales it provides support, while at the same time it can promote local collapse. Stellar birth is thus intimately linked to the dynamic behavior of parental gas clouds, which governs when and where protostellar cores form, and how they contract and grow in mass via accretion from the surrounding cloud material to build up stars. The equation of state plays a pivotal role in the fragmentation process. Under typical cloud conditions, massive stars form as part of dense clusters following the “normal” mass function observed, e.g. in the solar neighborhood. However, for gas with an effective polytropic index greater than unity star formation becomes biased towards isolated massive stars. This is relevant for understanding the properties of zero-metallicity stars (Population III) or stars that form under extreme environmental conditions like in the Galactic center or in luminous starbursts.

We present preliminary results of a high resolution simulation of globular cluster formation in a galaxy merger using GADGET (Springel et al. 2001). A barotropic equation of state (Li et al 2003) is implemented to include effects of cooling and heating. After one orbital period, a dozen proto-globular clusters are identified in the tidal tails.

Star formation is intimately linked to the dynamical evolution of molecular clouds. Turbulent fragmentation determines where and when protostellar cores form, and how they contract and grow in mass via accretion from the surrounding cloud material. Using numerical models of self-gravitating supersonic turbulence, efficiency, spatial distribution and timescale of star formation in turbulent interstellar clouds are estimated. Turbulence that is not continuously replenished or that is driven on large scales leads to a rapid formation of stars in a clustered mode, whereas interstellar turbulence that carries most energy on small scales results in isolated star formation with low efficiency. The clump mass spectrum for models of pure hydrodynamic turbulence is steeper than the observed one, but gets close to it when gravity is included. The mass spectrum of dense cores is log-normal for decaying and large-wavelength turbulence, similar to the IMF, but is too flat in the case of small-scale turbulence. The three-dimensional models of molecular cloud fragmentation can be combined with dynamical pre-main sequence stellar evolution calculations to obtain a consistent description of all phases of the star formation process. First results are reported for a one solar mass protostar.