The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on ‘Black holes, Gravitational waves and Fundamental Physics’.

We present a semi‐analytical model for the formation and evolution of a high‐redshift quasar (QSO). We reconstruct a set of hierarchical merger histories of a 1013‐M⊙ dark matter halo and model the evolution of the corresponding galaxy and of its central supermassive black hole. The code gamete/QSOdust consistently follows (i) the black hole assembly via both coalescence with other black holes and gas accretion; (ii) the build‐up and star formation history of the quasar host galaxy, driven by binary mergers and mass accretion; (iii) the evolution of gas, stars and metals in the interstellar medium (ISM), accounting for mass exchanges with the external medium (infall and outflow processes); (iv) the dust formation in supernova (SN) ejecta and in the stellar atmosphere of asymptotic giant branch (AGB) stars, dust destruction by interstellar shocks and grain growth in molecular clouds; and (v) the active galactic nucleus feedback which powers a galactic‐scale wind, self‐regulating the black hole growth and eventually halting star formation. We use this model to study the case of SDSS J1148+5251 observed at redshift 6.4. We explore different star formation histories for the QSO host galaxy and find that Population III stars give a negligible contribution to the final metal and dust masses due to rapid enrichment of the ISM to metallicities >Zcr= 10−6–10−4 Z⊙ in progenitor galaxies at redshifts >10. If Population II/I stars form with a standard initial mass function (IMF) and with a characteristic stellar mass of mch= 0.35 M⊙, a final stellar mass of (1–5) × 1011 M⊙ is required to reproduce the observed dust mass and gas metallicity of SDSS J1148+5251. This is a factor of 3–10 higher than the stellar mass inferred from observations and would shift the QSO closer or on to the stellar bulge–black hole relation observed in the local Universe; alternatively, the observed chemical properties can be reconciled with the inferred stellar mass, assuming that Population II/I stars form according to a top‐heavy IMF with mch= 5 M⊙. We find that SNe dominate the early dust enrichment and that, depending on the shape of the star formation history and on the stellar IMF, AGB stars contribute at z < 8–10. Yet, a dust mass of (2–6) × 108 M⊙ estimated for SDSS J1148+5251 cannot be reproduced considering only stellar sources, and the final dust mass is dominated by grain growth in molecular clouds. This conclusion is independent of the stellar IMF and star formation history.

With the aim of investigating whether stellar sources can account for the ≥10 8 M dust masses inferred from mm/sub-mm observations of samples of 5 < z < 6.4 quasars, we develop a chemical evolution model which follows the evolution of metals and dust on the stellar characteristic lifetimes, taking into account dust destruction mechanisms. Using a grid of stellar dust yields as a function of the initial mass and metallicity over the range 1-40 M and 0-1 Z , we show that the role of asymptotic giant branch (AGB) stars in cosmic dust evolution at high redshift might have been overlooked. In particular, we find that (i) for a stellar population forming according to a present-day Larson initial mass function (IMF) with m ch = 0.35 M , the characteristic time-scale at which AGB stars dominate dust production ranges between 150 and 500 Myr, depending both on the assumed star formation history and on the initial stellar metallicity; (ii) this result is only moderately dependent on the adopted stellar lifetimes, but it is significantly affected by variations of the IMF: for a m ch = 5 M , dust from AGB starts to dominate only on time-scales larger than 1 Gyr and SNe are found to dominate dust evolution when m ch ≥10 M . We apply the chemical evolution model with dust to the host galaxy of the most distant quasar at z = 6.4, SDSS J1148+5251. Given the current uncertainties on the star formation history of the host galaxy, we have considered two models: (i) the star formation history obtained in a numerical simulation by Li et al. which predicts that a large stellar bulge is already formed at z = 6.4, and (ii) a constant star formation rate of 1000 M yr −1 , as suggested by the observations if most of the far-infrared luminosity is due to young stars. The total mass of dust predicted at z = 6.4 by the first model is 2 × 10 8 M , within the range of values inferred by observations, with a substantial contribution (∼80 per cent) of AGB dust. When a constant star formation rate is adopted, the contribution of AGB dust decreases to ∼50 per cent but the total mass of dust formed is a factor of 2 smaller. Both models predict a rapid enrichment of the interstellar medium with metals and a relatively mild evolution of the carbon abundance, in agreement with observational constraints. This supports the idea that stellar sources can account for the dust observed but show that the contribution of AGB stars to dust production cannot be neglected, even at the most extreme redshifts currently accessible to observations.

The growth of the first super massive black holes (SMBHs) at z > 6 is still a major challenge for theoretical models. If it starts from black hole (BH) remnants of Population III stars (light seeds with mass ∼ 100 M ) it requires super-Eddington accretion. An alternative route is to start from heavy seeds formed by the direct collapse of gas onto a ∼ 10 5 M BH. Here we investigate the relative role of light and heavy seeds as BH progenitors of the first SMBHs. We use the cosmological, data constrained semi-analytic model GAMETE/QSOdust to simulate several independent merger histories of z > 6 quasars. Using physically motivated prescriptions to form light and heavy seeds in the progenitor galaxies, we find that the formation of a few heavy seeds (between 3 and 30 in our reference model) enables the Eddington-limited growth of SMBHs at z > 6. This conclusion depends sensitively on the interplay between chemical, radiative and mechanical feedback effects, which easily erase the conditions that allow the suppression of gas cooling in the low metallicity gas (Z < Z cr and J LW > J cr ). We find that heavy seeds can not form if dust cooling triggers gas fragmentation above a critical dust-to-gas mass ratio (D D cr ). In addition, the relative importance of light and heavy seeds depends on the adopted mass range for light seeds, as this dramatically affects the history of cold gas along the merger tree, by both SN and AGN-driven winds.

We interpret recent ALMA observations of z > 6 normal star forming galaxies by means of a semi-numerical method, which couples the output of a cosmological hydrodynamical simulation with a chemical evolution model which accounts for the contribution to dust enrichment from supernovae, asymptotic giant branch stars and grain growth in the interstellar medium. We find that while stellar sources dominate the dust mass of small galaxies, the higher level of metal enrichment experienced by galaxies with M star > 10 9 M ⊙ allows efficient grain growth, which provides the dominant contribution to the dust mass. Even assuming maximally efficient supernova dust production, the observed dust mass of the z = 7.5 galaxy A1689-zD1 requires very efficient grain growth. This, in turn, implies that in this galaxy the average density of the cold and dense gas, where grain growth occurs, is comparable to that inferred from observations of QSO host galaxies at similar redshifts. Although plausible, the upper limits on the dust continuum emission of galaxies at 6.5 < z < 7.5 show that these conditions must not apply to the bulk of the high redshift galaxy population.

The dust formation process in the winds of Asymptotic Giant Branch stars is discussed, based on full evolutionary models of stars with mass in the range 1M ⊙ M 8M ⊙ , and metallicities 0.001 < Z < 0.008. Dust grains are assumed to form in an isotropically expanding wind, by growth of pre-existing seed nuclei.Convection, for what concerns the treatment of convective borders and the efficiency of the schematization adopted, turns out to be the physical ingredient used to calculate the evolutionary sequences with the highest impact on the results obtained.Low-mass stars with M 3M ⊙ produce carbon type dust with also traces of silicon carbide. The mass of solid carbon formed, fairly independently of metallicity, ranges from a few 10 −4 M ⊙ , for stars of initial mass 1 − 1.5M ⊙ , to ∼ 10 −2 M ⊙ for M∼ 2 − 2.5M ⊙ ; the size of dust particles is in the range 0.1µm a C 0.2µm. On the contrary, the production of silicon carbide (SiC) depends on metallicity. For 10 −3 Z 8 × 10 −3 the size of SiC grains varies in the range 0.05µm < a SiC < 0.1µm, while the mass of SiC formed is 10 −5 M ⊙ < M SiC < 10 −3 M ⊙ .Models of higher mass experience Hot Bottom Burning, which prevents the formation of carbon stars, and favours the formation of silicates and corundum. In this case the results scale with metallicity, owing to the larger silicon and aluminium contained in higher-Z models. At Z=8 × 10 −3 we find that the most massive stars produce dust masses m d ∼ 0.01M ⊙ , whereas models of smaller mass produce a dust mass ten times smaller. The main component of dust are silicates, although corundum is also formed, in not negligible quantities (∼ 10 − 20%).

We investigate the evolutionary properties of a sample of quasars at 5 < z < 6.4 using the semi-analytical hierarchical model GAMETE/QSOdust. We find that the observed properties of these quasars are well reproduced by a common formation scenario in which stars form according to a standard IMF, via quiescent star formation and efficient merger-driven bursts, while the central BH grows via gas accretion and BH-BH mergers. Eventually, a strong AGN driven wind starts to clear up the ISM of dust and gas, damping the star formation and unobscuring the line of sight toward the QSO. In this scenario, all the QSOs hosts have final stellar masses in the range (4 − 6) × 10 11 M ⊙ , a factor 3-30 larger than the upper limits allowed by the observations. We discuss alternative scenarios to alleviate this apparent tension: the most likely explanation resides in the large uncertainties that still affect dynamical mass measurements in these high-z galaxies. In addition, during the transition between the starburstdominated and the active QSO phase, we predict that ∼ 40% of the progenitor galaxies can be classified as Sub Millimeter Galaxies, although their number rapidly decreases with redshift.

We explore the minimal conditions which enable the formation of metal-enriched solar and sub-solar mass stars. We find that in the absence of dust grains, gas fragmentation occurs at densities nH ~ [10^4-10^5]cm^{-3} when the metallicity exceeds Z ~ 10^{-4} Zsun. The resulting fragmentation masses are > 10 Msun. The inclusion of Fe and Si cooling does not affect the thermal evolution as this is dominated by molecular cooling even for metallicities as large as Z = 10^{-2} Zsun. The presence of dust is the key driver for the formation of low-mass stars. We focus on three representative core-collapse supernova (SN) progenitors, and consider the effects of reverse shocks of increasing strength: these reduce the depletion factors, fdep = Mdust/(Mdust+Mmet), alter the shape of the grain size distribution function and modify the relative abundances of grain species and of metal species in the gas phase. We find that the lowest metallicity at which fragmentation occurs is Z=10^{-6} Zsun for gas pre-enriched by the explosion of a 20 Msun primordial SN (fdep > 0.22) and/or by a 35 Msun, Z=10^{-4} Zsun SN (fdep > 0.26); it is ~ 1 dex larger, when the gas is pre-enriched by a Z = 10^{-4} Zsun, 20 Msun SN (fdep > 0.04). Cloud fragmentation depends on the depletion factor and it is suppressed when the reverse shock leads to a too large destruction of dust grains. These features are all consistent with the existence of a minimum dust-to-gas ratio, Dcr, above which fragmentation is activated. We derive a simple analytic expression for Dcr which, for grain composition and properties explored in the present study, reads Dcr = [2.6 - 6.3] x 10^{-9}. When the dust-to-gas ratio of star forming clouds exceeds this value, the fragmentation masses range between 0.01 Msun and 1 Msun, thus enabling the formation of the first low-mass stars.Comment: accepted by MNRAS, 12 pages, 8 figure