Statistical predictions for the first black holes

The recent observations of supermassive black holes (SMBHs) at high redshift challenge our understanding of their formation and growth. There are different proposed pathways to form black hole (BH) seeds, such as the remnants of the first stars (chapter 4), gas-dynamical processes (chapter 5), direct collapse (chapter 6), or stellar collisions in dense nuclear clusters (chapter 7). In this chapter, we discuss the probability of forming supermassive black holes (SMBHs) via these channels and determine the expected number density of the BH seeds. We start with a brief discussion of the observational constraints on SMBHs at low and high redshift that theoretical models have to reproduce (a more detailed account is provided in chapter 12). We further present the most popular formation channels of SMBHs, discuss under which conditions they can reproduce the observations, and compare various estimates in the literature on the expected number density of SMBHs. To account for the density of quasars at $z>6$ requires very efficient gas accretion mechanisms or high BH seeds masses. The bottleneck to obtain sufficiently high number densities of seed BHs with masses $>10^5$M$_\odot$ is the interplay between radiative and chemical feedback, which constrains the conditions for primordial, isothermal gas collapse.Comment: Preprint of the chapter "Statistical predictions for the first black holes", to be published in the review volume "Formation of the First Black Holes", Latif, M. and Schleicher, D. R. G., eds., World Scientific Publishing Company, 2018, pp 161-175 [see https://www.worldscientific.com/worldscibooks/10.1142/10652

Active Galactic Nuclei outflows in galaxy discs

Galactic outflows, driven by active galactic nuclei (AGN), play a crucial role in galaxy formation and in the self-regulated growth of supermassive black holes (BHs). AGN feedback couples to and affects gas, rather than stars, and in many, if not most, gas-rich galaxies cold gas is rotationally supported and settles in a disc. We present a 2D analytical model for AGN-driven outflows in a gaseous disc and demonstrate the main improvements, compared to existing 1D solutions. We find significant differences for the outflow dynamics and wind efficiency. The outflow is energy-driven due to inefficient cooling up to a certain AGN luminosity ($\sim 10^{43}$erg/s in our fiducial model), above which the outflow remains momentum-driven in the disc up to galactic scales. We reproduce results of 3D simulations that gas is preferentially ejected perpendicular to the disc and find that the fraction of ejected interstellar medium is lower than in 1D models. The recovery time of gas in the disc, defined as the freefall time from the radius to which the AGN pushes the ISM at most, is remarkably short, of the order 1Myr. This indicates that AGN-driven winds cannot suppress BH growth for long. Without the inclusion of supernova feedback, we find a scaling of the black hole mass with the halo velocity dispersion of $M_\mathrm{BH} \propto \sigma ^{4.8}$.Comment: 22 pages, 22 figures, published in MNRA

Witnessing the birth of a supermassive protostar

The detection of $\rm z>6$ quasars reveals the existence of supermassive black holes of a few $\rm 10^9~M_{\odot}$. One of the potential pathways to explain their formation in the infant universe is the so-called direct collapse model which provides massive seeds of $\rm 10^5-10^6~M_{\odot}$. An isothermal direct collapse mandates that halos should be of a primordial composition and the formation of molecular hydrogen remains suppressed in the presence of a strong Lyman Werner flux. In this study, we perform high resolution cosmological simulations for two massive primordial halos employing a detailed chemical model which includes $\rm H^-$ cooling as well as realistic opacities for both the bound-free $\rm H^-$ emission and the Rayleigh scattering of hydrogen atoms. We are able to resolve the collapse up to unprecedentedly high densities of $\rm \sim 10^{-3}~g/cm^3$ and to scales of about $\rm 10^{-4}$ AU. Our results show that the gas cools down to $\rm \sim$ 5000 K in the presence of $\rm H^-$ cooling, and induces fragmentation at scales of about 8000 AU in one of the two simulated halos, which may lead to the formation of a binary. In addition, fragmentation also occurs on the AU scale in one of the halos but the clumps are expected to merge on short time scales. Our results confirm that $\rm H^-$ cooling does not prevent the formation of a supermassive star and the trapping of cooling radiation stabilises the collapse on small scales.Comment: Accpeted version, to appear in MNRAS, comments are still welcome and high resolution version is available at http://www2.iap.fr/users/latif/DCBH.pd

Constraining the primordial initial mass function with stellar archaeology

We present a new near-field cosmological probe of the initial mass function (IMF) of the first stars. Specifically, we constrain the lower-mass limit of the Population III (Pop III) IMF with the total number of stars in large, unbiased surveys of the Milky Way. We model the early star formation history in a Milky Way-like halo with a semi-analytic approach, based on Monte-Carlo sampling of dark matter merger trees, combined with a treatment of the most important feedback mechanisms. Assuming a logarithmically flat Pop III IMF and varying its low mass limit, we derive the number of expected survivors of these first stars, using them to estimate the probability to detect any such Pop III fossil in stellar archaeological surveys. Following our analysis, the most promising region to find possible Pop III survivors is the stellar halo of the Milky Way, which is the best target for future surveys. We find that if no genuine Pop III survivor is detected in a sample size of $4 \times 10^6$ ($2 \times 10^7$) halo stars with well-controlled selection effects, then we can exclude the hypothesis that the primordial IMF extended down below $0.8 M_\odot$ at a confidence level of 68% (99%). With the sample size of the Hamburg/ESO survey, we can tentatively exclude Pop III stars with masses below $0.65 M_\odot$ with a confidence level of 95%, although this is subject to significant uncertainties. To fully harness the potential of our approach, future large surveys are needed that employ uniform, unbiased selection strategies for high-resolution spectroscopic follow-up.Comment: 19 pages, 14 figures, published in MNRA

A Photon Burst Clears the Earliest Dusty Galaxies: Modelling Dust in High-redshift Galaxies from ALMA to JWST

The generation and evolution of dust in galaxies are important tracers for star formation, and can characterize the rest-frame ultraviolet to infrared emission from the galaxies. In particular understanding dust in high-redshift galaxies are important for observational cosmology, as they would be necessary to extract information on star formation in the early universe. We update the public semi-analytical model A-SLOTH (Ancient Stars and Local Observables by Tracing Halos) to model the evolution of dust, focusing on high-redshift star-forming galaxies with stellar masses of $\sim 10^8$--$10^{10}M_\odot$ observed by ALMA ($z\approx 7$) and JWST ($z\approx 11$). We find that these galaxies should qualitatively differ in their star formation properties; while the samples in ALMA are explained by dust growth in normal star-forming galaxies, the lack of dust in the samples by JWST requires dust ejection by radiation pressure due to recent highly efficient star-formation within a few 10 Myr, with order 100 times higher efficiency than normal galaxies calibrated by A-SLOTH. Depending on where the JWST galaxies locate on the luminosity function, their bursty star formation histories inferred from our model can have impacts for rates of star formation, supernova explosion, stellar feedback, and detectability of dusty, mature galaxies in the very early universe.Comment: 13 pages, 7 figures. Revised after MNRAS referee report. Comments welcom

The Galaxy Assembly and Interaction Neural Networks (GAINN) for high-redshift JWST observations

We present the Galaxy Assembly and Interaction Neural Networks (GAINN), a series of artificial neural networks for predicting the redshift, stellar mass, halo mass, and mass-weighted age of simulated galaxies based on JWST photometry. Our goal is to determine the best neural network for predicting these variables at $11.5 < z < 15$. The parameters of the optimal neural network can then be used to estimate these variables for real, observed galaxies. The inputs of the neural networks are JWST filter magnitudes of a subset of five broadband filters (F150W, F200W, F277W, F356W, and F444W) and two medium-band filters (F162M and F182M). We compare the performance of the neural networks using different combinations of these filters, as well as different activation functions and numbers of layers. The best neural network predicted redshift with normalized root mean squared error NRMS = $0.009_{-0.002}^{+0.003}$, stellar mass with RMS = $0.073_{-0.008}^{+0.017}$, halo mass with MSE = $0.022_{-0.004}^{+0.006}$, and mass-weighted age with RMS = $10.866_{-1.410}^{+3.189}$. We also test the performance of GAINN on real data from MACS0647-JD, an object observed by JWST. Predictions from GAINN for the first projection of the object (JD1) have mean absolute errors $\langle \Delta z \rangle <0.00228$, which is significantly smaller than with template-fitting methods. We find that the optimal filter combination is F277W, F356W, F162M, and F182M when considering both theoretical accuracy and observational resources from JWST.Comment: 19 pages, 6 figures, submitted to Ap

How an improved implementation of H2 self-shielding influences the formation of massive stars and black holes

High redshift quasars at z>6 have masses up to ~$10^9$ M$_\odot$. One of the pathways to their formation includes direct collapse of gas, forming a supermassive star, precursor of the black hole seed. The conditions for direct collapse are more easily achievable in metal-free haloes, where atomic hydrogen cooling operates and molecular hydrogen (H2) formation is inhibited by a strong external UV flux. Above a certain value of UV flux (J_crit), the gas in a halo collapses isothermally at ~$10^4$ K and provides the conditions for supermassive star formation. However, H2 can self-shield, reducing the effect of photodissociation. So far, most numerical studies used the local Jeans length to calculate the column densities for self-shielding. We implement an improved method for the determination of column densities in 3D simulations and analyse its effect on the value of J_crit. This new method captures the gas geometry and velocity field and enables us to properly determine the direction-dependent self-shielding factor of H2 against photodissociating radiation. We find a value of J_crit that is a factor of two smaller than with the Jeans approach (~2000 J_21 vs. ~4000 J_21). The main reason for this difference is the strong directional dependence of the H2 column density. With this lower value of J_crit, the number of haloes exposed to a flux >J_crit is larger by more than an order of magnitude compared to previous studies. This may translate into a similar enhancement in the predicted number density of black hole seeds.Comment: 14 pages, 12 figures, published in MNRA

On the Detection of Supermassive Primordial Stars. II. Blue Supergiants

Supermassive primordial stars in hot, atomically-cooling haloes at $z \sim$ 15 - 20 may have given birth to the first quasars in the universe. Most simulations of these rapidly accreting stars suggest that they are red, cool hypergiants, but more recent models indicate that some may have been bluer and hotter, with surface temperatures of 20,000 - 40,000 K. These stars have spectral features that are quite distinct from those of cooler stars and may have different detection limits in the near infrared (NIR) today. Here, we present spectra and AB magnitudes for hot, blue supermassive primordial stars calculated with the TLUSTY and CLOUDY codes. We find that photometric detections of these stars by the James Webb Space Telescope (JWST) will be limited to $z \lesssim$ 10 - 12, lower redshifts than those at which red stars can be found, because of quenching by their accretion envelopes. With moderate gravitational lensing, Euclid and the Wide-Field Infrared Space Telescope (WFIRST) could detect blue supermassive stars out to similar redshifts in wide-field surveys.Comment: 9 pages, 5 figures, accepted by MNRA

Predicting the locations of possible long-lived low-mass first stars: Importance of satellite dwarf galaxies

The search for metal-free stars has so far been unsuccessful, proving that if there are surviving stars from the first generation, they are rare, they have been polluted, or we have been looking in the wrong place. To predict the likely location of Population~III (Pop~III) survivors, we semi-analytically model early star formation in progenitors of Milky Way-like galaxies and their environments. We base our model on merger trees from the high-resolution dark matter only simulation suite \textit{Caterpillar}. Radiative and chemical feedback are taken into account self-consistently, based on the spatial distribution of the haloes. Our results are consistent with the non-detection of Pop III survivors in the Milky Way today. We find that possible surviving Population III stars are more common in Milky Way satellites than in the main Galaxy. In particular, low mass Milky Way satellites contain a much larger fraction of Pop~III stars than the Milky Way. Such nearby, low mass Milky Way satellites are promising targets for future attempts to find Pop~III survivors, especially for high-resolution, high signal-to-noise spectroscopic observations. We provide the probabilities for finding a Pop~III survivor in the red giant branch phase for all known Milky Way satellites to guide future observations.Comment: 17 pages, 12 figures, 1 table, submitted to MNRA