arXiv subjects

Federico Marinacci

Publications and source records attributed to Federico Marinacci.

At least 199 records · Page 11Linked to original sources

arXiv2019

The fraction of dark matter within galaxies from the IllustrisTNG simulations

We use the IllustrisTNG (TNG) cosmological simulations to provide theoretical expectations for the dark matter mass fractions (DMFs) and circular velocity profiles of galaxies. TNG predicts flat circular velocity curves for $z = 0$ Milky Way (MW)-like galaxies beyond a few kpc from the galaxy centre, in better agreement with observational constraints than its predecessor, Illustris. TNG also predicts an enhancement of the dark matter mass within the 3D stellar half-mass radius ($r_\mathrm{half}$; $M_\mathrm{200c} = 10^{10}-10^{13}\mathrm{M}_{\odot}$, $z \le2$) compared to its dark matter only and Illustris counterparts. This enhancement leads TNG present-day galaxies to be dominated by dark matter within their inner regions, with $f_\mathrm{DM}(<r_\mathrm{half})\gtrsim0.5$ at all masses and with a minimum for MW-mass galaxies. The 1$σ$ scatter is $\lesssim$ 10~per~cent at all apertures, which is smaller than that inferred by some observational datasets, e.g. 40 per cent from the SLUGGS survey. TNG agrees with the majority of the observationally inferred values for elliptical galaxies once a consistent IMF is adopted (Chabrier) and the DMFs are measured within the same apertures. The DMFs measured within $r_\mathrm{half}$ increase towards lower redshifts: this evolution is dominated by the increase in galaxy size with time. At $z\sim2$, the DMF in disc-like TNG galaxies decreases with increasing galaxy mass, with $f_\mathrm{DM}(<r_\mathrm{half}) \sim 0.10-0.65$ for $10^{10} \lesssim M_{\rm stars}/\mathrm{M}_{\odot} \lesssim 10^{12}$, and are two times higher than if TNG galaxies resided in Navarro-Frenk-White dark matter haloes unaffected by baryonic physics. It remains to be properly assessed whether recent observational estimates of the DMFs at $z\sim2$ rule out the contraction of the dark matter haloes predicted by the TNG model.

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arXiv2019

The optical morphologies of galaxies in the IllustrisTNG simulation: a comparison to Pan-STARRS observations

We have generated synthetic images of $\sim$27,000 galaxies from the IllustrisTNG and the original Illustris hydrodynamic cosmological simulations, designed to match Pan-STARRS observations of $\log_{10}(M_{\ast}/{\rm M}_{\odot}) \approx 9.8$-$11.3$ galaxies at $z \approx 0.05$. Most of our synthetic images were created with the SKIRT radiative transfer code, including the effects of dust attenuation and scattering, and performing the radiative transfer directly on the Voronoi mesh used by the simulations themselves. We have analysed both our synthetic and real Pan-STARRS images with the newly developed $\tt{statmorph}$ code, which calculates non-parametric morphological diagnostics -- including the Gini-$M_{20}$ and concentration-asymmetry-smoothness (CAS) statistics -- and performs two-dimensional Sérsic fits. Overall, we find that the optical morphologies of IllustrisTNG galaxies are in good agreement with observations, and represent a substantial improvement compared to the original Illustris simulation. In particular, the locus of the Gini-$M_{20}$ diagram is consistent with that inferred from observations, while the median trends with stellar mass of all the morphological, size and shape parameters considered in this work lie within the $\sim$1$σ$ scatter of the observational trends. However, the IllustrisTNG model has some difficulty with more stringent tests, such as producing a strong morphology-colour relation. This results in a somewhat higher fraction of red discs and blue spheroids compared to observations. Similarly, the morphology-size relation is problematic: while observations show that discs tend to be larger than spheroids at a fixed stellar mass, such a trend is not present in IllustrisTNG.

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arXiv2018

A Quantification of the Butterfly Effect in Cosmological Simulations and Implications for Galaxy Scaling Relations

We study the chaotic-like behavior of cosmological simulations by quantifying how minute perturbations grow over time and manifest as macroscopic differences in galaxy properties. When we run pairs of 'shadow' simulations that are identical except for random minute initial displacements to particle positions (e.g. of order 1e-7pc), the results diverge from each other at the individual galaxy level (while the statistical properties of the ensemble of galaxies are unchanged). After cosmological times, the global properties of pairs of 'shadow' galaxies that are matched between the simulations differ from each other generally at a level of ~2-25%, depending on the considered physical quantity. We perform these experiments using cosmological volumes of (25-50Mpc/h)^3 evolved either purely with dark matter, or with baryons and star-formation but no feedback, or using the full feedback model of the IllustrisTNG project. The runs cover four resolution levels spanning a factor of 512 in mass. We find that without feedback the differences between shadow galaxies generally become smaller as the resolution increases, but with the IllustrisTNG model the results are mostly converging towards a 'floor'. This hints at the role of feedback in setting the chaotic properties of galaxy formation. Importantly, we compare the macroscopic differences between shadow galaxies to the overall scatter in various galaxy scaling relations, and conclude that for the star formation-mass and the Tully-Fisher relations the butterfly effect in our simulations contributes significantly to the overall scatter. We find that our results are robust to whether random numbers are used in the sub-grid models or not. We discuss the implications for galaxy formation theory in general and for cosmological simulations in particular.

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arXiv2018

Radiative AGN feedback on a moving mesh: the impact of the galactic disc and dust physics on outflow properties

Feedback from accreting supermassive black holes, active galactic nuclei (AGN), is now a cornerstone of galaxy formation models. In this work, we present radiation-hydrodynamic simulations of radiative AGN feedback using the novel Arepo-RT. A central black hole emits radiation at a constant luminosity and drives an outflow via radiation pressure on dust grains. Utilising an isolated NFW halo we validate our setup in the single and multi-scattering regimes, with the simulated shock front propagation in excellent agreement with the expected analytic result. For a spherically symmetric NFW halo, an examination of the simulated outflow properties generated by radiative feedback demonstrates that they are lower than typically observed at a fixed AGN luminosity, regardless of the collimation of the radiation. We then explore the impact of a central disc galaxy and the assumed dust model on the outflow properties. The contraction of the halo during the galaxy's formation and modelling the production of dust grains results in a factor $100$ increase in the halo's optical depth. Radiation is then able to couple momentum more efficiently to the gas, driving a stronger shock and producing a mass-loaded $\sim10^{3}\,\mathrm{M}_{\odot}\,\mathrm{yr}^{-1}$ outflow with a velocity of $\sim2000\,\mathrm{km}\,\mathrm{s}^{-1}$, in agreement with observations. However, the inclusion of dust destruction mechanisms, like thermal sputtering, leads to the rapid destruction of dust grains within the outflow, reducing its properties below typically observed values. We conclude that radiative AGN feedback can drive outflows, but a thorough numerical and physical treatment is required to assess its true impact.

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arXiv2018

Efficacy of early stellar feedback in low gas surface density environments

We present a suite of high resolution radiation hydrodynamic simulations of a small patch ($1 \ {\rm kpc}^2$) of the inter-stellar medium (ISM) performed with Arepo-RT, with the aim to quantify the efficacy of various feedback processes like supernovae explosions (SNe), photoheating and radiation pressure in low gas surface density galaxies ($Σ_{\rm gas} \simeq 10 \ {\rm M}_\odot \ {\rm pc}^{-2}$). We show that radiation fields decrease the star formation rate and therefore the total stellar mass formed by a factor of $\sim 2$. This increases the gas depletion timescale and brings the simulated Kennicutt-Schmidt relation closer to the observational estimates. Radiation feedback coupled with SNe is more efficient at driving outflows with the mass and energy loading increasing by a factor of $\sim 10$. This increase is mainly driven by the additional entrainment of medium density ($10^{-2} \leq n< 1 \ {\rm cm}^{-3}$), warm ($300 \ {\rm K}\leq T<8000 \ {\rm K}$) material. Therefore including radiation fields tends to launch colder, denser and higher mass and energy loaded outflows. This is because photoheating of the high density gas around a newly formed star over-pressurises the region, causing it to expand. This reduces the ambient density in which the SNe explode by a factor of $10-100$ which in turn increases their momentum output by a factor of $\sim 1.5-2.5$. Finally, we note that in these low gas surface density environments, radiation fields primarily impact the ISM via photoheating and radiation pressure has only a minimal role in regulating star formation.

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arXiv2018

A census of cool core galaxy clusters in IllustrisTNG

The thermodynamic structure of hot gas in galaxy clusters is sensitive to astrophysical processes and typically difficult to model with galaxy formation simulations. We explore the fraction of cool-core (CC) clusters in a large sample of $370$ clusters from IllustrisTNG, examining six common CC definitions. IllustrisTNG produces continuous CC criteria distributions, the extremes of which are classified as CC and non-cool-core (NCC), and the criteria are increasingly correlated for more massive clusters. At $z=0$, the CC fractions for $2$ criteria are in reasonable agreement with the observed fractions but the other $4$ CC fractions are lower than observed. This result is partly driven by systematic differences between the simulated and observed gas fraction profiles. The simulated CC fractions with redshift show tentative agreement with the observed fractions, but linear fits demonstrate that the simulated evolution is steeper than observed. The conversion of CCs to NCCs appears to begin later and act more rapidly in the simulations. Examining the fraction of CCs and NCCs defined as relaxed we find no evidence that CCs are more relaxed, suggesting that mergers are not solely responsible for disrupting CCs. A comparison of the median thermodynamic profiles defined by different CC criteria shows that the extent to which they evolve in the cluster core is dependent on the CC criteria. We conclude that the thermodynamic structure of galaxy clusters in IllustrisTNG shares many similarities with observations, but achieving better agreement most likely requires modifications of the underlying galaxy formation model.

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arXiv2018

Modeling the atomic-to-molecular transition in cosmological simulations of galaxy formation

Large-scale cosmological simulations of galaxy formation currently do not resolve the densities at which molecular hydrogen forms, implying that the atomic-to-molecular transition must be modeled either on the fly or in postprocessing. We present an improved postprocessing framework to estimate the abundance of atomic and molecular hydrogen and apply it to the IllustrisTNG simulations. We compare five different models for the atomic-to-molecular transition, including empirical, simulation-based, and theoretical prescriptions. Most of these models rely on the surface density of neutral hydrogen and the ultraviolet (UV) flux in the Lyman-Werner band as input parameters. Computing these quantities on the kiloparsec scales resolved by the simulations emerges as the main challenge. We show that the commonly used Jeans length approximation to the column density of a system can be biased and exhibits large cell-to-cell scatter. Instead, we propose to compute all surface quantities in face-on projections and perform the modeling in two dimensions. In general, the two methods agree on average, but their predictions diverge for individual galaxies and for models based on the observed midplane pressure of galaxies. We model the UV radiation from young stars by assuming a constant escape fraction and optically thin propagation throughout the galaxy. With these improvements, we find that the five models for the atomic-to-molecular transition roughly agree on average but that the details of the modeling matter for individual galaxies and the spatial distribution of molecular hydrogen. We emphasize that the estimated molecular fractions are approximate due to the significant systematic uncertainties.

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arXiv2018

Faraday rotation maps of disk galaxies

Faraday rotation is one of the most widely used observables to infer the strength and configuration of the magnetic field in the ionised gas of the Milky Way and nearby spiral galaxies. Here we compute synthetic Faraday rotation maps at $z=0$ for a set of disk galaxies from the Auriga high-resolution cosmological simulations, for different observer positions within and outside the galaxy. We find that the strength of the Faraday rotation of our simulated galaxies for a hypothetic observer at the solar circle is broadly consistent with the Faraday rotation seen for the Milky Way. The same holds for an observer outside the galaxy and the observed signal of the nearby spiral galaxy M51. However, we also find that the structure and angular power spectra of the synthetic all-sky Faraday rotation maps vary strongly with azimuthal position along the solar circle. We argue that this variation is a result of the structure of the magnetic field of the galaxy that is dominated by an azimuthal magnetic field ordered scales of several kpc, but has radial and vertical magnetic field components that are only ordered on scales of 1-2 kpc. Because the magnetic field strength decreases exponentially with height above the disk, the Faraday rotation for an observer at the solar circle is dominated by the local environment. This represents a severe obstacle for attempts to reconstruct the global magnetic field of the Milky Way from Faraday rotation maps alone without including additional observables.

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arXiv2018

The Supersonic Project: rotational effects of supersonic motions on the first structures in the Universe

We introduce the "Supersonic Project," aimed at investigating the effects of the supersonic relative velocity between dark matter (DM) and baryons at high redshift using a combination of analytical calculations and cosmological simulations. In this paper, we study the effect of this stream velocity on the angular momentum of the first structures in the early Universe using simulations. We focus on DM haloes and their gas component as well as the recently predicted supersonically-induced gas objects (SIGOs) that arise as a result of the stream velocity phase shift. We find that the spin parameter of the gas component in these first haloes is increased with the stream velocity. Moreover, we find that when the stream velocity is taken into account, the angular momentum vectors of the DM component and the gas component are typically misaligned and this misalignment angle has a nearly isotropic distribution. The spin parameter value of the gas component is higher than in the no stream velocity case, which even in the absence of cooling, may result in more prolate objects. We also generalize the spin parameter to the SIGOs and find that they typically have a larger spin parameter with respect to their dark matter counterparts and that there is no correlation of the spin parameter and the prolateness of such structures. We speculate that SIGOs may be observed as very low luminosity objects in the early Universe and may serve as potential progenitors of Little Blue Dot-like systems.

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arXiv2018

Assembly of supermassive black hole seeds

We present a suite of six fully cosmological, three-dimensional simulations of the collapse of an atomic cooling halo in the early Universe. We use the moving-mesh code arepo with an improved primordial chemistry network to evolve the hydrodynamical and chemical equations. The addition of a strong Lyman-Werner background suppresses molecular hydrogen cooling and permits the gas to evolve nearly isothermally at a temperature of about 8000 K. Strong gravitational torques effectively remove angular momentum and lead to the central collapse of gas, forming a supermassive protostar at the center of the halo. We model the protostar using two methods: sink particles that grow through mergers with other sink particles, and a stiff equation of state that leads to the formation of an adiabatic core. We impose threshold densities of $10^8$, $10^{10}$, and $10^{12}\,\text{cm}^{-3}$ for the sink particle formation and the onset of the stiff equation of state to study the late, intermediate, and early stages in the evolution of the protostar, respectively. We follow its growth from masses $\simeq 10\,\text{M}_\odot$ to $\simeq 10^5\,\text{M}_\odot$, with an average accretion rate of $\langle\dot{M}_\star\rangle \simeq 2\,\text{M}_\odot\,\text{yr}^{-1}$ for sink particles, and $\simeq 0.8 - 1.4\,\text{M}_\odot\,\text{yr}^{-1}$ for the adiabatic cores. At the end of the simulations, the HII region generated by radiation from the central object has long detached from the protostellar photosphere, but the ionizing radiation remains trapped in the inner host halo, and has thus not yet escaped into the intergalactic medium. Fully coupled, radiation-hydrodynamics simulations hold the key for further progress.

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arXiv2018

Aurigaia: mock Gaia DR2 stellar catalogues from the Auriga cosmological simulations

We present and analyse mock stellar catalogues that match the selection criteria and observables (including uncertainties) of the Gaia satellite data release 2 (DR2). The source are six cosmological high-resolution magneto-hydrodynamic $Λ$CDM zoom simulations of the formation of Milky Way analogues from the AURIGA project. Mock data are provided for stars with $V < 16$ mag, and $V < 20$ mag at $|b|>20$ degrees. The mock catalogues are made using two different methods: the public SNAPDRAGONS code, and a method based on that of Lowing et al. that preserves the phase-space distribution of the model stars. These publicly available catalogues contain 5-parameter astrometry, radial velocities, multi-band photometry, stellar parameters, dust extinction values, and uncertainties in all these quantities. In addition, we provide the gravitational potential and information on the origin of each star. By way of demonstration, we apply the mock catalogues to analyses of the young stellar disc and the stellar halo. We show that: i) the young outer stellar disc exhibits a flared distribution that is detectable in the height and vertical velocity distribution of A- and B-dwarf stars up to radii of ~15 kpc; and ii) the spin of the stellar halo out to 100 kpc can be accurately measured with Gaia DR2 RR Lyrae stars. These catalogues are well suited for comparisons with observations and should help to: i) develop and test analysis methods for the Gaia DR2 data; ii) gauge the limitations and biases of the data and iii) interpret the data in the light of theoretical predictions from realistic $ab$ $initio$ simulations of galaxy formation in the $Λ$CDM cosmological model.

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arXiv2018

First results from the IllustrisTNG simulations: radio haloes and magnetic fields

We introduce the IllustrisTNG project, a new suite of cosmological magnetohydrodynamical simulations performed with the moving-mesh code AREPO employing an updated Illustris galaxy formation model. Here we focus on the general properties of magnetic fields and the diffuse radio emission in galaxy clusters. Magnetic fields are prevalent in galaxies, and their build-up is closely linked to structure formation. We find that structure formation amplifies the initial seed fields ($10^{-14}$ comoving Gauss) to the values observed in low-redshift galaxies ($1-10\,μ{\rm G}$). The magnetic field topology is closely connected to galaxy morphology such that irregular fields are hosted by early-type galaxies, while large-scale, ordered fields are present in disc galaxies. Using two simple models for the energy distribution of relativistic electrons we predict the diffuse radio emission of $280$ clusters with a baryonic mass resolution of $1.1\times 10^{7}\,{\rm M_{\odot}}$, and generate mock observations for VLA, LOFAR, ASKAP and SKA. Our simulated clusters show extended radio emission, whose detectability correlates with their virial mass. We reproduce the observed scaling relations between total radio power and X-ray emission, $M_{500}$, and the Sunyaev-Zel'dovich $Y_{\rm 500}$ parameter. The radio emission surface brightness profiles of our most massive clusters are in reasonable agreement with VLA measurements of Coma and Perseus. Finally, we discuss the fraction of detected extended radio haloes as a function of virial mass and source count functions for different instruments. Overall our results agree encouragingly well with observations, but a refined analysis requires a more sophisticated treatment of relativistic particles in large-scale galaxy formation simulations.

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arXiv2018

Formation of a Malin 1 analogue in IllustrisTNG by stimulated accretion

The galaxy Malin 1 contains the largest stellar disk known but the formation mechanism of this structure has been elusive. In this paper, we report a Malin 1 analogue in the 100 Mpc IllustrisTNG simulation and describe its formation history. At redshift zero, this massive galaxy, having a maximum circular velocity $V_{\rm max}$ of 430 ${\rm km\ s^{-1}}$, contains a 100 kpc gas/stellar disk with morphology similar to Malin 1. The simulated galaxy reproduces well many observed features of Malin 1's vast disk, including its stellar ages, metallicities, and gas rotation curve. We trace the extended disk back in time and find that a large fraction of the cold gas at redshift zero originated from the cooling of hot halo gas, triggered by the merger of a pair of intruding galaxies. Our finding provides a novel way to form large galaxy disks as extreme as Malin 1 within the current galaxy formation framework.

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arXiv2018

On the relevance of chaos for halo stars in the solar neighbourhood II

In a previous paper based on dark matter only simulations we show that, in the approximation of an analytic and static potential describing the strongly triaxial and cuspy shape of Milky Way-sized haloes, diffusion due to chaotic mixing in the neighbourhood of the Sun does not efficiently erase phase space signatures of past accretion events. In this second paper we further explore the effect of chaotic mixing using multicomponent Galactic potential models and solar neighbourhood-like volumes extracted from fully cosmological hydrodynamic simulations, thus naturally accounting for the gravitational potential associated with baryonic components, such as the bulge and disc. Despite the strong change in the global Galactic potentials with respect to those obtained in dark matter only simulations, our results confirm that a large fraction of halo particles evolving on chaotic orbits exhibit their chaotic behaviour after periods of time significantly larger than a Hubble time. In addition, significant diffusion in phase space is not observed on those particles that do exhibit chaotic behaviour within a Hubble time.

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arXiv2018

Enhancing AGN efficiency and cool-core formation with anisotropic thermal conduction

Understanding how baryonic processes shape the intracluster medium (ICM) is of critical importance to the next generation of galaxy cluster surveys. However, most models of structure formation neglect potentially important physical processes, like anisotropic thermal conduction (ATC). In this letter, we explore the impact of ATC on the prevalence of cool-cores (CCs) using 12 pairs of magnetohydrodynamical galaxy cluster simulations, simulated using the IllustrisTNG model with and without ATC. Although the impact of ATC varies from cluster to cluster and with CC criterion, its inclusion produces a systematic shift to larger CC fractions at z = 0 for all CC criteria considered. Additionally, the inclusion of ATC yields a flatter CC fraction redshift evolution, easing the tension with the observed evolution. With ATC included, the energy required for the central black hole to achieve self-regulation is reduced and the gas fraction in the cluster core increases, resulting in larger CC fractions. ATC makes the ICM unstable to perturbations and the increased efficiency of AGN feedback suggests that its inclusion results in a greater level of mixing in the ICM. Therefore, ATC is potentially an important physical process in reproducing the thermal structure of the ICM.

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arXiv2018

Simulating galactic dust grain evolution on a moving mesh

Interstellar dust is an important component of the galactic ecosystem, playing a key role in multiple galaxy formation processes. We present a novel numerical framework for the dynamics and size evolution of dust grains implemented in the moving-mesh hydrodynamics code AREPO suited for cosmological galaxy formation simulations. We employ a particle-based method for dust subject to dynamical forces including drag and gravity. The drag force is implemented using a second-order semi-implicit integrator and validated using several dust-hydrodynamical test problems. Each dust particle has a grain size distribution, describing the local abundance of grains of different sizes. The grain size distribution is discretised with a second-order piecewise linear method and evolves in time according to various dust physical processes, including accretion, sputtering, shattering, and coagulation. We present a novel scheme for stochastically forming dust during stellar evolution and new methods for sub-cycling of dust physics time-steps. Using this model, we simulate an isolated disc galaxy to study the impact of dust physical processes that shape the interstellar grain size distribution. We demonstrate, for example, how dust shattering shifts the grain size distribution to smaller sizes resulting in a significant rise of radiation extinction from optical to near-ultraviolet wavelengths. Our framework for simulating dust and gas mixtures can readily be extended to account for other dynamical processes relevant in galaxy formation, like magnetohydrodynamics, radiation pressure, and thermo-chemical processes.

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arXiv2018

Ingredients for 21cm intensity mapping

[Abridged] We study the abundance and clustering properties of HI at redshifts $z\leqslant5$ using TNG100, a large state-of-the-art magneto-hydrodynamic simulation of a 75 Mpc/h box size. We show that most of the HI lies within dark matter halos and quantify the average HI mass hosted by halos of mass M at redshift z. We find that only halos with circular velocities larger than $\simeq$ 30 km/s contain HI. While the density profiles of HI exhibit a large halo-to-halo scatter, the mean profiles are universal across mass and redshift. The HI in low-mass halos is mostly located in the central galaxy, while in massive halos is concentrated in the satellites. We show that the HI and matter density probability distribution functions differ significantly. Our results point out that for small halos the HI bulk velocity goes in the same direction and has the same magnitude as the halo peculiar velocity, while in large halos differences show up. We find that halo HI velocity dispersion follows a power-law with halo mass. We find a complicated HI bias, with HI becoming non-linear already at $k=0.3$ h/Mpc at $z\gtrsim3$. Our simulation reproduces the DLAs bias value from observations. We find that the clustering of HI can be accurately reproduced by perturbative methods. We identify a new secondary bias, by showing that the clustering of halos depends not only on mass but also on HI content. We compute the amplitude of the HI shot-noise and find that it is small at all redshifts. We study the clustering of HI in redshift-space, and show that linear theory can explain the ratio between the monopoles in redshift- and real-space down to small scales at high redshift. We find that the amplitude of the Fingers-of-God effect is larger for HI than for matter. We point out that accurate 21 cm maps can be created from N-body or approximate simulations rather than full hydrodynamic simulations.

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arXiv2018

Opacity limit for supermassive protostars

We present a model for the evolution of supermassive protostars from their formation at $M_\star \simeq 0.1\,\text{M}_\odot$ until their growth to $M_\star \simeq 10^5\,\text{M}_\odot$. To calculate the initial properties of the object in the optically thick regime we follow two approaches: based on idealized thermodynamic considerations, and on a more detailed one-zone model. Both methods derive a similar value of $n_{\rm F} \simeq 2 \times 10^{17} \,\text{cm}^{-3}$ for the density of the object when opacity becomes important, i.e. the opacity limit. The subsequent evolution of the growing protostar is determined by the accretion of gas onto the object and can be described by a mass-radius relation of the form $R_\star \propto M_\star^{1/3}$ during the early stages, and of the form $R_\star \propto M_\star^{1/2}$ when internal luminosity becomes important. For the case of a supermassive protostar, this implies that the radius of the star grows from $R_\star \simeq 0.65 \,{\rm AU}$ to $R_\star \simeq 250 \,{\rm AU}$ during its evolution. Finally, we use this model to construct a sub-grid recipe for accreting sink particles in numerical simulations. A prime ingredient thereof is a physically motivated prescription for the accretion radius and the effective temperature of the growing protostar embedded inside it. From the latter, we can conclude that photo-ionization feedback can be neglected until very late in the assembly process of the supermassive object.

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