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We use the Evolution and Assembly of GaLaxies and their Environments (eagle) and IllustrisTNG (The Next Generation) cosmological simulations to investigate the properties of the baryonic specific angular momentum (j), baryonic mass (M), and atomic gas fraction (f atm) plane for nearby galaxies. We find EAGLE and TNG to be in excellent agreement with each other. These simulations are also consistent with the results obtained with eXtended GALEX Arecibo SDSS Survey (xGASS) for gas fractions greater than 0.01. This implies that the disagreements previously identified between xGASS and predictions from simple analytical disc stability arguments also holds true for eagle and tng. For lower gas fraction (the regime currently unconstrained by observations), both simulations deviate from the plane but still maintain good agreement with each other. Despite the challenges posed by resolution limits at low gas fractions, our findings suggest a potential disconnect between angular momentum and gas fraction in the gas-poor regime, implying that not all gas-poor galaxies have low specific angular momentum. [ABSTRACT FROM AUTHOR]

We employ the eagle hydrodynamical simulation to uncover the relationship between cluster environment and H2 content of star-forming galaxies at redshifts spanning 0 ≤ z ≤ 1. To do so, we divide the star-forming sample into those that are bound to clusters and those that are not. We find that, at any given redshift, the galaxies in clusters generally have less H2 than their non-cluster counterparts with the same stellar mass (corresponding to an offset of ≲0.5 dex), but this offset varies with stellar mass and is virtually absent at M ⋆ ≲ 109.3 M⊙. The H2 deficit in star-forming cluster galaxies can be traced back to a decline in their H2 content that commenced after first infall into a cluster, which occurred later than a typical cluster galaxy. Evolution of the full cluster population after infall is generally consistent with 'slow-then-rapid' quenching, but galaxies with M ⋆ ≲ 109.5 M⊙ exhibit rapid quenching. Unlike most cluster galaxies, star-forming ones were not pre-processed in groups prior to being accreted by clusters. For both of these cluster samples, the star formation efficiency remained oblivious to the infall. We track the particles associated with star-forming cluster galaxies and attribute the drop in H2 mass after infall to poor replenishment, depletion due to star formation, and stripping of H2 in cluster environments. These results provide predictions for future surveys, along with support and theoretical insights for existing molecular gas observations that suggest there is less H2 in cluster galaxies. [ABSTRACT FROM AUTHOR]

Using the eagle (Evolution and Assembly of GaLaxies and their Environments) suite of simulations, we demonstrate that both cold gas stripping and starvation of gas inflow play an important role in quenching satellite galaxies across a range of stellar and halo masses, M ⋆ and M 200. Quantifying the balance between gas inflows, outflows, and star formation rates, we show that even at z  = 2, only |$\approx 30{{\ \rm per\ cent}}$| of satellite galaxies are able to maintain equilibrium or grow their reservoir of cool gas – compared to |$\approx 50{{\ \rm per\ cent}}$| of central galaxies at this redshift. We find that the number of orbits completed by a satellite on first-infall to a group environment is a very good predictor of its quenching, even more so than the time since infall. On average, we show that intermediate-mass satellites with M ⋆ between will be quenched at |$10^{9}\, {\rm M}_{\odot }\, {\rm and}\, 10^{10}\, {\rm M}_{\odot }$| first pericenter in massive group environments, |$M_{200}\gt 10^{13.5}\, {\rm M}_{\odot }$|⁠ ; and will be quenched at second pericenter in less massive group environments, |$M_{200}\lt 10^{13.5}\, {\rm M}_{\odot }$|⁠. On average, more massive satellites (⁠|$M_{\star }\gt 10^{10}\, {\rm M}_{\odot }$|⁠) experience longer depletion time-scales, being quenched between first and second pericenters in massive groups, while in smaller group environments, just |$\approx 30{{\ \rm per\ cent}}$| will be quenched even after two orbits. Our results suggest that while starvation alone may be enough to slowly quench satellite galaxies, direct gas stripping, particularly at pericenters, is required to produce the short quenching time-scales exhibited in the simulation. [ABSTRACT FROM AUTHOR]

We study the shapes of spatially integrated |$\rm{H}\, \small {{I}}$| emission-line profiles of galaxies in the eagle simulation using three separate measures of the profile's asymmetry. We show that the subset of eagle galaxies whose gas fractions and stellar masses are consistent with those in the xGASS survey also have similar |$\rm{H}\, \small {{I}}$| line asymmetries. Central galaxies with symmetric |$\rm{H}\, \small {{I}}$| line profiles typically correspond to rotationally supported |$\rm{H}\, \small {{I}}$| and stellar discs, but those with asymmetric line profiles may or may not correspond to dispersion-dominated systems. Galaxies with symmetric |$\rm{H}\, \small {{I}}$| emission lines are, on average, more gas rich than those with asymmetric lines, and also exhibit systematic differences in their specific star formation rates, suggesting that turbulence generated by stellar or AGN feedback may be one factor contributing to |$\rm{H}\, \small {{I}}$| line asymmetry. The line asymmetry also correlates strongly with the dynamical state of a galaxy's host dark matter halo: older, more relaxed haloes host more-symmetric galaxies than those hosted by unrelaxed ones. At fixed halo mass, asymmetric centrals tend to be surrounded by a larger number of massive subhaloes than their symmetric counterparts, and also experience higher rates of gas accretion and outflow. At fixed stellar mass, central galaxies have, on average, more symmetric |$\rm{H}\, \small {{I}}$| emission lines than satellites; for the latter, ram pressure and tidal stripping are significant sources of asymmetry. [ABSTRACT FROM AUTHOR]

We study the clustering of H  i  intensity maps (IM) produced from simulations with a focus on baryonic acoustic oscillations (BAOs) and the effects induced by telescope beam smoothing and foreground cleaning. We start by creating an H  i catalogue at z  = 1.321 based on the Semi-Analytic Galaxy Evolution (SAGE) model applied to the UNIT simulations. With this catalogue, we investigate the relation between model H  i and the dark matter haloes and we also study the abundance of H  i , |$\Omega _\rm{H \small {\rm I}}$|⁠ , predicted by this model. We then create synthetic H  i IM with a nearest-grid-point approach. In order to simulate the telescope beam effect, a Gaussian smoothing is applied on the plane perpendicular to the line of sight. The effect of foreground removal methods is simulated by exponentially damping the largest wavelength Fourier modes on the radial direction. We study the anisotropic 2-point correlation function (2PCF) ξ(r ⊥, r ∥) and how it is affected by the aforementioned observational effects. In order to better isolate the BAO signal, we study several 2PCF μ -wedges (with a restricted range of orientations μ) tailored to address the systematics effects and we compare them with different definitions of radial 2PCFs. Finally, we discuss our findings in the context of an SKA-like survey, finding a clear BAO signal in most of the estimators here proposed. [ABSTRACT FROM AUTHOR]

We examine how the post-processed content of molecular hydrogen (H2) in galaxies from the TNG100 cosmological, hydrodynamic simulation changes with environment at z = 0, assessing central/satellite status and host halo mass. We make close comparisons with the carbon monoxide (CO) emission survey xCOLD GASS where possible, having mock-observed TNG100 galaxies to match the survey's specifications. For a representative sample of host haloes across 1011 ≲ M 200c/M⊙ < 1014.6, TNG100 predicts that satellites with |$m_* \ge 10^9\, {\rm M}_{\odot }$| should have a median deficit in their H2 fractions of ∼0.6 dex relative to centrals of the same stellar mass. Once observational and group-finding uncertainties are accounted for, the signature of this deficit decreases to ∼0.2 dex. Remarkably, we calculate a deficit in xCOLD GASS satellites' H2 content relative to centrals of 0.2–0.3 dex, in line with our prediction. We further show that TNG100 and SDSS data exhibit continuous declines in the average star formation rates of galaxies at fixed stellar mass in denser environments, in quantitative agreement with each other. By tracking satellites from their moment of infall in TNG100, we directly show that atomic hydrogen (H  i) is depleted at fractionally higher rates than H2 on average. Supporting this picture, we find that the H2/H  i  mass ratios of satellites are elevated relative to centrals in xCOLD GASS. We provide additional predictions for the effect of environment on H2 – both absolute and relative to H  i – that can be tested with spectral stacking in future CO surveys. [ABSTRACT FROM AUTHOR]

Observations of the cold neutral atomic hydrogen (H  i) in and around disc galaxies have revealed that spatial and kinematic asymmetries are common place, and are reflected in the global H  i spectra. We use the TNG100 box from the IllustrisTNG suite of cosmological simulations to study the conditions under which these asymmetries may arise in current theoretical galaxy formation models. We find that more than 50 per cent of the sample has at least a 10 per cent difference in integrated flux between the high- and low-velocity half of the spectrum, thus the typical TNG100 galaxy has an H  i profile that is not fully symmetric. We find that satellite galaxies are a more asymmetric population than centrals, consistent with observational results. Using halo mass as a proxy for environment, this trend appears to be driven by the satellite population within the virial radius of haloes more massive than 1013 M⊙, typical of medium/large groups. We show that, while the excess of H  i asymmetry in group satellites is likely driven by ram pressure, the bulk of the asymmetric H  i profiles observed in TNG100 are driven by physical processes able to affect both the central and satellite populations. Our results highlight how asymmetries are not driven solely by environment, and multiple physical processes can produce the same asymmetric shape in global H  i spectra. [ABSTRACT FROM AUTHOR]

We apply the spectral energy distribution (SED) fitting code ProSpect to multiwavelength imaging for ∼7000 galaxies from the GAMA survey at z < 0.06, in order to extract their star formation histories. We combine a parametric description of the star formation history with a closed-box evolution of metallicity where the present-day gas-phase metallicity of the galaxy is a free parameter. We show with this approach that we are able to recover the observationally determined cosmic star formation history (CSFH), an indication that stars are being formed in the correct epoch of the Universe, on average, for the manner in which we are conducting SED fitting. We also show the contribution to the CSFH of galaxies of different present-day visual morphologies and stellar masses. Our analysis suggests that half of the mass in present-day elliptical galaxies was in place 11 Gyr ago. In other morphological types, the stellar mass formed later, up to 6 Gyr ago for present-day irregular galaxies. Similarly, the most massive galaxies in our sample were shown to have formed half their stellar mass by 11 Gyr ago, whereas the least massive galaxies reached this stage as late as 4 Gyr ago (the well-known effect of 'galaxy downsizing'). Finally, our metallicity approach allows us to follow the average evolution in gas-phase metallicity for populations of galaxies and extract the evolution of the cosmic metal mass density in stars and in gas, producing results in broad agreement with independent, higher redshift observations of metal densities in the Universe. [ABSTRACT FROM AUTHOR]

We use the state-of-the-art semi-analytic galaxy formation model, shark , to investigate the physical processes involved in dictating the shape, scatter, and evolution of the Hi –halo mass (HIHM) relation at 0 ≤ z ≤ 2. We compare shark with Hi  clustering and spectral stacking of the HIHM relation derived from observations finding excellent agreement with the former and a deficiency of Hi in shark at M vir ≈ 1012–13 M⊙ in the latter. In shark , we find that the Hi mass increases with the halo mass up to a critical mass of ≈1011.8 M⊙; between ≈1011 and 1013 M⊙, the scatter in the relation increases by 0.7 dex and the Hi mass decreases with the halo mass on average (till |$M_{\rm vir}\sim 10^{12.5}\, \rm M_{\odot }$|⁠ , after which it starts increasing); at |$M_{\rm vir}\gtrsim 10^{13}\, \rm M_{\odot }$|⁠ , the Hi content continues to increase with increasing halo mass, as a result of the increasing Hi contribution from satellite galaxies. We find that the critical halo mass of ≈1012 M⊙ is set by feedback from active galactic nuclei (AGNs) which affects both the shape and scatter of the HIHM relation, with other physical processes playing a less significant role. We also determine the main secondary parameters responsible for the scatter of the HIHM relation, namely the halo spin parameter at |${M}_{\rm vir}\, \lt $| 1011.8 M⊙, and the fractional contribution from substructure to the total halo mass (⁠|$M_{\rm h}^{\rm sat}/M_{\rm vir}$|⁠) for |${M}_{\rm vir}\, \gt $| 1013 M⊙. The scatter at 1011.8 M⊙ |$\lt \, {M}_{\rm vir}\, \lt $| 1013 M⊙ is best described by the black hole-to-stellar mass ratio of the central galaxy, reflecting the relevance of AGN feedback. We present a numerical model to populate dark matter-only simulations with Hi at 0 ≤ z ≤ 2 based solely on halo parameters that are measurable in such simulations. [ABSTRACT FROM AUTHOR]

We present a comparison of galaxy atomic and molecular gas properties in three recent cosmological hydrodynamic simulations, namely SIMBA, EAGLE, and IllustrisTNG, versus observations from z ∼ 0 to 2. These simulations all rely on similar subresolution prescriptions to model cold interstellar gas that they cannot represent directly, and qualitatively reproduce the observed z ≈ 0 H  i and H2 mass functions (HIMFs and H2MFs, respectively), CO(1–0) luminosity functions (COLFs), and gas scaling relations versus stellar mass, specific star formation rate, and stellar surface density μ*, with some quantitative differences. To compare to the COLF, we apply an H2-to-CO conversion factor to the simulated galaxies based on their average molecular surface density and metallicity, yielding substantial variations in αCO and significant differences between models. Using this, predicted z = 0 COLFs agree better with data than predicted H2MFs. Out to z ∼ 2, EAGLE's and SIMBA's HIMFs and COLFs strongly increase, while IllustrisTNG's HIMF declines and COLF evolves slowly. EAGLE and simba reproduce high- L CO(1–0) galaxies at z ∼ 1–2 as observed, owing partly to a median αCO(z = 2) ∼ 1 versus αCO(z = 0) ∼ 3. Examining H  i , H2, and CO scaling relations, their trends with M * are broadly reproduced in all models, but EAGLE yields too little H  i in green valley galaxies, IllustrisTNG and SIMBA overproduce cold gas in massive galaxies, and SIMBA overproduces molecular gas in small systems. Using SIMBA variants that exclude individual active galactic nucleus (AGN) feedback modules, we find that SIMBA's AGN jet feedback is primarily responsible by lowering cold gas contents from z ∼ 1 → 0 by suppressing cold gas in |$M_*\gtrsim 10^{10}{\rm \,M}_\odot$| galaxies, while X-ray feedback suppresses the formation of high-μ* systems. [ABSTRACT FROM AUTHOR]

We investigate the influence of environment on the cold-gas properties of galaxies at |$z$|  = 0 within the TNG100 cosmological, magnetohydrodynamic simulation, part of the IllustrisTNG suite. We extend previous post-processing methods for breaking gas cells into their atomic and molecular phases, and build detailed mocks to comprehensively compare to the latest surveys of atomic hydrogen (H  i) in nearby galaxies, namely ALFALFA and xGASS. We use TNG100 to explore the H  i content, star formation activity, and angular momentum of satellite galaxies, each as a function of environment, and find that satellites are typically a factor of ≳3 poorer in H  i than centrals of the same stellar mass, with the exact offset depending sensitively on parent halo mass. Due to the large physical scales on which H  i measurements are made (∼45–245 kpc), contributions from gas not bound to the galaxy of interest but in the same line of sight crucially lead to larger H  i mass measurements in the mocks in many cases, ultimately aligning with observations. This effect is mass-dependent and naturally greater for satellites than centrals, as satellites are never isolated by definition. We also show that H  i stripping in TNG100 satellites is closely accompanied by quenching, in tension with observational data that instead favour that H  i is preferentially stripped before star formation is reduced. [ABSTRACT FROM AUTHOR]

We explore the connection between the atomic gas fraction, f atm, and 'global disc stability' parameter, q, of galaxies within a fully cosmological context by examining galaxies in the Dark Sage semi-analytic model. The q parameter is determined by the ratio of disc specific angular momentum to mass, i.e. q ∝ j disc/ m disc. Dark Sage is well suited to our study, as it includes the numerical evolution of one-dimensional disc structure, making both j discand q predicted quantities. We show that Dark Sage produces a clear correlation between gas fraction and j discat fixed disc mass, in line with recent results from observations and hydrodynamic simulations. This translates to a tight q – f atmsequence for star-forming central galaxies, which closely tracks the analytic prediction of Obreschkow et al. The scatter in this sequence is driven by the probability distribution function of mass as a function of j (PDF of j) within discs, specifically where it peaks. We find that halo mass is primarily responsible for the peak location of the PDF of j, at least for low values of q. Two main mechanisms of equal significance are then identified for disconnecting f atmfrom q. Mergers in the model can trigger quasar winds, with the potential to blow out most of the gas disc, while leaving the stellar disc relatively unharmed. Ram-pressure stripping of satellite galaxies has a similar effect, where f atmcan drop drastically with only a minimal effect to q. We highlight challenges associated with following these predictions up with observations. [ABSTRACT FROM AUTHOR]

We apply the Jeans Anisotropic Multi-Gaussian Expansion dynamical modelling method to SAGES Legacy Unifying Globulars and GalaxieS (SLUGGS) survey data of early-type galaxies in the stellar mass range 1010 < M*/Mʘ < 1011.6 that cover a large radial range of 0.1-4.0 effective radii.We combine SLUGGS and ATLAS3D data sets to model the total-mass profiles of a sample of 21 fast-rotator galaxies, utilizing a hyperparameter method to combine the two independent data sets. The total-mass density profile slope values derived for these galaxies are consistent with those measured in the inner regions of galaxies by other studies. Furthermore, the total-mass density slopes (γ tot) appear to be universal over this broad stellar mass range, with an average value of γ tot= -2.24± 0.05 , i.e. slightly steeper than isothermal. We compare our results to model galaxies from the Magneticum and EAGLE cosmological hydrodynamic simulations, in order to probe the mechanisms that are responsible for varying total-mass density profile slopes. The simulated-galaxy slopes are shallower than the observed values by ***0.3--0.5, indicating that the physical processes shaping the mass distributions of galaxies in cosmological simulations are still incomplete. For galaxies with M* > 1010.7Mʘ in the Magneticum simulations, we identify a significant anticorrelation between total-mass density profile slopes and the fraction of stellar mass formed ex situ (i.e. accreted), whereas this anticorrelation is weaker for lower stellar masses, implying that the measured total-mass density slopes for low-mass galaxies are less likely to be determined by merger activity. [ABSTRACT FROM AUTHOR]

We combine the latest spectrally stacked data of 21-cm emission from the Arecibo Legacy Fast ALFA survey with an updated version of the DARK SAGE semi-analytic model to investigate the relative contributions of secular and environmental astrophysical processes on shaping the HI fractions and quiescence of galaxies in the local Universe.We calibrate the model to match the observed mean HI fraction of all galaxies as a function of stellar mass. Without consideration of stellar feedback, disc instabilities and active galactic nuclei, we show how the slope and normalization of this relation would change significantly. We find DARK SAGE can reproduce the relative impact that halo mass is observed to have on satellites' HI fractions and quiescent fraction. However, the model satellites are systematically gas-poor. We discuss how this could be affected by satellite-central cross-contamination from the group-finding algorithm applied to the observed galaxies, but that it is not the full story. From our results, we suggest the anticorrelation between satellites' HI fractions and host halo mass, seen at fixed stellar mass and fixed specific star formation rate, can be attributed almost entirely to ram-pressure stripping of cold gas. Meanwhile, stripping of hot gas from around the satellites drives the correlation of quiescent fraction with halo mass at fixed stellar mass. Further detail in the modelling of galaxy discs' centres is required to solidify this result, however. We contextualize our results with those from other semi-analytic models and hydrodynamic simulations. [ABSTRACT FROM AUTHOR]

We use the hydrodynamic, cosmological EAGLE simulations to investigate how the hot gas in haloes condenses to form and grow galaxies. We select haloes from the simulations that are actively cooling and study the temperature, distribution and metallicity of their hot, cold and transitioning 'cooling' gas, placing these in the context of semi-analytic models. Our selection criteria lead us to focus on Milky Way-like haloes. We find that the hot-gas density profiles of the haloes form a progressively stronger core over time, the nature of which can be captured by a β profile that has a simple dependence on redshift. In contrast, the hot gas that will cool over a time-step is broadly consistent with a singular isothermal sphere.We find that cooling gas carries a few times the specific angular momentum of the halo and is offset in spin direction from the rest of the hot gas. The gas loses ∼60 per cent of its specific angular momentum during the cooling process, generally remaining greater than that of the halo and it precesses to become aligned with the cold gas already in the disc.We find tentative evidence that angular-momentum losses are slightly larger when gas cools on to dispersion-supported galaxies.We show that an exponential surface density profile for gas arriving on a disc remains a reasonable approximation, but a cusp containing ∼20 per cent of the mass is always present, and disc scale radii are larger than predicted by a vanilla Fall & Efstathiou model. These scale radii are still closely correlated with the halo spin parameter, for which we suggest an updated prescription for galaxy formation models. [ABSTRACT FROM AUTHOR]

We use the EAGLE cosmological hydrodynamic simulation suite to study the specific angular momentum of galaxies, j, with the aims of (i) investigating the physical causes behind the wide range of j at fixed mass and (ii) examining whether simple, theoretical models can explain the seemingly complex and non-linear nature of the evolution of j. We find that j of the stars, jstars, and baryons, jbar, are strongly correlated with stellar and baryon mass, respectively, with the scatter being highly correlated with morphological proxies such as gas fraction, stellar concentration, (u-r) intrinsic colour, stellar age and the ratio of circular velocity to velocity dispersion. We compare with available observations at z = 0 and find excellent agreement. We find that jbar follows the theoretical expectation of an isothermal collapsing halo under conservation of specific angular momentum to within ≈50 per cent, while the subsample of rotation-supported galaxies are equally well described by a simple model in which the disc angular momentum is just enough to maintain marginally stable discs. We extracted evolutionary tracks of the stellar spin parameter of EAGLE galaxies and found that the fate of their jstars at z = 0 depends sensitively on their star formation and merger histories. From these tracks, we identified two distinct physical channels behind low jstars galaxies at z = 0: (i) galaxy mergers, and (ii) early star formation quenching. The latter can produce galaxies with low jstars and early-type morphologies even in the absence of mergers. [ABSTRACT FROM AUTHOR]

We present the new semi-analytic model of galaxy evolution, DARK SAGE, a heavily modified version of the publicly available SAGE code. The model is designed for detailed evolution of galactic discs. We evolve discs in a series of annuli with fixed specific angular momentum, which allows us to make predictions for the radial and angular-momentum structure of galaxies. Most physical processes, including all channels of star formation and associated feedback, are performed in these annuli. We present the surface density profiles of our model spiral galaxies, both as a function of radius and specific angular momentum, and find that the discs naturally build a pseudo-bulge-like component. Our main results are focused on predictions relating to the integrated mass-specific angular momentum relation of stellar discs. The model produces a distinct sequence between these properties in remarkable agreement with recent observational literature. We investigate the impact Toomre disc instabilities have on shaping this sequence and find they are crucial for regulating both the mass and spin of discs. Without instabilities, high-mass discs would be systematically deficient in specific angular momentum by a factor of ~2.5, with increased scatter. Instabilities also appear to drive the direction in which the mass-spin sequence of spiral galaxy discs evolves. With them, we find galaxies of fixed mass have higher specific angular momentum at later epochs. [ABSTRACT FROM AUTHOR]

Using the suite of high-resolution zoom re-simulations of individual haloes by Martig et al., and the large-scale simulation MassiveBlack-II, we examine the differences in measured galaxy properties from techniques with various aperture definitions of where galaxies end. We perform techniques popular in the literature and present a new technique of our own, where the aperture radius is based on the baryonic mass profiles of simulated (sub)haloes. For the average Milky Way-mass system, we find the two most popular techniques in the literature return differences of the order of 30 per cent for stellar mass, a factor of 3 for gas mass, 40 per cent for star formation rate, and factors of several for gas accretion and ejection rates. Individual cases can show variations greater than this, with the severity dependent on the concentration of a given system. The average difference in integrated properties for a more general galaxy population is not as striking, but is still significant for stellar and gas mass, especially for optical-limit apertures. The large differences that can occur are problematic for comparing results from various publications. We stress the importance of both defining and justifying a technique choice and discourage using popular apertures that use an exact fraction of the virial radius, due to the unignorable variation in galaxy-to-(sub)halo size. Finally, we note that technique choice does not greatly affect simulated galaxies from lying within the scatter of observed scaling relations, but it can alter the derived best-fitting slope for the Kennicutt–Schmidt relation. [ABSTRACT FROM PUBLISHER]

The revised equation (21) from the original paper is as follows: a low 0 =-0.477 + 0.142z - 0.006 z 2, a low 1 = 1.920 - 0.592z + 0.1999 z 2 - 0.0352 z 3, a low 2 =-0.348 + 0.321z - 0.176 z 2 + 0.035z 3, (2) where a low 0-2 are the coefficients for the polynomial fit of equation (1) for the low-mass region, and z is redshift. Our initial equations (equations 20, 21 and 25) had to be revised by introducing normalising factors to make the execution of these equations simpler and to correct an error that was introduced. The median HIHM relation of SHARK is fitted with a polynomial function f M H I (M vir,z), with the fit done in bins of 0.1 dex of halo mass. [Extracted from the article]