arXiv subjects

Camila A. Correa

Publications and source records attributed to Camila A. Correa.

At least 19 recordsLinked to original sources

arXiv2026

A subgrid model for chemical enrichment in cosmological simulations

We present the modules for stellar nucleosynthesis, stellar mass loss, and turbulent diffusion of the new COLIBRE subgrid model for cosmological hydrodynamical simulations of galaxy formation. COLIBRE models the thermal evolution of the multi-phase interstellar medium, dust grains, star formation, and stellar and AGN feedback. This work focuses on the model for chemical enrichment. We track the evolution of 12 chemical elements produced by a broad range of nucleosynthetic channels, including core-collapse supernovae and stellar winds, Type Ia supernovae, and asymptotic giant branch (AGB) stars. Enrichment from $s$- and $r$-process elements is modelled via contributions from AGB stars, neutron star mergers, common envelope supernovae, and collapsars. We present an updated compilation of stellar yields taken from the literature, which we release alongside this work. Small-scale element mixing is implemented through a turbulent diffusion process. While diffusion has only a minimal impact on basic integrated galaxy properties, it does reduce the slope of the gas-phase metallicity-mass relation compared with simulations that do not include it. The distribution of element ratios of individual stellar particles is sensitive to diffusion, but only at low metallicities ($Z \lesssim 10^{-1}\,\rm{Z}_\odot$). The model is tested using redshift $z=0$ results from a set of cosmological simulations, mostly of (25 Mpc)$^3$ volumes, demonstrating generally good agreement with Milky Way stellar abundance trends from the APOGEE survey. The model also reproduces the alpha-element enhancement relations observed in galaxies from SDSS, ATLAS-3D, and the Local Group.

astro-ph.GA↗

arXiv2024

In-Situ Spheroid Formation in Distant Submillimeter-Bright Galaxies

The majority of stars in today's Universe reside within spheroids, which are bulges of spiral galaxies and elliptical galaxies. Their formation is still an unsolved problem. Infrared/submm-bright galaxies at high redshifts have long been suspected to be related to spheroids formation. Proving this connection has been hampered so far by heavy dust obscuration when focusing on their stellar emission or by methodologies and limited signal-to-noise ratios when looking at submm wavelengths. Here we show that spheroids are directly generated by star formation within the cores of highly luminous starburst galaxies in the distant Universe. This follows from the ALMA submillimeter surface brightness profiles which deviate significantly from those of exponential disks, and from the skewed-high axis-ratio distribution. The majority of these galaxies are fully triaxial rather than flat disks: the ratio of the shortest to the longest of their three axes is half, on average, and increases with spatial compactness. These observations, supported by simulations, reveal a cosmologically relevant pathway for in-situ spheroid formation through starbursts likely preferentially triggered by interactions (and mergers) acting on galaxies fed by non-co-planar gas accretion streams.

astro-ph.GA↗

arXiv2023

Influence of local structure on relic neutrino abundances and anisotropies

Gravitational potentials of the Milky Way and extragalactic structures can influence the propagation of the cosmic neutrino background (CNB). Of particular interest to future CNB observatories, such as PTOLEMY, is the CNB number density on Earth. In this study, we have developed a simulation framework that maps the trajectories of relic neutrinos as they move through the local gravitational environment. The potentials are based on the dark matter halos found in state-of-the-art cosmological N-body simulations, resulting in a more nuanced and realistic input than the previously employed analytical models. We find that the complex dark matter distributions, along with their dynamic evolution, influence the abundance and anisotropies of the CNB in ways unaccounted for by earlier analytical methods. Importantly, these cosmological simulations contain multiple instances of Milky Way-like halos that we employ to model a variety of gravitational landscapes. Consequently, we notice a variation in the CNB number densities that can be primarily attributed to the differences in the masses of these individual halos. For neutrino masses between $0.01$ and $0.3$ eV, we note clustering factors within the range of $1+\mathcal{O}(10^{-3})$ to $1+\mathcal{O}(1)$. Furthermore, the asymmetric nature of the underlying dark matter distributions within the halos results in not only overdense, but intriguingly, underdense regions within the full-sky anisotropy maps. Gravitational clustering appears to have a significant impact on the angular power spectra of these maps, leading to orders of magnitude more power on smaller scales beyond multipoles of $\ell = 3$ when juxtaposed against predictions by primordial fluctuations. We discuss how our results reshape our understanding of relic neutrino clustering and how this might affect observability of future CNB observatories such as PTOLEMY.

astro-ph.CO↗

arXiv2023

Warm Dark Matter Constraints Using Milky-Way Satellite Observations and Subhalo Evolution Modeling

Warm dark matter (WDM) can potentially explain small-scale observations that currently challenge the cold dark matter (CDM) model, as warm particles suppress structure formation due to free-streaming effects. Observing small-scale matter distribution provides a valuable way to distinguish between CDM and WDM. In this work, we use observations from the Dark Energy Survey and PanSTARRS1, which observe 270 Milky-Way satellites after completeness corrections. We test WDM models by comparing the number of satellites in the Milky Way with predictions derived from the Semi-Analytical SubHalo Inference ModelIng (SASHIMI) code, which we develop based on the extended Press-Schechter formalism and subhalos' tidal evolution prescription. We robustly rule out WDM with masses lighter than 4.4 keV at 95% confidence level for the Milky-Way halo mass of $10^{12} M_\odot$. The limits are a weak function of the (yet uncertain) Milky-Way halo mass, and vary as $m_{\rm WDM}>3.6$-$5.1$ keV for $(0.6$-$2.0) \times 10^{12} M_\odot$. For the sterile neutrinos that form a subclass of WDM, we obtain the constraints of $m_{ν_s}>11.6$ keV for the Milky-Way halo mass of $10^{12} M_{\odot}$. These results based on SASHIMI do not rely on any assumptions of galaxy formation physics or are not limited by numerical resolution. The models, therefore, offer a robust and fast way to constrain the WDM models. By applying a satellite forming condition, however, we can rule out the WDM mass lighter than 9.0 keV for the Milky-Way halo mass of $10^{12} M_\odot$.

astro-ph.CO↗

arXiv2022

Towards reconstructing the halo clustering and halo mass function of N-body simulations using neural ratio estimation

High-resolution cosmological N-body simulations are excellent tools for modelling the formation and clustering of dark matter haloes. These simulations suggest complex physical theories of halo formation governed by a set of effective physical parameters. Our goal is to extract these parameters and their uncertainties in a Bayesian context. We make a step towards automatising this process by directly comparing dark matter density projection maps extracted from cosmological simulations, with density projections generated from an analytical halo model. The model is based on a toy implementation of two body correlation functions. To accomplish this we use marginal neural ratio estimation, an algorithm for simulation-based inference that allows marginal posteriors to be estimated by approximating marginal likelihood-to-evidence ratios with a neural network. In this case, we train a neural network with mock images to identify the correct values of the physical parameters that produced a given image. Using the trained neural network on cosmological N-body simulation images we are able to reconstruct the halo mass function, to generate mock images similar to the N-body simulation images and to identify the lowest mass of the haloes of those images, provided that they have the same clustering with our training data. Our results indicate that this is a promising approach in the path towards developing cosmological simulations assisted by neural networks.

astro-ph.CO↗

arXiv2022

TangoSIDM: Tantalizing models of Self-Interacting Dark Matter

We introduce the TangoSIDM project, a suite of cosmological simulations of structure formation in a $Λ$-Self-Interacting Dark Matter (SIDM) universe. TangoSIDM explores the impact of large dark matter (DM) scattering cross sections over dwarf galaxy scales. Motivated by DM interactions that follow a Yukawa potential, the cross section per unit mass, $σ/m_χ$, assumes a velocity dependent form that avoids violations of current constraints on large scales. We demonstrate that our implementation accurately models not only core formation in haloes, but also gravothermal core collapse. For central haloes in cosmological volumes, frequent DM particle collisions isotropise the particles orbit, making them largely spherical. We show that the velocity-dependent $σ/m_χ$ models produce a large diversity in the circular velocities of satellites haloes, with the spread in velocities increasing as the cross sections reach 20, 60 and 100 cm$^2$/g in $10^9~\rm{M}_{\odot}$ haloes. The large variation in the haloes internal structure is driven by DM particles interactions, causing in some haloes the formation of extended cores, whereas in others gravothermal core collapse. We conclude that the SIDM models from the Tango project offer a promising explanation for the diversity in the density and velocity profiles of observed dwarf galaxies.

astro-ph.GA↗

arXiv2022

Simulations of $^{60}$Fe entrained in ejecta from a near-Earth supernova: Effects of observer motion

Recent studies have shown that live (not decayed) radioactive $^{60}$Fe is present in deep-ocean samples, Antarctic snow, lunar regolith, and cosmic rays. $^{60}$Fe represents supernova (SN) ejecta deposited in the Solar System around $3 \, \rm Myr$ ago, and recently an earlier pulse $\approx 7 \ \rm Myr $ ago has been found. These data point to one or multiple near-Earth SN explosions that presumably participated in the formation of the Local Bubble. We explore this theory using 3D high-resolution smooth-particle hydrodynamical simulations of isolated supernovae with ejecta tracers in a uniform interstellar medium (ISM). The simulation allows us to trace the supernova ejecta in gas form and those eject in dust grains that are entrained with the gas. We consider two cases of diffused ejecta: when the ejecta are well-mixed in the shock and when they are not. In the latter case, we find that these ejecta remain far behind the forward shock, limiting the distance to which entrained ejecta can be delivered to $\approx 100$ pc in an ISM with $n_\mathrm{H}=0.1\; \rm cm^{-3}$ mean hydrogen density. We show that the intensity and the duration of $^{60}$Fe accretion depend on the ISM density and the trajectory of the Solar System. Furthermore, we show the possibility of reproducing the two observed peaks in $^{60}$Fe concentration with this model by assuming two linear trajectories for the Solar System with $30$-km s$^{-1}$ velocity. The fact that we can reproduce the two observed peaks further supports the theory that the $^{60}$Fe signal was originated from near-Earth SNe.

astro-ph.HE↗

arXiv2021

Revealing the physical properties of gas accreting to haloes in the EAGLE simulations

The inflow of cosmological gas onto haloes, while challenging to directly observe and quantify, plays a fundamental role in the baryon cycle of galaxies. Using the EAGLE suite of hydrodynamical simulations, we present a thorough exploration of the physical properties of gas accreting onto haloes -- namely, its spatial characteristics, density, temperature, and metallicity. Classifying accretion as ``hot'' or `` cold'' based on a temperature cut of $10^{5.5}{\rm K}$, we find that the covering fraction ($f_{\rm cov}$) of cold-mode accreting gas is significantly lower than the hot-mode, with $z=0$ $f_{\rm cov}$ values of $\approx 50\%$ and $\approx 80\%$ respectively. Active Galactic Nuclei (AGN) feedback in EAGLE reduces inflow $f_{\rm cov}$ values by $\approx 10\%$, with outflows decreasing the solid angle available for accretion flows. Classifying inflow by particle history, we find that gas on first-infall onto a halo is metal-depleted by $\approx 2$~dex compared to pre-processed gas, which we find to mimic the circum-galactic medium (CGM) in terms of metal content. We also show that high (low) halo-scale gas accretion rates are associated with metal-poor (rich) CGM in haloes below $10^{12}M_{\odot}$, and that variation in halo-scale gas accretion rates may offer a physical explanation for the enhanced scatter in the star-forming main sequence at low ($\lesssim10^{9}M_{\odot}$) and high ($\gtrsim10^{10}M_{\odot}$) stellar masses. Our results highlight how gas inflow influences several halo- and galaxy-scale properties, and the need to combine kinematic and chemical data in order to confidently break the degeneracy between accreting and outgoing gas in CGM observations.

astro-ph.GA↗

arXiv2020

The dependence of the galaxy stellar-to-halo mass relation on galaxy morphology

We investigate the dependence of the local galaxy stellar-to-halo mass relation (SHMR) on galaxy morphology. We use data from the Sloan Digital Sky Survey DR7 with morphological classifications from Galaxy Zoo, and compare with the EAGLE cosmological simulation. At fixed halo mass in the mass range $10^{11.7}-10^{12.9}M_{\odot}$, the median stellar masses of SDSS disc galaxies are up to a factor of 1.4 higher than the median masses of their elliptical counterparts. However, when we switch from the stellar masses from Kauffmann et al. to those calculated by Chang et al. or Brinchmann et al., the median SHMR from discs and ellipticals coincide in this mass range. For halo masses larger than $10^{13}M_{\odot}$, discs are less massive than ellipticals in same-mass haloes, regardless of whose stellar mass estimates we use. However, we find that for these high halo masses the results for discs may be affected by central/satellite misclassifications. The EAGLE simulation predicts that discs are up to a factor of 1.5 more massive than elliptical galaxies residing in same-mass haloes less massive than $10^{13}M_{\odot}$, in agreement with the Kauffmann et al. data. Haloes with masses between $10^{11.5}$ and $10^{12}M_{\odot}$, that host disc galaxies, were assembled earlier than those hosting ellipticals. This suggests that the discs are more massive because they had more time for gas accretion and star formation. In $10^{12}-10^{12.5}M_{\odot}$ haloes, the central black holes in elliptical galaxies grew faster and became more massive than their counterparts in disc galaxies. This suggests that in this halo mass range the ellipticals are less massive because AGN feedback ejected more of the halo's gas reservoir, reducing star formation, and suppressing the (re)growth of stellar discs.

astro-ph.GA↗

arXiv2020

Constraining Velocity-dependent Self-Interacting Dark Matter with the Milky Way's dwarf spheroidal galaxies

The observed anti-correlation between the central dark matter (DM) densities of the bright Milky Way (MW) dwarf spheroidal galaxies (dSphs) and their orbital pericenter distances poses a potential signature of self-interacting dark matter (SIDM). In this work we investigate this possibility by analysing the range of SIDM scattering cross section per unit mass, $σ/m_χ$, able to explain such anti-correlation. We simulate the orbital evolution of dSphs subhaloes around the MW assuming an analytical form for the gravitational potential, adopting the proper motions from the Gaia mission and including a consistent characterization of gravitational tidal stripping. The evolution of the subhaloes density profile is modelled using the gravothermal fluid formalism, where DM particle collisions induce thermal conduction that depends on $σ/m_χ$. We find that models of dSphs, such as Carina and Fornax, reproduce the observed central DM densities with fixed $σ/m_χ$ ranging between $30$ and $50$ cm$^{2}$g$^{-1}$, whereas other dSphs prefer larger values ranging between $70$ and $100$ cm$^{2}$g$^{-1}$. These cross sections correlate with the average collision velocity of DM particles within each subhalo's core, so that systems modelled with large cross sections have lower collision velocities. We fit the cross section-velocity correlation with a SIDM particle model, where a DM particle of mass $m_χ=0.648\pm 0.154$ GeV interacts under the exchange of a light mediator of mass $m_ϕ=0.636\pm 0.055$ MeV, with the self-interactions being described by a Yukawa potential. The outcome is a cross section-velocity relation that explains the diverse DM profiles of MW dSph satellites and is consistent with observational constraints on larger scales.

astro-ph.GA↗

arXiv2020

The effect of gas accretion on the radial gas metallicity profile of simulated galaxies

We study the effect of the gas accretion rate ($\dot M_{\rm accr}$) on the radial gas metallicity profile (RMP) of galaxies using the EAGLE cosmological hydrodynamic simulations, focusing on central galaxies of stellar mass $M_\star \gtrsim 10^9 \, {\rm M_\odot}$ at $z \le 1$. We find clear relations between $\dot M_{\rm accr}$ and the slope of the RMP (measured within an effective radius), where higher $\dot M_{\rm accr}$ are associated with more negative slopes. The slope of the RMPs depends more strongly on $\dot M_{\rm accr}$ than on stellar mass, star formation rate or gas fraction, suggesting $\dot M_{\rm accr}$ to be a more fundamental driver of the RMP slope of galaxies. We find that eliminating the dependence on stellar mass is essential for pinning down the properties that shape the slope of the RMP. Although $\dot M_{\rm accr}$ is the main property modulating the slope of the RMP, we find that it causes other correlations that are more easily testable observationally: at fixed stellar mass, galaxies with more negative RMP slopes tend to have higher gas fractions and SFRs, while galaxies with lower gas fractions and SFRs tend to have flatter metallicity profiles within an effective radius.

astro-ph.GA↗

arXiv2018

The origin of the red sequence galaxy population in the EAGLE simulation

We investigate the evolution in colour and morphology of the progenitors of red-sequence galaxies in the EAGLE cosmological hydrodynamical simulation. We quantify colours with $u^{*}-r^{*}$ intrinsic magnitudes and morphologies with a measure of the stellar kinematics. The time when galaxies moved onto the red sequence depends on their morphology. Disc-type galaxies tend to have become red during the last 3 Gyr, while elliptical-type galaxies joined the red sequence earlier, with half the sample already being red 5 Gyr ago. The time-scale, $τ_{\rm{Green}}$, of colour transition through the `green valley' depends weakly on the galaxy's morphological type. Elliptical-type galaxies cross the green valley slightly faster ($τ_{\rm{Green}}{\approx}1$ Gyr) than disc-type galaxies ($τ_{\rm{Green}}{\approx}$1.5 Gyr). While $τ_{\rm{Green}}$ is similar for central and satellite galaxies, for satellites $τ_{\rm{Green}}$ decreases with increasing stellar mass to host-halo mass ratio. Coupled with our finding that galaxies tend to become green after becoming satellites, this indicates that satellite-specific processes are important for quenching red-sequence galaxies. The last time central, elliptical-type red-sequence galaxies left the blue cloud is strongly correlated with the time the luminosity of the central black hole peaked, but this is not the case for discs. This suggests that AGN feedback is important for quenching ellipticals, particularly centrals, but not for discs. We find only a weak connection between transformations in colour and morphology.

astro-ph.GA↗

arXiv2018

The impact of feedback and the hot halo on the rates of gas accretion onto galaxies

We investigate the physics that drives the gas accretion rates onto galaxies at the centers of dark matter haloes using the EAGLE suite of hydrodynamical cosmological simulations. We find that at redshifts $z{\le}2$ the accretion rate onto the galaxy increases with halo mass in the halo mass range $10^{10}-10^{11.7}M_{\odot}$, flattens between the halo masses $10^{11.7}-10^{12.7}M_{\odot}$, and increases again for higher-mass haloes. However, the galaxy gas accretion does not flatten at intermediate halo masses when AGN feedback is switched off. To better understand these trends, we develop a physically motivated semi-analytic model of galaxy gas accretion. We show that the flattening is produced by the rate of gas cooling from the hot halo. The ratio of the cooling radius and the virial radius does not decrease continuously with increasing halo mass as generally thought. While it decreases up to ${\sim}10^{13}M_{\odot}$ haloes, it increases for higher halo masses, causing an upturn in the galaxy gas accretion rate. This may indicate that in high-mass haloes AGN feedback is not sufficiently efficient. When there is no AGN feedback, the density of the hot halo is higher, the ratio of the cooling and virial radii does not decrease as much and the cooling rate is higher. Changes in the efficiency of stellar feedback can also increase or decrease the accretion rates onto galaxies. The trends can plausibly be explained by the re-accretion of gas ejected by progenitor galaxies and by the suppression of black hole growth, and hence AGN feedback, by stellar feedback.

astro-ph.GA↗

arXiv2017

The formation of hot gaseous haloes around galaxies

We use a suite of hydrodynamical cosmological simulations from the Evolution and Assembly of GaLaxies and their Environments (EAGLE) project to investigate the formation of hot hydrostatic haloes and their dependence on feedback mechanisms. We find that the appearance of a strong bimodality in the probability density function (PDF) of the ratio of the radiative cooling and dynamical times for halo gas provides a clear signature of the formation of a hot corona. Haloes of total mass $10^{11.5}-10^{12}{\rm{M}}_{\odot}$ develop a hot corona independent of redshift, at least in the interval $z=0-4$ where the simulation has sufficiently good statistics. We analyse the build up of the hot gas mass in the halo, $M_{\rm{hot}}$, as a function of halo mass and redshift and find that while more energetic galactic winds powered by SNe increases $M_{\rm{hot}}$, AGN feedback reduces it by ejecting gas from the halo. We also study the thermal properties of gas accreting onto haloes and measure the fraction of shock-heated gas as a function of redshift and halo mass. We develop analytic and semianalytic approaches to estimate a `critical halo mass', $M_{\rm{crit}}$, for hot halo formation. We find that the mass for which the heating rate produced by accretion shocks equals the radiative cooling rate, reproduces the mass above which haloes develop a significant hot atmosphere. This yields a mass estimate of $M_{\rm{crit}} \approx 10^{11.7}{\rm{M}}_{\odot}$ at $z=0$, which agrees with the simulation results. The value of $M_{\rm{crit}}$ depends more strongly on the cooling rate than on any of the feedback parameters.

astro-ph.GA↗

arXiv2017

The relation between galaxy morphology and colour in the EAGLE simulation

We investigate the relation between kinematic morphology, intrinsic colour and stellar mass of galaxies in the EAGLE cosmological hydrodynamical simulation. We calculate the intrinsic u-r colours and measure the fraction of kinetic energy invested in ordered corotation of 3562 galaxies at z=0 with stellar masses larger than $10^{10}M_{\odot}$. We perform a visual inspection of gri-composite images and find that our kinematic morphology correlates strongly with visual morphology. EAGLE produces a galaxy population for which morphology is tightly correlated with the location in the colour- mass diagram, with the red sequence mostly populated by elliptical galaxies and the blue cloud by disc galaxies. Satellite galaxies are more likely to be on the red sequence than centrals, and for satellites the red sequence is morphologically more diverse. These results show that the connection between mass, intrinsic colour and morphology arises from galaxy formation models that reproduce the observed galaxy mass function and sizes.

astro-ph.GA↗

arXiv2016

The environmental dependence of gas accretion onto galaxies: quenching satellites through starvation

Galaxies that have fallen into massive haloes may no longer be able to accrete gas from their surroundings, a process referred to as 'starvation' or 'strangulation' of satellites. We study the environmental dependence of gas accretion onto galaxies using the cosmological, hydrodynamical EAGLE simulation. We quantify the dependence of gas accretion on stellar mass, redshift, and environment, using halo mass and galaxy overdensity as environmental indicators. We find a strong suppression, by many orders of magnitude, of the gas accretion rate in dense environments, primarily for satellite galaxies. This suppression becomes stronger at lower redshift. However, the scatter in accretion rates is very large for satellites. This is (at least in part) due to the variation in halocentric radius, since gas accretion is more suppressed at smaller radii. Central galaxies are influenced less strongly by their environment and exhibit less scatter in their gas accretion rates. The star formation rates of both centrals and satellites show similar behaviour to their gas accretion rates. The relatively small differences between gas accretion and star formation rates demonstrate that galaxies generally exhaust their gas reservoir somewhat faster at higher stellar mass, lower redshift, and in denser environments. We conclude that the environmental suppression of gas accretion could directly result in the quenching of star formation.

astro-ph.GA↗

arXiv2015

The accretion history of dark matter halos III: A physical model for the concentration-mass relation

We present a semi-analytic, physically motivated model for dark matter halo concentration as a function of halo mass and redshift. The semi-analytic model combines an analytic model for the halo mass accretion history (MAH), based on extended Press Schechter (EPS) theory, with an empirical relation between concentration and formation time obtained through fits to the results of numerical simulations. Because the semi-analytic model is based on EPS theory, it can be applied to wide ranges in mass, redshift and cosmology. The resulting concentration-mass (c-M) relations are found to agree with the simulations, and because the model applies only to relaxed halos, they do not exhibit the upturn at high masses or high redshifts found by some recent works. We predict a change of slope in the z=0 c-M relation at a mass scale of $10^{11}\rm{M}_{\odot}$. We find that this is due to the change in the functional form of the halo MAH, which goes from being dominated by an exponential (for high-mass halos) to a power-law (for low-mass halos). During the latter phase, the core radius remains approximately constant, and the concentration grows due to the drop of the background density. We also analyse how the c-M relation predicted by this work affects the power produced by dark matter annihilation, finding that at z = 0 the power is two orders of magnitude lower than that obtained from extrapolating best-fitting c-M relations. We provide fits to the c-M relations as well as numerical routines to compute concentrations and MAHs.

astro-ph.CO↗

arXiv2015

The accretion history of dark matter halos I: The physical origin of the universal function

Understanding the universal accretion history of dark matter halos is the first step towards determining the origin of their structure. We use the extended Press-Schechter formalism to derive the halo mass accretion history from the growth rate of initial density perturbations. We show that the halo mass history is well described by an exponential function of redshift in the high-redshift regime. However, in the low-redshift regime the mass history follows a power law because the growth of density perturbations is halted in the dark energy dominated era due to the accelerated expansion of the Universe. We provide an analytic model that follows the expression $M(z) = M_{0}(1+z)^{af(M_{0})}e^{-f(M_{0})z}$, where $M_{0} = M(z=0)$, $a$ depends on cosmology and $f(M_{0})$ depends only on the linear matter power spectrum. The analytic model does not rely on calibration against numerical simulations and is suitable for any cosmology. We compare our model with the latest empirical models for the mass accretion history in the literature and find very good agreement. We provide numerical routines for the model online.

astro-ph.GA↗