We predict the 21-cm global signal and power spectra during the Epoch of Reionisation using the MERAXES semi-analytic galaxy formation and reionisation model, updated to include X-ray heating and thermal evolution of the intergalactic medium. Studying the formation and evolution of galaxies together with the reionisation of cosmic hydrogen using semi-analytic models (such as MERAXES) requires N-body simulations within large volumes and high mass resolutions. For this, we use a simulation of side-length $210~h^{-1}$ Mpc with $4320^3$ particles resolving dark matter haloes to masses of $5\times10^8~h^{-1}~M_\odot$. To reach the mass resolution of atomically cooled galaxies, thought to be the dominant population contributing to reionisation, at $z=20$ of $\sim 2\times10^7~h^{-1}~M_\odot$, we augment this simulation using the DARKFOREST Monte-Carlo merger tree algorithm (achieving an effective particle count of $\sim10^{12}$). Using this augmented simulation we explore the impact of mass resolution on the predicted reionisation history as well as the impact of X-ray heating on the 21-cm global signal and the 21-cm power spectra. We also explore the cosmic variance of 21-cm statistics within $70^{3}$ $h^{-3}$ Mpc$^3$ sub-volumes. We find that the midpoint of reionisation varies by $Δz\sim0.8$ and that the cosmic variance on the power spectrum is underestimated by a factor of $2-4$ at $k\sim 0.1-0.4$ Mpc$^{-1}$ due to the non-Gaussian nature of the 21-cm signal. To our knowledge, this work represents the first model of both reionisation and galaxy formation which resolves low-mass atomically cooled galaxies while simultaneously sampling sufficiently large scales necessary for exploring the effects of X-rays in the early Universe.
Motivated by the current constraints on the epoch of reionisation from recent cosmic microwave background observations, ionising background measurements of star-forming galaxies, and low redshifts line-of-sight probes, we propose a new data-motivated parameterisation of the history of the average ionisation fraction. This parameterisation describes a flexible redshift-asymmetric reionisation process in two regimes that is capable of fitting all the current constraints.
We use cosmological hydrodynamical simulations to assess the feasibility of constraining the thermal history of the intergalactic medium during reionisation with the Ly$α$ forest at $z\simeq5$. The integrated thermal history has a measureable impact on the transmitted flux power spectrum that can be isolated from Doppler broadening at this redshift. We parameterise this using the cumulative energy per proton, $u_0$, deposited into a gas parcel at the mean background density, a quantity that is tightly linked with the gas density power spectrum in the simulations. We construct mock observations…
Using a Bayesian framework, we quantify what current observations imply about the history of the epoch of reionisation (EoR). We use a popular, three-parameter EoR model, flexible enough to accommodate a wide range of physically-plausible reionisation histories. We study the impact of various EoR observations: (i) the optical depth to the CMB measured by Planck 2016; (ii) the dark fraction in the Lyman $α$ and $β$ forests; (iii) the redshift evolution of galactic Ly$α$ emission (so-called "Ly$α$ fraction"); (iv) the clustering of Ly$α$ emitters; (v) the IGM damping wing imprint in the spectrum…
Measurements of the intergalactic medium (IGM) temperature provide a potentially powerful constraint on the reionisation history due to the thermal imprint left by the photo-ionisation of neutral hydrogen. However, until recently IGM temperature measurements were limited to redshifts 2 < z < 4.8, restricting the ability of these data to probe the reionisation history at z > 6. In this work, we use recent measurements of the IGM temperature in the near-zones of seven quasars at z ~ 5.8 - 6.4, combined with a semi-numerical model for inhomogeneous reionisation, to establish new constraints on th…
We discuss constraints on cosmic reionisation and their implications on a cosmic SFR density $ρ_\mathrm{SFR}$ model; we study the influence of key-parameters such as the clumping factor of ionised hydrogen in the intergalactic medium (IGM) $C_{H_{II}}$ and the fraction of ionising photons escaping star-forming galaxies to reionise the IGM $f_\mathrm{esc}$. Our analysis uses SFR history data coming from luminosity functions, assuming that star-forming galaxies were sufficient to lead the reionisation process at high redshift. We add two other sets of constraints: measurements of the IGM ionised…
A consistent, physical, and analytical model for CMB observables of reionisation I. Derivation, constraining power, and detectability of the auto-spectra
Revealing the cosmic reionisation history is at the frontier of extragalactic astronomy. The power spectrum of the cosmic microwave background (CMB) polarisation can be used to constrain the reionisation history. Here we propose a CMB-independent method using fast radio bursts (FRBs) to directly measure the ionisation fraction of the intergalactic medium (IGM) as a function of redshift. FRBs are new astronomical transients with millisecond timescales. Their dispersion measure (DM$_{\rm IGM}$) is an indicator of the amount of ionised material in the IGM. Since the differential of DM$_{\rm IGM}$…
We show that, in the context of patchy reionisation, an accurate description of the angular power spectrum of the kinetic Sunyaev-Zel'dovich (kSZ) effect is not possible with simple scaling relations between the amplitude of the spectrum and global parameters, such as the reionisation midpoint and its duration. We introduce a new parameterisation of this spectrum, based on a novel description of the power spectrum of the free electrons density contrast Pee (k,z) in terms of the reionisation global history and morphology. We directly relate features of the spectrum to the typical ionised bubble…
We study the E and B mode polarisation of the cosmic microwave background (CMB) originating from the transverse peculiar velocity of free electrons, at second order in perturbation theory, during the reionisation and post-reionisation eras. Interestingly, the spectrum of this polarised kinetic Sunyaev-Zeldovich (SZ) effect can be decomposed into a blackbody part and a y-type distortion. The y-distortion part is distinguishable from the primary E and B modes and also the lensing B modes. Furthermore, it is also differentiable from the other y-type signals, such as the thermal SZ effect, which a…
Intergalactic medium temperature is a powerful probe of the epoch of reionisation, as information is retained long after reionisation itself. However, mean temperatures are highly degenerate with the timing of reionisation, with the amount heat injected during the epoch, and with the subsequent cooling rates. We post-process a suite of semi-analytic galaxy formation models to characterise how different thermal statistics of the intergalactic medium can be used to constrain reionisation. Temperature is highly correlated with redshift of reionisation for a period of time after the gas is heated.…
Intensity mapping of the 21cm signal of neutral hydrogen will yield exciting insights into the Epoch of Reionisation and the nature of the first galaxies. However, the large amount of data that will be generated by the next generation of radio telescopes, such as the Square Kilometre Array (SKA), as well as the numerous observational obstacles to overcome, require analysis techniques tuned to extract the reionisation history and morphology. In this context, we introduce a one-point statistic, to which we refer as the local variance, $σ_\mathrm{loc}$, that describes the distribution of the mean…
We use a suite of cosmological hydrodynamic simulations including a self-consistent treatment for inhomogeneous reionisation to study the impact of galactic outflows and photoionisation heating on the volume-averaged recombination rate of the intergalactic medium (IGM). By incorporating an evolving ionising escape fraction and a treatment for self-shielding within Lyman limit systems, we have run the first simulations of "photon-starved" reionisation scenarios that simultaneously reproduce observations of the abundance of galaxies, the optical depth to electron scattering of cosmic microwave b…
A Portrait of the Cosmic Reionisation History in the Context of the Early Dark Energy Model
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；University of Chinese Academy of Sciences（中国科学院大学）；Peking University（北京大学）；Swinburne University of Technology（斯威本科技大学）；University of Arizona（亚利桑那大学）
We explore the impact of incorporating physically motivated ionisation and recombination rates on the history and topology of cosmic reionisation, by incorporating inputs from small-volume hydrodynamic simulations into a semi-numerical code, SimFast21, that evolves reionisation on large scales. We employ radiative hydrodynamic simulations to parameterize the ionisation rate Rion and recombination rate Rrec as functions of halo mass, overdensity and redshift. We find that Rion is super-linearly dependent on halo mass (Rion ~ Mh^1.41), in contrast to previous assumptions. We implement these scal…
Resolving faint galaxies in large volumes is critical for accurate cosmic reionisation simulations. While less demanding than hydrodynamical simulations, semi-analytic reionisation models still require very large N-body simulations in order to resolve the atomic cooling limit across the whole reionisation history within box sizes $\gtrsim 100 \, h^{-1} {\rm Mpc}$. To facilitate this, we extend the mass resolution of N-body simulations using a Monte Carlo algorithm. We also propose a method to evolve positions of Monte Carlo halos, which can be an input for semi-analytic reionisation models. To…
Recent results of ground-based telescopes, giving high-quality measurements of the CMB temperature power spectrum on small scales motivate the need for an accurate model of foregrounds, which dominate the primary signal at these multipoles. In a previous work, we have shown that cosmological information could be retrieved from the power spectrum of the thermal SZ effect. In this work, we introduce a physically motivated model of the Epoch of Reionisation in the cosmological analysis of CMB data, which is coherent on all scales. In particular, at high multipoles, the power spectrum of the kinet…
The contribution of stars in galaxies to cosmic reionisation depends on the star formation history in the Universe, the abundance of galaxies during reionisation, the escape fraction of ionising photons and the clumping factor of the inter-galactic medium (IGM). We compute the star formation rate and clumping factor during reionisation in a cosmological volume using a high-resolution hydrodynamical simulation. We post-process the output with detailed radiative transfer simulations to compute the escape fraction of ionising photons. Together, this gives us the opportunity to assess the contribu…
Discriminating Planck Reionisation Histories with the kSZ Effect
Université Paris-Saclay（巴黎萨克雷大学）；CNRS, Institut d’Astrophysique Spatiale（法国国家科学研究中心，空间天体物理学研究所）；Observatoire de Paris, PSL Research University, Sorbonne Université, CNRS, LUX（巴黎天文台，PSL研究大学，索邦大学，法国国家科学研究中心，LUX）；Institut du Développement et des Ressources en Informatique Scientifique (IDRIS)（科学计算资源开发研究所）；Inria Saclay-Île-de-France（INRIA 塞纳-圣但尼大区研究所）；Institut de Radioastronomie Millimétrique (IRAM)（毫米波射电天文学研究所）；IRAP, CNRS, Université de Toulouse, CNES, UT3-UPS（空间研究与天体物理学研究所，法国国家科学研究中心，图卢兹大学，法国国家太空研究中心）；IJCLab, Université Paris-Saclay, CNRS/IN2P3（IJCLab，巴黎萨克雷大学，法国国家科学研究中心/欧洲核子研究组织）
Interferometry of the cosmic 21-cm signal is set to revolutionise our understanding of the Epoch of Reionisation (EoR) and the Cosmic Dawn (CD). The culmination of ongoing efforts will be the upcoming Square Kilometre Array (SKA), which will provide tomography of the 21-cm signal from the first billion years of our Universe. Using a galaxy formation model informed by high-$z$ luminosity functions, here we forecast the accuracy with which the first phase of SKA-low (SKA1-low) can constrain the properties of the unseen galaxies driving the astrophysics of the EoR and CD. We consider three observ…
We show that the star formation history, the reionization history and the present luminosity function of galaxies are reproduced in a simple gravitational collapse model within the $Λ$CDM regime to almost a quantitative accuracy, when the physical conditions, the Jeans criterion and the cooling process, are taken into account. Taking a reasonable set of the model parameters, the reionisation takes place sharply at around redshift $1+z\simeq 7.5$, and the resulting luminosity function turns off at $L\simeq 10^{10.7}L_\odot$, showing the consistency between the star formation history and the rei…
Measurement of redshifted 21-cm emission from neutral hydrogen promises to be the most effective method for studying the reionisation history of hydrogen and, indirectly, the first galaxies. These studies will be limited not by raw sensitivity to the signal, but rather, by bright foreground radiation from Galactic and extragalactic radio sources and the Galactic continuum. In addition, leakage due to gain errors and non-ideal feeds conspire to further contaminate low-frequency radio obsevations. This leakage leads to a portion of the complex linear polarisation signal finding its way into Stok…
The cosmic 21 cm signal is set to revolutionise our understanding of the early Universe, allowing us to probe the 3D temperature and ionisation structure of the intergalactic medium (IGM). It will open a window onto the unseen first galaxies, showing us how their UV and X-ray photons drove the cosmic milestones of the epoch of reionisation (EoR) and epoch of heating (EoH). To facilitate parameter inference from the 21 cm signal, we previously developed 21CMMC: a Monte Carlo Markov Chain sampler of 3D EoR simulations. Here we extend 21CMMC to include simultaneous modelling of the EoH, resulting…
We present a new semi-analytical model of the population of satellite galaxies of the Milky Way, aimed at estimating the effect of the spatial structure of reionisation at galaxy scale on the properties of the satellites. In this model reionisation can be either: (A) externally-driven and uniform, or (B) internally-driven, by the most massive progenitor of the Milky-Way. In the latter scenario the propagation of the ionisation front and photon dilution introduce a delay in the photo-evaporation of the outer satellites' gas with respect to the inner satellites. As a consequence, outer satellite…
The (re)ionisation of hydrogen in the early universe has a profound effect on the formation of the first galaxies: by raising the gas temperature and pressure, it prevents gas from cooling into small haloes thus affecting the abundance of present-day small galaxies. Using the Galform semi-analytic model of galaxy formation, we show that two key aspects of the reionisation process -- when reionisation takes place and the characteristic scale below which it suppresses galaxy formation -- are imprinted in the luminosity function of dwarf galaxies. We focus on the luminosity function of satellites…
Starlight from galaxies plays a pivotal role throughout the process of cosmic reionisation. We present the statistics of dwarf galaxy properties at z > 7 in haloes with masses up to 10^9 solar masses, using a cosmological radiation hydrodynamics simulation that follows their buildup starting with their Population III progenitors. We find that metal-enriched star formation is not restricted to atomic cooling ($T_{\rm vir} \ge 10^4$ K) haloes, but can occur in haloes down to masses ~10^6 solar masses, especially in neutral regions. Even though these smallest galaxies only host up to 10^4 solar m…
The UV escape fraction from high-redshift galaxies plays a key role in models of cosmic reionisation. Because it is currently not possible to deduce the escape fractions during the epoch of reionisation from observations, we have to rely on numerical simulations. Our aim is to better constrain the escape fraction from high-redshift dwarf galaxies, as these are the most likely sources responsible for reionising the Universe. We employ a N-body/SPH method that includes realistic prescriptions for the physical processes that are important for the evolution of dwarf galaxies. These models are post…
Context: Population III (Pop III) stars may be fast rotating. An expected consequence of fast rotation is strong internal mixing that deeply affects their evolutionary tracks in the Hertzsprung-Russell diagram and hence their ionising power. aims: We investigate the impact on the ionising power of Pop III stars in an extreme case of internal mixing, the one leading to chemically homogeneous evolution (CHE). In that situation, during the main sequence phase, the star keeps the same chemical composition from its center to its surface. Homogeneous stars have larger effective temperatures and lumi…
We investigate the process of reionisation in a model in which the dark matter is a warm elementary particle such as a sterile neutrino. We focus on models that are consistent with the dark matter decay interpretation of the recently detected line at 3.5 keV in the X-ray spectra of galaxies and clusters. In warm dark matter models the primordial spectrum of density perturbations has a cut-off on the scale of dwarf galaxies. Structure formation therefore begins later than in the standard cold dark matter (CDM) model and very few objects form below the cut-off mass scale. To calculate the number…
Emulation of the Global (sky-averaged) 21-cm signal with neural networks has been shown to be an essential tool for physical signal modelling. In this paper we present globalemu, a Global 21-cm signal emulator that uses redshift as a character defining variable alongside a set of astrophysical parameters to estimate the signal brightness temperature. Combined with physically-motivated data pre-processing this makes for a reliable and fast emulator that is relatively insensitive to the network design. globalemu can emulate a high resolution signal in 1.3 ms in comparison to 133 ms, a factor of …
Recently, Planck measured a value of the cosmic microwave background (CMB) optical depth due to electron scattering of $τ=0.066 \pm 0.016$. Here we show that this low value leaves essentially no room for an early partial reionisation of the intergalactic medium (IGM) by high-redshift Population III (Pop III) stars, expected to have formed in low-mass minihaloes. We perform semi-analytic calculations of reionisation which include the contribution from Pop II stars in atomic cooling haloes, calibrated with high-redshift galaxy observations, and Pop III stars in minihaloes with feedback due to Ly…
The reionisation of the Universe is thought to have ended around z~6, as inferred from spectroscopy of distant bright background sources, such as quasars (QSO) and gamma-ray burst (GRB) afterglows. Furthermore, spectroscopy of a GRB afterglow provides insight in its host galaxy, which is often too dim and distant to study otherwise. We present the high S/N VLT/X-shooter spectrum of GRB130606A at z=5.913. We aim to measure the degree of ionisation of the IGM between 5.02<z<5.84 and to study the chemical abundance pattern and dust content of its host galaxy. We measured the flux decrement due to…
Dark matter annihilation or decay could have a significant impact on the ionisation and thermal history of the universe. In this paper, we study the potential contribution of dark matter annihilation (s-wave- or p-wave-dominated) or decay to cosmic reionisation, via the production of electrons, positrons and photons. We map out the possible perturbations to the ionisation and thermal histories of the universe due to dark matter processes, over a broad range of velocity-averaged annihilation cross-sections/decay lifetimes and dark matter masses. We have employed recent numerical studies of the …
We explore the relation between the structure and mass accretion histories of dark matter halos using a suite of cosmological simulations. We confirm that the formation time, defined as the time when the virial mass of the main progenitor equals the mass enclosed within the scale radius, correlates strongly with concentration. We provide a semi-analytic model for halo mass history that combines analytic relations with fits to simulations. This model has the functional form, $M(z) = M_{0}(1+z)^αe^{βz}$, where the parameters $α$ and $β$ are directly correlated with concentration. We then combine…
Using the publicly available VESPA database of SDSS Data Release 7 spectra, we calculate the stellar Mass Weighted Age (hereafter MWA) as a function of local galaxy density and dark matter halo mass. We compare our results with semi-analytic models from the public Millennium Simulation. We find that the stellar MWA has a large scatter which is inherent in the data and consistent with that seen in semi-analytic models. The stellar MWA is consistent with being independent (to first order) with local galaxy density, which is also seen in semi-analytic models. As a function of increasing dark matt…
Ultrafaint dwarf galaxies ($M_\star\lesssim10^{5-6}\,{\rm M}_\odot$) are relics of an early phase of galaxy formation. They contain some of the oldest and most metal-poor stars in the Universe which likely formed before the epoch of hydrogen reionisation. These galaxies are so faint that they can only be detected as satellites of the Milky Way. They are so small that they are just barely resolved in current cosmological hydrodynamics simulations. Here we combine very high resolution cosmological $N$-body simulations with a semi-analytic model of galaxy formation to study the demographics and s…
Physical Calibration of a Minimal Effective Field Theory of the Three-Dimensional Lyman-$α$ Forest
SISSA - International School for Advanced Studies（国际高等研究院）；INFN – National Institute for Nuclear Physics（意大利国家核物理研究所）；IFPU, Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；Centre for Astrophysics Research, Department of Physics, Astronomy and Mathematics, University of Hertfordshire（赫特福德大学天体物理学研究中心）；INAF - Osservatorio Astronomico di Trieste（的里雅斯特天文台）
We present a detailed analysis of predicted galaxy-galaxy merger fractions and rates in the Millennium simulation and compare these with the most up to date observations of the same quantities up to z~3. We carry out our analysis by considering the predicted merger history in the Millennium simulation within a given time interval, as a function of stellar mass. This method, as opposed to pair fraction counts, considers mergers that have already taken place, and allows a more direct comparison with the observed rates and fractions measured with the concentration-asymmetry-clumpiness (CAS) metho…
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 t…
We study the impact of early dark energy (EDE) cosmologies on galaxy properties by coupling high-resolution numerical simulations with semi-analytic modeling (SAM) of galaxy formation and evolution. EDE models are characterized by a non-vanishing high-redshift contribution of dark energy, producing an earlier growth of structures and a modification of large-scale structure evolution. They can be viewed as typical representatives of non-standard dark energy models in which only the expansion history is modified, and hence the impact on galaxy formation is indirect. We show that in EDE cosmologi…
TeV-blazars potentially heat the intergalactic medium (IGM) as their gamma rays interact with photons of the extragalactic background light to produce electron-positron pairs, which lose their kinetic energy to the surrounding medium through plasma instabilities. This results in a heating mechanism that is only weakly sensitive to the local density, and therefore approximately spatially uniform, naturally producing an inverted temperature-density relation in underdense regions. In this paper we go beyond the approximation of uniform heating and quantify the heating rate fluctuations due to the…
We present charm (cosmic history agnostic reconstruction method), a novel inference algorithm that reconstructs the cosmic expansion history as encoded in the Hubble parameter $H(z)$ from SNe Ia data. The novelty of the approach lies in the usage of information field theory, a statistical field theory that is very well suited for the construction of optimal signal recovery algorithms. The charm algorithm infers non-parametrically $s(a)=\ln(ρ(a)/ρ_{\mathrm{crit}0})$, the density evolution which determines $H(z)$, without assuming an analytical form of $ρ(a)$ but only its smoothness with the sca…
Over the past several decades, galaxy formation theory has met with significant successes. In order to test current theories thoroughly we require predictions for as yet unprobed regimes. To this end, we describe a new implementation of the Galform semi-analytic model of galaxy formation. Our motivation is the success of the model described by Bower et al. in explaining many aspects of galaxy formation. Despite this success, the Bower et al. model fails to match some observational constraints and certain aspects of its physical implementation are not as realistic as we would like. The model de…
The strong dependence of the large-scale dark matter halo bias on the (local) non-Gaussianity parameter, f_NL, offers a promising avenue towards constraining primordial non-Gaussianity with large-scale structure surveys. In this paper, we present the first detection of the dependence of the non-Gaussian halo bias on halo formation history using N-body simulations. We also present an analytic derivation of the expected signal based on the extended Press-Schechter formalism. In excellent agreement with our analytic prediction, we find that the halo formation history-dependent contribution to the…
We extend the existing analytical model of reionization by Furlanetto et al. (2004) to include the biasing of reionization sources and additional absorption by Lyman Limit systems. Our model is, by construction, consistent with the observed evolution of the galaxy luminosity function at z<8 and with the observed evolution of Ly-α forest at z<6. We also find that, for a wide range of values for the relative escape fraction that we consider reasonable, and which are consistent with the observational constraints on the relative escape fraction from lower redshifts, our reionization model is consi…
At low densities the standard ionisation history of the intergalactic medium (IGM) predicts a decreasing temperature of the IGM with decreasing density once hydrogen (and helium) reionisation is complete. Heating the high-redshift, low-density IGM above the temperature expected from photo-heating is difficult, and previous claims of high/rising temperatures in low density regions of the Universe based on the probability density function (PDF) of the opacity in Lyman-$α$ forest data at $2<z<4$ have been met with considerable scepticism, particularly since they appear to be in tension with other…
The fitting formula for the location of the first acoustic peak in the matter power spectrum is revised. We discuss the physics that leads to baryon acoustic oscillations: the recombination history, the tight coupling approximation and the velocity overshoot effect. A new fitting formula is proposed, which is in accordance within 5% with numerical results for a suitable range of cosmological parameters, whereas previous results yield deviations of up to 20%. The crucial improvement turns out to be the accuracy of the recombination history.
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 …
We study the minimal ``bathtub" toy model as an analytic tool for capturing key processes of galaxy evolution and identifying robust successes and challenges in reproducing observations at high redshift. The source and sink terms of the continuity equations for gas and stars are expressed in simple terms from first principles. The assumed dependence of star-formation rate (SFR) on gas mass self-regulates the system into a unique asymptotic behavior, which is approximated by an analytic quasi-steady-state solution (QSS). We address the validity of the QSS at different epochs independent of earl…
We examine whether large-scale environment affects the mass assembly history of their central galaxies. To facilitate this, we constructed dark matter halo merger trees from a cosmological N-body simulation and calculated the formation and evolution of galaxies using a semi-analytic method. We confirm earlier results that smaller halos show a notable difference in formation time with a mild dependence on large-scale environment. However, using a semi-analytic model, we found that on average the growth rate of the stellar mass of central galaxies is largely insensitive to large-scale environmen…
