Simulated Dark Matter Halos Research Articles

MAMBO: An empirical galaxy and AGN mock catalogue for the exploitation of future surveys

Current and future large surveys will produce unprecedented amounts of data. Realistic simulations have become essential for the design and development of these surveys, as well as for the interpretation of the results. We present MAMBO, a flexible and efficient workflow to build empirical galaxy and active galactic nucleus (AGN) mock catalogues that reproduce the physical and observational properties of these sources. We started with simulated dark matter (DM) haloes, to preserve the link with the cosmic web, and we populated them with galaxies and AGN using abundance matching techniques. We followed an empirical methodology, using stellar mass functions, host galaxy AGN mass functions, and AGN accretion rate distribution functions studied at different redshifts to assign, among other properties, stellar masses, the fraction of quenched galaxies, or the AGN activity (demography, obscuration, multiwavelength emission, etc.). As a proof test, we applied the method to a Millennium DM lightcone of 3.14 $ deg^2$ up to a redshift of $z=10$ and down to stellar masses of $ M \, M_ We show that the AGN population from the mock lightcone presented here reproduces with good accuracy various observables, such as state-of-the-art luminosity functions in the X-ray up to $z 7$ and in the ultraviolet up to $z 5$, optical/near-infrared colour-colour diagrams, and narrow emission line diagnostic diagrams. Finally, we demonstrate how this catalogue can be used to make useful predictions for large surveys. Using Euclid as a case example, we compute, among other forecasts, the expected surface densities of galaxies and AGN detectable in the Euclid $H_ E $ band. We find that Euclid might observe (on $H_ E $ only) about $10^ $ and $8 $ type 1 and 2 AGN, respectively, and $2 $ galaxies at the end of its $ deg^2$ Wide survey, in good agreement with other published forecasts.

Towards including super-sample covariance in the unbinned likelihood for cluster abundance cosmology

ABSTRACT The measurement of the abundance of galaxy clusters in the Universe is a sensitive probe of cosmology, which depends on both the expansion history of the Universe and the growth of structure. Density fluctuations across the finite survey volume add noise to this measurement, this is often referred to as super-sample covariance (SSC). For an unbinned cluster analysis, such noise has not been included in the cluster likelihood, since the effect of SSC was small compared to the Poisson shot-noise for samples of a few hundred clusters. For upcoming large cluster surveys such as the Rubin LSST, which will deliver catalogues of tens of thousands of clusters, this effect will no longer be negligible. In this paper, we propose a new hybrid likelihood based on the Gauss-Poisson Compound model (GPC), by using infinitesimal mass bins and standard redshift bins. This likelihood has the advantages of an unbinned Poisson likelihood while successfully incorporating the effects of SSC. Using a simulated dark matter halo catalogue, we find that the hybrid likelihood, accounting for both Poisson noise and SSC, increases the dispersion of the parameter posteriors by 20 per cent when using 100 000 clusters compared to the standard unbinned likelihood, based on Poisson statistics only.

Machine Learning the Dark Matter Halo Mass of Milky Way-Like Systems

Despite the Milky Way’s proximity to us, our knowledge of its dark matter halo is fairly limited, and there is still considerable uncertainty in its halo mass. Many past techniques have been limited by assumptions such as the Galaxy being in dynamical equilibrium as well as nearby galaxies being true satellites of the Galaxy, and/or the need to find large samples of Milky Way analogs in simulations.Here, we propose a new technique based on neural networks that obtains high precision (<0.14 dex mass uncertainty with perfect measurements of 30 neighboring galaxies; <0.14 dex including fiducial observational errors) without assuming halo dynamical equilibrium or that neighboring galaxies are all satellites, and which can use information from a wide variety of simulated halos (even those dissimilar to the Milky Way) to improve its performance. This method uses only observable information including satellite orbits, distances to nearby larger halos, and the maximum circular velocity of the largest satellite galaxy. In this paper, we demonstrate a proof-of-concept method on simulated dark matter halos; in future papers in this series, we will apply neural networks to estimate the masses of the Milky Way’s and M31’s dark matter halos, and we will train variations of these networks to estimate other halo properties including concentration, assembly history, and spin axis.

Cosmological and idealized simulations of dark matter haloes with velocity-dependent, rare and frequent self-interactions

ABSTRACT Dark matter self-interactions may have the capability to solve or at least mitigate small-scale problems of the cosmological standard model, Lambda cold dark matter. There are a variety of self-interacting dark matter models that lead to distinguishable astrophysical predictions and hence varying success in explaining observations. Studies of dark matter (DM) density cores on various mass scales suggest a velocity-dependent scattering cross-section. In this work, we investigate how a velocity dependence alters the evolution of the DM distribution for frequent DM scatterings and compare to the velocity-independent case. We demonstrate that these cases are qualitatively different using a test problem. Moreover, we study the evolution of the density profile of idealized DM haloes and find that a velocity dependence can lead to larger core sizes and different time-scales of core formation and core collapse. In cosmological simulations, we investigate the effect of velocity-dependent self-interaction on haloes and satellites in the mass range of ≈1011–$10^{14} \, \mathrm{M_\odot }$. We study the abundance of satellites, density, and shape profiles and try to infer qualitative differences between velocity-dependent and velocity-independent scatterings as well as between frequent and rare self-interactions. We find that a strongly velocity-dependent cross-section can significantly amplify the diversity of rotation curves, independent of the angular dependence of the differential cross-section. We further find that the abundance of satellites in general depends on both the velocity dependence and the scattering angle, although the latter is less important for strongly velocity-dependent cross-sections.

Statistical characteristics of observed and simulated dark matter haloes

ABSTRACT A simple model of spherical dark matter haloes is proposed in terms of two structure functions. In the framework of this model, we analysed the properties of 450 000 simulated haloes with masses Mvir > 1011 M⊙. We compared the mean characteristics of simulated haloes with the corresponding characteristics of 641 galaxies and found that the basic characteristics of the two populations are similar but that their probability distribution functions are different. This disagreement may be caused by technical factors such as the halo identification algorithm, which does not reproduce the observed dark matter haloes correctly.

Topological data analysis reveals differences between simulated galaxies and dark matter haloes

ABSTRACT We use topological summaries based on Betti curves to characterize the large-scale spatial distribution of simulated dark matter haloes and galaxies. Using the IllustrisTNG and CAMELS-SAM simulations, we show that the topology of the galaxy distribution is significantly different from the topology of the dark matter halo distribution. Further, there are significant differences between the distributions of star-forming and quiescent galaxies. These topological differences are broadly consistent across all simulations, while at the same time there are noticeable differences when comparing between different models. Finally, using the CAMELS-SAM simulations, we show that the topology of the quiescent galaxies, in particular, depends strongly on the amount of supernova feedback. These results suggest that topological summary statistics could be used to help better understand the processes of galaxy formation and evolution.

Constraining the shape of dark matter haloes with globular clusters and diffuse stellar light in the E-MOSAICS simulations

ABSTRACTWe explore how diffuse stellar light and globular clusters (GCs) can be used to trace the matter distribution of their host halo using an observational methodology. For this, we use 117 simulated dark matter (DM) haloes from the $(34.4~\rm cMpc)^3$ periodic volume of the E-MOSAICS project. For each halo, we compare the stellar surface brightness and GC projected number density maps to the surface density of DM. We find that the dominant structures identified in the stellar light and GCs correspond closely with those from the DM. Our method is unaffected by the presence of satellites and its precision improves with fainter GC samples. We recover tight relations between the dimensionless profiles of stellar-to-DM surface density and GC-to-DM surface density, suggesting that the profile of DM can be accurately recovered from the stars and GCs (σ ≤ 0.5 dex). We quantify the projected morphology of DM, stars, and GCs and find that the stars and GCs are more flattened than the DM. Additionally, the semimajor axes of the distribution of stars and GCs are typically misaligned by ∼10 degrees from that of DM. We demonstrate that deep imaging of diffuse stellar light and GCs can place constraints on the shape, profile, and orientation of their host halo. These results extend down to haloes with central galaxies M⋆ ≥ 1010 M⊙, and the analysis will be applicable to future data from the Euclid, Roman, and the Rubin observatories

Testing the accuracy of likelihoods for cluster abundance cosmology

ABSTRACTThe abundance of galaxy clusters is a sensitive probe to the amplitude of matter density fluctuations, the total amount of matter in the Universe as well as its expansion history. Inferring correct values and accurate uncertainties of cosmological parameters requires accurate knowledge of cluster abundance statistics, encoded in the likelihood function. In this paper, we test the accuracy of cluster abundance likelihoods used in the literature, namely the Poisson and Gaussian likelihoods as well as the more complete description of the Gauss–Poisson Compound likelihood. This is repeated for a variety of binning choices and analysis setups. In order to evaluate the accuracy of a given likelihood, this work compares individual posterior covariances to the covariance of estimators over the 1000 simulated dark matter halo catalogues obtained from PINOCCHIO algorithm. We find that for Rubin/LSST and Euclid-like surveys the Gaussian likelihood gives robust constraints over a large range of binning choices. The Poisson likelihood, that does not account for sample covariance, always underestimates the errors on the parameters, even when the sample volume is reduced or only high-mass clusters are considered. We find no benefit in using the more complex Gauss–Poisson Compound likelihood as it gives essentially the same results as the Gaussian likelihood, but at a greater computational cost. Finally, in this ideal setup, we note only a small gain on the parameter error bars when using a large number of bins in the mass–redshift plane.

How galaxies populate halos in extreme density environments: An analysis of the halo occupation distribution in SDSS

Context. Recent works have shown that the properties of galaxy populations in simulated dark matter halos vary with large-scale environments. These results suggest a variation in the halo occupation distribution (HOD) in extreme density environments since the dynamical and astrophysical conditions prevailing in these regions may significantly affect the formation and evolution of their halos and residing galaxies, influencing the mean number of satellite galaxies. To analyze these effects, we identify cosmic voids and future virialized structures (FVSs) in the Sloan Digital Sky Server Data Release 12 (SDSS-DR12) and estimate the HOD within these super-structures using group catalogs as dark matter halo proxies. Aims. Our goal is to use observational galaxy data to characterize the HOD within cosmic voids and FVSs, explore the different properties of these galaxies’ populations, and compare them with the general results outside of these super-structures. Methods. We used a publicly available observational galaxy catalog with information on redshifts, positions, magnitudes, and other astrophysical features to build a volume complete galaxy sample and identify cosmic voids and FVSs. Using a publicly available galaxy group catalog as a proxy to dark matter halos, we computed the HOD within both types of super-structures for different absolute magnitude thresholds. We also studied the dependence of the results on the main void and FVS properties, density, and volume. We also analyzed the main characteristics of the stellar content of galaxies inside these extreme-density regions such as the mean stellar age and the stellar mass. In all cases, we compared the results with those derived from the field sample, defined by objects outside of both types of environments. Results. Inside cosmic voids, we find a strong decrease in the HOD concerning the field results. In the most extreme cases, that is to say groups with masses above ∼1013 h−1 M⊙, the mean number of satellites fall to ∼50%. Inside FVSs, the HOD shows a significant increase to the field, with a ∼40% excess in the mean number of satellites for groups with masses around 1014 h−1 M⊙. These results are present for the different galaxy luminosity ranges explored. In both environments, the differences with respect to the field increases for the extreme values of the density environments. However, we obtain no signs of variations related to intrinsic characteristics of the super-structures, indicating that the effects mainly depend on the density of the large-scale environment. In addition, we find that the cumulative distribution of the mean age of stars of the central galaxy also varies in the different regions; this suggests that the history of the formation of the dark matter halos may be different. Finally, we explore the HOD for the 25% youngest (oldest) galaxies, based on the mean age of their stars. We find that for the low-mass groups the youngest galaxies are only present inside voids, and they are generally central galaxies. On the other hand, for the high-mass groups, the FVS environments show the same increase in the HOD concerning the field as previously mentioned. We find that cosmic voids lack a significant fraction of galaxies with the oldest stellar population.

On the Effect of the Large Magellanic Cloud on the Orbital Poles of Milky Way Satellite Galaxies

The reflex motion and distortion of the Milky Way (MW) halo caused by the infall of a massive Large Magellanic Cloud (LMC) has been demonstrated to result in an excess of orbital poles of dark matter halo particles toward the LMC orbital pole. This was suggested to help explain the observed preference of MW satellite galaxies to coorbit along the Vast Polar Structure (VPOS). We test this idea by correcting the positions and velocities of the MW satellites for the Galactocentric-distance-dependent shifts inferred from a LMC-infall simulation. While this should substantially reduce the observed clustering of orbital poles if it were mainly caused by the LMC, we instead find that the strong clustering remains preserved. We confirm the initial study’s main result with our simulation of an MW-LMC-like interaction, and use it to identify two reasons why this scenario is unable to explain the VPOS: (1) the orbital pole density enhancement in our simulation is very mild (∼10% within 50–250 kpc) compared to the observed enhancement (∼220%–300%), and (2) it is very sensitive to the specific angular momenta (AM) of the simulation particles, with the higher-AM particles being affected the least. Particles in simulated dark matter halos tend to follow more radial orbits (lower AM), so their orbital poles are more easily affected by small offsets in position and velocity caused by a LMC infall than objects with more tangential velocity (higher AM), such as the observed dwarf galaxies surrounding the MW. The origin of the VPOS thus remains unexplained.

Cosmic Tidal Reconstruction with Halo Fields

Abstract The gravitational coupling between large-scale perturbations and small-scale perturbations leads to anisotropic distortions of the small-scale matter distribution. The measured local small-scale power spectrum can thus be used to infer the large-scale matter distribution. In this paper, we present a new tidal reconstruction algorithm for reconstructing large-scale modes using the full three-dimensional tidal shear information. We apply it to simulated dark matter halo fields and find the reconstructed large-scale density field correlates well with the original matter density field on large scales, improving upon the previous tidal reconstruction method, which only uses two transverse shear fields. This has profound implications for recovering lost 21 cm radial modes due to foreground subtraction and constraining primordial non-Gaussianity using the multitracer method with future cosmological surveys.

Weak lensing mass modeling bias and the impact of miscentring

ABSTRACT Parametric modeling of galaxy cluster density profiles from weak lensing observations leads to a mass bias, whose detailed understanding is critical in deriving accurate mass-observable relations for constraining cosmological models. Drawing from existing methods, we develop a robust framework for calculating this mass bias in one-parameter fits to simulations of dark matter haloes. We show that our approach has the advantage of being independent of the absolute noise level, so that only the number of haloes in a given simulation and the representativeness of the simulated haloes for real clusters limit the accuracy of the bias estimation. While we model the bias as a lognormal distribution and the haloes with a Navarro–Frenk–White profile, our method can be generalized to any bias distribution and parametric model of the radial mass distribution. We find that the lognormal assumption is not strictly valid in the presence of miscentring of haloes. We investigate the use of cluster centres derived from weak lensing in the context of mass bias, and tentatively find that such centroids can yield sensible mass estimates if the convergence peak has a signal-to-noise ratio (SNR) approximately greater than 4. In this context we also find that the standard approach to estimating the positional uncertainty of weak lensing mass peaks using bootstrapping severely underestimates the true positional uncertainty for peaks with low SNRs. Though we determine the mass and redshift dependence of the bias distribution for a few experimental setups, our focus remains providing a general approach to computing such distributions.

Emerge: constraining merging probabilities and time-scales of close galaxy pairs

ABSTRACT Theoretical models are vital for exploring the galaxy merger process, which plays a crucial role in the evolution of galaxies. Recent advances in modelling have placed tight constraints on the build-up of stellar material in galaxies across cosmic time. Despite these successes, extracting the merger rates from observable data remains a challenge. Differences in modelling techniques, combined with limited observational data, drive conflicting conclusions on the merging time-scales of close pairs. We employ an empirical model for galaxy formation that links galaxy properties to the growth of simulated dark matter haloes, along with mock light-cone galaxy catalogues, to probe the dependences of pair merging probabilities and merging time-scales. In this work, we demonstrate that the pair merging probabilities are best described by a logistic function and that mean merging time-scales can be well approximated by a linear relation in the projected separation and line of sight velocity difference in observed pairs. Together, our fitting formulas can accurately predict merger rates from galaxy pairs to at least z ∼ 4 under a wide variety of pair selection criteria. Additionally, we show that some commonly used pair selection criteria may not represent a suitable sample of galaxies to reproduce underlying merger rates. Finally, we conclude from our analysis that observation time-scales are primarily driven by dynamics and are not strongly impacted by the star formation properties of the component galaxies.

The Dekel-Zhao profile: a mass-dependent dark-matter density profile with flexible inner slope and analytic potential, velocity dispersion, and lensing properties

ABSTRACTWe explore a function with two shape parameters for the dark-matter halo density profile subject to baryonic effects, which is a special case of the general Zhao family of models applied to simulated dark-matter haloes by Dekel et al. This profile has variable inner slope and concentration parameter, and analytic expressions for the gravitational potential, velocity dispersion, and lensing properties. Using the Numerical Investigation of a Hundred Astrophysical Objects cosmological simulations, we find that it provides better fits than the Einasto profile and the generalized NFW profile with variable inner slope, in particular towards the halo centres. We show that the profile parameters are correlated with the stellar-to-halo mass ratio Mstar/Mvir. This defines a mass-dependent density profile describing the average dark-matter profiles in all galaxies, which can be directly applied to observed rotation curves of galaxies, gravitational lenses, and semi-analytic models of galaxy formation or satellite–galaxy evolution. The effect of baryons manifests itself by a significant flattening of the inner density slope and a 20 per cent decrease of the concentration parameter for Mstar/Mvir = 10−3.5–10−2, corresponding to $M_{\rm star} \!\sim \! 10^{7-10}\, \mathrm{ M}_\odot$. The accuracy by which this profile fits simulated galaxies is similar to certain multiparameter mass-dependent profiles, but its fewer parameters and analytic nature make it most desirable for many purposes.

Power-law Pseudo-phase-space Density Profiles of Dark Matter Halos: A Fluke of Physics?

It has been known for nearly 20 years that the pseudo phase-space density profile of equilibrium simulated dark matter halos, $\rho(r)/\sigma^3(r)$, is well described by a power law over 3 decades in radius, even though both the density $\rho(r)$, and the velocity dispersion $\sigma(r)$ deviate significantly from power laws. The origin of this scale-free behavior is not understood. It could be an inherent property of self-gravitating collisionless systems, or it could be a mere coincidence. To address the question we work with equilibrium halos, and more specifically, the second derivative of the Jeans equation, which, under the assumptions of (i) Einasto density profile, (ii) linear velocity anisotropy - density slope relation, and (iii) $\rho/\sigma^3\propto r^{-\alpha}$, can be transformed from a differential equation to a cubic algebraic equation. Relations (i)-(iii) are all observed in numerical simulations, and are well parametrized by a total of 4 or 6 model parameters. We do not consider dynamical evolution of halos; instead, taking advantage of the fact that the algebraic Jeans equation for equilibrium halos puts relations (i)-(iii) on the same footing, we study the (approximate) solutions of this equation in the 4 and 6 dimensional spaces. We argue that the distribution of best solutions in these parameter spaces is inconsistent with $\rho/\sigma^3\propto r^{-\alpha}$ being an fundamental property of gravitational evolution, and conclude that the scale-free nature of this quantity is likely to be a fluke.

Cosmological exploitation of the size function of cosmic voids identified in the distribution of biased tracers

Abstract Cosmic voids are large underdense regions that, together with galaxy clusters, filaments and walls, build-up the large-scale structure of the Universe. The void size function provides a powerful probe to test the cosmological framework. However, to fully exploit this statistics, the void sample has to be properly cleaned from spurious objects. Furthermore, the bias of the mass tracers used to detect these regions has to be taken into account in the size function model. In our work, we test a cleaning algorithm and a new void size function model on a set of simulated dark matter halo catalogues, with different mass and redshift selections, to investigate the statistics of voids identified in a biased mass density field. We then investigate how the density field tracers’ bias affects the detected size of voids. The main result of this analysis is a new model of the size function, parametrized in terms of the linear effective bias of the tracers used, which is straightforwardly inferred from the large-scale two-point correlation function. This method is a crucial step in exploiting real surveys. The proposed size function model has been accurately calibrated on halo catalogues, and used to validate the possibility to provide forecasts on the cosmological constraints, namely on the matter density contrast, ΩM, and on the normalization of the linear matter power spectrum, σ8, at different redshifts.

The mass of the Milky Way from satellite dynamics

Abstract We present and apply a method to infer the mass of the Milky Way (MW) by comparing the dynamics of MW satellites to those of model satellites in the eagle cosmological hydrodynamics simulations. A distribution function (DF) for galactic satellites is constructed from eagle using specific angular momentum and specific energy, which are scaled so as to be independent of host halo mass. In this two-dimensional space, the orbital properties of satellite galaxies vary according to the host halo mass. The halo mass can be inferred by calculating the likelihood that the observed satellite population is drawn from this DF. Our method is robustly calibrated on mock eagle systems. We validate it by applying it to the completely independent suite of 30 auriga high-resolution simulations of MW-like galaxies: the method accurately recovers their true mass and associated uncertainties. We then apply it to 10 classical satellites of the MW with six-dimensional phase-space measurements, including updated proper motions from the Gaia satellite. The mass of the MW is estimated to be $M_{200}^{\rm {MW}}=1.17_{-0.15}^{+0.21}\times 10^{12}\, \mathrm{M}_{\odot }$ (68 per cent confidence limits). We combine our total mass estimate with recent mass estimates in the inner regions of the Galaxy to infer an inner dark matter (DM) mass fraction $M^\rm {DM}(\lt 20~\rm {kpc})/M^\rm {DM}_{200}=0.12$, which is typical of ${\sim }10^{12}\, \mathrm{M}_{\odot }$ lambda cold dark matter haloes in hydrodynamical galaxy formation simulations. Assuming a Navarro, Frenk and White (NFW) profile, this is equivalent to a halo concentration of $c_{200}^{\rm {MW}}=10.9^{+2.6}_{-2.0}$.

A rigorous EFT-based forward model for large-scale structure

Conventional approaches to cosmology inference from galaxy redshift surveys are based on n-point functions, which are under rigorous perturbative control on sufficiently large scales. Here, we present an alternative approach, which employs a likelihood at the level of the galaxy density field. By integrating out small-scale modes based on effective-field theory arguments, we prove that this likelihood is under perturbative control if certain specific conditions are met. We further show that the information captured by this likelihood is equivalent to the combination of the next-to-leading order galaxy power spectrum, leading-order bispectrum, and BAO reconstruction. Combined with MCMC sampling and MAP optimization techniques, our results allow for fully Bayesian cosmology inference from large-scale structure that is under perturbative control. We illustrate this via a first demonstration of unbiased cosmology inference from nonlinear large-scale structure using this likelihood. In particular, we show unbiased estimates of the power spectrum normalization σ8 from a catalog of simulated dark matter halos, where nonlinear information is crucial in breaking the b1−σ8 degeneracy.

The Information Content in Cold Stellar Streams

Abstract Cold stellar streams—produced by tidal disruptions of globular clusters—are long-lived, coherent dynamical features in the halo of the Milky Way. They hold the promise of delivering precise information about the gravitational potential, including constraints on the shape of the dark matter halo. Because of their different ages and different positions in phase space, different streams tell us different things about the Galaxy. Here we employ a Cramér–Rao lower bound (CRLB) or Fisher-matrix approach to understand the quantitative information content in (toy versions of) 11 known streams: ATLAS, GD-1, Hermus, Kwando, Orinoco, PS1A, PS1C, PS1D, PS1E, Sangarius, and Triangulum. This approach depends on a generative model, which we have developed previously, and which permits calculation of derivatives of predicted stream properties with respect to Galaxy and stream parameters. We find that in simple analytic models of the Milky Way, streams on eccentric orbits contain the most information about the halo shape. For each stream, there are near degeneracies between dark matter halo properties and parameters of the bulge, the disk, and the stream progenitor itself, but simultaneous fitting of multiple streams will constrain all parameters at the percent level. At this precision, simulated dark matter halos deviate from simple analytic parameterizations, so we add an expansion of basis functions as a first step in giving the gravitational potential more freedom. As freedom increases, the information about the halo reduces overall, and it becomes more localized to the current position of the stream. In the limit of high model freedom, a stellar stream appears to measure the local acceleration at its current position; this motivates thinking about future nonparametric approaches. The CRLB formalism also permits us to assess the value of future measurements of stellar velocities, distances, and proper motions. We show that velocities of stream stars are essential for producing competitive constraints on the distribution of dark matter.

Dependence on the environment of the abundance function of light-cone simulation dark matter haloes

Aims. We study the dependence of the halo abundance function (AF) on different environments in a whole-sky ΛCDM light-cone halo catalogue extending to z ~ 0.65, using a simple and well-defined halo isolation criterion. Methods. The isolation status of each individual dark matter halo is determined by the distance to its nearest neighbour, which defines the maximum spherical region devoid of halos above a threshold mass around it (although the true size of such region may be much larger since it is not necessarily spherical). A versatile double power-law Schechter function is used to fit the dark matter halo AF, and its derived parameters are studied as a function of halo isolation status. Results. (a) Our function fits the halo abundances for all halo isolation statuses extremely well, while the well-established theoretical mass functions, integrated over the volume of the light-cone, provide an adequate but poorer fit than our phenomenological model. (b) As expected, and in agreement with other studies based on snap-shot simulations, we find significant differences of the halo abundance function as a function of halo isolation, indicating different rates of halo formation. The slope of the power law and the characteristic mass of the Schechter-like fitting function decrease with isolation, a result consistent with the formation of less massive haloes in lower density regions. (c) We find an unexpected upturn of the characteristic mass of the most isolated haloes of our sample. This upturn originates and characterises only the higher redshift regime (z ≳ 0.45), which probably implies a significant and recent evolution of the isolation status of the most isolated and most massive haloes.