Halo Properties Research Articles

Computationally efficient reionization in a large hydrodynamic galaxy formation simulation

ABSTRACT Accuracy in the topology and statistics of a simulated epoch of reionization (EoR) are vital to draw connections between observations and physical processes. While full radiative transfer models produce the most accurate reionization models, they are highly computationally expensive, and are infeasible for the largest cosmological simulations. Instead, large simulations often include EoR models that are pre-computed via the initial density field, or post-processed where feedback effects are ignored. We introduce astrid-es, a resimulation of the astrid epoch of reionization 20 > z > 5.5 which includes an on-the-fly excursion-set reionization algorithm. astrid-es produces more accurate reionization histories without significantly impacting the computational time. This model directly utilizes the star particles produced in the simulation to calculate the EoR history and includes an ultraviolet (UV) background which heats the gas particles after their reionization. We contrast the reionization topology and statistics in astrid-es with the previously employed parametric reionization model, finding that in astrid-es, ionized regions are more correlated with galaxies, and the 21cm power spectrum shows an increase in large-scale power. We calculate the relation between the size of H ii regions and the UV luminosity of the brightest galaxy within them. Prior to the overlap phase, we find a power-law fit of log(R) = −0.314MUV − 2.550log(1 + z) + 7.408 with a standard deviation σR < 0.15 dex across all mass bins. We also examine the properties of haloes throughout reionization, finding that while the properties of haloes in the simulation are correlated with the redshift of reionization, they are not greatly affected by reionization itself.

Inferring the impact of feedback on the matter distribution using the Sunyaev Zel’dovich effect: insights from CAMELS simulations and ACT + DES data

ABSTRACT Feedback from active galactic nuclei and stellar processes changes the matter distribution on small scales, leading to significant systematic uncertainty in weak lensing constraints on cosmology. We investigate how the observable properties of group-scale haloes can constrain feedback’s impact on the matter distribution using Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS). Extending the results of previous work to smaller halo masses and higher wavenumber, k, we find that the baryon fraction in haloes contains significant information about the impact of feedback on the matter power spectrum. We explore how the thermal Sunyaev Zel’dovich (tSZ) signal from group-scale haloes contains similar information. Using recent Dark Energy Survey weak lensing and Atacama Cosmology Telescope tSZ cross-correlation measurements and models trained on CAMELS, we obtain 10 per cent constraints on feedback effects on the power spectrum at $k \sim 5\, h\, {\rm Mpc}^{-1}$. We show that with future surveys, it will be possible to constrain baryonic effects on the power spectrum to $\mathcal {O}(\lt 1~{{\ \rm per\ cent}})$ at $k = 1\, h\, {\rm Mpc}^{-1}$ and $\mathcal {O}(3~{{\ \rm per\ cent}})$ at $k = 5\, h\, {\rm Mpc}^{-1}$ using the methods that we introduce here. Finally, we investigate the impact of feedback on the matter bispectrum, finding that tSZ observables are highly informative in this case.

QUOTAS: A New Research Platform for the Data-driven Discovery of Black Holes

We present QUOTAS, a novel research platform for the data-driven investigation of supermassive black hole (SMBH) populations. While SMBH data—observations and simulations—have grown in complexity and abundance, our computational environments and tools have not matured commensurately to exhaust opportunities for discovery. To explore the BH, host galaxy, and parent dark matter halo connection—in this pilot version—we assemble and colocate the high-redshift, z > 3 quasar population alongside simulated data at the same cosmic epochs. As a first demonstration of the utility of QUOTAS, we investigate correlations between observed Sloan Digital Sky Survey (SDSS) quasars and their hosts with those derived from simulations. Leveraging machine-learning algorithms (ML), to expand simulation volumes, we show that halo properties extracted from smaller dark-matter-only simulation boxes successfully replicate halo populations in larger boxes. Next, using the Illustris-TNG300 simulation that includes baryonic physics as the training set, we populate the larger LEGACY Expanse dark-matter-only box with quasars, and show that observed SDSS quasar occupation statistics are accurately replicated. First science results from QUOTAS comparing colocated observational and ML-trained simulated data at z3 are presented. QUOTAS demonstrates the power of ML, in analyzing and exploring large data sets, while also offering a unique opportunity to interrogate theoretical assumptions that underpin accretion and feedback models. QUOTAS and all related materials are publicly available at the Google Kaggle platform. (The full data set—observational data and simulation data—are available at: https://www.kaggle.com/ and the codes are available at:https://www.kaggle.com/datasets/quotasplatform/quotas)

The MillenniumTNG Project: an improved two-halo model for the galaxy–halo connection of red and blue galaxies

ABSTRACT Approximate methods to populate dark-matter haloes with galaxies are of great utility to galaxy surveys. However, the limitations of simple halo occupation models (HODs) preclude a full use of small-scale galaxy clustering data and call for more sophisticated models. We study two galaxy populations, luminous red galaxies (LRGs) and star-forming emission-line galaxies (ELGs), at two epochs, z = 1 and z = 0, in the large-volume, high-resolution hydrodynamical simulation of the MillenniumTNG project. In a partner study we concentrated on the small-scale, one-halo regime down to r ∼ 0.1 h−1 Mpc, while here we focus on modelling galaxy assembly bias in the two-halo regime, r ≳ 1 h−1 Mpc. Interestingly, the ELG signal exhibits scale dependence out to relatively large scales (r ∼ 20 h−1 Mpc), implying that the linear bias approximation for this tracer is invalid on these scales, contrary to common assumptions. The 10–15 per cent discrepancy is only reconciled when we augment our halo occupation model with a dependence on extrinsic halo properties (‘shear’ being the best-performing one) rather than intrinsic ones (e.g. concentration, peak mass). We argue that this fact constitutes evidence for two-halo galaxy conformity. Including tertiary assembly bias (i.e. a property beyond mass and ‘shear’) is not an essential requirement for reconciling the galaxy assembly bias signal of LRGs, but the combination of external and internal properties is beneficial for recovering ELG the clustering. We find that centrals in low-mass haloes dominate the assembly bias signal of both populations. Finally, we explore the predictions of our model for higher order statistics such as nearest neighbour counts. The latter supplies additional information about galaxy assembly bias and can be used to break degeneracies between halo model parameters.

Halo assembly bias from a deep learning model of halo formation

ABSTRACT We build a deep learning framework that connects the local formation process of dark matter haloes to the halo bias. We train a convolutional neural network (CNN) to predict the final mass and concentration of dark matter haloes from the initial conditions. The CNN is then used as a surrogate model to derive the response of the haloes’ mass and concentration to long-wavelength perturbations in the initial conditions, and consequently the halo bias parameters following the ‘response bias’ definition. The CNN correctly predicts how the local properties of dark matter haloes respond to changes in the large-scale environment, despite no explicit knowledge of halo bias being provided during training. We show that the CNN recovers the known trends for the linear and second-order density bias parameters b1 and b2, as well as for the local primordial non-Gaussianity linear bias parameter bϕ. The expected secondary assembly bias dependence on halo concentration is also recovered by the CNN: at fixed mass, halo concentration has only a mild impact on b1, but a strong impact on bϕ. Our framework opens a new window for discovering which physical aspects of the halo’s Lagrangian patch determine assembly bias, which in turn can inform physical models of halo formation and bias.

Constraining interacting dark energy models with the halo concentration–mass relation

ABSTRACT The interacting dark energy (IDE) model is a promising alternative cosmological model that has the potential to solve the fine-tuning and coincidence problems by considering the interaction between dark matter and dark energy. Previous studies have shown that the energy exchange between the dark sector components in this model can significantly affect the dark matter halo properties. In this study, by utilizing a large set of cosmological N-body simulations, we analyse the redshift evolution of the halo concentration–mass (c–M) relation in the IDE model, and show that the c–M relation is a sensitive proxy of the interaction strength parameter ξ2, especially at lower redshifts. Furthermore, we construct parametrized formulae to quantify the dependence of the c–M relation on ξ2 at redshifts ranging from z = 0 to z = 0.6. Our parametrized formulae provide a useful theoretical tool in constraining ξ2 with the observational c–M relation. As a first attempt, we use the data from X-ray, gravitational lensing, and galaxy rotational curve observations and obtain a tight constraint on ξ2, i.e. ξ2 = 0.071 ± 0.034. Our work demonstrates that the halo c–M relation, which reflects the halo assembly history, is a powerful probe to constrain the IDE model.

Multi-epoch machine learning 2: identifying physical drivers of galaxy properties in simulations

ABSTRACT Using a novel machine learning method, we investigate the buildup of galaxy properties in different simulations, and in various environments within a single simulation. The aim of this work is to show the power of this approach at identifying the physical drivers of galaxy properties within simulations. We compare how the stellar mass is dependent on the value of other galaxy and halo properties at different points in time by examining the feature importance values of a machine learning model. By training the model on IllustrisTNG, we show that stars are produced at earlier times in higher density regions of the universe than they are in low density regions. We also apply the technique to the Illustris, EAGLE, and CAMELS simulations. We find that stellar mass is built up in a similar way in EAGLE and IllustrisTNG, but significantly differently in the original Illustris, suggesting that subgrid model physics is more important than the choice of hydrodynamics method. These differences are driven by the efficiency of supernova feedback. Applying principal component analysis to the CAMELS simulations allows us to identify a component associated with the importance of a halo’s gravitational potential and another component representing the time at which galaxies form. We discover that the speed of galactic winds is a more critical subgrid parameter than the total energy per unit star formation. Finally, we find that the Simba black hole feedback model has a larger effect on galaxy formation than the IllustrisTNG black hole feedback model.

MultiCAM: a multivariable framework for connecting the mass accretion history of haloes with their properties

ABSTRACT Models that connect galaxy and halo properties often summarize a halo’s mass accretion history (MAH) with a single value and use this value as the basis for predictions. However, a single-value summary fails to capture the complexity of MAHs and information can be lost in the process. We present MultiCAM, a generalization of traditional abundance matching frameworks, which can simultaneously connect the full MAH of a halo with multiple halo and/or galaxy properties. As a first case study, we apply MultiCAM to the problem of connecting dark matter halo properties to their MAHs in the context of a dark matter-only simulation. While some halo properties, such as concentration, are more strongly correlated to the early-time mass growth of a halo, others, like the virial ratio, have stronger correlations with late-time mass growth. This highlights the necessity of considering the impact of the entire MAH on halo properties. For most of the halo properties we consider, we find that MultiCAM models that use the full MAH achieve higher accuracy than conditional abundance matching models that use a single epoch. We also demonstrate an extension of MultiCAM that captures the covariance between predicted halo properties. This extension provides a baseline model for applications where the covariance between predicted properties is important.

Halos of dark energy

We investigate the properties of dark energy halos in models with a nonminimal coupling in the dark sector. We show, using a quasistatic approximation, that a coupling of the mass of dark matter particles to a standard quintessence scalar field $\phi$ generally leads to the formation of dark energy concentrations in and around compact dark matter objects. These are associated with regions where scalar field gradients are large and the dark energy equation of state parameter is close to $-1/3$. We find that the energy and radius of a dark energy halo are approximately given by $E_{\rm halo} \sim \boldsymbol{\beta}^2 \varphi \, m$ and $r_{\rm halo} \sim \sqrt{\boldsymbol{\beta} \,\varphi ({R}/{H})}$, where $\varphi=Gm/(R c^2)$, $m$ and $R$ are, respectively, the mass and radius of the associated dark matter object, $\boldsymbol{\beta} = -(8\pi G)^{-1/2} d \ln m/d \phi$ is the nonminimal coupling strength parameter, $H$ is the Hubble parameter, $G$ is the gravitational constant, and $c$ is the speed of light in vacuum. We further show that current observational limits on $\boldsymbol{\beta}$ over a wide redshift range lead to stringent constraints on $E_{\rm halo}/m$ and, therefore, on the impact of dark energy halos on the value of the dark energy equation of state parameter. We also briefly comment on potential backreaction effects that may be associated with the breakdown of the quasistatic approximation and determine the regions of parameter space where such a breakdown might be expected to occur.

Inferring dark matter halo properties for H i-selected galaxies

ABSTRACT We set constraints on the dark matter halo mass and concentration of ∼22 000 individual galaxies visible both in $\rm{H}\, {\small I}$ (from the ALFALFA survey) and optical light (from the Sloan Digital Sky Survey). This is achieved by combining two Bayesian models, one for the $\rm{H}\, {\small I}$ line width as a function of the stellar and neutral hydrogen mass distributions in a galaxy using kinematic modelling, and the other for the galaxy’s total baryonic mass using the technique of inverse subhalo abundance matching. We hence quantify the constraining power on halo properties of spectroscopic and photometric observations, and assess their consistency. We find good agreement between the two sets of posteriors, although there is a sizeable population of low-line width galaxies that favour significantly smaller dynamical masses than expected from abundance matching (especially for cuspy halo profiles). Abundance matching provides significantly more stringent bounds on halo properties than the $\rm{H}\, {\small I}$ line width, even with a mass–concentration prior included, although combining the two provides a mean gain of 40 per cent for the sample when fitting an NFW profile. We also use our kinematic posteriors to construct a baryonic mass–halo mass relation, which we find to be near power law, and with a somewhat shallower slope than expected from abundance matching. Our method demonstrates the potential of combining photometric and spectroscopic observations to precisely map out the dark matter distribution at the galaxy scale using upcoming $\rm{H}\, {\small I}$ surveys such as the SKA.

Negligible Effects of Baryons on the Angular Momentum Scaling Relations of Galactic Dark Matter Halos

In cosmological simulations without baryons, the relation between the specific angular momentum j h and mass M h of galactic dark matter halos has the well-established form . This is invariably adopted as the starting point in efforts to understand the analogous relation between the specific angular momentum j * and mass M * of the stellar parts of galaxies, which are often re-expressed relative to the corresponding halo properties through the retention fractions f j = j */j h and f M = M */M h. An important caveat here is that the adopted relation could, in principle, be modified by the gravitational back-reaction of baryons on dark matter (DM). We have tested for this possibility by comparing the j h–M h relations in the IllustrisTNG100 and TNG50 simulations that include baryons (full-physics runs) with their counterparts that do not (DM-only runs). In all cases, we find scaling relations of the form , with α ≈ 2/3 over the ranges of mass and redshift studied here: M h ≥ 1010 M ⊙ and 0 ≤ z ≤ 2. The values of α are virtually identical in the full-physics and DM-only runs at the same redshift. The only detectable effect of baryons on the j h–M h relation is a slightly higher normalization, by 12%–15% at z = 0 and by 5% at z = 2. This implies that existing estimates of f j based on DM-only simulations should be adjusted downward by similar amounts. Finally, we discuss briefly some implications of this work for studies of galaxy formation.

DESI mock challenge

Context. We present a novel approach to the construction of mock galaxy catalogues for large-scale structure analysis based on the distribution of dark matter halos obtained with effective bias models at the field level. Aims. We aim to produce mock galaxy catalogues capable of generating accurate covariance matrices for a number of cosmological probes that are expected to be measured in current and forthcoming galaxy redshift surveys (e.g. two- and three-point statistics). The construction of the catalogues shown in this paper is part of a mock-comparison project within the Dark Energy Spectroscopic Instrument (DESI) collaboration. Methods. We use the bias assignment method (BAM) to model the statistics of halo distribution through a learning algorithm using a few detailed N-body simulations, and approximated gravity solvers based on Lagrangian perturbation theory. We introduce cosmic-web-dependent corrections to modelling redshift-space distortions at the N-body level – both in the halo and galaxy distributions –, as well as a multi-scale approach for accurate assignment of halo properties. Using specific models of halo occupation distributions to populate halos, we generate galaxy mocks with the expected number density and central-satellite fraction of emission-line galaxies, which are a key target of the DESI experiment. Results. BAM generates mock catalogues with per cent accuracy in a number of summary statistics, such as the abundance, the two- and three-point statistics of halo distributions, both in real and redshift space. In particular, the mock galaxy catalogues display ∼3%−10% accuracy in the multipoles of the power spectrum up to scales of k ∼ 0.4 h−1Mpc. We show that covariance matrices of two- and three-point statistics obtained with BAM display a similar structure to the reference simulation. Conclusions. BAM offers an efficient way to produce mock halo catalogues with accurate two- and three-point statistics, and is able to generate a variety of multi-tracer catalogues with precise covariance matrices of several cosmological probes. We discuss future developments of the algorithm towards mock production in DESI and other galaxy-redshift surveys.

High-fidelity reproduction of central galaxy joint distributions with neural networks

ABSTRACT The relationship between galaxies and haloes is central to the description of galaxy formation and a fundamental step towards extracting precise cosmological information from galaxy maps. However, this connection involves several complex processes that are interconnected. Machine Learning methods are flexible tools that can learn complex correlations between a large number of features, but are traditionally designed as deterministic estimators. In this work, we use the IllustrisTNG300-1 simulation and apply neural networks in a binning classification scheme to predict probability distributions of central galaxy properties, namely stellar mass, colour, specific star formation rate, and radius, using as input features the halo mass, concentration, spin, age, and the overdensity on a scale of 3 h−1 Mpc. The model captures the intrinsic scatter in the relation between halo and galaxy properties, and can thus be used to quantify the uncertainties related to the stochasticity of the galaxy properties with respect to the halo properties. In particular, with our proposed method, one can define and accurately reproduce the properties of the different galaxy populations in great detail. We demonstrate the power of this tool by directly comparing traditional single-point estimators and the predicted joint probability distributions, and also by computing the power spectrum of a large number of tracers defined on the basis of the predicted colour–stellar mass diagram. We show that the neural networks reproduce clustering statistics of the individual galaxy populations with excellent precision and accuracy.

Halo-independent dark matter electron scattering analysis with in-medium effects

Dark matter (DM)-electron scattering is a prime target of a number of direct DM detection experiments and constitutes a promising avenue for exploring interactions of DM in the sub-GeV mass-range, challenging to probe with nuclear recoils. We extend the recently proposed halo-independent analysis method for DM-electron scattering, which allows to infer the local DM halo properties without any additional assumptions about them, to include in-medium effects through dielectric functions of the target material. We show that in-medium effects could significantly affect halo-independent analysis response functions for germanium and silicon and thus are essential for proper inference of local DM halo characteristics from direct DM detection data.

Modelling dark matter halo spin using observations and simulations: application to UGC 5288

ABSTRACT Dark matter (DM) halo properties are extensively studied in cosmological simulations but are very challenging to estimate from observations. The DM halo density profile of observed galaxies is modelled using multiple probes that trace the DM potential. However, the angular momentum distribution of DM halos is still a subject of debate. In this study, we investigate a method for estimating the halo spin and halo concentration of low surface brightness (LSB), gas-rich dwarf barred galaxy UGC 5288, by forward modelling disc properties derived from observations – stellar and gas surface densities, disc scalelength, H i rotation curve, bar length, and bar ellipticity. We combine semi-analytical techniques, N-body/SPH, and cosmological simulations to model the DM halo of UGC 5288 with both a cuspy Hernquist profile and a flat-core pseudo-isothermal profile. We find that the best match with observations is a pseudo-isothermal halo model with a core radius of rc = 0.23 kpc and halo spin of λ = 0.08 at the virial radius. Although our findings are consistent with previous core radius estimates of the halo density profile of UGC 5288, as well as with the halo spin profiles of similar mass analogues of UGC 5288 in the high-resolution cosmological-magneto-hydrodynamical simulation TNG50, there still remain some uncertainties as we are limited in our knowledge of the formation history of the galaxy. Additionally, we find that the inner halo spin (r < 10 kpc) in barred galaxies is different from the unbarred ones, and the halo spin shows weak correlations with bar properties.

The Planck clusters in the LOFAR sky

Context. Diffuse cluster-scale synchrotron radio emission is discovered in an increasing number of galaxy clusters in the form of radio haloes, probing the presence of relativistic electrons and magnetic fields in the intra-cluster medium (ICM). The favoured scenario to explain their origin is that they trace turbulent regions that are generated during cluster-cluster mergers, where particles are re-accelerated. In this framework, radio haloes are expected to probe cluster dynamics and are predicted to be more frequent in massive systems, in which more energy becomes available for the re-acceleration of relativistic electrons. For these reasons, statistical studies of galaxy cluster samples have the power to derive fundamental information on the radio haloes populations and on their connection with cluster dynamics, and hence to constrain theoretical models. Furthermore, low-frequency cluster surveys have the potential to shed light on the existence of radio haloes with very steep radio spectra, which are a key prediction of turbulent models and are thought to be generated in less energetic merger events and thus be more common in the Universe. Aims. The main question we address is whether we can explain the observed properties of the radio halo population within the framework of current models. Methods. We study the occurrence and properties of radio haloes from clusters of the second catalogue of Planck Sunyaev Zel’dovich-detected sources that lie within the 5634 deg2 that are covered by the second data release (DR2) of the LOFAR Two-meter Sky Survey. We derive their integral number, flux density, and redshift distributions. We compare these observations with expectations of theoretical models. We also study the connection between radio haloes and cluster mergers by using cluster morphological parameters derived through Chandra and/or XMM-Newton data. Results. We find that the number of observed radio haloes, their radio flux density, and their redshift distributions agree with what is expected in the framework of the re-acceleration scenario. In line with model expectations, the fraction of clusters with radio haloes increases with the cluster mass, confirming the leading role of the gravitational process of cluster formation in the generation of radio haloes. These models predict a large fraction of radio haloes with very steep spectra in the DR2 Planck sample. This will be tested in future studies, but a comparison of the occurrence of haloes in GMRT and LOFAR samples indeed shows a more frequent occurrence of haloes at lower frequencies, suggesting the presence of a population of haloes with very steep spectra that is preferentially detected by LOFAR. Using morphological information, we confirm that radio haloes are preferentially located in merging systems, and that the fraction of newly LOFAR-discovered radio haloes is larger in less strongly disturbed systems.

What sets the splashback radius of dark matter haloes: accretion history or other properties?

ABSTRACT The density profiles of dark matter haloes contain rich information about their growth history and physical properties. One particularly interesting region is the splashback radius, Rsp, which marks the transition between particles orbiting in the halo and particles undergoing first infall. While the dependence of Rsp on the recent accretion rate is well-established and theoretically expected, it is not clear exactly what parts of the accretion history Rsp responds to, and what other halo properties might additionally influence its position. We comprehensively investigate these questions by correlating the dynamically measured splashback radii of a large set of simulated haloes with their individual growth histories as well as their structural, dynamical, and environmental properties. We find that Rsp is sensitive to the accretion over one crossing time but largely insensitive to the prior history (in contrast to concentration, which probes earlier epochs). All secondary correlations are much weaker, but we discern a relatively higher Rsp in less massive, older, more elliptical, and more tidally deformed haloes. Despite these minor influences, we conclude that the splashback radius is a clean indicator of a halo’s growth over the past dynamical time. We predict that the magnitude gap should be a promising observable indicator of a halo’s accretion rate and splashback radius.

Ionizing photon production and escape fractions during cosmic reionization in the TNG50 simulation

ABSTRACTIn this work, we investigate the dependence of the escape fraction of ionizing photons, fesc, on various galaxy and host halo properties during the epoch of reionization. We post-process the TNG50 magnetohydrodynamical simulation from the IllustrisTNG project using the three-dimensional multifrequency radiative transfer code CRASH. Our work covers the stellar mass range of 106 ≲ M⋆/M⊙ ≲ 108 at redshifts 6 < z < 10. Adopting an unresolved, cloud-scale escape fraction parameter of unity, the average halo escape fraction fesc increases with mass from ∼0.3 at M⋆ = 106 M⊙ to ∼0.6 at M⋆ = 107.5 M⊙, after which we find hints of a turnover and decreasing escape fractions for even more massive galaxies. However, we demonstrate a strong and non-linear dependence of fesc on the adopted subgrid escape fraction, resulting in uncertainties for the absolute value of the escape fraction. In addition, fesc has significant scatter at fixed mass, driven by diversity in the ionizing photon rate together with a complex relationship between (stellar) source positions and the underling density distribution. The global emissivity is consistent with observations for reasonable cloud-scale absorption values, and haloes with a stellar mass ≲107.5 M⊙ contribute the majority of escaping ionizing photons at all redshifts. Incorporating dust reduces fesc by a few per cent at M⋆ ≲ 106.5 M⊙, and up to 10 per cent for larger haloes. Our multifrequency approach shows that fesc depends on photon energy, and is reduced substantially at E > 54.4 eV versus lower energies. This suggests that the impact of high-energy photons from binary stars is reduced when accounting for an energy-dependent escape fraction.

Accurate analytic mass–scale relations for dark matter haloes of all masses and redshifts

ABSTRACTCUSP is a powerful formalism that recovers, from first principles and with no free parameter, all the macroscopic properties of dark matter haloes found in cosmological N-body simulations and unveils the origin of their characteristic features. Since it is not restricted by the limitations of simulations, it covers the whole mass and redshift ranges. In the present Paper we use CUSP to calculate the mass–scale relations holding for halo density profiles fitted to the usual NFW and Einasto functions in the most relevant cosmologies and for the most usual mass definitions. We clarify the origin of these relations and provide accurate analytic expressions holding for all masses and redshifts. The performance of those expressions is compared to that of previous models and to the mass–concentration relation spanning more than 20 orders of magnitude in mass at z = 0 obtained in recent simulations of a 100 GeV WIMP universe.

The impact of the dark matter on galaxy formation

Contemporarily, dark matter exerts dominant impacts on galaxy formation, which is the spine bone of the galaxy. Herein, we investigate the attraction effect of initial dark matter distribution on the normal matter (hydrogen and other gases), which will form the dark matter halos. Subsequently, an introduction to the properties of dark matter halos and some disputes about it are demonstrated. Besides, the cold dark matter (CDM) is chosen to fit the current observation and interpret the influences of dark matter on galaxy formation. Overall, this paper offers a clear procession of the impact of dark matter on galaxy formation, which will be guideline for future development of both galaxy formation theory as well as dark matter detection.