Formation Of Dark Matter Halos Research Articles

The shape of dark matter halos: A new fundamental cosmological invariance

In this article, we focus on the complex relationship between the shape of dark matter (DM) halos and the cosmological models underlying their formation. We have used three realistic cosmological models from the DEUS numerical simulation project. These three models have very distinct cosmological parameters (Ωm, σ8, and w) but their cosmic matter fields beyond the scale of DM halos are quasi-indistinguishable, providing an exemplary framework to examine the cosmological dependence of DM halo morphology. First, we developed a robust method for measuring the halo shapes detected in numerical simulations. This method avoids numerical artifacts on DM halo shape measurements, induced by the presence of substructures depending on the numerical resolution or by any spherical prior that does not respect the triaxiality of DM halos. We then obtain a marked dependence of the halo’s shape both on their mass and the cosmological model underlying their formation. As it is well known, the more massive the DM halo, the less spherical it is and we find that the higher the σ8 of the cosmological model, the more spherical the DM halos. Then, by reexpressing the properties of the shape of the halos in terms of the nonlinear fluctuations of the total cosmic matter field or only of the cosmic matter field which is internal to the halos, we managed to make the cosmological dependence disappear completely. This new fundamental cosmological invariance is a direct consequence of the nonlinear dynamics of the cosmic matter field. As the universe evolves, the nonlinear fluctuations of the cosmic field increase, driving the dense matter halos toward sphericity. The deviation from sphericity, measured by the prolaticity, triaxiality, and ellipticity of the DM halos, is therefore entirely encapsulated in the nonlinear power spectrum of the cosmic field. From this fundamental invariant relation, we retrieve with remarkable accuracy the root-mean-square of the nonlinear fluctuations and, consequently, the power spectrum of the cosmic matter field in which the halos formed. We also recover the σ8 amplitude of the cosmological model that governs the cosmic matter field at the origin of the DM halos. Our results therefore highlight, not only the nuanced relationship between DM halo formation and the underlying cosmology but also the potential of DM halo shape analysis of being a powerful tool for probing the nonlinear dynamics of the cosmic matter field.

Dwarf galaxies as a probe of a primordially magnetized Universe

Aims. The true nature of primordial magnetic fields (PMFs) and their role in the formation of galaxies remains elusive. To shed light on these unknowns, we investigated their impact by varying two sets of properties: (i) accounting for the effect of PMFs on the initial matter power spectrum and (ii) accounting for their magneto-hydrodynamical effects on the formation of galaxies. By comparing both, we can determine the dominant agent in shaping galaxy evolution. Methods. We used the magneto-hydrodynamics code RAMSES to generate multiple new zoom-in simulations for eight different host halos of dwarf galaxies across a wide luminosity range of 103 − 106 L⊙. These halos were selected from a ΛCDM cosmological box, tracking their evolution down to redshift z = 0. We explored a variety of primordial magnetic field (comoving) strengths of Bλ ranging from 0.05 to 0.50 nG. Results. We find that magnetic fields in the interstellar medium not only modify star formation processes in dwarf spheroidal galaxies, but these fields also entirely prevent the formation of stars in less compact, ultra-faint galaxies with halo masses and stellar masses below, respectively, ∼2.5 × 109 and 3 × 106 M⊙. At high redshifts, the impact of PMFs on host halos of dwarf galaxies through the modification of the matter power spectrum is more dominant than the influence of magneto-hydrodynamics in shaping their gaseous structure. Through the amplification of small perturbations ranging in mass from 107 to 109 M⊙ in the ΛCDM+PMFs matter power spectrum, primordial fields expedite the formation of the first dark matter halos, leading to an earlier onset and a higher star formation rate at redshifts of z > 9. We investigated the evolution of various energy components and demonstrated that magnetic fields with an initial strength of Bλ ≥ 0.05 nG exhibit a strong growth of magnetic energy, accompanied by a saturation phase that begins soon after the growth phase. These trends persist consistently, regardless of the initial conditions or whether it is the classical ΛCDM model or ΛCDM modified by PMFs. Lastly, we investigated the impact of PMFs on the present-time observable properties of dwarf galaxies, namely: the half light radius, V-band luminosity, mean metallicity, and velocity dispersion profile. We find that PMFs with moderate strengths of Bλ ≤ 0.10 nG show an impressive agreement with the scaling relations of the observed Local Group dwarfs. However, stronger fields lead to larger sizes and higher velocity dispersions.

Neutral hydrogen lensing simulations in the hubble frontier fields

ABSTRACT Cold gas evolution ties the formation of dark matter haloes to the star formation history of the universe. A primary component of cold gas, neutral atomic hydrogen (HI), can be traced by its 21-cm emission line. However, the faintness of this emission typically limits individual detections to low redshifts ($z\lesssim 0.2$). To address this limitation, we investigate the potential of targeting gravitationally lensed systems. Building on our prior galaxy–galaxy simulations, we have developed a ray-tracing code to simulate lensed HI images for known galaxies situated behind the massive hubble frontier field galaxy clusters. Our findings reveal the existence of high HI mass, high HI magnification systems in these cluster-lensing scenarios. Through simulations of hundreds of sources, we have identified compelling targets within the redshift range $z\approx 0.7 - 1.5$. The most promising candidate from our simulations is the Great Arc at z = 0.725 in Abell 370, which should be detectable by MeerKAT in approximately 50 h. Importantly, the derived HI mass is predicted to be relatively insensitive to systematic uncertainties in the lensing model, and should be constrained within a factor of ${\sim }2.5$ for a 95 per cent confidence interval.

Excess of high-z galaxies as a test for bumpy power spectrum of density perturbations

ABSTRACT Modified matter power spectra with approximately Gaussian bump on sub-Mpc scales can be a result of a complex inflation. We consider five spectra with different Gaussian amplitudes A and locations k0 and run N-body simulations in a cube (5 Mpc h−1)3 at z > 8 to reveal the halo mass functions and their evolution with redshift. We have found that the Sheth–Tormen formula provides a good approximation to a such kind of halo mass functions. In the considered models, the dark matter halo formation starts much more earlier than in Lambda cold dark matter (ΛCDM), which in turn can result in an earlier star formation and a nuclear activity in galaxies and can be detected and tested by, e.g. JWST. At z = 0, the halo mass functions are hardly distinguishable from the standard ΛCDM, therefore the models with the bumpy spectra can be identified in observations by their excess in number of bright sources at high redshift only.

Analysis of dark matter halo structure formation in N -body simulations with machine learning

The properties of the matter density field in the initial conditions have a decisive impact on the features of the large-scale structure of the Universe as observed today. These need to be studied via $N$-body simulations, which are imperative to analyze high density collapsed regions into dark matter halos. In this paper, we train machine learning algorithms with information from $N$-body simulations to infer two properties: dark matter particle halo classification that leads to halo formation prediction with the characteristics of the matter density field traced back to the initial conditions, and dark matter halo formation by calculating the halo mass function, which offers the number density of dark matter halos with a given threshold. We map the initial conditions of the density field into classification labels of dark matter halo structures. The halo mass function of the simulations is calculated and reconstructed with theoretical methods as well as our trained algorithms. We test several machine learning techniques where we could find that the random forest and neural networks proved to be the better performing tools to classify dark matter particles in cosmological simulations. We also show that, by using only a few data points, we can effectively train the algorithms to reconstruct the halo mass function in a model-independent way, giving us a highly accurate fitting function that aligns well with both simulation and theoretical results.

The Structure of the Universe in the Quasar Absorption Spectra

An analysis of the absorption lines observed in the spectra of quasars makes it possible to study the evolution of the structure of the Universe up to redshifts z∼5. The observed clustering of C IV lines demonstrates the multiple birth of low-mass galaxies in separate structural elements—filaments and “pancakes.” This ensures their subsequent regular hierarchical merger in the central galaxy or group of galaxies. Remnants of the early “pancakes” are observed today as the Local Group, groups around the Andromeda and Centaurus galaxies, and other small groups of galaxies. In turn, the observed clustering of Lyman-alpha lines shows that starless dark matter (DM) halos are also formed in structural elements and their hierarchical clustering leads to the formation of massive starless dark matter halos of moderate density, which also appear in numerical models.

Iterative mean-field approach to the spherical collapse of dark matter haloes

ABSTRACT Gravitational collapse of dark matter overdensities leads to the formation of dark matter haloes which embed galaxies and galaxy clusters. An intriguing feature of dark matter haloes is that their density profiles closely follow a universal form irrespective of the initial condition or the corresponding growth history. This represents a class of dynamical systems with emergent universalities. We propose an ‘iterative mean-field approach’ to compute the solutions of the gravitational collapse dynamics. This approach iteratively searches for the evolution of the interaction field ϕ(t) – in this case the enclosed mass profile M(r, t) – that is consistent with the dynamics, thus that ϕ(t) is the fix-point of the iterative mapping, $\mathcal {H}(\phi) = \phi$. The formalism replaces the N-body interactions with one-body interactions with the coarse-grained interaction field, and thus shares the spirit of the mean-field theory in statistical physics. This ‘iterative mean-field approach’ combines the versatility of numerical simulations and the comprehensiveness of analytical solutions, and is particularly powerful in searching for and understanding intermediate asymptotic states in a wide range of dynamical systems where the solutions can not be obtained through the traditional self-similar analysis.

Neutrino bound states and bound systems

Yukawa interactions of neutrinos with a new light scalar boson ϕ can lead to formation of stable bound states and bound systems of many neutrinos (ν-clusters). For allowed values of the coupling y and the scalar mass mϕ, the bound state of two neutrinos would have the size larger than 1012 cm. Bound states with sub-cm sizes are possible for keV scale sterile neutrinos with coupling y > 10−4. For ν-clusters we study in detail the properties of final stable configurations. If there is an efficient cooling mechanism, these configurations are in the state of degenerate Fermi gas. We formulate and solve equations of the density distributions in ν-clusters. In the non-relativistic case, they are reduced to the Lane-Emden equation. We find that (i) stable configurations exist for any number of neutrinos, N; (ii) there is a maximal central density ∼ 109 cm−3 determined by the neutrino mass; (iii) for a given mϕ there is a minimal value of Ny3 for which stable configurations can be formed; (iv) for a given strength of interaction, Sϕ = (ymν/mϕ)2, the minimal radius of ν-clusters exists. We discuss the formation of ν-clusters from relic neutrino background in the process of expansion and cooling of the Universe. One possibility realized for Sϕ > 700 is the development of instabilities in the ν-background at T < mν which leads to its fragmentation. For Sϕ ∈ [70, 700]) they might be formed via the growth of initial density perturbations in the ν-background and virialiazation, in analogy with the formation of Dark Matter halos. For allowed values of y, cooling of ν-clusters due to ϕ-bremsstrahlung and neutrino annihilation is negligible. The sizes of ν-clusters may range from ∼ km to ∼ 5 Mpc.

Semi-annihilating dark matter coupled with Majorons

The thermal production mechanism of dark matter is attractive and well-motivated by predictivity. A representative of this type of dark matter candidate is the canonical, weakly interacting massive particles. An alternative is semi-annihilating dark matter, which exhibits different phenomenological aspects from the former example. In this study, we constructed a model of dark matter semi-annihilating into a pair of anti-dark matter and a Majoron based on a global U(1)B−L symmetry, and show that semi-annihilation induces the core formation of dark matter halos, which can alleviate the so-called small-scale problems. In addition, the box-shaped spectrum of neutrinos was produced by the subsequent decay of the Majoron. This can be a distinctive signature of the dark matter in the model. We find a parameter space where the produced neutrinos can be detected by the future large-volume neutrino detector Hyper-Kamiokande. We also compared the dark matter scenario with the case of halo core formation by the strongly self-interacting dark matter.

Beyond mass: detecting secondary halo properties with galaxy-galaxy lensing

ABSTRACTSecondary halo properties beyond mass, such as the mass accretion rate (MAR), concentration, and the half mass scale, are essential in understanding the formation of large-scale structure and dark matter haloes. In this paper, we study the impact of secondary halo properties on the galaxy-galaxy lensing observable, ΔΣ. We build an emulator trained on N-body simulations to model ΔΣ and quantify the impact of different secondary parameters on the ΔΣ profile. We focus on the impact of MAR on ΔΣ. We show that a 3σ detection of variations in MAR at fixed halo mass could be achieved with the Hyper Suprime Cam survey assuming no baryonic effects and a proxy for MAR with scatter &amp;lt;1.5. We show that the full radial profile of ΔΣ depends on secondary properties at fixed halo mass. Consequently, an emulator that can perform full shape fitting yields better than two times improvement upon the constraints on MAR than only using the outer part of the halo. Finally, we highlight that miscentring and MAR impact the radial profile of ΔΣ in a similar fashion, implying that miscentring and MAR need to be modelled jointly for unbiased estimates of both effects. We show that present-day lensing data sets have the statistical capability to place constraints on halo MAR within our assumptions. Our analysis opens up new possibilities for observationally measuring the assembly history of the dark matter haloes that host galaxies and clusters.

Constraint on the early-formed dark matter halos using the free-free emission in the Planck foreground analysis

We provide a new constraint on the small-scale density fluctuations, evaluating the diffuse background free-free emission from dark matter halos in the dark ages. If there exists a large amplitude of the matter density fluctuations on small scales, the excess enhances the early formation of dark matter halos. When the virial temperature is sufficiently high, the gas in a halo is heated up and ionized by thermal collision. The heated ionized gas emits photons by the free-free process. We would observe the sum of these photons as the diffuse background free-free emission. Assuming the analytical dark matter halo model including the gas density and temperature profile, we calculate the intensity of the diffuse background free-free emission from early-formed dark matter halos in the microwave frequency range. Comparing with the recent foreground analysis on cosmic microwave background, we obtain the constraint on the excess of the density fluctuations on small scales. Our constraint corresponds to $P_\zeta \lesssim 10^{-7}$ for $k \simeq 1-100~\mathrm{Mpc}^{-1}$ with assuming the delta-function-type curvature power spectrum. Therefore, our constraint is the most stringent constraint on the perturbations below $1~\rm Mpc$ scales.

Constructing high-fidelity halo merger trees inabacussummit

ABSTRACTTracking the formation and evolution of dark matter haloes is a critical aspect of any analysis of cosmological N-body simulations. In particular, the mass assembly of a halo and its progenitors, encapsulated in the form of its merger tree, serves as a fundamental input for constructing semi-analytic models of galaxy formation and, more generally, for building mock catalogues that emulate galaxy surveys. We present an algorithm for constructing halo merger trees from abacussummit, the largest suite of cosmological N-body simulations performed to date consisting of nearly 60 trillion particles, and which has been designed to meet the Cosmological Simulation Requirements of the Dark Energy Spectroscopic Instrument (DESI) survey. Our method tracks the cores of haloes to determine associations between objects across multiple time slices, yielding lists of halo progenitors and descendants for the several tens of billions of haloes identified across the entire suite. We present an application of these merger trees as a means to enhance the fidelity of abacussummit halo catalogues by flagging and ‘merging’ haloes deemed to exhibit non-monotonic past merger histories. We show that this cleaning technique identifies portions of the halo population that have been deblended due to choices made by the halo finder, but which could have feasibly been part of larger aggregate systems. We demonstrate that by cleaning halo catalogues in this post-processing step, we remove potentially unphysical features in the default halo catalogues, leaving behind a more robust halo population that can be used to create highly accurate mock galaxy realizations from abacussummit.

Star Formation Histories of Ultra-faint Dwarf Galaxies: Environmental Differences between Magellanic and Non-Magellanic Satellites?*

Abstract We present the color–magnitude diagrams and star formation histories (SFHs) of seven ultra-faint dwarf galaxies: Horologium 1, Hydra 2, Phoenix 2, Reticulum 2, Sagittarius 2, Triangulum 2, and Tucana 2, derived from high-precision Hubble Space Telescope photometry. We find that the SFH of each galaxy is consistent with them having created at least 80% of the stellar mass by z ∼ 6. For all galaxies, we find quenching times older than 11.5 Gyr ago, compatible with the scenario in which reionization suppresses the star formation of small dark matter halos. However, our analysis also reveals some differences in the SFHs of candidate Magellanic Cloud satellites, i.e., galaxies that are likely satellites of the Large Magellanic Cloud and that entered the Milky Way potential only recently. Indeed, Magellanic satellites show quenching times about 600 Myr more recent with respect to those of other Milky Way satellites, on average, even though the respective timings are still compatible within the errors. This finding is consistent with theoretical models that suggest that satellites’ SFHs may depend on their host environment at early times, although we caution that within the error bars all galaxies in our sample are consistent with being quenched at a single epoch.

Excursion set peaks in energy as a model for haloes

ABSTRACT The simplest models of dark matter halo formation rely on the heuristic assumption, motivated by spherical collapse, that virialized haloes originate from initial regions that are maxima of the smoothed matter density field. Here, we replace this notion with the dynamical requirement that protohaloes be regions where the local gravitational flow converges to a point. For this purpose, we look for spheres whose acceleration at the boundary – relative to their centre of mass – points towards their geometric centre: that is, spheres with null dipole moment. We show that these configurations are minima of the energy, corresponding to the most energetically bound spheres. Therefore, we study peaks of the smoothed energy overdensity field. This significant conceptual change is technically trivial to implement: to change from density to energy one need only modify the standard top-hat smoothing filter. However, this comes with the important benefit that, for power spectra of cosmological interest, the model is no longer plagued by divergences: improving the physics mends the mathematics. In addition, the ‘excursion set’ requirement that the smoothed matter density crosses a critical value can be naturally replaced by a threshold in energy. Measurements in simulations of haloes more massive than 1013h−1M⊙ show very good agreement with a number of generic predictions of our model.

The causal effect of environment on halo mass and concentration

ABSTRACT Understanding the impact of environment on the formation and evolution of dark matter haloes and galaxies is a crucial open problem. Studying statistical correlations in large simulated populations sheds some light on these impacts, but the causal effect of an environment on individual objects is harder to pinpoint. Addressing this, we present a new method for resimulating a single dark matter halo in multiple large-scale environments. In the initial conditions, we ‘splice’ (i.e. insert) the Lagrangian region of a halo into different Gaussian random fields, while enforcing consistency with the statistical properties of Lambda cold dark matter. Applying this technique, we demonstrate that the mass of haloes is primarily determined by the density structure inside their Lagrangian patches, while the haloes’ concentration is more strongly affected by environment. The splicing approach will also allow us to study, for example, the impact of the cosmic web on accretion processes and galaxy quenching.

On the formation and stability of fermionic dark matter haloes in a cosmological framework

ABSTRACT The formation and stability of collisionless self-gravitating systems are long-standing problems, which date back to the work of D. Lynden-Bell on violent relaxation and extends to the issue of virialization of dark matter (DM) haloes. An important prediction of such a relaxation process is that spherical equilibrium states can be described by a Fermi–Dirac phase-space distribution, when the extremization of a coarse-grained entropy is reached. In the case of DM fermions, the most general solution develops a degenerate compact core surrounded by a diluted halo. As shown recently, the latter is able to explain the galaxy rotation curves, while the DM core can mimic the central black hole. A yet open problem is whether these kinds of astrophysical core–halo configurations can form at all, and whether they remain stable within cosmological time-scales. We assess these issues by performing a thermodynamic stability analysis in the microcanonical ensemble for solutions with a given particle number at halo virialization in a cosmological framework. For the first time, we demonstrate that the above core–halo DM profiles are stable (i.e. maxima of entropy) and extremely long-lived. We find the existence of a critical point at the onset of instability of the core–halo solutions, where the fermion-core collapses towards a supermassive black hole. For particle masses in the keV range, the core-collapse can only occur for $M_{\rm vir} \gtrsim 10^{9}{\, \mathrm{M}_\odot}$ starting at zvir ≈ 10 in the given cosmological framework. Our results prove that DM haloes with a core–halo morphology are a very plausible outcome within non-linear stages of structure formation.

Jeans Instability of Dissipative Self-Gravitating Bose–Einstein Condensates with Repulsive or Attractive Self-Interaction: Application to Dark Matter

We study the Jeans instability of an infinite homogeneous dissipative self-gravitating Bose–Einstein condensate described by generalized Gross–Pitaevskii–Poisson equations [Chavanis, P.H. Eur. Phys. J. Plus2017, 132, 248]. This problem has applications in relation to the formation of dark matter halos in cosmology. We consider the case of a static and an expanding universe. We take into account an arbitrary form of repulsive or attractive self-interaction between the bosons (an attractive self-interaction being particularly relevant for the axion). We consider both gravitational and hydrodynamical (tachyonic) instabilities and determine the maximum growth rate of the instability and the corresponding wave number. We study how they depend on the scattering length of the bosons (or more generally on the squared speed of sound) and on the friction coefficient. Previously obtained results (notably in the dissipationless case) are recovered in particular limits of our study.

On the phase-space structure of galaxy clusters from cosmological simulations

ABSTRACT Cosmological N-body simulations represent an excellent tool to study the formation and evolution of dark matter (DM) haloes and the mechanisms that have originated the universal profile at the largest mass scales in the Universe. In particular, the combination of the velocity dispersion σv with the density ρ can be used to define the pseudo-entropy $S(r)=\sigma _\mathrm{v}^2/\rho ^{\, 2/3}$, whose profile is well described by a simple power law $S\propto \, r^{\, \alpha }$. We analyse a set of cosmological hydrodynamical re-simulations of massive galaxy clusters and study the pseudo-entropy profiles as traced by different collisionless components in simulated galaxy clusters: DM, stars, and substructures. We analyse four sets of simulations, exploring different resolution and physics (N-body and full hydrodynamical simulations) to investigate convergence and the impact of baryons. We find that baryons significantly affect the inner region of pseudo-entropy profiles as traced by substructures, while DM particles profiles are characterized by an almost universal behaviour, thus suggesting that the level of pseudo-entropy could represent a potential low-scatter mass-proxy. We compare observed and simulated pseudo-entropy profiles and find good agreement in both normalization and slope. We demonstrate, however, that the method used to derive observed pseudo-entropy profiles could introduce biases and underestimate the impact of mergers. Finally, we investigate the pseudo-entropy traced by the stars focusing our interest in the dynamical distinction between intracluster light and the stars bound to the brightest cluster galaxy: the combination of these two pseudo-entropy profiles is well described by a single power law out to almost the entire cluster virial radius.

Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics

We develop the theory of weak wave turbulence in systems described by the Schr\"odinger-Helmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schr\"odinger equation, and the Schr\"odinger-Newton equations. The latter, in three dimensions, are a nonrelativistic model of fuzzy dark matter which has a nonlocal gravitational self-potential, and in two dimensions they describe nonlocal nonlinear optics in the paraxial approximation. We show that in the weakly nonlinear limit the Schr\"odinger-Helmholtz equations have a simultaneous inverse cascade of particles and a forward cascade of energy. We interpret the inverse cascade as a nonequilibrium condensation process, which is a precursor to structure formation at large scales (for example the formation of galactic dark matter haloes or optical solitons). We show that for the Schr\"odinger-Newton equations in two and three dimensions, and in the two-dimensional nonlinear Schr\"odinger equation, the particle and energy fluxes are carried by small deviations from thermodynamic distributions, rather than the Kolmogorov-Zakharov cascades that are familiar in wave turbulence. We develop a differential approximation model to characterise such "warm cascade" states.

Dark matter simulations with primordial black holes in the early Universe

ABSTRACTPrimordial black holes (PBH) with masses of order $10\!-\!30 \, \mathrm{M}_\odot$ have been proposed as a possible explanation of the gravitational waves emission events recently discovered by the Laser Interferometer Gravitational-Wave Observatory (LIGO). If true, then PBHs would constitute a sizeable fraction of the dark matter component in the Universe. Using a series of cosmological N-body simulations that include both dark matter and a variable fraction of PBHs ranging from fPBH = 10−4 to fPBH = 1, we analyse the processes of formation and disruption of gravitationally bound PBH pairs, as well as the merging of both bound and unbound pairs, and estimate the probabilities of such events. We show that they are in good agreement with the constrains to the PBH abundance obtained by the LIGO and other research groups. We find that pair stability, while being a main factor responsible for the merger rate, is significantly affected by the effects of dark matter halo formation and clustering. As a side result, we also evaluate the effects of numerical errors in the stability of bound pairs, which can be useful for future research using this methodology.