Fuzzy dark matter (FDM) or wave dark matter is an alternative theory designed to solve the small-scale problems faced by the standard cold dark matter proposal for the primary material component of the universe. It is made up of ultra-light axions having mass $\sim 10^{-22}$ eV that typically have de Broglie wavelength of several kpc, alleviating some of the apparent small-scale discrepancies faced by the standard $Λ$CDM paradigm. In this paper, we calculate the halo mass function for the fuzzy dark matter using a sharp-k window function and compare it with one calculated using numerical simulations, finding the peak mass at roughly $10^{10} {M_{\odot}}$ for a particle mass of $2\times 10^{-22}$ eV. We also constrain the mass of FDM particle to be $\gtrapprox 2\times10^{-22}$ eV using the observations of high-redshift ($z\sim 10$) lensed galaxies from CLASH survey.
Ultralight bosonic dark matter called fuzzy dark matter (FDM) has attracted much attention as an alternative to the cold dark matter. An intriguing feature of the FDM model is the presence of a soliton core, a stable dense core formed at the center of halos. In this paper, we analytically study the dependence of the soliton core properties on the halo characteristics by solving approximately the Schrödinger-Poisson equation. Focusing on the ground-state eigenfunction, we derive a key expression for the soliton core radius, from which we obtain the core-halo mass relations similar to those foun…
Dark matter models involving a very light bosonic particle, generally known as Fuzzy Dark Matter (FDM), have been recently attracting great interest in the cosmology community, as their wave-like phenomenology would simultaneously explain the longstanding mis-detection of a dark matter particle and help easing the small-scale issues related to the standard Cold Dark Matter (CDM) scenario. With the present work, we initiate a series of papers aiming at investigating the evolution of FDM structures in a cosmological framework performed with our N-body code AX-GADGET, detailing for the first time…
Fuzzy dark matter (FDM), a scalar particle coupled to the gravitational field without self-interaction whose mass range is $m \sim 10^{-24} - 10^{-20}\ \rm{eV}$, is one of the promising alternative dark matter candidates to cold dark matter. The quantum interference pattern, which is a unique structure of FDM, can be seen in halos in cosmological FDM simulations. In this paper, we first provide an analytic model of the sub-galactic matter power spectrum originating from quantum clumps in FDM halos, in which the density distribution of the FDM is expressed by a superposition of quantum clumps w…
The fuzzy dark matter (FDM) scenario has received increased attention in recent years due to the small-scale challenges of the vanilla Lambda cold dark matter ($Λ$CDM) cosmological model and the lack of any experimental evidence for any candidate particle. In this study, we use cosmological $N$-body simulations to investigate high-redshift dark matter halos and their responsiveness to an FDM-like power spectrum cutoff on small scales in the primordial density perturbations. We study halo density profiles, shapes and alignments in FDM-like cosmologies (the latter two for the first time) by prov…
A Fuzzy Dark Matter (FDM) halo consists of a soliton core close to the center and an NFW-like density profile in the outer region. Previous investigations found that the soliton core exhibits temporal oscillations and random walk excursions around the halo center. Analyzing a set of numerical simulations, we show that both phenomena can be understood as the results of wave interference -- a suitable superposition of the ground (solitonic) state and excited states in a fixed potential suffices to account for the main features of these phenomena. Such an eigenmode analysis can shed light on the …
In the fuzzy dark matter (FDM) model, gravitationally collapsed objects always consist of a solitonic core located within a virialised halo. Although various numerical simulations have confirmed that the collapsed structure can be described by a cored NFW like density profile, there is still disagreement about the relation between the core mass and the halo mass. To fully understand this relation, we have assembled a large sample of cored haloes based on both idealised soliton mergers and cosmological simulations with various box sizes. We find that there exists a sizeable dispersion in the co…
We numerically study the movement of two colliding fuzzy dark matter solitons without explicit self-interaction and find the effective cross section of dissipative change in velocity. The cross section turns out to be inversely proportional to the velocity cubed, and we present its analytic interpretation. Using the result we roughly estimate spatial offsets during head-on collisions of two fuzzy dark matter halos, which can be related to the spatial offsets between stars and dark matter in collisions of some galaxy clusters. We also show that the gravitational cooling plays an important role …
We present zoom-in simulations of fuzzy dark matter (FDM) halos including baryons and star-formation with sufficient resolution to follow the formation and evolution of central solitons. We find that their properties are determined by the local dark matter velocity dispersion in the combined dark matter-baryon gravitational potential. This motivates a simple prescription to estimate the radial density profiles of FDM cores in the presence of baryons. As cores become more massive and compact if baryons are included, galactic rotation curve measurements are likely harder to reconcile with FDM.
We perform a numerical comparison between the fuzzy dark matter model and the cold dark matter model, focusing on formation of satellite galaxy planes around massive galaxies. Such galactic dynamics with controlled initial subhalo configurations are investigated using GADGET2 for the cold dark matter and PyUltraLight for the fuzzy dark matter, respectively. We demonstrate that satellite galaxies in the fuzzy dark matter side have a tendency to form more flattened and corotating satellite systems than in the cold dark matter side mainly due to the dissipation by the gravitational cooling effect…
We present the results of a full cosmological simulation with the new code SCALAR, where dark matter is in form of fuzzy dark matter, described by a light scalar field with a mass of $m_{\rm B} = 2.5 \times 10^{-22}$ eV and evolving according to the Schrödinger-Poisson system of equations. In comoving units, the simulation volume is $2.5 ~ h^{-1} {\rm Mpc}$ on a side, with a resolution of $20~h^{-1}{\rm pc}$ at the finest refinement level. We analyse the formation and the evolution of central solitonic cores, which are found to leave their imprints on dark matter density profiles, resulting in…
Based on a set of cosmological N-body simulations we analyze properties of the dark matter haloes (DM) in a galaxy mass range ($10^{11} - 10^{13} h^{-1}M_{\odot}$) in modified $\lcdm$ cosmology with additional dynamically screened scalar interactions in DM sector. Our simulations show that scalar interactions support picture of the Island Universe. Rapid structure formation processes are shifted into higher redshifts resulting in a much smaller accretion and merging rates for galactic haloes at low redshifts. Finally, we present how this "fifth" force affects halo properties, like density prof…
We present a method for generating suites of dark-matter halo catalogs with only a few $N$-body simulations, focusing on making small changes to the underlying cosmology of a simulation with high precision. In the context of blind challenges, this allows us to reuse a simulation by giving it a new cosmology after the original cosmology is revealed. Starting with full $N$-body realizations of an original cosmology and a target cosmology, we fit a transfer function that displaces halos in the original so that the galaxy/HOD power spectrum matches that of the target cosmology. This measured trans…
We study the distribution of intragroup dark matter in small groups of dark matter halos of galaxy-like size in a LCDM cosmology. These groups are identified using a physical criterion and may be an appropriate representation of small galaxy groups. We quantify the amount of intragroup dark matter and characterize its distribution. We find that compact associations of halos, as well as those intermediate and loose groups, have rather flat intragroup dark matter profiles with logarithmic slopes of gamma ~0 and ~-0.2$, respectively. Hence, the intragroup dark matter of these halo systems does no…
Axion-like particle (ALP) dark matter shows distinctive behavior on scales where wavelike effects dominate over self-gravity. Ultralight axions are candidates for fuzzy dark matter (FDM) whose de Broglie wavelength in virialized halos reaches scales of kiloparsecs. Important features of FDM scenarios are the formation of solitonic halo cores, suppressed small-scale perturbations, and enhanced gravitational relaxation. More massive ALPs, including the QCD axion, behave like CDM on galactic scales but may be clumped into axion miniclusters if they were produced after inflation. Just as FDM halos…
The statistics of dark matter halos is an essential component of understanding the nonlinear evolution in modified gravity cosmology. Based on a series of modified gravity N-body simulations, we investigate the halo mass function, concentration and bias. We model the impact of modified gravity by a single parameter ζ, which determines the enhancement of particle acceleration with respect to GR, given the identical mass distribution (ζ=1 in GR). We select snapshot redshifts such that the linear matter power spectra of different gravity models are identical, in order to isolate the impact of gra…
Stability properties of gravitationally bound condensates composed of ultralight axionic Fuzzy Dark Matter (FDM) are studied. Previous work has shown that astrophysical collisions could make self-gravitating condensates structurally unstable, making them prone to collapse and decay; in the context of FDM, we reexamine the relevant timescales using the time-dependent variational method. We show that FDM condensates can be made unstable through gravitational interactions with central black holes, for black hole masses in a phenomenologically relevant range. Instability could also be stimulated b…
We derive the halo mass function (HMF) for fuzzy dark matter (FDM) by solving the excursion set problem explicitly with a mass-dependent barrier function, which has not been done before. We find that compared to the naive approach of the Sheth--Tormen HMF for FDM, our approach has a higher cut off mass and the cut off mass changes less strongly with redshifts. Using merger trees constructed with a modified version of the Lacey & Cole formalism that accounts for suppressed small scale power and the scale-dependent growth of FDM haloes and the semi-analytic GALACTICUS code, we study the statisti…
We use a large suite of N-body simulations to study departures from universality in halo abundances and clustering in cosmologies with non-vanishing neutrino masses. To this end, we study how the halo mass function and halo bias factors depend on the scaling variable $σ^2(M,z)$, the variance of the initial matter fluctuation field, rather than on halo mass $M$ and redshift $z$ themselves. We show that using the variance of the cold dark matter rather than the total mass field, i.e., $σ^2_{cdm}(M,z)$ rather than $σ^2_{m}(M,z)$, yields more universal results. Analysis of halo bias yields similar…
The mass assembly of a whole population of sub-Milky Way galaxies is studied by means of hydrodynamical simulations within the $Λ$-CDM cosmology. Our results show that while dark halos assemble hierarchically, in stellar mass this trend is inverted in the sense that the smaller the galaxy, the later is its stellar mass assembly on average. Our star formation and supernovae feedback implementation in a multi-phase interstellar medium seems to play a key role on this process. However, the obtained downsizing trend is not yet as strong as observations show.
The EDGES experiment recently announced evidence for a broad absorption feature in the sky-averaged radio spectrum around 78 MHz, as may result from absorption in the 21 cm line by neutral hydrogen at z~15-20. If confirmed, one implication is that the spin temperature of the 21 cm line is coupled to the gas temperature by z=20. The known mechanism for accomplishing this is the Wouthuysen-Field effect, whereby Lyman-alpha photons scatter in the intergalactic medium (IGM) and impact the hyperfine level populations. This suggests that early star formation had already produced a copious Lyman-alph…
Fuzzy Dark Matter (FDM) represents an alternative and intriguing description of the standard Cold Dark Matter (CDM) fluid, able to explain the lack of direct detection of dark matter particles in the GeV sector and to alleviate small scales tensions in the cosmic large-scale structure formation. Cosmological simulations of FDM models in the literature were performed either with very expensive high-resolution grid-based simulations of individual haloes or through N-body simulations encompassing larger cosmic volumes but resorting on significant approximations in the FDM non-linear dynamics to r…
In this paper we study the triaxial properties of dark matter haloes of a wide range of masses extracted from a set of cosmological N-body simulations. We measure the shape at different distances from the halo centre (characterised by different overdensity thresholds), both in three and in two dimensions. We discuss how halo triaxiality increases with mass, redshift and distance from the halo centre. We also examine how the orientation of the different ellipsoids are aligned with each other and what is the gradient in internal shapes for halos with different virial configurations. Our findings…
We use high resolution N-body simulations to investigate the Lagrangian bias of cold dark matter haloes within the LCDM cosmology. Our analysis focuses on "proto-haloes", which we identify in the simulation initial conditions with the subsets of particles belonging to individual redshift-zero haloes. We then calculate the number-density and velocity-divergence fields of proto-haloes and estimate their auto spectral densities. We also measure the corresponding cross spectral densities with the linear matter distribution. We use our results to test a Lagrangian-bias model presented by Desjacques…
We study the concentration of dark matter halos and its evolution in N-body simulations of the standard LCDM cosmology. The results presented in this paper are based on 4 large N-body simulations with about 10 billion particles each: the Millennium-I and II, Bolshoi, and MultiDark simulations. The MultiDark (or BigBolshoi) simulation is introduced in this paper. This suite of simulations with high mass resolution over a large volume allows us to compute with unprecedented accuracy the concentration over a large range of scales (about six orders of magnitude in mass), which constitutes the stat…
We use observations of ultra-faint dwarf (UFD) galaxies to constrain the particle mass of ultra-light dark matter. Potential fluctuations created by wave interference in virialized "fuzzy" dark matter (FDM) halos dynamically heat stellar orbits in UFDs, some of which exhibit velocity dispersions of $\lesssim$ 3 km/s and sizes $\lesssim$ 40 pc. Using simulations of FDM halos, and existing measurements of sizes and stellar radial velocities in Segue 1 and Segue 2 UFDs, we derive a lower limit on the dark matter particle mass of $m_{fdm} > 3\times 10^{-19}$ eV at 99% confidence, marginalized over…
Fuzzy dark matter (FDM) made of ultra-light bosonic particles is a viable alternative to cold dark matter (CDM) with clearly distinguishable small-scale features in collapsed structures. On large scales, it behaves gravitationally like CDM deviating only by a cut-off in the initial power spectrum and can be studied using N-body methods. In contrast, wave interference effects near the de Broglie scale result in new phenomena unique to FDM. Interfering modes in filaments and halos yield a stochastically oscillating granular structure which condenses into solitonic cores during halo formation. In…
We study the impact of theoretical uncertainty in the dark matter halo mass function and halo bias on dark energy constraints from imminent galaxy cluster surveys. We find that for an optical cluster survey like the Dark Energy Survey, the accuracy required on the predicted halo mass function to make it an insignificant source of error on dark energy parameters is ~ 1%. The analogous requirement on the predicted halo bias is less stringent (~ 5%), particularly if the observable-mass distribution can be well constrained by other means. These requirements depend upon survey area but are relative…
New statistical properties of dark matter halos in Lagrangian space are presented. Tracing back the dark matter particles constituting bound halos resolved in a series of N-body simulations, we measure quantitatively the correlations of the proto-halo's inertia tensors with the local tidal tensors and investigate how the correlation strength depends on the proto-halo's sphericity, local density and filtering scale. It is shown that the majority of the proto-halos exhibit strong correlations between the two tensors provided that the tidal field is smoothed on the proto-halo's mass scale. The co…
Whereas cold dark matter (CDM) simulations predict central dark matter cusps with densities that diverge as $ρ$(r)$\sim$ 1/r observations often indicate constant density cores with finite central densities $ρ_0$ and a flat density distribution within a core radius r$_0$. This paper investigates whether this core-cusp problem can be solved by fuzzy dark matter (FDM), a hypothetical particle with a mass of order m$\approx$10$^{-22}$eV and a corresponding de Broglie wavelength on astrophysical scales. We show that galaxies with CDM halo virial masses M$_{vir} \leq 10^{11}$M$_{\odot}$ follow two c…
The concentrations of dark matter haloes provide crucial information about their internal structure and how it depends on mass and redshift -- the so-called concentration-mass-redshift relation, denoted $c(M,z)$. We present here an extensive study of the cosmology-dependence of $c(M,z)$ that is based on a suite of 72 gravity-only, full N-body simulations in which the following cosmological parameters were varied: $σ_{8}$, $Ω_{\mathrm{M}}$, $Ω_{\mathrm{b}}$, $n_{\mathrm{s}}$, $h$, $M_ν$, $w_{0}$ and $w_{\mathrm{a}}$. We characterize the impact of these parameters on concentrations for different…
We present the results obtained from the full-shape cosmology analysis of the redshift-space power spectra for 4 galaxy samples of the SDSS-III BOSS DR12 galaxy catalog over $0.2 < z < 0.75$. For the theoretical template, we use an emulator that was built from an ensemble set of $N$-body simulations, which enables fast and accurate computation of the redshift-space power spectrum of halos. Combining with the halo occupation distribution to model the halo-galaxy connection, we can compute the redshift-space power spectrum of BOSS-like galaxies in the flat $Λ$CDM cosmology. In our cosmology infe…
Institute of Astrophysics, National Taiwan University（台湾大学天文研究所）；Department of Physics, National Taiwan University（台湾大学物理系）；Center for Theoretical Physics, National Taiwan University（台湾大学理论物理中心）；National Center for Theoretical Sciences（国家理论科学中心）
Fuzzy dark matter of ultra-light axions has gained attention, largely in light of the galactic scale problems associated with cold dark matter. But the large de Broglie wavelength, believed to possibly alleviate these problems, also leads to fluctuations that place constraints on ultra-light axions. We adapt and extend a method, previously devised to describe the effect of gaseous fluctuations on cold dark matter cusps, in order to determine the imprints of ultra-light axion haloes on the motion of classical test particles. We first evaluate the effect of fluctuations in a statistically homoge…
The halo mass function (HMF) is a critical element in cosmological analyses of galaxy cluster catalogs. We quantify the impact of uncertainties in HMF parameters on cosmological constraints from cluster catalogs similar to those from Planck, those expected from the Euclid, Roman and Rubin surveys, and from a hypothetical larger future survey. We analyse simulated catalogs in each case, gradually loosening priors on HMF parameters to evaluate the degradation in cosmological constraints. While current uncertainties on HMF parameters do not substantially impact Planck-like surveys, we find that t…
The splashback radius $R_{\rm sp}$, the apocentric radius of particles on their first orbit after falling into a dark matter halo, has recently been suggested as a physically motivated halo boundary that separates accreting from orbiting material. Using the SPARTA code presented in Paper I, we analyze the orbits of billions of particles in cosmological simulations of structure formation and measure $R_{\rm sp}$ for a large sample of halos that span a mass range from dwarf galaxy to massive cluster halos, reach redshift 8, and include WMAP, Planck, and self-similar cosmologies. We analyze the d…
Using cosmological N-body simulations, we study the abundance of local maxima (peaks) and minima (dips) identified in the smoothed distribution of halos and dark matter (DM) on scales of $10-100$s Mpcs. The simulations include Gaussian and local-type $f_{\rm NL}$ non-Gaussian initial conditions. The expression derived in the literature for the abundance (irrespective of height) of peaks for Gaussian fields is surprisingly accurate for the evolved halo and DM density fields for all initial conditions considered. Furthermore, the height distribution is very well fitted by a log-normal on quasi-l…
The structural and dynamic properties of the dark matter halos, though an important ingredient in understanding large-scale structure formation, require more conservative particle resolution than those required by halo mass alone in a simulation. This reduces the parameter space of the simulations, more severely for high-redshift and large-volume mocks which are required by the next-generation large sky surveys. Here, we incorporate redshift and cosmology dependence into an algorithm that assigns accurate halo properties such as concentration, spin, velocity, and spatial distribution to the su…
Recent advances in observational astronomy allow to study various groups of Dark Matter (DM) dominated objects from the dwarf spheroidal (dSph) galaxies to clusters of galaxies that span the mass range from $10^{6} M_{\odot}$ to $10^{15} M_{\odot}$. To analyze data of this divers collection of objects we used a simple toy model of spherical DM halo formation that was initially proposed by Peebles. This model introduced the concept of the epoch or redshift of halo formation. Using this concept we analyzed selected sample of DM dominated objects and we have found empirical correlations between t…
The evolution of galaxy cluster counts is a powerful probe of several fundamental cosmological parameters. A number of recent studies using this probe have claimed tension with the cosmology preferred by the analysis of the Planck primary CMB data, in the sense that there are fewer clusters observed than predicted based on the primary CMB cosmology. One possible resolution to this problem is systematic errors in the absolute halo mass calibration in cluster studies, which is required to convert the standard theoretical prediction (the halo mass function) into counts as a function of the observ…
Scalar Field Dark Matter (SFDM), comprised of ultralight ($\gtrsim 10^{-22}$ eV) bosons, is distinguished from massive ($\gtrsim$ GeV), collisionless Cold Dark Matter (CDM) by its novel structure-formation dynamics as Bose-Einstein condensate (BEC) and quantum superfluid with wave-like properties, described by the Gross-Pitaevski and Poisson (GPP) equations. In the free-field (fuzzy) limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength $λ_{\text{deB}}$, but resembles CDM on larger scales. Virialized haloes have solitonic cores of radius $\sim λ_{\text{deB}}$ that follow …
