The halo spin-spin correlation function, $η(r)$, measures how rapidly the strength of the alignments of the spin directions between the neighbor halos change with the separation distance, $r$. The previous model based on the tidal torque theory expresses the halo spin-spin correlation function as a power of the linear density two-point correlation function, $η(r)\propto ξ^{n}(r)$, predicting $n=2$ in the linear regime and $n=1$ in the non-linear regime. Using a high-resolution N-body simulation, we show that the halo spin-spin correlation function in fact drops much less rapidly with $r$ than the prediction of the previous model, finding $η(r)$ to be statistically significant even at $r\ge 10\,h^{-1}$Mpc on the dwarf galaxy scale. Claiming that the anisotropic tidal effect is responsible for the failure of the previous model, we propose a new formula for the halo spin-spin correlation function expressed in terms of the integrals of $ξ(r)$. The new formula with the best-fit parameters turns out to agree excellently with the numerical results in a broad mass range, $0.05\le M/(10^{11}\,h^{-1}\,M_{\odot})\le 50$, describing well the large-scale tail of $η(r)$. We discuss a possibility of using the large-scale spin-spin correlations of the dwarf galactic halos as a complementary probe of dark matter.
We study how halo intrinsic dynamical properties are linked to their formation processes for halos in two mass ranges, $10^{12}-10^{12.5}h^{-1}{\rm M_\odot}$ and $\ge 10^{13}h^{-1}{\rm M_\odot}$, and how both are correlated with the large scale tidal field within which the halos reside at present. Halo merger trees obtained from cosmological $N$-body simulations are used to identify infall halos that are about to merge with their hosts. We find that the tangential component of the infall velocity increases significantly with the strength of the local tidal field, but no strong correlation is f…
Large scale tidal field estimated directly from the distribution of dark matter halos is used to investigate how halo shapes and spin vectors are aligned with the cosmic web. The major, intermediate and minor axes of halos are aligned with the corresponding tidal axes, and halo spin axes tend to be parallel with the intermediate axes and perpendicular to the major axes of tidal field. The strengths of these alignments generally increase with halo mass and redshift, but the dependencies are only through the peak height, ν. The scaling relations of the alignment strengths with the value of ν ind…
We use seven high-resolution $N$-body simulations to study the correlations among different halo properties (assembly time, spin, shape and substructure), and how these halo properties are correlated with the large-scale environment in which halos reside. The large-scale tidal field estimated from halos above a mass threshold is used as our primary quantity to characterize the large-scale environment, while other parameters, such as the local overdensity and the morphology of large-scale structure, are used for comparison. For halos at a fixed mass, all the halo properties depend significantly…
We delineate the conditions under which the consistency relation for the non-Gaussian bias and the universality of the halo mass function hold in the context of microscopic Lagrangian descriptions of halos. The former is valid provided that the collapse barrier depends only on the physical fields (instead of fields normalized by their variance for example) and explicitly includes the effect of {\it all} physical fields such as the tidal shear. The latter holds provided that the response of the halo number density to a long-wavelength density fluctuation is equivalent to the response induced by…
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 the reconstructed large-scale density field correlates well with the original matter density field on large scales, …
We investigate impacts of long-wavelength gravitational waves (GWs) on nonlinear structure formation by utilizing the tidal separate universe simulations. Based on the equivalence of a long-wavelength GW to a uniform tidal field in a local frame, we provide a way to incorporate a long-wavelength GW into the tidal separate universe simulation as an effective anisotropic expansion. This methodology enables us to study effects of GWs on large-scale structure efficiently. We measure the anisotropic imprint in the local power spectrum from the tidal separate universe simulations with GWs, which cor…
Galaxies on the largest scales of the Universe are observed to be embedded in the filamentary cosmic web which is shaped by the nonlinear tidal field. As an efficient tool to quantitatively describe the statistics of this cosmic web, we present the anisotropic two-point correlation functions of the nonlinear traceless tidal field in the principal-axis frame, which are measured using numerical data from an N-body simulation. We show that both of the nonlinear density and traceless tidal fields are more strongly correlated along the directions perpendicular to the eigenvectors associated with th…
A numerical evidence for the dependence of the substructure abundance of cluster halos on the orientation coherence of the surrounding tidal fields is presented. Applying the adapted minimal spanning tree (MST) algorithm to the cluster halos with $M\ge 10^{14}\,h^{-1}\,M_{\odot}$ from the Big MultiDark-Planck Simulations, we identify primary MST stems composed of multiple nodes as the filaments and measure their specific sizes (spatial extents per node), which quantify the orientation coherence of the tidal field on the cluster scales. Classifying the cluster halos into five samples by the spe…
We present anisotropic "separate universe" simulations which modify the N-body code Gadget-4 in order to represent a large-scale tidal field through an anisotropic expansion factor. These simulations are used to measure the linear, quasi-linear and nonlinear response of the matter power spectrum to a spatially uniform trace-free tidal field up to wavenumber $k = 7 h \text{Mpc}^{-1}$. Together with the response to a large-scale overdensity measured in previous work, this completely describes the nonlinear matter bispectrum in the squeezed limit. We find that the response amplitude does not appr…
The relation between the clustering properties of luminous matter in the form of galaxies and the underlying dark matter distribution is of fundamental importance for the interpretation of ongoing and upcoming galaxy surveys. The so called local bias model, where galaxy density is a function of local matter density, is frequently discussed as a means to infer the matter power spectrum or correlation function from the measured galaxy correlation. However, gravitational evolution generates a term quadratic in the tidal tensor and thus non-local in the density field, even if this term is absent i…
The tidal torque theory (TTT) relates the origin and evolution of angular momentum with the environment in which dark matter (DM) haloes form. The deviations introduced by late non-linearities are commonly thought as noise in the model. In this work, we analyze a cosmological simulation looking for systematics on these deviations, finding that the classification of DM haloes according to their angular momentum growth results in samples with different internal alignment, spin parameter distribution and assembly history. Based on this classification, we obtain that low mass haloes are embedded i…
N-body simulations have revealed a wealth of information about dark matter halos however their results are largely empirical. Using analytic means, we attempt to shed light on simulation results by generalizing the self-similar secondary infall model to include tidal torque. In this first of two papers, we describe our halo formation model and compare our results to empirical mass profiles inspired by N-body simulations. Each halo is determined by four parameters. One parameter sets the mass scale and the other three define how particles within a mass shell are torqued throughout evolution. We…
In the present work, we extend the classic halo model for the large-scale matter distribution including a triaxial model for the halo profiles and their alignments. In particular, we derive general expressions for the halo-matter cross correlation function. In addition, by numerical integration, we obtain instances of the cross-correlation function depending on the directions given by halo shape axes. These functions are called anisotropic cross-correlations. With the aim of comparing our theoretical results with the simulations, we compute averaged anisotropic correlations in cones with their…
Gravitational lensing observations of massive X-ray clusters imply a steep characteristic density profile marked by a central concentration of dark matter. The observed mass fraction within a projected radius of 150 kpc is twice that found in state-of-the-art dark matter simulations of the standard Lambda-CDM cosmology. A central baryon enhancement that could explain this discrepancy is not observed, leaving a major puzzle. We propose a solution based on the merger histories of clusters. A significant fraction of the final dark matter content of a cluster halo originates within galaxy-sized ha…
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…
We revisit the question of what mechanism is responsible for the spins of halos of dark matter. The answer to this question is of high importance for modeling galaxy intrinsic alignment, which can potentially contaminate current and future lensing data. In particular, we show that when the dark matter halos pass nearly by each other in dense environments-- namely halo assemblies-- they swing and spin each other via exerting mutual tidal torques. We show that this has a significant contribution to the spin of dark matter halos comparable to that of calculated by the so-called tidal torque theor…
We study the alignment of dark matter haloes with the cosmic web characterized by the tidal and velocity shear fields. We focus on the alignment of their shape, angular momentum and peculiar velocities. We use a cosmological N-body simulation that allows to study dark matter halos spanning almost five orders of magnitude in mass ($10^{9}$-$10^{14}$) $h^{-1}$$M_{\odot}$ and spatial scales of $(0.5$-$1.0)$ $h^{-1}$ Mpc to define the cosmic web. We find that the halo shape presents the strongest alignment along the smallest tidal eigenvector, e.g. along filaments and walls, with a signal that get…
The well-developed separate universe technique enables accurate calibration of the response of any observable to an isotropic long-wavelength density fluctuation. The large-scale environment also hosts tidal modes that perturb all observables anisotropically. As in the separate universe, both the long tidal and density modes can be absorbed by an effective anisotropic background, on which the interaction and evolution of the short modes change accordingly. We further develop the tidal simulation method, including proper corrections to the second order Lagrangian perturbation theory (2LPT) to g…
We discuss the properties of subhalos in cluster-size halos, using a high-resolution statistical sample: the Rhapsody simulations introduced in Wu et al. (2012). We demonstrate that the criteria applied to select subhalos have significant impact on the inferred properties of the sample, including the scatter in the number of subhalos, the correlation between the subhalo number and formation time, and the shape of subhalos' spatial distribution and velocity structure. We find that the number of subhalos, when selected using the peak maximum circular velocity in their histories (a property expec…
In this paper we carry out anisotropic "separate universe" simulations by including a large-scale tidal field in the N-body code \textsc{gadget}4 using an anisotropic expansion factor $A_{ij}$. We use the code in a pure \textit{particle-mesh} (PM) mode to simulate the evolution of 16 realizations of an initial density field with and without a large-scale tidal field, which are then used to measure the \textit{response function} describing how the tidal field influences structure formation in the linear and non-linear regimes. Together with the previously measured response to a large scale over…
We use deep V-band surface photometry of five of the brightest elliptical galaxies in the Virgo cluster to search for diffuse tidal streams, shells, and plumes in their outer halos (r > 50 kpc). We fit and subtract elliptical isophotal models from the galaxy images to reveal a variety of substructure, with surface brightnesses in the range mu_V= 26-29 mag/arcsec^2. M49 possesses an extended, interleaved shell system reminiscent of the radial accretion of a satellite companion, while M89's complex system of shells and plumes suggests a more complicated accretion history involving either multipl…
The non-linear cosmic web environment of dark matter haloes plays a major role in shaping their growth and evolution, and potentially also affects the galaxies that reside in them. We develop an analytical (halo model) formalism to describe the tidal field of anisotropic halo-centric density distributions, as characterised by the halo-centric tidal tensor $\langle T_{ij} \rangle(<R)$ spherically averaged on scale $R\sim4R_{\rm vir}$ for haloes of virial radius $R_{\rm vir}$. We focus on axisymmetric anisotropies, which allows us to explore simple and intuitive toy models of (sub)halo configura…
We present a numerical evidence supporting the claim that the mass-dependent transitions of the halo spin orientations from the intermediate to the minor principal directions of the local tidal fields can in principle be a useful discriminator of dark energy models. We first define a spin transition zone as the mass range of the halos, $Δm_{t}$, for which the intrinsic spin alignments with the minor tidal principal directions become as strong as that with the intermediate principal directions. Then, utilizing the halo samples from the DEUS simulations performed separately for the WMAP7 $Λ$CDM,…
We study the effect of large-scale tidal fields on internal halo properties using a set of N-body simulations. We measure significant cross-correlations between large-scale tidal fields and several non-scalar halo properties: shapes, velocity dispersion, and angular momentum. Selection effects that couple to these non-scalar halo properties can produce anisotropic clustering even in real-space. We investigate the size of this effect and show that it can produce a non-zero quadrupole similar in size to the one generated by linear redshift-space distortions (RSD). Finally, we investigate the clu…
To generate initial conditions for cosmological $N$-body simulations, one needs to prepare a uniform distribution of simulation particles, so-called the pre-initial condition (pre-IC). The standard method to construct the pre-IC is to place the particles on the lattice grids evenly spaced in the three-dimensional spatial coordinates. However, even after the initial displacement of each particle according to cosmological perturbations, the particle distribution remains to display an artificial anisotropy. Such an artifact causes systematic effects in simulations at later time until the evolved …
In the cold dark matter paradigm, structures form hierarchically, implying that large structures contain smaller substructures. These subhalos will enhance signatures of dark matter annihilation such as gamma rays. In the literature, typical estimates of this boost factor assume a concentration-mass relation for field halos, to calculate the luminosity of subhalos. However, since subhalos accreted in the gravitational potential of their host loose mass through tidal stripping and dynamical friction, they have a quite characteristic density profile, different from that of the field halos of the…
Extensive photometric and spectroscopic surveys of the Andromeda galaxy (M31) have discovered tidal debris features throughout M31's stellar halo. We present stellar kinematics and metallicities in fields with identified substructure from our on-going SPLASH survey of M31 red giant branch stars with the DEIMOS spectrograph on the Keck II 10-m telescope. Radial velocity criteria are used to isolate members of the kinematically-cold substructures. The substructures are shown to be metal-rich relative to the rest of the dynamically hot stellar population in the fields in which they are found. We …
The anisotropy or triaxiality of massive dark matter haloes largely defines the structure of the cosmic web, in particular the filaments that join the haloes together. Here we investigate such oriented correlations in mass-Peak Patch halo catalogues by using the initial strain tensor of spherical proto-halo regions to orient the haloes. To go beyond the spherically averaged two-point correlation function of haloes we use oriented stacks to compute oriented two-point correlations: we explicitly break isotropy by imposing a local frame set by the strain tensor of the reference halo before stacki…
In the hierarchical formation model, galaxy clusters grow by accretion of smaller groups or isolated galaxies. During the infall into the centre of a cluster, the properties of accreted galaxies change. In particular, both observations and numerical simulations suggest that its dark matter halo is stripped by the tidal forces of the host. We use galaxy-galaxy weak lensing to measure the average mass of dark matter haloes of satellite galaxies as a function of projected distance to the centre of the host, for different stellar mass bins. Assuming that the stellar component of the galaxy is less…
Using $N$-body simulations of cosmological large-scale structure formation, for the first time, we show that the anisotropic primordial non-Gaussianity (PNG) causes a scale-dependent modification, given by $1/k^2$ at small $k$ limit, in the three-dimensional power spectra of halo shapes (intrinsic alignments), whilst the conventional power spectrum of halo number density field remains unaffected. We discuss that wide-area imaging and spectrocopic surveys observing the same region of the sky allow us to constrain the quadrupole PNG coefficient $f_{\rm NL}^{s=2}$ at a precision comparable with o…
We study the role of the local tidal environment in determining the assembly bias of dark matter haloes. Previous results suggest that the anisotropy of a halo's environment (i.e, whether it lies in a filament or in a more isotropic region) can play a significant role in determining the eventual mass and age of the halo. We statistically isolate this effect using correlations between the large-scale and small-scale environments of simulated haloes at $z=0$ with masses between $10^{11.6}\lesssim (m/h^{-1}M_{\odot})\lesssim10^{14.9}$. We probe the large-scale environment using a novel halo-by-ha…
We present direct measurements of cubic bias parameters of dark matter halos from the halo-matter-matter-matter trispectrum. We measure this statistic efficiently by cross-correlating the halo field measured in N-body simulations with specific third-order nonlocal transformations of the initial density field in the same simulation. Together with the recent Abidi & Baldauf (2018), these are the first measurements of halo bias using the four-point function that have been reported to date. We also obtain constraints on the quadratic bias parameters. For all individual cubic parameters involving t…
The gravitational coupling between large- and small-scale density perturbations leads to anisotropic distortions to the local small-scale matter fluctuations. Such local anisotropic distortions can be used to reconstruct the large-scale matter distribution, known as tidal reconstruction. In this paper, we apply the tidal reconstruction methods to simulated galaxies in redshift space. We find that redshift-space distortions lead to anisotropic reconstruction results. While the reconstructed radial modes are more noisy mainly due to the small-scale velocity dispersion, the transverse modes are s…
We propose a new method for generating equilibrium models of spherical systems of collisionless particles that are finite in extent, but whose central regions resemble dark matter halos from cosmological simulations. This method involves iteratively removing unbound particles from a Navarro-Frenk-White profile truncated sharply at some radius. The resulting models are extremely stable, and thus provide a good starting point for N-body simulations of isolated halos. We provide a code to generate such models for NFW and a variety of other common density profiles. We then develop an analytic appr…
The dark matter halos that surround Milky Way-like galaxies in cosmological simulations are, to first order, triaxial. Nearly 30 years ago it was predicted that such triaxial dark matter halos should exhibit steady figure rotation or tumbling motions for durations of several gigayears. The angular frequency of figure rotation predicted by cosmological simulations is described by a log-normal distribution of pattern speed with a median value 0.15hkm/s/kpc (~ 0.15h rad/Gyr ~ 9h deg/Gyr) and a width of 0.83km/s/kpc. These pattern speeds are so small that they have generally been considered both u…
The long-wavelength coherent overdensity and tidal force, which are not direct observables for a finite-volume survey, affect time evolution of cosmic structure formation and therefore clustering observables through the mode coupling. In this paper we develop an "anisotropic" separate universe (SU) simulation technique to simulate large-scale structure formation taking into account the effect of large-scale tidal force into the anisotropic expansion of local background. We modify the TreePM N-body simulation code to implement the anisotropic SU simulations, and then study the "response" functi…
Understanding the non-linear dynamics of satellite halos (a.k.a. "sub-halos") is important for predicting the abundance and distribution of dark matter substructures and satellite galaxies, and for distinguishing among microphysical dark matter models using observations. Typically, modeling these dynamics requires large N-body simulations with high resolution. Semi-analytic models can provide a more efficient way to describe the key physical processes such as dynamical friction, tidal mass loss, and tidal heating, with only a few free parameters. In this work, we present a fast Monte Carlo Mar…
We analyse the coarse-grained phase-space structure of the six Galaxy-scale dark matter haloes of the Aquarius Project using a state-of-the-art 6D substructure finder. Within r_50, we find that about 35% of the mass is in identifiable substructures, predominantly tidal streams, but including about 14% in self-bound subhaloes. The slope of the differential substructure mass function is close to -2, which should be compared to around -1.9 for the population of self-bound subhaloes. Near r_50 about 60% of the mass is in substructures, with about 30% in self-bound subhaloes. The inner 35 kpc of th…
We investigate the dependence of the mass function of dark-matter haloes on their environment within the cosmic web of large-scale structure. A dependence of the halo mass function on large-scale mean density is a standard element of cosmological theory, allowing mass-dependent biasing to be understood via the peak-background split. On the assumption of a Gaussian density field, this analysis can be extended to ask how the mass function depends on the geometrical environment: clusters, filaments, sheets and voids, as classified via the tidal tensor (the Hessian matrix of the gravitational pote…
We present a method to couple N-body star cluster simulations to a cosmological tidal field, using the Astrophysical Multipurpose Software Environment. We apply this method to star clusters embedded in the CosmoGrid dark matter-only LambdaCDM simulation. Our star clusters are born at z = 10 (corresponding to an age of the Universe of about 500 Myr) by selecting a dark matter particle and initializing a star cluster with 32,000 stars on its location. We then follow the dynamical evolution of the star cluster within the cosmological environment. We compare the evolution of star clusters in two M…
Observations of the lengthy tidal streams produced by the destruction of the Sagittarius dwarf spheroidal (Sgr dSph) are capable of providing strong constraints on the shape of the Galactic gravitational potential. However, previous work, based on modeling different stream properties in axisymmetric Galactic models has yielded conflicting results: while the angular precession of the Sgr leading arm is most consistent with a spherical or slightly oblate halo, the radial velocities of stars in this arm are only reproduced by prolate halo models. We demonstrate that this apparent paradox can be r…
Tunneling and tidal stripping in multifield ultralight dark matter halos
Center for Theoretical Physics—a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）；Department of Physics, Harvard University（哈佛大学物理系）；Universidad Autonoma de Madrid（马德里自治大学）；IFT-UAM/CSIC（乌阿姆/西班牙国家科学研究委员会理论物理研究所）
Dark matter halos grow by hierarchical clustering as they merge together to produce ever larger structures. During these merger processes, the smaller halo can potentially survive as a subhalo of the larger halo, so a galaxy-scale halo today likely possesses a rich abundance of substructure. This substructure can greatly boost the rate of dark matter annihilation within the host halo, but the precise magnitude of this boost is clouded by uncertainty about the survival prospects of these subhalos. In particular, tidal forces gradually strip material from the subhalos, reducing their annihilatio…
The alignment between halo spins and the cosmic web is still poorly understood despite being a widely studied topic. Here, we study this alignment within the context of tidal torque theory (TTT) and deviations from it. To this end, we analyze the evolution of the shape and spin direction of proto-haloes, i.e. of all the volume elements associated to a $z=0$ halo, with respect to the present-day filaments. We find that the major axis of proto-haloes undergoes a major change, from being strongly perpendicular to the filament spine in the initial conditions, to being preferentially aligned at the…
Gravitational collapse of a massive primordial gas cloud is thought to be a promising path for the formation of supermassive blackholes in the early universe. We study conditions for the so-called direct collapse (DC) blackhole formation in a fully cosmological context. We combine a semianalytic model of early galaxy formation with halo merger trees constructed from dark matter $N$-body simulations. We locate a total of 68 possible DC sites in a volume of $20\;h^{-1}\;\mathrm{Mpc}$ on a side. We then perform hydrodynamics simulations for 42 selected halos to study in detail the evolution of th…
The dwarf satellite galaxies of the Milky Way Crater II and Antlia II have uncommonly low dynamical mass densities, due to their large size and low velocity dispersion. Previous work have failed to identify formation scenarios within the $Λ$CDM framework and have invoked cored dark matter haloes, processed by tides. I show that the tidal evolution of $Λ$CDM NFW haloes is richer than previously recognised: tidal heating causes the innermost regions of haloes that fall short of the mass-concentration relation to expand significantly, resulting in the formation of giant, kinematically cold satell…
We develop an analytic model for galaxy intrinsic alignments (IA) based on the theory of tidal alignment. We calculate all relevant nonlinear corrections at one-loop order, including effects from nonlinear density evolution, galaxy biasing, and source density weighting. Contributions from density weighting are found to be particularly important and lead to bias dependence of the IA amplitude, even on large scales. This effect may be responsible for much of the luminosity dependence in IA observations. The increase in IA amplitude for more highly biased galaxies reflects their locations in regi…
The influence of the Cosmic Web on galaxy formation and evolution is of great observational and theoretical interest. We investigate whether the Cosmic Web leaves an imprint in the spatial clustering of galaxies in the Sloan Digital Sky Survey (SDSS), using the group catalog of Yang et al. and tidal field estimates at $\sim2h^{-1}$Mpc scales from the Mass-Tides-Velocity data set of Wang et al. We use the $\textit{tidal anisotropy}$ $α$ (Paranjape et al.) to characterise the tidal environment of groups, and measure the redshift-space 2-point correlation function (2pcf) of group positions and th…
There is a growing interest of using the intrinsic alignment (IA) of galaxy images as a tool to extract cosmological information complimentary to galaxy clustering analysis. Recently, Okumura & Taruya derived useful formulas for the intrinsic ellipticity--ellipticity correlation, the gravitational shear--intrinsic ellipticity correlation, and the velocity--intrinsic ellipticity correlation functions based on the linear alignment (LA) model. In this paper, using large-volume $N$-body simulations, we measure these alignment statistics in real and redshift space and compare them to the LA and non…
We present surface photometry of a giant, low surface brightness stellar arc in the halo of the nearby spiral galaxy M63 (NGC 5055) that is consistent with being a part of a stellar stream resulting from the disruption of a dwarf satellite galaxy. Using the stream's "great-circle" morphology and its photometric properties, we estimate that the stream originates from the accretion of a 10^8 M_sun satellite in the last few Gyr. The B-R color of the stream's stars is consistent with Local Group dwarfs and is also similar to the outer regions of M63's disk and stellar halo within our measurement u…
