Tidal Effects and the Environment Dependence of Halo Assembly
Oliver Hahn, Cristiano Porciani, Avishai Dekel, C. Marcella Carollo
备注：
16 pages, 13 figures, MNRASaccepted. significantly expanded discussion of the connection of tides, shear and assembly. Version with high-resolution figures available at http://www.exp-astro.phys.ethz.ch/hahn/pub/HPDC09.pdf
We explore a possible origin for the puzzling anti-correlation between the formation epoch of galactic dark-matter haloes and their environment density. This correlation has been revealed from cosmological N-body simulations and is in conflict with the Extended Press-Schechter model of halo clustering. Using similar simulations, we first quantify the straightforward association of an early formation epoch with a reduced mass growth rate at late times. We then find that a primary driver of suppressed growth, by accretion and mergers, is tidal effects dominated by a neighbouring massive halo. The tidal effects range from a slowdown of the assembly of haloes due to the shear along the large-scale filaments that feed the massive halo to actual mass loss in haloes that pass through the massive halo. Using the restricted three-body problem, we show that haloes are prone to tidal mass loss within 1.5 virial radii of a larger halo. Our results suggest that the dependence of formation epoch on environment density is a secondary effect induced by the enhanced density of haloes in filaments near massive haloes where the tides are strong. Our measures of assembly rate are particularly correlated with the tidal field at high redshifts z~1.
We investigate the origin of halo assembly bias, the dependence of halo clustering on assembly history. We relate halo assembly to peak properties measured in the Lagrangian space of the initial linear Gaussian random density field, and show how these same Lagrangian properties determine large-scale bias. We focus on the two regimes where assembly bias has been observed to be significant: at masses very large and very small compared to the nonlinear mass scale. At high masses, we show that assembly bias is expected from the statistics of the peaks of Gaussian random fluctuations, and we show t…
Using a high-resolution cosmological $N$-body simulation, we identify the ejected population of subhalos, which are halos at redshift $z=0$ but were once contained in more massive `host' halos at high redshifts. The fraction of the ejected subhalos in the total halo population of the same mass ranges from 9% to 4% for halo masses from $\sim 10^{11}$ to $\sim 10^{12}\msun$. Most of the ejected subhalos are distributed within 4 times the virial radius of their hosts. These ejected subhalos have distinct velocity distribution around their hosts in comparison to normal halos. The number of subhalo…
The clustering of dark halos depends not only on their mass but also on their assembly history, a dependence we term `assembly bias'. Using a galaxy formation model grafted onto the Millennium Simulation of the LCDM cosmogony, we study how assembly bias affects galaxy clustering. We compare the original simulation to `shuffled' versions where the galaxy populations are randomly swapped among halos of similar mass, thus isolating the effects of correlations between assembly history and environment at fixed mass. Such correlations are ignored in the halo occupation distribution models often used…
In this paper we use the ``Millennium Simulation'' to re-examine the mass assembly history of dark matter halos and the age dependence of halo clustering. We use eight different definitions of halo formation times to characterize the different aspects of the assembly history of a dark matter halo. We find that these formation times have different dependence on halo mass. While some formation times characterize well the hierarchical nature of halo formation, in the sense that more massive halos have later formation, the trend is reversed for other definitions of the formation time. In particula…
Massive and extended dark halos can inhibit the formation of long tidal tails in galaxy collisions. We examine this effect using an extensive survey of simulations with different dark halo potentials to constrain halo properties of interacting galaxies. These constraints are compared to other observational limits and theoretical predictions of halo structure. The dark halos predicted by $Ω=1$ cosmological models like CDM are too massive and extended to produce the long tidal tails seen in nearby galaxy collisions. There is also a conflict with the halo potentials inferred from satellite kinema…
We examine the effect of different dark matter halo potentials on the morphology and kinematics of tidals tails in a merger model of NGC 7252. We find that models of merging galaxies with low halo masses of Mh = 4-8 M{disk+bulge} (Mdb) can fit the observed morphology and kinematics of the NGC 7252 tails while galaxies with high mass halos (Mh = 16-32 Mdb) fail in this respect. In high mass models, the deep potential only allows weakly bound disk material (stars or gas) at R > 5 disk scale lengths to be ejected in tidal tails which tend to fall back onto the parent galaxies before the final mer…
We use a very large simulation of structure growth in a LCDM universe -- the Millennium Simulation -- to study assembly bias, the fact that the large-scale clustering of haloes of given mass varies significantly with their assembly history. We extend earlier work based on the same simulation by superposing results for redshifts from 0 to 3, by defining a less noisy estimator of clustering amplitude, and by considering halo concentration, substructure mass fraction and spin, as well as formation time, as additional parameters. These improvements lead to results with less noise than previous stu…
We use simulations of merging galaxies to explore the sensitivity of the morphology of tidal tails to variations of the halo mass distributions in the parent galaxies. Our goal is to constrain the mass of dark halos in well-known merging pairs. We concentrate on prograde encounters between equal mass galaxies which represent the best cases for creating tidal tails, but also look at systems with different relative orientations, orbital energies and mass ratios. As the mass and extent of the dark halo increase in the model galaxies, the resulting tidal tails become shorter and less massive, even…
We present an extensive parameter survey to study the influence of halo mass profiles on the development of tidal tails in interacting disk galaxies. We model the galaxies using a fixed exponential disk with a central bulge and vary the halo potential over a range of parameters using both the Hernquist and NFW mass distributions, probing the effect of the halo mass, extent and concentration. We examine the consistency of the results against both observational and theoretical constraints on halo profiles and comment on the failures and weaknesses of different models. Galaxies with rising or fla…
The dwarf galaxies orbiting a main galaxy suffer strong tidal forces produced by its dark halo. As a consequence, substructures and tidal tails could appear in the satellites. These structures could give us information about the dark matter content of the main and the dwarf galaxies. The Milky Way satellites, because of their proximity, are a good sample to study the effects of the tidal forces. The shape of the Milky Way potential could be inferred from the observational data of the tidal tails of its satellites. The Sagittarius dwarf is one of the most interesting satellites as it presents a…
We address the question of whether or not assembly bias arises in the absence of highly non-linear effects such as tidal stripping of halos near larger mass concentrations. Therefore, we use a simplified dynamical scheme where these effects are not modeled. We choose the punctuated Zel'dovich (PZ) approximation, which prevents orbit mixing by coalescing particles coming within a critical distance of each other. A numerical implementation of this approximation is fast, allowing us to run a large number of simulations to study assembly bias. We measure an assembly bias from 60 PZ simulations, ea…
We use a suite of high-resolution N-body simulations to study the properties, abundance and clustering of high mass halos at high redshift, including their mass assembly histories and mergers. We find that the analytic form which best fits the abundance of halos depends sensitively on the assumed definition of halo mass, with common definitions of halo mass differing by a factor of two for these low concentration, massive halos. A significant number of massive halos are undergoing rapid mass accretion, with major merger activity being common. We compare the mergers and mass accretion histories…
(abridged) We study the mass assembly history (MAH) of dark matter haloes. We compare MAHs obtained using (i) merger trees constructed with the extended Press-Schechter (EPS) formalism, (ii) numerical simulations, and (iii) the Lagrangian perturbation code PINOCCHIO. We show that the PINOCCHIO MAHs are in excellent agreement with those obtained using numerical simulations. Using a suite of 55 PINOCCHIO simulations, with 256^3 particles each, we study the MAHs of 12,924 cold dark matter haloes in a \LambdaCDM concordance cosmology. We show that haloes less massive than the characteristic non-li…
In several interacting systems, gas accumulations as massive as 10^9 solar masses are observed near the tip of tidal tails, and are thought to be possible progenitors of Tidal Dwarf Galaxies. Using N-body simulations of galaxy interactions, we show that the existence of such features requires that dark matter haloes around spiral galaxies extend at least ten times further than the stellar disks. The massive gas clouds formed in our simulations have a kinematical origin and gravitationally collapse into dwarf galaxies that often survive for a few billion years.
We explain in simple terms how the buildup of dark haloes by merging compact satellites, as in the CDM cosmology, inevitably leads to an inner cusp of density profile $ρ\propto r^{-α}$ with $α\gsim 1$, as seen in cosmological N-body simulations. A flatter halo core with $α<1$ exerts on the satellites tidal compression in all directions, which prevents deposit of stripped satellite material in the core region. This makes the satellite orbits decay from the radius where $α\sim 1$ to the halo centre with no local tidal mass transfer and thus causes a rapid steepening of the inner profile to $α>1$…
In this second paper in our series, we continue to test primordial scenarios of globular cluster formation which predict that globular clusters formed in the early universe in the potential of dark matter minihalos. In this paper we use high-resolution N-body simulations to model tidal stripping experienced by primordial dark-matter dominated globular clusters in the static gravitational potential of the host dwarf galaxy. We test both cuspy Navarro-Frenk-White (NFW) and flat-core Burkert models of dark matter halos. Our primordial globular cluster with an NFW dark matter halo survives severe …
We discuss recent observational and numerical work on tidal tails in globular clusters. Evidence of tidal tails has now been found in 16 Galactic globulars and 4 globulars in M31. Simulations indicate that mapping of these tidal tails over most of a typical cluster's orbit may be quite feasible. A relatively modest effort in this regard would yield reliable space velocities for those clusters whose tidal tails could be traced to angular separations of a few degrees or more. Mining of forthcoming databases should allow us to trace the individual orbital paths of globular clusters over large por…
Models for the formation and growth of structure in a cold dark matter dominated universe predict that galaxy halos should contain significant substructure. Studies of the Milky Way, however, have yet to identify the expected few hundred sub-halos with masses greater than about 10^6 Msun. Here we propose a test for the presence of sub-halos in the halos of galaxies. We show that the structure of the tidal tails of ancient globular clusters is very sensitive to heating by repeated close encounters with the massive dark sub-halos. We discuss the detection of such an effect in the context of the …
We have simulated the evolution of tidal debris in the Galactic halo in order to guide our ongoing survey to determine the fraction of halo mass accreted via satellite infall. Contrary to naive expectations that the satellite debris will produce a single narrow velocity peak on a smooth distribution, there are many different signatures of substructure, including multiple peaks and broad but asymmetrical velocity distributions. Observations of the simulations show that there is a high probability of detecting the presence of tidal debris with a pencil beam survey of 100 square degrees. In the l…
We study the relation between the density profiles of dark matter halos and their mass assembly histories, using a statistical sample of halos in a high-resolution N-body simulation of the LCDM cosmology. For each halo at z=0, we identify its merger-history tree, and determine concentration parameters c_vir for all progenitors, thus providing a structural merger tree for each halo. We fit the mass accretion histories by a universal function with one parameter, the formation epoch a_c, defined when the log mass accretion rate dlog M/doga falls below a critical value. We find that late forming g…
We present a technique for constructing equilibrium triaxial N-body haloes with nearly arbitrary density profiles, axial ratios and spin parameters. The method is based on the way in which structures form in hierarchical cosmological simulations, where prolate and oblate haloes form via mergers with low and high angular momentum, respectively. We show that major mergers between equilibrium spherical cuspy haloes produce similarly cuspy triaxial remnants and higher angular-momentum mergers produce systems with lower concentrations. Triaxial haloes orbiting within deeper potentials become more s…
(abridged) We present a detailed analysis of the properties of tidally stripped material from disrupting substructure haloes or subhaloes in a sample of high resolution cosmological N-body host haloes ranging from galaxy- to cluster-mass scales. We focus on devising methods to recover the infall mass and infall eccentricity of subhaloes from the properties of their tidally stripped material (i.e. tidal streams). Our analysis reveals that there is a relation between the scatter of stream particles about the best-fit debris plane and the infall mass of the progenitor subhalo. This allows us to r…
Tidal disruption of dark matter halos around proto-globular clusters in a halo of a small galaxy is studied in the context of the hierarchical clustering scenario by using semi-cosmological N-body/SPH simulations assuming the standard cold dark matter model ($Ω_0 = 1$). Our analysis on formation and evolution of the galaxy and its substructures archives until $z = 2.0$. In such a high-redshift universe, the Einstein-de Sitter universe is still a good approximation for a recently favored $Λ$-dominated universe, and then our results does not depend on the choice of cosmology. In order to resolve…
We show how the buildup of halos by merging satellites forces an inner cusp, with a density profile ρ\propto r^{-α} where α\to α_a \gsim 1$. Our analysis is based on a new prescription for tidal stripping as a function of α(r), using a simple toy model which matches N-body simulations. In a core of α< 1 there is tidal compression rather than stripping and the satellites sink towards the halo center, causing a rapid steepening of the profile to α> 1. Where α> 1, the stripping of each satellite shell is preceded by gradual puffing up, which makes the stripping more efficient at larger α, causing…
Self-calibration techniques for analyzing galaxy cluster counts utilize the abundance and the clustering amplitude of dark matter halos. These properties simultaneously constrain cosmological parameters and the cluster observable-mass relation. It was recently discovered that the clustering amplitude of halos depends not only on the halo mass, but also on various secondary variables, such as the halo formation time and the concentration; these dependences are collectively termed assembly bias. Applying modified Fisher matrix formalism, we explore whether these secondary variables have a signif…
We explore whether stellar tidal streams can provide information on the secular, cosmological evolution of the Milky Way's gravitational potential and on the presence of subhalos. We carry out long-term (~t_hubble) N-body simulations of disrupting satellite galaxies in a semi-analytic Galaxy potential where the dark matter halo and the subhalos evolve according to a LCDM cosmogony. All simulations are constrained to end up with the same position and velocity at present. Our simulations account for: (i) the secular evolution of the host halo's mass, size and shape, (ii) the presence of subhalos…
We evaluate the success of linear tidal-torque theory (TTT) in predicting galactic-halo spin using a cosmological N-body simulation with thousands of well-resolved haloes. The proto-haloes are identified by tracing today's haloes back to the initial conditions. The TTT predictions for the proto-haloes match, on average, the spin amplitudes of today's virialized haloes if linear growth is assumed until ~t_0/3, or 55-70 per cent of the halo effective turn-around time. This makes it a useful qualitative tool for understanding certain average properties of galaxies, such as total spin and angular-…
We study the formation of tidal tails in pairs of merging disk galaxies with structural properties motivated by current theories of cold dark matter (CDM) cosmologies. In a recent study, Dubinski, Mihos & Hernquist (1996) showed that the formation of prominent tidal tails can be strongly suppressed by massive and extended dark haloes. For the large halo-to-disk mass ratio expected in CDM cosmologies their sequence of models failed to produce strong tails like those observed in many well-known pairs of interacting galaxies. In order to test whether this effect can constrain the viability of CDM…
Standard cosmology predicts that dwarfs were the first galaxies to be formed in the Universe and that many of them merge afterwards to form bigger galaxies such as the Milky Way. This process would have left behind traces such as tidal debris or star streams in the outer halo. We report here the detection of a very low density stellar system at 50+/- 10 kpc from the Galactic center that could be related to the merger process. It could form part of the Sagittarius northern stream or, alternatively, could be the trace of a hitherto unknown dwarf galaxy. The dwarf galaxy in Sagittarius, the close…
How fast a satellite decays its orbit depends on how slowly its mass is lost by tide. Motivated by inner halo satellite remnants like the Sgr and Omega Cen, we develop fully analytical models to study the orbital decay and tidal massloss of satellites. The orbital decay rate is often severely overestimated if applying the ChandraSekhar's formula without correcting for (a) the evaporation and tidal loss of the satellite and (b) the contraction of satellite orbits due to adiabatic growth of the host galaxy potential over the Hubble time. As a satellite migrates inwards, the increasing halo densi…
Two studies have recently reported the discovery of pronounced Halo substructure in the Sloan Digital Sky Survey (SDSS) commissioning data. Here we show that this Halo substructure is almost in its entirety due to the expected tidal stream torn off the Sagittarius dwarf galaxy during the course of its many close encounters with the Milky Way. This interpretation makes strong predictions on the kinematics and distances of these stream stars. Comparison of the structure in old horizontal branch stars, detected by the SDSS team, with the carbon star structure discovered in our own survey, indicat…
We show by means of a high-resolution N-body simulation how the mass assembly histories of galaxy-size cold dark matter (CDM) halos depend on environment. Halos in high density environments form earlier and a higher fraction of their mass is assembled in major mergers, compared to low density environments. The distribution of the present-day specific mass aggregation rate is strongly dependent on environment. While in low density environments only ~20% of the halos are not accreting mass at the present epoch, this fraction rises to ~80% at high densities. At z=1 the median of the specific aggr…
