arXiv subjects

Arif Babul

Publications and source records attributed to Arif Babul.

At least 109 records · Page 6Linked to original sources

arXiv2006

On the formation of extended galactic disks by tidally disrupted dwarf galaxies

We explore the possibility that extended disks, such as that recently discovered in M31, are the result of a single dwarf (10^9--10^10 Msun) satellite merger. We carry out N-body simulations of dwarf NFW halos with embedded spheriodal stellar components on co-planar, prograde orbits in a M31-like host galaxy. As the orbit decays due to dynamical friction and the system is disrupted, the stellar particles form an extended, exponential disk-like structure that spans the radial range 30--200 kpc once they have relaxed. The disk scale-length correlates with the initial extent of the stellar component within the satellite halo: the more embedded the stars, the smaller the resulting disk scale-length. If the progenitors start on circular orbits, the kinematics of the stars that make up the extended disk have an average rotational motion that is 30--50 km/s lower than the host's circular velocity. For dwarf galaxies moving on highly eccentric orbits (e=0.7), the stellar debris exhibits a much lower rotational velocity. Our results imply that extended galactic disks might be a generic feature of the hierarchical formation of spiral galaxies such as M31 and the Milky Way.

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arXiv2006

The impact of mergers on relaxed X-ray clusters - I. Dynamical evolution and emergent transient structures

We report on the analysis of a suite of SPH simulations (incorporating cooling and star formation) of mergers involving idealised X-ray clusters whose initial conditions resemble relaxed clusters with cool compact cores observed by Chandra and XMM. The simulations sample the most interesting, theoretically plausible, range of impact parameters and progenitor mass ratios. We find that all mergers evolve via a common progression. We illustrate this progression in the projected gas density, X-ray surface brightness, SZ, temperature, and gas entropy maps. Several different classes of transient ``cold front''-like features can arise over the course of a merger. We find that all of these classes are present in Chandra and XMM observations of merging systems and propose a naming scheme for these features: ``comet-like'' tails, bridges, plumes, streams and edges. In none of the cases considered do the initial cool compact cores of the primary and the secondary get destroyed during the course of the mergers. We quantify the evolving morphology of our mergers using centroid variance, power ratios and offset between the X-ray and the projected mass maps. We find that the centroid variance best captures the dynamical state of the cluster. Placing the system at z=0.1, we find that all easily identified observable traces of the secondary disappear from a simulated 50 ks Chandra image following the second pericentric passage. The system, however, takes approximately 2 additional Gyrs to relax and virialize. Temperature fluctuations at the level of 20% can persist in the final systems well past the point of virialization, suggesting that that the existence of temperature fluctuations, in and of themselves, do not necessarily indicate a disturbed or unrelaxed system.

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arXiv2006

Density Profiles of Collisionless Equilibria. I. Spherical Isotropic Systems

We investigate the connection between collisionless equilibria and the phase-space relation between density $ρ$ and velocity dispersion $σ$ found in simulations of dark matter halo formation, $F=\psd \propto r^{-α}$. Understanding this relation will shed light on the physics relevant to collisionless collapse and on the subsequent structures formed. We show that empirical density profiles that provide good fits to N-body halos also happen to have nearly scale-free \psd distributions when in equilibrium. We have also done a preliminary investigation of variables other than $r$ that may match or supercede the correlation with $F$. In the same vein, we show that $ρ/σ^m$, where $m=3$ is the most appropriate combination to use in discussions of the power-law relationship. Since the mechanical equilibrium condition that characterizes the final systems does not by itself lead to power-law $F$ distributions, our findings prompt us to posit that dynamical collapse processes (such as violent relaxation) are responsible for the radial power-law nature of the \psd distributions of virialized systems.

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arXiv2006

An analytic investigation of the scatter in the integrated X-ray properties of galaxy groups and clusters

(Abridged) We revisit the scaling relationships between the dark matter mass and observed X-ray luminosity and temperature of galaxy clusters and groups in the local Universe. Specifically, we compare recent observations with analytic models of the intracluster medium in which the gas entropy distribution has been shifted by a variable amount, K0, to investigate the origin of the scatter in these scaling relations, and its influence on the luminosity and temperature functions. We find that variations in halo concentration or formation epoch (which might determine the time available for low entropy gas to cool out) are insufficient to explain the amount of scatter in the mass-luminosity relation. Instead, a range of entropy floors at a fixed halo mass, spanning approximately 50 keV sq.cm to 700 keV sq.cm, is required to match the data. This range is likely related to the variance in heating and/or cooling efficiency from halo to halo. We demonstrate that these models are consistent with the observed temperature and luminosity functions of clusters, if scatter in the mass-luminosity relation is accounted for. Finally, we present predictions for the redshift evolution of these scaling relations and luminosity/temperature functions. Comparison with recent data at z<0.7 shows reasonable agreement with a model that assumes a median entropy floor of K0=200 keV sq.cm. When observations are extended to group scales (kT < 1 keV), this evolution will have the potential to discriminate between an entropy floor that is independent of redshift (for example, in a preheating scenario) and one that depends on the cooling time of the halo.

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arXiv2005

A Simple and Accurate Model for Intra-Cluster Gas

Starting with the well-known NFW dark matter halo distribution, we construct a simple polytropic model for the intracluster medium which is in good agreement with high resolution numerical hydrodynamical simulations, apply this model to a very large scale concordance dark matter simulation, and compare the resulting global properties with recent observations of X-ray clusters, including the mass-temperature and luminosity-temperature relations. We make allowances for a non-negligible surface pressure, removal of low entropy (short cooling time) gas, energy injection due to feedback, and for a relativistic (non-thermal) pressure component. A polytropic index n=5 (Gamma=1.2) provides a good approximation to the internal gas structure of massive clusters (except in the very central regions where cooling becomes important), and allows one to recover the observed M_500-T, L_x-T, and T/n_e^{2/3} ~ T^0.65 relations. Using these concepts and generalizing this method so that it can be applied to fully three-dimensional N-body simulations, one can predict the global X-ray and SZE trends for any specified cosmological model. We find a good fit to observations when assuming that twelve percent of the initial baryonic mass condenses into stars, the fraction of rest mass of this condensed component transferred back to the remaining gas (feedback) is 3.9E-5, and the fraction of total pressure from a nonthermal component is near ten percent.

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arXiv2005

Semi-analytical dark matter halos and the Jeans equation

Although N-body studies of dark matter halos show that the density profiles, rho(r), are not simple power-laws, the quantity rho/sigma^3, where sigma(r) is the velocity dispersion, is in fact a featureless power-law over ~3 decades in radius. In the first part of the paper we demonstrate, using the semi-analytic Extended Secondary Infall Model (ESIM), that the nearly scale-free nature of rho/sigma^3 is a robust feature of virialized halos in equilibrium. By examining the processes in common between numerical N-body and semi-analytic approaches, we argue that the scale-free nature of rho/sigma^3 cannot be the result of hierarchical merging, rather it must be an outcome of violent relaxation. The empirical results of the first part of the paper motivate the analytical work of the second part of the paper, where we use rho/sigma^3 proportional to r^{-alpha} as an additional constraint in the isotropic Jeans equation of hydrostatic equilibrium. Our analysis shows that the constrained Jeans equation has different types of solutions, and in particular, it admits a unique ``periodic'' solution with alpha=1.9444. We derive the analytic expression for this density profile, which asymptotes to inner and outer profiles of rho ~ r^{-0.78}, and rho ~ r^{-3.44}, respectively.

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arXiv2005

The phase-space density distribution of dark matter halos

High resolution N-body simulations have all but converged on a common empirical form for the shape of the density profiles of halos, but the full understanding of the underlying physics of halo formation has eluded them so far. We investigate the formation and structure of dark matter halos using analytical and semi-analytical techniques. Our halos are formed via an extended secondary infall model (ESIM); they contain secondary perturbations and hence random tangential and radial motions which affect the halo's evolution at it undergoes shell-crossing and virialization. Even though the density profiles of NFW and ESIM halos are different their phase-space density distributions are the same: ρ/σ^3 ~ r^{-α}, with α=1.875 over ~3 decades in radius. We use two approaches to try to explain this ``universal'' slope: (1) The Jeans equation analysis yields many insights, however, does not answer why α=1.875. (2) The secondary infall model of the 1960's and 1970's, augmented by ``thermal motions'' of particles does predict that halos should have α=1.875. However, this relies on assumptions of spherical symmetry and slow accretion. While for ESIM halos these assumptions are justified, they most certainly break down for simulated halos which forms hierarchically. We speculate that our argument may apply to an ``on-average'' formation scenario of halos within merger-driven numerical simulations, and thereby explain why α=1.875 for NFW halos. Thus, ρ/σ^3 ~ r^{-1.875} may be a generic feature of violent relaxation.

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arXiv2005

The Effects of Radiative Cooling on the Entropy Distribution of Intracluster Gas

High resolution X-ray observations indicate that the entropy profiles in the central regions of some massive cooling flow clusters are well approximated by powerlaws. McCarthy and coworkers recently accounted for this trend with an analytic model that includes the detailed effects of radiative cooling. Interestingly, these authors found that cooling (and subsequent inflow of the gas) naturally establishes approximate steady-state powerlaw entropy profiles in the cores of clusters. However, the origin of this behavior and its dependence on initial conditions have yet to be elucidated. In the present study, we explain this trend in the context of the self-similar cooling wave model developed previously by Bertschinger (1989). It is shown that the logarithmic slope of the entropy profile in the cores of relaxed cooling flow clusters is given by a simple analytic function that depends only on the logarithmic slopes of the local gravitational potential and the cooling function. We discuss a number of potentially interesting uses of the above result, including: (1) a way of measuring the shapes of gravitational potentials of cooling flow clusters (which may, for example, be compared with the results of the standard hydrostatic equilibrium method); (2) a simple method for constructing realistic analytic cluster models that include the effects of radiative cooling; and (3) a test of the reliability of cooling routines implemented in analytic models and hydrodynamic simulations.

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arXiv2004

The Evolution of Substructure in Galaxy, Group and Cluster Haloes III: Comparison with Simulations

In a previous paper, we described a new method for including detailed information about substructure in semi-analytic models of halo formation based on merger trees. In this paper, we compare the predictions of our model with results from self-consistent numerical simulations. We find that in general the two methods agree extremely well, particularly once numerical effects and selection effects in the choice of haloes are taken into account. As expected from the original analyses of the simulations, we see some evidence for artificial overmerging in the innermost regions of the simulated haloes, either because substructure is being disrupted artificially or because the group-finding algorithms used to identify substructure are not detecting all the bound clumps in the highest-density regions. Our analytic results suggest that greater mass and force resolution may be required before numerical overmerging becomes negligible in all current applications. We discuss the implications of this result for observational and experimental tests of halo substructure, such as the analysis of discrepant magnification ratios in strongly lensed systems, terrestrial experiments to detect dark matter particles directly, or indirect detection experiments searching for positrons, gamma-rays, neutrinos or other dark matter decay products.

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arXiv2004

The Evolution of Substructure in Galaxy, Group and Cluster Haloes II: Global Properties

In a previous paper, we described a new method for including detailed information about substructure in semi-analytic models of dark matter halo formation based on merger trees. In this paper, we present the basic predictions of our full model of halo formation. We first describe the overall properties of substructure in galaxy, group or cluster haloes at the present day. We then discuss the evolution of substructure, and the effect of the mass accretion history of an individual halo on the mass function and orbital grouping of its subhalo population. We show, in particular, that the shape of the subhalo mass function is strongly correlated with the formation epoch of the halo. In a third paper in this series we will compare the results of our semi-analytic method with the results of self-consistent numerical simulations of halo formation.

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arXiv2004

Predicting Substructure in CDM Haloes

Observations of multiple-image gravitational lens systems suggest that the projected mass distributions of galaxy haloes may contain substantial inhomogeneities. The fraction of the halo mass in dense substructure is still highly uncertain, but could be as large as a few percent. While halo substructure is seen in numerical simulations of CDM haloes, little of this substructure survives in the innermost regions of haloes, and thus the observational claims for substructure at small projected radii are slightly surprising. There is evidence, however, that even the highest-resolution simulations published to-date are still limited by numerical effects that heat and disrupt substructure artificially in high-density regions. By comparing numerical and semi-analytic models of halo substructure, we show that current simulations probably underestimate the mass fraction in substructure at small projected radii, by a factor of at least 2-3. We discuss the prospects for using lensing observations as a fundamental test of the nature of dark matter.

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arXiv2004

Models of the ICM with Heating and Cooling: Explaining the Global and Structural X-ray Properties of Clusters

(Abridged) Theoretical models that include only gravitationally-driven processes fail to match the observed mean X-ray properties of clusters. As a result, there has recently been increased interest in models in which either radiative cooling or entropy injection play a central role in mediating the properties of the intracluster medium. Both sets of models give reasonable fits to the mean properties of clusters, but cooling only models result in fractions of cold baryons in excess of observationally established limits and the simplest entropy injection models do not treat the "cooling core" structure present in many clusters and cannot account for entropy profiles revealed by recent X-ray observations. We consider models that marry radiative cooling with entropy injection, and confront model predictions for the global and structural properties of massive clusters with the latest X-ray data. The models successfully and simultaneously reproduce the observed L-T and L-M relations, yield detailed entropy, surface brightness, and temperature profiles in excellent agreement with observations, and predict a cooled gas fraction that is consistent with observational constraints. The model also provides a possible explanation for the significant intrinsic scatter present in the L-T and L-M relations and provides a natural way of distinguishing between clusters classically identified as "cooling flow" clusters and dynamically relaxed "non-cooling flow" clusters. The former correspond to systems that had only mild levels (< 300 keV cm^2) of entropy injection, while the latter are identified as systems that had much higher entropy injection. This is borne out by the entropy profiles derived from Chandra and XMM-Newton.

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arXiv2003

Small-scale Substructure in Dark Matter Haloes: Where Does Galaxy Formation Come to an End?

Models of structure formation based on cold dark matter predict that most of the small dark matter haloes that first formed at high redshift would have merged into larger systems by the present epoch. Substructure in present-day haloes preserves the remains of these ancient systems, providing the only direct information we may ever have about the low-mass end of the power spectrum. I describe some recent attempts to model halo substructure down to very small masses, using a semi-analytic model of halo formation. I make a preliminary comparison between the model predictions, observations of substructure in lensed systems, and the properties of local satellite galaxies.

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arXiv2003

The Satellite-substructure Connection

We describe our recent attempts to model substructure in dark matter halos down to very small masses, using a semi-analytic model of halo formation. The results suggest that numerical simulations of halo formation may still be missing substructure in the central regions of halos due to purely numerical effects. If confirmed, this central 'overmerging' problem will have important consequences for the interpretation of lensing measurements of substructure. We also show that the spatial distribution of subhalos relative to the satellite companions of the Milky Way rules out at least one simple model of how dwarf galaxies form in low-mass halos.

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arXiv2003

Investigating the Origins of Dark Matter Halo Density Profiles

Although high-resolution N-body simulations make robust empirical predictions for the density distribution within cold dark matter halos, these studies have yielded little physical insight into the origins of the distribution. We investigate the problem using analytic and semi-analytic approaches. Simple analytic considerations suggest that the inner slope of dark matter halos cannot be steeper than alpha=2 (rho ~ r^-alpha), with alpha=1.5-1.7 being a more realistic upper limit. Our analysis suggests that any number of effects, both real (angular momentum from tidal torques, secondary perturbations) and artificial (two-body interactions, the accuracy of the numerical integrator, round-off errors), will result in shallower slopes. We also find that the halos should exhibit a well-defined relation between r_peri/r_apo and j_theta/j_r. We derive this relation analytically and speculate that it may be "universal". Using a semi-analytic scheme based on Ryden & Gunn (1987), we further explore the relationship between the specific angular momentum distribution in a halo and its density profile. For now we restrict ourselves to halos that form primarily via nearly-smooth accretion of matter, and only consider the specific angular momentum generated by secondary perturbations associated with the cold dark matter spectrum of density fluctuations. Compared to those formed in N-body simulations, our ``semi-analytic'' halos are more extended, have flatter rotation curves and have higher specific angular momentum, even though we have not yet taken into account the effects of tidal torques. Whether the density profiles of numerical halos is indeed the result of loss in angular momentum outside the central region, and whether this loss is a feature of hierarchical merging and major mergers in particular, is under investigation.

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arXiv2003

On the Intracluster Medium in Cooling Flow & Non-Cooling Flow Clusters

Recent X-ray observations have highlighted clusters that lack entropy cores. At first glance, these results appear to invalidate the preheated ICM models. We show that a self-consistent preheating model, which factors in the effects of radiative cooling, is in excellent agreement with the observations. Moreover, the model naturally explains the intrinsic scatter in the L-T relation, with ``cooling flow'' and ``non-cooling flow'' systems corresponding to mildly and strongly preheated systems, respectively. We discuss why preheating ought to be favoured over merging as a mechanism for the origin of ``non-cooling flow'' clusters.

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arXiv2003

The SZ Effect Signature of Excess Entropy in Distant, Massive Clusters

Studies of cluster X-ray scaling relations have led to suggestions that non-gravitational processes, e.g., radiative cooling and/or "preheating", have significantly modified the entropy of the intracluster medium (ICM). For the first time, we test this hypothesis through a comparison of predicted thermal Sunyaev-Zeldovich (SZ) effect scaling relations with available data from the literature. One of the relations that we explore, in principle, depends solely on SZ effect observations, thus offering an X-ray independent probe of the ICM. A detailed comparison of the theoretical relations with the largest compilation of high redshift SZ effect data to date indicates that the presence of an entropy floor is favored by the data. Furthermore, the inferred level of that floor, 300 keV cm^2 or higher, is comparable to that found in studies of X-ray scaling relations of nearby massive clusters. Thus, we find no evidence for significant evolution of the entropy floor out to z = 0.7. We further demonstrate that the high quality data to be obtained from the upcoming Sunyaev-Zeldovich Array (SZA) and the (soon-to-be) upgraded Owens Valley Radio Observatory (OVRO) array will open powerful new windows into the properties of the ICM. Specifically, the new measurements will allow for accurate measurements of the ICM entropy for even the most distant galaxy clusters.

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arXiv2003

On the Relationship between Cooling Flows and Bubbles

A common feature of the X-ray bubbles observed in Chandra images of some "cooling flow" clusters is that they appear to be surrounded by bright, cool shells. Temperature maps of a few nearby luminous clusters reveal that the shells consist of the coolest gas in the clusters -- much cooler than the surrounding medium. Using simple models, we study the effects of this cool emission on the inferred cooling flow properties of clusters. We find that the introduction of bubbles into model clusters that do NOT have cooling flows results in temperature and surface brightness profiles that resemble those seen in nearby "cooling flow" clusters. They also approximately reproduce the recent XMM-Newton and Chandra observations of a high minimum temperature of 1-3 keV. Hence, bubbles, if present, must be taken into account when inferring the physical properties of the ICM. In the case of some clusters, bubbles may account entirely for these observed features, calling into question their designation as clusters with cooling flows. However, since not all nearby "cooling flow" clusters show bubble-like features, we suggest that there may be a diverse range of physical phenomena that give rise to the same observed features.

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