The outer profile of dark matter halos: an analytical approach

A steepening feature in the outer density profiles of dark matter halos indicating the splashback radius has drawn much attention recently. Possible observational detections have even been made for galaxy clusters. Theoretically, Adhikari et al. have estimated the location of the splashback radius by computing the secondary infall trajectory of a dark matter shell through a growing dark matter halo with an NFW profile. However, since they imposed a shape of the halo profile rather than computing it consistently from the trajectories of the dark matter shells, they could not provide the full shape of the dark matter profile around the splashback radius. We improve on this by extending the self-similar spherical collapse model of Fillmore \& Goldreich to a $\Lambda$CDM universe. This allows us to compute the dark matter halo profile and the trajectories simultaneously from the mass accretion history. Our results on the splashback location agree qualitatively with Adhikari et al. but with small quantitative differences at large mass accretion rates. We present new fitting formulae for the splashback radius $R_{\rm sp}$ in various forms, including the ratios of $R_{\rm sp} / R_{\rm 200c}$ and $R_{\rm sp} / R_{\rm 200m}$. Numerical simulations have made the puzzling discovery that the splashback radius scales well with $R_{\rm 200m}$ but not with $R_{\rm 200c}$. We trace the origin of this to be the correlated increase of $\Omega_{\rm m}$ and the average halo mass accretion rate with an increasing redshift.Comment: 10 pages, 10 figures, published in MNRA

Turbulence decay in the density-stratified intracluster medium

Turbulence evolution in a density-stratified medium differs from that of homogeneous isotropic turbulence described by the Kolmogorov picture. We evaluate the degree of this effect in the intracluster medium (ICM) with hydrodynamical simulations. We find that the buoyancy effect induced by ICM density stratification introduces qualitative changes to the turbulence energy evolution, morphology, and the density fluctuation - turbulence Mach number relation, and likely explains the radial dependence of the ICM turbulence amplitude as found previously in cosmological simulations. A new channel of energy flow between the kinetic and the potential energy is opened up by buoyancy. When the gravitational potential is kept constant with time, this energy flow leaves oscillations to the energy evolution, and leads to a balanced state of the two energies where both asymptote to power-law time evolution with slopes shallower than that for the turbulence kinetic energy of homogeneous isotropic turbulence. We discuss that the energy evolution can differ more significantly from that of homogeneous isotropic turbulence when there is a time variation of the gravitational potential. Morphologically, ICM turbulence can show a layered vertical structure and large horizontal vortical eddies in the central regions with the greatest density stratification. In addition, we find that the coefficient in the linear density fluctuation - turbulence Mach number relation caused by density stratification is in general a variable with position and time.Comment: 10 pages, 9 figures, published in MNRA

Analytical model for non-thermal pressure in galaxy clusters

Non-thermal pressure in the intracluster gas has been found ubiquitously in numerical simulations, and observed indirectly. In this paper we develop an analytical model for intracluster non-thermal pressure in the virial region of relaxed clusters. We write down and solve a first-order differential equation describing the evolution of non-thermal velocity dispersion. This equation is based on insights gained from observations, numerical simulations, and theory of turbulence. The non-thermal energy is sourced, in a self-similar fashion, by the mass growth of clusters via mergers and accretion, and dissipates with a time-scale determined by the turnover time of the largest turbulence eddies. Our model predicts a radial profile of non-thermal pressure for relaxed clusters. The non-thermal fraction increases with radius, redshift, and cluster mass, in agreement with numerical simulations. The radial dependence is due to a rapid increase of the dissipation time-scale with radii, and the mass and redshift dependence comes from the mass growth history. Combing our model for the non-thermal fraction with the Komatsu-Seljak model for the total pressure, we obtain thermal pressure profiles, and compute the hydrostatic mass bias. We find typically 10% bias for the hydrostatic mass enclosed within $r_{500}$.Comment: 12 pages, 9 figures, published in MNRAS. Discussions and references added. A factor of 2 corrected in t_dyn (Fig. 2), definition of t_d (Eq. 3) changed accordingl

How well do third-order aperture mass statistics separate E- and B-modes?

With 3rd-order statistics of gravitational shear it will be possible to extract valuable cosmological information from ongoing and future weak lensing surveys which is not contained in standard 2nd-order statistics, due to the non-Gaussianity of the shear field. Aperture mass statistics are an appropriate choice for 3rd-order statistics due to their simple form and their ability to separate E- and B-modes of the shear. However, it has been demonstrated that 2nd-order aperture mass statistics suffer from E-/B-mode mixing because it is impossible to reliably estimate the shapes of close pairs of galaxies. This finding has triggered developments of several new 2nd-order statistical measures for cosmic shear. Whether the same developments are needed for 3rd-order shear statistics is largely determined by how severe this E-/B-mixing is for 3rd-order statistics. We test 3rd-order aperture mass statistics against E-/B-mode mixing, and find that the level of contamination is well-described by a function of $\theta/\theta_{\rm min}$, with $\theta_{\rm min}$ being the cut-off scale. At angular scales of $\theta > 10 \;\theta_{\rm min}$, the decrease in the E-mode signal due to E-/B-mode mixing is smaller than 1 percent, and the leakage into B-modes is even less. For typical small-scale cut-offs this E-/B-mixing is negligible on scales larger than a few arcminutes. Therefore, 3rd-order aperture mass statistics can safely be used to separate E- and B-modes and infer cosmological information, for ground-based surveys as well as forthcoming space-based surveys such as Euclid.Comment: references added, A&A publishe

Multi-scale analysis of turbulence evolution in the density stratified intracluster medium

The diffuse hot medium inside clusters of galaxies typically exhibits turbulent motions whose amplitude increases with radius, as revealed by cosmological hydrodynamical simulations. However, its physical origin remains unclear. It could either be due to an excess injection of turbulence at large radii, or faster turbulence dissipation at small radii. We investigate this by studying the time evolution of turbulence in the intracluster medium (ICM) after major mergers, using the Omega500 non-radiative hydrodynamical cosmological simulations. By applying a novel wavelet analysis to study the radial dependence of the ICM turbulence spectrum, we discover that faster turbulence dissipation in the inner high density regions leads to the increasing turbulence amplitude with radius. We also find that the ICM turbulence at all radii decays in two phases after a major merger: an early fast decay phase followed by a slow secular decay phase. The buoyancy effects resulting from the ICM density stratification becomes increasingly important during turbulence decay, as revealed by a decreasing turbulence Froude number $Fr \sim \mathcal{O}(1)$. Our results indicate that the stronger density stratification and smaller eddy turn-over time are the likely causes of the faster turbulence dissipation rate in the inner regions of the cluster.Comment: 8 pages, 7 figures, accepted to MNRA

The Role of Early Recurrence in Improving Visual Representations

This dissertation proposes a computational model of early vision with recurrence, termed as early recurrence. The idea is motivated from the research of the primate vision. Specifically, the proposed model relies on the following four observations. 1) The primate visual system includes two main visual pathways: the dorsal pathway and the ventral pathway; 2) The two pathways respond to different visual features; 3) The neurons of the dorsal pathway conduct visual information faster than that of the neurons of the ventral pathway; 4) There are lower-level feedback connections from the dorsal pathway to the ventral pathway. As such, the primate visual system may implement a recurrent mechanism to improve visual representations of the ventral pathway. Our work starts from a comprehensive review of the literature, based on which a conceptualization of early recurrence is proposed. Early recurrence manifests itself as a form of surround suppression. We propose that early recurrence is capable of refining the ventral processing using results of the dorsal processing. Our work further defines a set of computational components to formalize early recurrence. Although we do not intend to model the true nature of biology, to verify that the proposed computation is biologically consistent, we have applied the model to simulate a neurophysiological experiment of a bar-and-checkerboard and a psychological experiment involving a moving contour illusion. Simulation results indicated that the proposed computation behaviourally reproduces the original observations. The ultimate goal of this work is to investigate whether the proposal is capable of improving computer vision applications. To do this, we have applied the model to a variety of applications, including visual saliency and contour detection. Based on comparisons against the state-of-the-art, we conclude that the proposed model of early recurrence sheds light on a generally applicable yet lightweight approach to boost real-life application performance

Dynamical heating of the X-ray emitting intracluster medium: the roles of merger shocks and turbulence dissipation

The diffuse plasma inside clusters of galaxies has X-ray emitting temperatures of a few keV. The physical mechanisms that heat this intracluster medium (ICM) to such temperatures include the accretion shock at the periphery of a galaxy cluster, the shocks driven by merger events, as well as a somewhat overlooked mechanism -- the dissipation of intracluster turbulent motions. We study the relative role of these heating mechanisms using galaxy clusters in Lagrangian tracer particle re-simulations of the Omega500 cosmological simulation. We adopt a novel analysis method of decomposing the temperature increase at each time step into the contribution from dissipative heating and that from adiabatic heating. In the high-resolution spatial-temporal map of these heating rates, merger tracks are clearly visible, demonstrating the dominant role of merger events in heating the ICM. The dissipative heating contributed by each merger event is extended in time and also occurs in the rarefaction regions, suggesting the importance of heating by the dissipation of merger-induced turbulence. Quantitative analysis shows that turbulence heating, rather than direct heating at merger shocks, dominates the temperature increase of the ICM, especially at inner radii $r < r_{\rm 500c}$. In addition, we find that many merger shocks can propagate with almost constant velocity to very large radii $r \gg r_{\rm 500c}$, some even reach and join with the accretion shock and becoming the outer boundary of the ICM. Altogether, these results suggest that the ICM is heated more in an `inside-out' fashion rather than `outside-in' as depicted in the classical smooth accretion picture.Comment: 12 pages, 13 figures, published in MNRA

Analytical model for non-thermal pressure in galaxy clusters - III. Removing the hydrostatic mass bias

Non-thermal pressure in galaxy clusters leads to underestimation of the mass of galaxy clusters based on hydrostatic equilibrium with thermal gas pressure. This occurs even for dynamically relaxed clusters that are used for calibrating the mass-observable scaling relations. We show that the analytical model for non-thermal pressure developed in Shi & Komatsu 2014 can correct for this so-called 'hydrostatic mass bias', if most of the non-thermal pressure comes from bulk and turbulent motions of gas in the intracluster medium. Our correction works for the sample average irrespective of the mass estimation method, or the dynamical state of the clusters. This makes it possible to correct for the bias in the hydrostatic mass estimates from X-ray surface brightness and the Sunyaev-Zel'dovich observations that will be available for clusters in a wide range of redshifts and dynamical states.Comment: 9 pages, 8 figures, published in MNRA