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Register a new userThe splashback radius of halos from particle dynamics. II. Dependence on mass, accretion rate, redshift, and cosmology
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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 dependence of $R_{rm sp}/R_{rm 200m}$ and $M_{rm sp}/M_{rm 200m}$ on the mass accretion rate $Gamma$, halo mass, redshift, and cosmology. The scatter in these relations varies between 0.02 and 0.1 dex. While we confirm the known trend that $R_{rm sp}/R_{rm 200m}$ decreases with $Gamma$, the relationships turn out to be more complex than previously thought, demonstrating that $R_{rm sp}$ is an independent definition of the halo boundary that cannot trivially be reconstructed from spherical overdensity definitions. We present fitting functions for $R_{rm sp}/R_{rm 200m}$ and $M_{rm sp}/M_{rm 200m}$ as a function of accretion rate, peak height, and redshift, achieving an accuracy of 5% or better everywhere in the parameter space explored. We discuss the physical meaning of the distribution of particle apocenters and show that the previously proposed definition of $R_{rm sp}$ as the radius of the steepest logarithmic density slope encloses roughly three-quarters of the apocenters. Finally, we conclude that no analytical model presented thus far can fully explain our results.
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The lensing signal around galaxy clusters can, in principle, be used to test detailed predictions for their average mass profile from numerical simulations. However, the intrinsic shape of the profiles can be smeared out when a sample that spans a wide range of cluster masses is averaged in physical length units. This effect especially conceals rapid changes in gradient such as the steep drop associated with the splashback radius, a sharp edge corresponding to the outermost caustic in accreting halos. We optimize the extraction of such local features by scaling individual halo profiles to a number of spherical overdensity radii, and apply this method to 16 X-ray-selected high-mass clusters targeted in the Cluster Lensing And Supernova survey with Hubble. By forward-modeling the weak- and strong-lensing data presented by Umetsu et al., we show that, regardless of the scaling overdensity, the projected ensemble density profile is remarkably well described by an NFW or Einasto profile out to $R sim 2.5h^{-1}$Mpc, beyond which the profiles flatten. We constrain the NFW concentration to $c_{200c} = 3.66 pm 0.11$ at $M_{200c} simeq 1.0 times 10^{15}h^{-1}M_odot$, consistent with and improved from previous work that used conventionally stacked lensing profiles, and in excellent agreement with theoretical expectations. Assuming the profile form of Diemer & Kravtsov and generic priors calibrated from numerical simulations, we place a lower limit on the splashback radius of the cluster halos, if it exists, of $R_{sp}/r_{200m} > 0.89$ ($R_{sp} > 1.83h^{-1}$Mpc) at 68% confidence. The corresponding density feature is most pronounced when the cluster profiles are scaled by $r_{200m}$, and smeared out when scaled to higher overdensities.
We compiled a catalogue of about 4000 SDSS quasars including individual estimators V for the variability strength, virial black hole masses M, and mass accretion rates dM/dt from the Davis-Laor scaling relation. We confirm significant anti-correlations between V and dM/dt, the Eddington ratio, and the bolometric luminosity L, respectively. A weak, statistically not significant positive trend is indicated for the dependence of V on M. As a side product, we find a strong correlation of the radiative efficiency with M and show that this trend is most likely produced by selection effects in combination with the mass errors and the use of the scaling relation for dM/dt. The anti-correlations found for V cannot be explained in such a way. The strongest anti-correlation is found with dM/dt. However, it is difficult to decide which of the quantities (L, Eddington ratio, dM/dt) is intrinsically correlated with V and which of the observed correlations are produced by the relations between these quantities. A V-dM/dt anti-correlation is qualitatively expected for the strongly inhomogeneous accretion disks. We argue that several observed variability properties are not adequately explained by the simple multi-temperature black-body model of a standard disk and suggest to check whether the strongly inhomogeneous disk model is capable of reproducing these observations better.
The density field in the outskirts of dark matter halos is discontinuous due to a caustic formed by matter at its first apocenter after infall. In this paper, we present an algorithm to identify the splashback shell formed by these apocenters in individual simulated halos using only a single snapshot of the density field. We implement this algorithm in the code SHELLFISH (SHELL Finding In Spheroidal Halos) and demonstrate that the code identifies splashback shells correctly and measures their properties with an accuracy of $<5%$ for halos with more than 50,000 particles and mass accretion rates of $Gamma_textrm{DK14}>0.5$. Using SHELLFISH, we present the first estimates for several basic properties of individual splashback shells, such as radius, $R_textrm{sp}$, mass, and overdensity, and provide fits to the distribution of these quantities as functions of $Gamma_textrm{DK14}$, $ u_textrm{200m}$, and $z.$ We confirm previous findings that $R_textrm{sp}$ decreases with increasing $Gamma_textrm{DK14}$, but we show that independent of accretion rate, it also decreases with increasing $ u_textrm{200m}$. We also study the 3D structures of these shells and find that they generally have non-ellipsoidal oval shapes. We find that splashback radii estimated by SHELLFISH are $20%-30%$ larger than those estimated in previous studies from stacked density profiles at high accretion rates. We demonstrate that the latter are biased low due to the contribution of high-mass subhalos to these profiles and show that using the median instead of mean density in each radial bin mitigates the effect of substructure on density profiles and removes the bias.
We present the direct detection of the splashback feature using the sample of massive galaxy clusters from the Local Cluster Substructure Survey (LoCuSS). This feature is clearly detected (above $5sigma$) in the stacked luminosity density profile obtained using the K-band magnitudes of spectroscopically confirmed cluster members. We obtained the best-fit model by means of Bayesian inference, which ranked models including the splashback feature as more descriptive of the data with respect to models that do not allow for this transition. In addition, we have assessed the impact of the cluster dynamical state on the occurrence of the splashback feature. We exploited the extensive multi-wavelength LoCuSS dataset to test a wide range of proxies for the cluster formation history, finding the most significant dependence of the splashback feature location and scale according to the presence or absence of X-ray emitting galaxy groups in the cluster infall regions. In particular, we report for the first time that clusters that do not show massive infalling groups present the splashback feature at a smaller clustercentric radius $ r_{rm{sp}}/r_{rm{200,m}} = 1.158 pm 0.071$ than clusters that are actively accreting groups $r_{rm{sp}}/r_{rm{200,m}} = 1.291 pm 0.062$. The difference between these two sub-samples is significant at $4.2sigma$, suggesting a correlation between the properties of the cluster potential and its accretion rate and merger history. Similarly, clusters that are classified as old and dynamically inactive present stronger signatures of the splashback feature, with respect to younger, more active clusters. We are directly observing how fundamental dynamical properties of clusters reverberate across vastly different physical scales.
We have examined a sample of 13 sub-Eddington supermassive black holes hosted by galaxies spanning a variety of morphological classifications to further understand the empirical fundamental plane of black hole activity. This plane describes black holes from stellar-mass to supermassive and relates the mass of an accreting black hole and its radio and X-ray luminosities. A key factor in studying the fundamental plane is the turnover frequency, the frequency at which the radio continuum emission becomes optically thin. We measured this turnover frequency using new VLA observations combined, when necessary, with archival Chandra observations. Radio observations are in the range of 5--40 GHz across four frequency bands in B-configuration, giving high spatial resolution to focus on the core emission. We use Markov Chain Monte Carlo methods to fit the continuum emission in order to find the turnover frequency. After testing for correlations, the turnover frequency does not display a significant dependence on either mass or mass accretion rate, indicating that more complicated physics than simple scaling and optical depth effects are at play, as has been suggested by recent theoretical work.
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