Comparison of simple mass estimators for slowly rotating elliptical galaxies

We compare the performance of mass estimators for elliptical galaxies that rely on the directly observable surface brightness and velocity dispersion profiles, without invoking computationally expensive detailed modeling. These methods recover the mass at a specific radius where the mass estimate is expected to be least sensitive to the anisotropy of stellar orbits. One method (Wolf et al. 2010) uses the total luminosity-weighted velocity dispersion and evaluates the mass at a 3D half-light radius $r_{1/2}$, i.e., it depends on the GLOBAL galaxy properties. Another approach (Churazov et al. 2010) estimates the mass from the velocity dispersion at a radius $R_2$ where the surface brightness declines as $R^{-2}$, i.e., it depends on the LOCAL properties. We evaluate the accuracy of the two methods for analytical models, simulated galaxies and real elliptical galaxies that have already been modeled by the Schwarzschild's orbit-superposition technique. Both estimators recover an almost unbiased circular speed estimate with a modest RMS scatter ($\lesssim 10 \%$). Tests on analytical models and simulated galaxies indicate that the local estimator has a smaller RMS scatter than the global one. We show by examination of simulated galaxies that the projected velocity dispersion at $R_2$ could serve as a good proxy for the virial galaxy mass. For simulated galaxies the total halo mass scales with $\sigma_p(R_2)$ as $M_{vir} \left[M_{\odot}h^{-1}\right] \approx 6\cdot 10^{12} \left( \frac{\sigma_p(R_2)}{200\, \rm km\, s^{-1}} \right)^{4}$ with RMS scatter $\approx 40 \%$.Comment: 19 pages, 14 figures, 4 tables, accepted for publication in MNRA

Time-frequency analysis of locally stationary Hawkes processes

Locally stationary Hawkes processes have been introduced in order to generalise classical Hawkes processes away from stationarity by allowing for a time-varying second-order structure. This class of self-exciting point processes has recently attracted a lot of interest in applications in the life sciences (seismology, genomics, neuro-science,...), but also in the modelling of high-frequency financial data. In this contribution we provide a fully developed nonparametric estimation theory of both local mean density and local Bartlett spectra of a locally stationary Hawkes process. In particular we apply our kernel estimation of the spectrum localised both in time and frequency to two data sets of transaction times revealing pertinent features in the data that had not been made visible by classical non-localised approaches based on models with constant fertility functions over time.Comment: Bernoulli journal, A Para{\^i}tr

zCOSMOS 10k-bright spectroscopic sample: Exploring mass and environment dependence in early-type galaxies

Aims. We present the analysis of the U – V rest-frame color distribution and some spectral features as a function of mass and environment for a sample of early-type galaxies up to z = 1 extracted from the zCOSMOS spectroscopic survey. This analysis is used to place constraints on the relative importance of these two properties in controlling galaxy evolution. Methods. We used the zCOSMOS 10k-bright sample, limited to the AB magnitude range 15 < I < 22.5, from which we extracted two different subsamples of early-type galaxies. The first sample (“red galaxies”) was selected using a photometric classification (2098 galaxies), while in the second case (“ETGs”) we combined morphological, photometric, and spectroscopic properties to obtain a more reliable sample of elliptical, red, passive, early-type galaxies (981 galaxies). The analysis is performed at fixed mass to search for any dependence of the color distribution on environment, and at fixed environment to search for any mass dependence. Results. In agreement with the low redshift results of the SDSS, we find that the color distribution of red galaxies is not strongly dependent on environment for all mass bins, exhibiting only a weak trend such that galaxies in overdense regions (log_(10)(1+Δ) ~ 1.2) are redder than galaxies in underdense regions (log_(10)(1+Δ) ~ 0.1), 
with a difference of = 0.027±0.008 mag. On the other hand, the dependence on mass is far more significant, and we find that the average colors of massive galaxies (log_(10)(M/M_☉) ~ 10.8) are redder by = 0.093±0.007 mag than low-mass galaxies (log_(10)(M/M_☉) ~ 10) 
throughout the entire redshift range. We study the color-mass (U – V)_(rest) ∝ S_M ·log_(10)(M/M_☉) relation, finding a mean slope = 0.12±0.005, while the color-environment (U – V)_(rest) ∝ S_δ · log_(10)(1+Δ) relation is flatter, with a slope always smaller than S_δ ≈ 0.04. 
 The spectral analysis that we perform on our ETGs sample is in good agreement with our photometric results: we study the 4000 Å  break and the equivalent width of the Hδ Balmer line, finding for D4000 a dependence on mass ( =0.11±0.02 between log_(10)(M/M_☉) ~ 10.2 and log_(10)(M/M_☉) ~ 10.8), and a much weaker dependence on environment ( = 0.05±0.02 between high and low environment quartiles). The same is true for the equivalent width of Hδ, for which we measure a difference of ΔEW0(Hδ) = 0.28±0.08 Å  across the same mass range and no significant dependence on environment. By analyzing the lookback time of early-type galaxies, we support the possibility of a downsizing scenario, in which massive galaxies with a stronger D4000 and an almost constant equivalent width of Hδ formed their mass at higher redshift than lower mass ones. We also conclude that the main driver of galaxy evolution is the galaxy mass, the environment playing a subdominant role

Halo assembly bias and the tidal anisotropy of the local halo environment

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-halo estimator of linear bias. For the small-scale environment, we identify a variable $\alpha_R$ that captures the $\textit{tidal anisotropy}$ in a region of radius $R=4R_{\textrm{200b}}$ around the halo and correlates strongly with halo bias at fixed mass. Segregating haloes by $\alpha_R$ reveals two distinct populations. Haloes in highly isotropic local environments ($\alpha_R\lesssim0.2$) behave as expected from the simplest, spherically averaged analytical models of structure formation, showing a $\textit{negative}$ correlation between their concentration and large-scale bias at $\textit{all}$ masses. In contrast, haloes in anisotropic, filament-like environments ($\alpha_R\gtrsim0.5$) tend to show a $\textit{positive}$ correlation between bias and concentration at any mass. Our multi-scale analysis cleanly demonstrates how the overall assembly bias trend across halo mass emerges as an average over these different halo populations, and provides valuable insights towards building analytical models that correctly incorporate assembly bias. We also discuss potential implications for the nature and detectability of galaxy assembly bias.Comment: 19 pages, 15 figures; v2: revised in response to referee comments, added references and discussion, conclusions unchanged. Accepted in MNRA