We propose a novel method to constrain turbulence and bulk motions in massive galaxies, galaxy groups and clusters, exploring both simulations and observations. As emerged in the recent picture of the top-down multiphase condensation, the hot gaseous halos are tightly linked to all other phases in terms of cospatiality and thermodynamics. While hot halos (∼ 10 7 K) are perturbed by subsonic turbulence, warm (∼ 10 4 K) ionized and neutral filaments condense out of the turbulent eddies. The peaks condense into cold molecular clouds (< 100 K) raining in the core via chaotic cold accretion (CCA). We show all phases are tightly linked in terms of the ensemble (wide-aperture) velocity dispersion along the line of sight. The correlation arises in complementary long-term AGN feedback simulations and high-resolution CCA runs, and is corroborated by the combined Hitomi and new Integral Field Unit measurements in Perseus cluster. The ensemble multiphase gas distributions (from UV to radio band) are characterized by substantial spectral line broadening (σ v,los ≈ 100 -200 km s −1 ) with mild line shift. On the other hand, pencil-beam detections (as HI absorption against the AGN backlight) sample the small-scale clouds displaying smaller broadening and significant line shift up to several 100 km s −1 (for those falling toward the AGN), with increased scatter due to the turbulence intermittency. We present new ensemble σ v,los of the warm Hα+[NII] gas in 72 observed cluster/group cores: the constraints are consistent with the simulations and can be used as robust proxies for the turbulent velocities, in particular for the challenging hot plasma (otherwise requiring extremely long X-ray exposures). Finally, we show the physically motivated criterion C ≡ t cool /t eddy ≈ 1 best traces the condensation extent region and presence of multiphase gas in observed clusters and groups. The ensemble method can be applied to many available spectroscopic datasets and can substantially advance our understanding of multiphase halos in light of the next-generation multiwavelength missions.

The Fast Radio Burst FRB121102 has been observed to repeat in an irregular fashion. Using published timing data of the observed bursts, we show that Poissonian statistics are not a good description of this random process. As an alternative we suggest to describe the intervals between bursts with a Weibull distribution with a shape parameter smaller than one, which allows for the clustered nature of the bursts. We quantify the amount of clustering using the parameters of the Weibull distribution and discuss the consequences that it has for the detection probabilities of future observations and for the optimization of observing strategies. Allowing for this generalization, we find a mean repetition rate of r = 5.7 +3.0 −2.0 per day and index k = 0.34 +0.06 −0.05 for a correlation function ξ(t) = (t/t 0 ) k−1 .

We present a direct approach to nonparametrically reconstruct the linear density field from an observed nonlinear map. We solve for the unique displacement potential consistent with the nonlinear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to the nonlinear scale (r δr δ L > 0.5 for k 1 h/Mpc) with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully nonlinear fields, potentially substantially expanding the baryon acoustic oscillations and redshift space distortions information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping initiatives.