Halo masses for optically selected and for radio-loud AGN from clustering and galaxy–galaxy lensing

We compute two-point correlation functions and measure the shear signal due to galaxy–galaxy lensing for 80 000 optically identified and 5700 radio-loud active galactic nuclei (AGN) from Data Release 4 of the Sloan Digital Sky Survey. Halo occupation models are used to estimate halo masses and satellite fractions for these two types of AGN. The large sample size allows us to separate AGN according to the stellar mass of their host galaxies. We study how the halo masses of optical and radio AGN differ from those of the parent population at fixed   M _*  . Halo masses deduced from clustering and from lensing agree satisfactorily. Radio AGN are found in more massive haloes than optical AGN: in our samples, their mean halo masses are  1.6 × 10¹³  and  8 × 10¹¹  h ⁻¹ M_⊙  , respectively. Optical AGN follow the same relation between stellar mass and halo mass as galaxies selected without regard to nuclear properties, but radio-loud AGN deviate significantly from this relation. The dark matter haloes of radio-loud AGN are about twice as massive as those of control galaxies of the same stellar mass. This boost is independent of radio luminosity, and persists even when our analysis is restricted to field galaxies. The large-scale gaseous environment of the galaxy clearly plays a crucial role in producing observable radio emission. The dark matter halo masses that we derive for the AGN in our two samples are in good agreement with recent models in which feedback from radio AGN becomes dominant in haloes where gas cools quasi-statically.     

Tidal effects and the environment dependence of halo assembly

We explore a possible origin for the puzzling anti-correlation between the formation epoch of galactic dark-matter haloes and their environment density. This correlation has been revealed from cosmological N -body simulations and is in conflict with the extended Press–Schechter model of halo clustering. Using similar simulations, we first quantify the straightforward association of an early formation epoch with a reduced mass-growth rate at late times. We then find that a primary driver of suppressed growth, by accretion and mergers, is tidal effects dominated by a neighbouring massive halo. The tidal effects range from a slowdown of the assembly of haloes due to the shear along the large-scale filaments that feed the massive halo to actual mass loss in haloes that pass through the massive halo. Using the restricted three-body problem, we show that haloes are prone to tidal mass loss within 1.5 virial radii of a larger halo. Our results suggest that the dependence of the formation epoch on environment density is a secondary effect induced by the enhanced density of haloes in filaments near massive haloes where the tides are strong. Our measures of assembly rate are particularly correlated with the tidal field at high redshifts   z ∼ 1  .     

Theoretical estimates of intrinsic galaxy alignment

It has recently been argued that the observed ellipticities of galaxies may be determined at least in part by the primordial tidal gravitational field in which the galaxy formed. Long-range correlations in the tidal field could thus lead to an ellipticity–ellipticity correlation for widely separated galaxies. We present a new model relating ellipticity to angular momentum, which can be calculated in linear theory. We use this model to calculate the angular power spectrum of intrinsic galaxy shape correlations. We show that, for low-redshift galaxy surveys, our model predicts that intrinsic correlations will dominate correlations induced by weak lensing, in good agreement with previous theoretical work and observations. We find that our model produces ' E -mode' correlations enhanced by a factor of 3.5 over B -modes on small scales, making it harder to disentangle intrinsic correlations from those induced by weak gravitational lensing.     

Weak gravitational flexion

Flexion is the significant third-order weak gravitational lensing effect responsible for the weakly skewed and arc-like appearance of lensed galaxies. Here we demonstrate how flexion measurements can be used to measure galaxy halo density profiles and large-scale structure on non-linear scales, via galaxy–galaxy lensing, dark matter mapping and cosmic flexion correlation functions. We describe the origin of gravitational flexion, and discuss its four components, two of which are first described here. We also introduce an efficient complex formalism for all orders of lensing distortion. We proceed to examine the flexion predictions for galaxy–galaxy lensing, examining isothermal sphere and Navarro–Frenk–White (NFW) profiles and both circularly symmetric and elliptical cases. We show that in combination with shear we can precisely measure galaxy masses and NFW halo concentrations. We also show how flexion measurements can be used to reconstruct mass maps in two-dimensional projection on the sky, and in three dimensions in combination with redshift data. Finally, we examine the predictions for cosmic flexion, including convergence–flexion cross-correlations, and we find that the signal is an effective probe of structure on non-linear scales.     

Intrinsic and extrinsic galaxy alignment

We show with analytic models that the assumption of uncorrelated intrinsic ellipticities of target sources that is usually made in searches for weak gravitational lensing arising from large-scale mass inhomogeneities ('field lensing') is unwarranted. If the orientation of the galaxy image is determined either by the angular momentum or by the shape of the halo in which it forms, then the image should be aligned preferentially with the component of the tidal gravitational field perpendicular to the line of sight. Long-range correlations in the tidal field will thus lead to long-range ellipticity–ellipticity correlations that mimic the shear correlations arising from weak gravitational lensing. We calculate the ellipticity–ellipticity correlation expected if halo shapes determine the observed galaxy shape, and we discuss uncertainties (which are still considerable) in the predicted amplitude of this correlation. The ellipticity–ellipticity correlation induced by angular momenta should be smaller. We consider several methods for discriminating between the weak-lensing (extrinsic) and intrinsic correlations, including the use of redshift information. An ellipticity–tidal-field correlation also implies the existence of an alignment of images of galaxies near clusters. Although the intrinsic alignment may complicate the interpretation of field-lensing results, it is inherently interesting as it may shed light on galaxy formation as well as on structure formation.     

An analytic model for the epoch of halo creation

In this paper we describe the Bayesian link between the cosmological mass function and the distribution of times at which isolated haloes of a given mass exist. By assuming that clumps of dark matter undergo monotonic growth on the time-scales of interest, this distribution of times is also the distribution of 'creation' times of the haloes. This monotonic growth is an inevitable aspect of gravitational instability. The spherical top-hat collapse model is used to estimate the rate at which clumps of dark matter collapse. This gives the prior for the creation time given no information about halo mass. Applying Bayes' theorem then allows any mass function to be converted into a distribution of times at which haloes of a given mass are created. This general result covers both Gaussian and non-Gaussian models. We also demonstrate how the mass function and the creation time distribution can be combined to give a joint density function, and discuss the relation between the time distribution of major merger events and the formula calculated. Finally, we determine the creation time of haloes within three N -body simulations, and compare the link between the mass function and creation rate with the analytic theory.     

The Hubble constant from galaxy lenses: impacts of triaxiality and model degeneracies

The Hubble constant can be constrained using the time delays between multiple images of gravitationally lensed sources. In some notable cases, typical lensing analyses assuming isothermal galaxy density profiles produce low values for the Hubble constant, inconsistent with the result of the HST Key Project  (72 ± 8 km s⁻¹ Mpc⁻¹)  . Possible systematics in the values of the Hubble constant derived from galaxy lensing systems can result from a number of factors, for example, neglect of environmental effects, assumption of isothermality, or contamination by line-of-sight structures. One additional potentially important factor is the triaxial structure of the lensing galaxy halo; most lens models account for halo shape simply by perturbing the projected spherical lensing potential, an approximation that is often necessary but that is inadequate at the levels of triaxiality predicted in the cold dark matter paradigm. To quantify the potential error introduced by this assumption in estimates of the Hubble parameter, we strongly lens a distant galaxy through a sample of triaxial softened isothermal haloes and use an Markov Chain Monte Carlo method to constrain the lensing halo profile and the Hubble parameter from the resulting multiple image systems. We explore the major degeneracies between the Hubble parameter and several parameters of the lensing model, finding that without a way to accurately break these degeneracies accurate estimates of the Hubble parameter are not possible. Crucially, we find that triaxiality does not significantly bias estimates of the Hubble constant, and offer an analytic explanation for this behaviour in the case of isothermal profiles. Neglected triaxial halo shape cannot contribute to the low Hubble constant values derived in a number of galaxy lens systems.