We present a semi-analytic, physically motivated model for dark matter halo concentration as a function of halo mass and redshift. The semi-analytic model combines an analytic model for the halo mass accretion history (MAH), based on extended Press Schechter (EPS) theory, with an empirical relation between concentration and formation time obtained through fits to the results of numerical simulations. Because the semi-analytic model is based on EPS theory, it can be applied to wide ranges in mass, redshift and cosmology. The resulting concentration-mass (c − M ) relations are found to agree with the simulations, and because the model applies only to relaxed halos, they do not exhibit the upturn at high masses or high redshifts found by some recent works. We predict a change of slope in the z ∼ 0 c − M relation at a mass scale of 10 11 M ⊙ . We find that this is due to the change in the functional form of the halo MAH, which goes from being dominated by an exponential (for high-mass halos) to a power-law (for low-mass halos). During the latter phase, the core radius remains approximately constant, and the concentration grows due to the drop of the background density. We also analyse how the c − M relation predicted by this work affects the power produced by dark matter annihilation, finding that at z = 0 the power is two orders of magnitude lower than that obtained from extrapolating best-fitting c − M relations. We provide fits to the c − M relations as well as numerical routines to compute concentrations and MAHs †.

We present seven epochs of spectroscopy on the quadruply imaged quasar SDSS J1004+4112, spanning observed-frame time delays from 1 to 322 days. The spectra reveal differences in the emission lines between the lensed images. Specifically, component A showed a strong enhancement in the blue wings of -2several high-ionization lines relative to component B, which lasted at least 28 days (observed frame) then faded. Since the predicted time delay between A and B is 30 days, our time coverage suggests that the event was not intrinsic to the quasar. We attribute these variations to microlensing of part of the broad emission line region of the quasar, apparently resolving structure in the source plane on a scale of ∼ 10 16 cm at z = 1.734. In addition, we observed smaller differences in the emission line profiles between components A and B that persisted throughout the time span, which may also be due to microlensing or millilensing. Further spectroscopic monitoring of this system holds considerable promise for resolving the structure of the broad emission line region in quasars.

Exceptionally bright quasars with redshifts up to z=6.28 have recently been discovered 1 . Quasars are thought to be powered by the accretion of gas onto supermassive black holes at the centres of galaxies. Their maximum (Eddington) luminosity is proportional to the mass of the black hole, and so these bright quasars are inferred to have black holes with masses of more than a few billion solar masses. The existence of such massive black holes poses a challenge to models for the formation of structures in the early Universe, as it requires that the black holes would grow so massive in less than a billion years after the Big Bang. Here we show that up to a third of known quasars with z∼6 will have their observed flux magnified by a factor of 10 or more through gravitational lensing by galaxies along the line of sight. The inferred abundance of quasar host galaxies, as well as the luminosity density provided by the quasars, are therefore substantially overestimated.The four highest redshift quasars known 1 with z ∼ > 5.8 (SDSS 1044-0125 was later found 4 to have z = 5.73), were selected in the SDSS photometric system to have magnitudes z * < 20.2 and colors i * − z * > 2.2. The masses of the black holes powering these quasars are estimated to be ∼ > 3 × 10 9 M ⊙ , implying 3 that the mass of their host galaxies is ∼ > 10 13 M ⊙ . Such massive hosts lie on the steep exponential tail of the Press-Schechter 5

We examine the properties of the host galaxies of z = 7 quasars using the large volume, cosmological hydrodynamical simulation BlueTides. We find that the 10 most massive black holes and the 191 quasars in the simulation (with MUV, AGN &lt; MUV, host) are hosted by massive galaxies with stellar masses log (M*/M⊙) = 10.8 ± 0.2, and 10.2 ± 0.4,which have large star formation rates, of $513\substack{+1225 \\-351}M_\odot /\rm {yr}$ and $191\substack{+288 \\-120}M_\odot /\rm {yr}$, respectively. The hosts of the most massive black holes and quasars in BlueTides are generally bulge-dominated, with bulge-to-total mass ratio B/T ≃ 0.85 ± 0.1, however their morphologies are not biased relative to the overall z = 7 galaxy sample. We find that the hosts of the most massive black holes and quasars are compact, with half-mass radii $R_{0.5}=0.41\substack{+0.18 \\-0.14}$ kpc and $0.40\substack{+0.11 \\-0.09}$ kpc respectively; galaxies with similar masses and luminosities have a wider range of sizes with a larger median value, $R_{0.5}=0.71\substack{+0.28 \\-0.25}$ kpc. We make mock James Webb Space Telescope (JWST) images of these quasars and their host galaxies. We find that distinguishing the host from the quasar emission will be possible but still challenging with JWST, due to the small sizes of quasar hosts. We find that quasar samples are biased tracers of the intrinsic black hole–stellar mass relation, following a relation that is 0.2 dex higher than that of the full galaxy sample. Finally, we find that the most massive black holes and quasars are more likely to be found in denser environments than the typical MBH &gt; 106.5M⊙ black hole, indicating that minor mergers play at least some role in growing black holes in the early Universe.

Determination of microlensing parameters in the gravitationally lensed quasar Q2237+0305 from the statistics of high magnification events will require monitoring for more than 100 years (Wambsganss, Paczynski & Schneider 1990). However we show that the effective transverse velocity of the lensing galaxy can be determined on a more realistic time-scale through consideration of the distribution of light-curve derivatives. The 10 years of existing monitoring data for Q2237+0305 are analysed. These data display strong evidence for microlensing that is not associated with a high magnification event. An upper limit of v < 500 km/sec is obtained for the galactic transverse velocity which is smaller than previously assumed values. The analysis suggests that the observed microlensing variation may be predominantly due to stellar proper motions. The statistical significance of the results obtained from our method will be increased by the addition of data points from current and future monitoring campaigns. However reduced photometric errors will be more valuable than an increased sampling rate.Comment: 16 pages, including 17 figures. Accepted for publication in M.N.R.A.