The first objects to arise in a cold dark matter universe present a daunting challenge for models of structure formation. In the ultra small-scale limit, CDM structures form nearly simultaneously across a wide range of scales. Hierarchical clustering
no longer provides a guiding principle for theoretical analyses and the computation time required to carry out credible simulations becomes prohibitively high. To gain insight into this problem, we perform high-resolution (N=720^3 - 1584^3) simulations of an Einstein-de Sitter cosmology where the initial power spectrum is P(k) propto k^n, with -2.5 < n < -1. Self-similar scaling is established for n=-1 and n=-2 more convincingly than in previous, lower-resolution simulations and for the first time, self-similar scaling is established for an n=-2.25 simulation. However, finite box-size effects induce departures from self-similar scaling in our n=-2.5 simulation. We compare our results with the predictions for the power spectrum from (one-loop) perturbation theory and demonstrate that the renormalization group approach suggested by McDonald improves perturbation theorys ability to predict the power spectrum in the quasilinear regime. In the nonlinear regime, our power spectra differ significantly from the widely used fitting formulae of Peacock & Dodds and Smith et al. and a new fitting formula is presented. Implications of our results for the stable clustering hypothesis vs. halo model debate are discussed. Our power spectra are inconsistent with predictions of the stable clustering hypothesis in the high-k limit and lend credence to the halo model. Nevertheless, the fitting formula advocated in this paper is purely empirical and not derived from a specific formulation of the halo model.
We show that current clustering observations of quasars and luminous AGN can be explained by a merger model augmented by feedback from outflows. Using numerical simulations large enough to study clustering out to 25 comoving h^{-1} Mpc, we calculate
correlation functions, biases, and correlation lengths as a function of AGN redshift and optical and X-ray luminosity. At optical wavelengths, our results match a wide range of current observations and generate predictions for future data sets. We reproduce the weak luminosity dependence of clustering over the currently well-measured range, and predict a much stronger dependence at higher luminosities. The increase in the amplitude of binary quasar clustering observed in the Sloan Digital Sky Survey (SDSS) is also reproduced and is predicted to occur at higher redshift, an effect that is due to the one halo term in the correlation function. On the other hand, our results do not match the rapid evolution of the correlation length observed in the SDSS at zsimeq 3, a discrepancy that is at least partially due to differences in the scales probed by our simulation versus this survey. In fact, we show that changing the distances sampled from our simulations can produce changes as large as 40% in the fitted correlation lengths. Finally, in the X-ray, our simulations produce correlation lengths similar to that observed in the Chandra Deep Field (CDF) North, but not the significantly larger correlation length observed in the CDF South.
One of the most important and poorly-understood issues in structure formation is the role of outflows driven by active galactic nuclei (AGN). Using large-scale cosmological simulations, we compute the impact of such outflows on the small-scale distri
bution of the cosmic microwave background (CMB). Like gravitationally-heated structures, AGN outflows induce CMB distortions both through thermal motions and peculiar velocities, by processes known as the thermal and kinetic Sunyaev-Zeldovich (SZ) effects, respectively. For AGN outflows the thermal SZ effect is dominant, doubling the angular power spectrum on arcminute scales. But the most distinct imprint of AGN feedback is a substantial increase in the thermal SZ distortions around elliptical galaxies, post-starburst ellipticals, and quasars, which is linearly proportional to the outflow energy. While point source subtraction is difficult for quasars, we show that by appropriately stacking microwave measurements around early-type galaxies, the new generation of small-scale microwave telescopes will be able to directly measure AGN feedback at the level important for current theoretical models.
