Eisenstein DJ, Loeb A.

An analytical model for the triaxial collapse of cosmological perturbations. The Astrophysical Journal. 1995;439 :520-541.

Publisher's VersionAbstractWe present an analytical model for the nonspherical collapse ofoverdense regions out of a Gaussian random field of initial cosmologicalperturbations. The collapsing region is treated as an ellipsoid ofconstant density, acted upon by the quadrupole tidal shear from thesurrounding matter. The dynamics of the ellipsoid is set by theellipsoid self-gravity and the external quadrupole shear. Both forcesare linear in the coordinates and therefore maintain homogeneity of theellipsoid at all times. The amplitude of the external shear is evolvedinto the nonlinear regime in thin spherical shells that are allowed tomove only radially according to mass interior to them. The fulldynamical equations then reduce to a set of nine second-order ordinarydifferential equations, which reproduce the linear regime behavior butcan be evolved past turnaround, well into the nonlinear regime. Wedescribe how the initial conditions can be drawn in the appropriatecorrelated way from a random field of initial density perturbations. Themodel is applied to a restricted set of initial conditions that are moresuitable to the above approximations; most notable we focus on theproperties of rare high-density peaks (greater than of approximately = 2sigma). By considering many random realization of the initialconditions, we calculate the distributions of shapes and angular momentaacquired by objects through the coupling of their quadruole moment tothe tidal shear. The average value of the spin parameter, (mean value ofa lambda) approximately = 0.04, is found to be only weakly dependent onthe system mass, the mean cosmological density, or the initial powerspectrum of perturbations, in agreement with N-body simulations. For thecold dark matter power spectrum, most objects evolve from aquasi-spherical initial state to a pancake or filament and then tocomplete virialization. Low-spin objects tend to be more spherical. Theevolution history of shapes is primarily induced by the external shearand not by the initial triaxially of the objects. The statisticaldistribution of the triaxial shapes of collapsing region can be used totest cosmological models against galaxy surveys on large scales.

Eisenstein DJ, Loeb A.

Origin of quasar progenitors from the collapse of low-spin cosmological perturbations. The Astrophysical Journal. 1995;443 :11-17.

Publisher's VersionAbstractWe show that seeds for quasar black holes could have originated from theinitial cosmological collapse of overdense regions with unusually smallrotation. The gas in these rare regions collapses into a compact diskthat shrinks on a short viscous timescale. Using an analytical model, wecalculate the low-pin tail of the probability distribution of angularmomenta for objects that collapse out of a Gaussian random field ofinitial density peturbations. The population of low-spin systems issignificant for any viable power spectrum of primordial densityperturbations. Most objects from just above the cosmological Jeans massapproximately 10^{5} solar mass at high redshifts z greater thanand approximately 10. In the standard cold dark matter cosmology, thecomoving density of 10^{6-7} solar mass objects with viscousevolution times shorter than approximately 10^{6-7} years isapproximately 10^{-3}(h/0.5)^{3}/cubic Mpc, comparableto the local density of bright galaxies. The seed black holes tend toreside within larger mass systems that collapse later and supply the gasneeded for the bright quasar activity.

Loeb A, Eisenstein DJ.

Probing Early Clustering with LY alpha Absorption Lines beyond the Quasar Redshift. The Astrophysical Journal. 1995;448 :17.

Publisher's VersionAbstractGroups and clusters of galaxies hosting a quasar can be found throughthe detection of Lyα absorption lines beyond the quasar redshift.The effect occurs whenever the distortion to the redshift distributionof Lyα clouds induced by the cluster potential extends beyond theproximity effect of the quasar. Based on cold dark matter (CDM)cosmological models for the evolution of structure, we predict theprobability for finding lines beyond the quasar redshift(Ζ_{abs} > Ζ_{Q}) under the assumption thatthe physical properties of Lyman alpha clouds are not affected by flowson large scales (≳Mpc) in the quasi-linear regime. If quasarsrandomly sample the underlying galaxy distribution, the expected numberof lines with Ζ_{abs} > Ζ_{Q} per quasarcan be as high as ˜0.5 × [(dN/dΖ)/350] at Ζ = 2,where dN/dΖ is the number of Lyα lines per unit redshift farfrom the quasar. The probability is enhanced if quasars typically residein small groups of galaxies. A statistical excess of Lyα lines isexpected near very dim quasars or around metal absorption systems. Dueto clustering, the standard approach to the proximity effectoverestimates the ionizing background flux at high redshifts by up to afactor of ˜3. This result weakens the discrepancy between thededuced background flux and the contribution from known populations ofquasars.