Luminosity Functions of Elliptical Galaxies at z < 1.2

The luminosity functions of E/S0 galaxies are constructed in 3 different redshift bins (0.2 < z < 0.55, 0.55 < z < 0.8, 0.8 < z < 1.2), using the data from the Hubble Space Telescope Medium Deep Survey (HST MDS) and other HST surveys. These independent luminosity functions show the brightening in the luminosity of E/S0s by about 0.5~1.0 magnitude at z~1, and no sign of significant number evolution. This is the first direct measurement of the luminosity evolution of E/S0 galaxies, and our results support the hypothesis of a high redshift of formation (z > 1) for elliptical galaxies, together with weak evolution of the major merger rate at z < 1.Comment: To be published in ApJ Letters, 4 pages, AAS Latex, 4 figures, and 2 table

Spectrum of the Product of Independent Random Gaussian Matrices

We show that the eigenvalue density of a product X=X_1 X_2 ... X_M of M independent NxN Gaussian random matrices in the large-N limit is rotationally symmetric in the complex plane and is given by a simple expression rho(z,\bar{z}) = 1/(M\pi\sigma^2} |z|^{-2+2/M} for |z|<\sigma, and is zero for |z|> \sigma. The parameter \sigma corresponds to the radius of the circular support and is related to the amplitude of the Gaussian fluctuations. This form of the eigenvalue density is highly universal. It is identical for products of Gaussian Hermitian, non-Hermitian, real or complex random matrices. It does not change even if the matrices in the product are taken from different Gaussian ensembles. We present a self-contained derivation of this result using a planar diagrammatic technique for Gaussian matrices. We also give a numerical evidence suggesting that this result applies also to matrices whose elements are independent, centered random variables with a finite variance.Comment: 16 pages, 6 figures, minor changes, some references adde

A Slow Merger History of Field Galaxies Since z~1

Using deep infrared observations conducted with the CISCO imager on the Subaru Telescope, we investigate the field-corrected pair fraction and the implied merger rate of galaxies in redshift survey fields with Hubble Space Telescope imaging. In the redshift interval, 0.5 < z < 1.5, the fraction of infrared-selected pairs increases only modestly with redshift to 7% +- 6% at z~1. This is nearly a factor of three less than the fraction, 22% +- 8%, determined using the same technique on HST optical images and as measured in a previous similar study. Tests support the hypothesis that optical pair fractions at z~1 are inflated by bright star-forming regions that are unlikely to be representative of the underlying mass distribution. By determining stellar masses for the companions, we estimate the mass accretion rate associated with merging galaxies. At z~1, we estimate this to be 2x10^{9 +- 0.2} solar masses per galaxy per Gyr. Although uncertainties remain, our results suggest that the growth of galaxies via the accretion of pre-existing fragments remains as significant a phenomenon in the redshift range studied as that estimated from ongoing star formation in independent surveys.Comment: 5 pages, accepted for publication in ApJ Letter

Symplectic formulation of the type IIA nongeometric scalar potential

We study the four-dimensional (4D) scalar potential arising from a generalized type IIA flux superpotential including the (non-)geometric fluxes. First, we show that using a set of peculiar flux combinations, the 4D scalar potential can be formulated into a very compact form. This is what we call as the `symplectic formulation' from which one could easily anticipate the ten-dimensional origin of the effective scalar potential. We support our formulation through an alternate derivation of the scalar potential via considering the Double Field Theory (DFT) reduction on a generic Calabi Yau orientifold. In addition, we also exemplify the insights of our formulation with explicit computations for two concrete toroidal examples using orientifolds of the complex threefolds ${\mathbb T}^6/{({\mathbb Z}_2 \times {\mathbb Z}_2)}$ and ${\mathbb T}^6/{\mathbb Z}_4$.Comment: v4: 33 pages, typos fixed in eqn. (4.22) and (4.23), and some cosmetic changes in the title; version to appear in PR