Limits on the evolution of galaxies from the statistics of gravitational lenses

We use gravitational lenses from the Cosmic Lens All-Sky Survey (CLASS) to constrain the evolution of galaxies since redshift $z \sim 1$ in the current \LCDM cosmology. This constraint is unique as it is based on a mass-selected lens sample of galaxies. Our method of statistical analysis is the same as in Chae (2003). We parametrise the early-type number density evolution in the form of $(1+z)^{\nu_n}$ and the velocity dispersion as $(1+z)^{\nu_v}$. We find that $\nu_n=-0.11^{+0.82}_{-0.89}$ ($1\sigma$) if we assume $\nu_v =0$, implying that the number density of early-type galaxies is within 50% to 164% of the present-day value at redshift $z=1$. Allowing the velocity dispersion to evolve, we find that $\nu_v=-0.4^{+0.5}_{-0.4}$ ($1\sigma$), indicating that the velocity dispersion must be within 57% and 107% of the present-day value at $z=1$. These results are consistent with the early formation and passive evolution of early-type galaxies. More stringent limits from lensing can be obtained from future large lens surveys and by using very high-redshift quasars (z \ga 5) such as those found from the Sloan Digital Sky Survey.Comment: 10 pages (preprint format), 2 figures, ApJL in press (December 20th issue

Biased-estimations of the Variance and Skewness

Nonlinear combinations of direct observables are often used to estimate quantities of theoretical interest. Without sufficient caution, this could lead to biased estimations. An example of great interest is the skewness $S_3$ of the galaxy distribution, defined as the ratio of the third moment \xibar_3 and the variance squared \xibar_2^2. Suppose one is given unbiased estimators for \xibar_3 and \xibar_2^2 respectively, taking a ratio of the two does not necessarily result in an unbiased estimator of $S_3$. Exactly such an estimation-bias affects most existing measurements of $S_3$. Furthermore, common estimators for \xibar_3 and \xibar_2 suffer also from this kind of estimation-bias themselves: for \xibar_2, it is equivalent to what is commonly known as the integral constraint. We present a unifying treatment allowing all these estimation-biases to be calculated analytically. They are in general negative, and decrease in significance as the survey volume increases, for a given smoothing scale. We present a re-analysis of some existing measurements of the variance and skewness and show that most of the well-known systematic discrepancies between surveys with similar selection criteria, but different sizes, can be attributed to the volume-dependent estimation-biases. This affects the inference of the galaxy-bias(es) from these surveys. Our methodology can be adapted to measurements of analogous quantities in quasar spectra and weak-lensing maps. We suggest methods to reduce the above estimation-biases, and point out other examples in LSS studies which might suffer from the same type of a nonlinear-estimation-bias.Comment: 28 pages of text, 9 ps figures, submitted to Ap

Extending the halo mass resolution of NN-body simulations

We present a scheme to extend the halo mass resolution of N-body simulations of the hierarchical clustering of dark matter. The method uses the density field of the simulation to predict the number of sub-resolution dark matter haloes expected in different regions. The technique requires as input the abundance of haloes of a given mass and their average clustering, as expressed through the linear and higher order bias factors. These quantities can be computed analytically or, more accurately, derived from a higher resolution simulation as done here. Our method can recover the abundance and clustering in real- and redshift-space of haloes with mass below $\sim 7.5 \times 10^{13}h^{-1}M_{\odot}$ at $z=0$ to better than 10%. We demonstrate the technique by applying it to an ensemble of 50 low resolution, large-volume $N$-body simulations to compute the correlation function and covariance matrix of luminous red galaxies (LRGs). The limited resolution of the original simulations results in them resolving just two thirds of the LRG population. We extend the resolution of the simulations by a factor of 30 in halo mass in order to recover all LRGs. With existing simulations it is possible to generate a halo catalogue equivalent to that which would be obtained from a $N$-body simulation using more than 20 trillion particles; a direct simulation of this size is likely to remain unachievable for many years. Using our method it is now feasible to build the large numbers of high-resolution large volume mock galaxy catalogues required to compute the covariance matrices necessary to analyse upcoming galaxy surveys designed to probe dark energy.Comment: 11 pages, 7 Figure

Measuring the galaxy power spectrum and scale-scale correlations with multiresolution-decomposed covariance -- I. method

We present a method of measuring galaxy power spectrum based on the multiresolution analysis of the discrete wavelet transformation (DWT). Since the DWT representation has strong capability of suppressing the off-diagonal components of the covariance for selfsimilar clustering, the DWT covariance for popular models of the cold dark matter cosmogony generally is diagonal, or $j$(scale)-diagonal in the scale range, in which the second scale-scale correlations are weak. In this range, the DWT covariance gives a lossless estimation of the power spectrum, which is equal to the corresponding Fourier power spectrum banded with a logarithmical scaling. In the scale range, in which the scale-scale correlation is significant, the accuracy of a power spectrum detection depends on the scale-scale or band-band correlations. This is, for a precision measurements of the power spectrum, a measurement of the scale-scale or band-band correlations is needed. We show that the DWT covariance can be employed to measuring both the band-power spectrum and second order scale-scale correlation. We also present the DWT algorithm of the binning and Poisson sampling with real observational data. We show that the alias effect appeared in usual binning schemes can exactly be eliminated by the DWT binning. Since Poisson process possesses diagonal covariance in the DWT representation, the Poisson sampling and selection effects on the power spectrum and second order scale-scale correlation detection are suppressed into minimum. Moreover, the effect of the non-Gaussian features of the Poisson sampling can be calculated in this frame.Comment: AAS Latex file, 44 pages, accepted for publication in Ap

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

The Angular Power Spectrum of EDSGC Galaxies

We determine the angular power spectrum, C_l, of the Edinburgh/Durham Southern Galaxy Catalog (EDSGC) and use this statistic to constrain cosmological parameters. Our methods for determining C_l, and the parameters that affect it are based on those developed for the analysis of cosmic microwave background maps. We expect them to be useful for future surveys. Assuming flat cold dark matter models with a cosmological constant (constrained by COBE/DMR and local cluster abundances), and a scale--independent bias, b, we find good fits to the EDSGC angular power spectrum with 1.11 < b < 2.35 and 0.2 < Omega_m < 0.55 at 95% confidence. These results are not significantly affected by the ``integral constraint'' or extinction by interstellar dust, but may be by our assumption of Gaussianity.Comment: 11 pages, 9 figures, version to appear in Ap

Multi-spin dynamics of the solid-state NMR Free Induction Decay

We present a new experimental investigation of the NMR free induction decay (FID) in a lattice of spin-1/2 nuclei in a strong Zeeman field. Following a pi/2 pulse, evolution under the secular dipolar Hamiltonian preserves coherence number in the Zeeman eigenbasis, but changes the number of correlated spins in the state. The observed signal is seen to decay as single-spin, single-quantum coherences evolve into multiple-spin coherences under the action of the dipolar Hamiltonian. In order to probe the multiple-spin dynamics during the FID, we measured the growth of coherence orders in a basis other than the usual Zeeman eigenbasis. This measurement provides the first direct experimental observation of the growth of coherent multiple-spin correlations during the FID. Experiments were performed with a cubic lattice of spins (19F in calcium fluoride) and a linear spin chain (19F in fluorapatite). It is seen that the geometrical arrangement of the spins plays a significant role in the development of higher order correlations. The results are discussed in light of existing theoretical models.Comment: 7 pages, 6 figure