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

The effect of the environment on the Faber Jackson relation

We investigate the effect of the environment on the Faber Jackson (FJ) relation, using a sample of 384 nearby elliptical galaxies and estimating objectively their environment on the typical scale of galaxy clusters. We show that the intrinsic scatter of the FJ is significantly reduced when ellipticals in high density environments are compared to ellipticals in low density ones. This result, which holds on a limited range of overdensities, is likely to provide an important observational link between scaling relations and formation mechanisms in galaxies.Comment: accepted by Ap

Does the Number Density of Elliptical Galaxies Change at z<1?

We have performed a detailed V/Vmax test for a sample of the Canada-France Redshift Survey (CFRS) for the purpose of examining whether the comoving number density of field galaxies changes significantly at redshifts of z<1. Taking into account the luminosity evolution of galaxies which depends on their morphological type through different history of star formation, we obtain \sim 0.5 in the range of 0.3<z<0.8, where reliable redshifts were secured by spectroscopy of either absorption or emission lines for the CFRS sample. This indicates that a picture of mild evolution of field galaxies without significant mergers is consistent with the CFRS data. Early-type galaxies, selected by their (V-I)_{AB} color, become unnaturally deficient in number at z>0.8 due to the selection bias, thereby causing a fictitious decrease of . We therefore conclude that a reasonable choice of upper bound of redshift z \sim 0.8 in the V/Vmax test saves the picture of passive evolution for field ellipticals in the CFRS sample, which was rejected by Kauffman, Charlot, & White (1996) without confining the redshift range. However, about 10% of the CFRS sample consists of galaxies having colors much bluer than predicted for irregular galaxies, and their \avmax is significantly larger than 0.5. We discuss this population of extremely blue galaxies in terms of starburst that has just turned on at their observed redshifts.Comment: 11 pages including 3 figures, to appear in ApJ Letter

Probing Dark Energy with Baryonic Acoustic Oscillations from Future Large Galaxy Redshift Surveys

We show that the measurement of the baryonic acoustic oscillations in large high redshift galaxy surveys offers a precision route to the measurement of dark energy. The cosmic microwave background provides the scale of the oscillations as a standard ruler that can be measured in the clustering of galaxies, thereby yielding the Hubble parameter and angular diameter distance as a function of redshift. This, in turn, enables one to probe dark energy. We use a Fisher matrix formalism to study the statistical errors for redshift surveys up to z=3 and report errors on cosmography while marginalizing over a large number of cosmological parameters including a time-dependent equation of state. With redshifts surveys combined with cosmic microwave background satellite data, we achieve errors of 0.037 on Omega_x, 0.10 on w(z=0.8), and 0.28 on dw(z)/dz for cosmological constant model. Models with less negative w(z) permit tighter constraints. We test and discuss the dependence of performance on redshift, survey conditions, and fiducial model. We find results that are competitive with the performance of future supernovae Ia surveys. We conclude that redshift surveys offer a promising independent route to the measurement of dark energy.Comment: submitted to ApJ, 24 pages, LaTe

Numerical Analyses of Weakly Nonlinear Velocity-Density Coupling

We study evolution of various statistical quantities of smoothed cosmic density and velocity fields using N-body simulations. The parameter $C\equiv /( )$ characterizes nonlinear coupling of these two fields and determines behavior of bulk velocity dispersion as a function of local density contrast. It is found that this parameter depends strongly on the smoothing scale even in quasi-linear regimes where the skewness parameter $S_3$ is nearly constant and close to the predicted value by the second-order perturbation theory. We also analyze weakly nonlinear effects caused by an adaptive smoothing known as the gather approach.Comment: 22 pages, 4 figures, to appear in ApJ (558, Sep 10

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

Galaxy Formation by Galactic Magnetic Fields

Galaxies exhibit a sequence of various morphological types, i.e., the Hubble sequence, and they are basically composed of spheroidal components (elliptical galaxies and bulges in spiral galaxies) and disks. It is known that spheroidal components are found only in relatively massive galaxies with M=10^{10-12} M_sun, and all stellar populations in them are very old, but there is no clear explanation for these facts. Here we present a speculative scenario for the origin of the Hubble sequence, in which magnetic fields ubiquitously seen in galaxies have played a crucial role. We first start from a strange observational fact that magnetic field strengths observed in spiral galaxies sharply concentrate at a few microgauss, for a wide range of galaxy luminosity and types. We then argue that this fact and the observed correlation between star formation activity and magnetic field strength in spiral galaxies suggest that spheroidal galaxies have formed by starbursts induced by strong magnetic fields. Then we show that this idea naturally leads to the formation of spheroidal systems only in massive and high-redshift objects in hierarchically clustering universe, giving a simple explanation for various observations.Comment: 7 pages including 2 figures. Accepted by ApJ Letter

A High Merger Fraction in the Rich Cluster MS1054-03 at z=0.83: Direct Evidence for Hierarchical Formation of Massive Galaxies

We present a morphological study of the galaxy population of the luminous X-ray cluster MS1054-03 at z=0.83. The sample consists of 81 spectroscopically confirmed cluster members in a 3 x 2 Mpc area imaged in F606W and F814W with WFPC2. We find thirteen ongoing mergers in MS1054-03, comprising 17% of the L > L* cluster population. Most of these mergers will likely evolve into luminous (\sim 2 L*) elliptical galaxies, and some may evolve into S0 galaxies. Assuming the galaxy population in MS1054-03 is typical for its redshift it is estimated that \sim 50% of present-day cluster ellipticals experienced a major merger at z < 1. The mergers are preferentially found in the outskirts of the cluster, and probably occur in small infalling clumps. Morphologies, spectra, and colors of the mergers show that their progenitors were typically E/S0s or early-type spirals with mean stellar formation redshifts z* \gtrsim 1.7. The red colors of the merger remnants are consistent with the low scatter in the color-magnitude relation in rich clusters at lower redshift. The discovery of a high fraction of mergers in this young cluster is direct evidence against formation of ellipticals in a single ``monolithic'' collapse at high redshift, and in qualitative agreement with predictions of hierarchical models for structure formation.Comment: Added GIF version of Figure 1. At http://www.astro.rug.nl/~dokkum/preprints/merger_fig1.eps.gz the PS file is available. Accepted for publication in ApJ Letter

How limiting is optical follow-up for fast radio burst applications? Forecasts for radio and optical surveys

Fast radio bursts (FRBs) are the first cosmological radio sources that vary on millisecond timescales, which makes them a unique probe of the Universe. Many proposed applications of FRBs require associated redshifts. These can only be obtained by localizing FRBs to their host galaxies and subsequently measuring their redshifts. Upcoming FRB surveys will provide arcsecond localization for many FRBs, not all of which can be followed up with dedicated optical observations. We aim to estimate the fraction of FRB hosts that will be catalogued with redshifts by existing and future optical surveys. We use the population synthesis code frbpoppy to simulate several FRB surveys, and the semi-analytical galaxy formation code GALFORM to simulate their host galaxies. We obtain redshift distributions for the simulated FRBs and the fraction with host galaxies in a survey. Depending on whether FRBs follow the cosmic star formation rate or stellar mass, 20 to 40 per cent of CHIME FRB hosts will be observed in an SDSS-like survey, all at $z<0.5$. The deeper DELVE survey will detect 63 to 85 per cent of ASKAP FRBs found in its coherent search mode. CHIME FRBs will reach $z\sim 3$, SKA1-Mid FRBs $z\sim 5$, but ground based follow-up is limited to $z\lesssim 1.5$. We discuss consequences for several FRB applications. If $\sim1/2$ of ASKAP FRBs have measured redshifts, 1000 detected FRBs can be used to constrain $\Omega_\text{b} h_{70}$ to within $\sim10$ per cent at 95 per cent credibility. We provide strategies for optimized follow-up, when building on data from existing surveys. Data and codes are made available.Comment: 18 pages, 16 figures, 4 tables, accepted for publication in MNRAS. Code available at https://github.com/JoschaJ/mockFRBhost