ANNz: estimating photometric redshifts using artificial neural networks

We introduce ANNz, a freely available software package for photometric redshift estimation using Artificial Neural Networks. ANNz learns the relation between photometry and redshift from an appropriate training set of galaxies for which the redshift is already known. Where a large and representative training set is available ANNz is a highly competitive tool when compared with traditional template-fitting methods. The ANNz package is demonstrated on the Sloan Digital Sky Survey Data Release 1, and for this particular data set the r.m.s. redshift error in the range 0 < z < 0.7 is 0.023. Non-ideal conditions (spectroscopic sets which are small, or which are brighter than the photometric set for which redshifts are required) are simulated and the impact on the photometric redshift accuracy assessed.Comment: 6 pages, 6 figures. Replaced to match version accepted by PASP (minor changes to original submission). The ANNz package may be obtained from http://www.ast.cam.ac.uk/~aa

Faint Blue Galaxies as a Probe of the X-ray Background at High Redshift

We present a formalism describing the physical content of cross-correlation functions between a diffuse background and a population of discrete sources. The formalism is used to interpret cross-correlation signals between the unresolved X-ray background and a galaxy population resolved to high redshift in another spectral band. Specifically, we apply it to the so-called faint blue galaxy population and constrain their X-ray emissivity and clustering properties. A model is presented which satisfies the recently measured constraints on all 3 correlation functions (galaxy/galaxy, background/background and galaxy/background). This model predicts that faint galaxies in the magnitude range B=18-23 (cvering redshifts z \lsim 0.5) make up $\sim 22 \%$ of the X-ray background in the 0.5-2 keV band. At the mean redshift of the galaxy sample, $\bar z=0.26$, the comoving volume emissivity is $\rho_X \sim 6-9 \times 10^{38}h$ ergs s$^{-1}$Mpc$^{-3}$ . When extrapolated to fainter magnitudes, the faint blue galaxy population can account for most of the residual background at soft energy. We show how the measurement of the angular and zero-lag cross-correlation functions between increasingly faint galaxies and the X-ray background can allow us to map the X-ray emissivity as a function of redshift.Comment: uuencoded compressed postscript, without figures. The preprint is available with figures at http://www.ast.cam.ac.uk/preprint/PrePrint.htm

Variance and Skewness in the FIRST survey

We investigate the large-scale clustering of radio sources in the FIRST 1.4-GHz survey by analysing the distribution function (counts in cells). We select a reliable sample from the the FIRST catalogue, paying particular attention to the problem of how to define single radio sources from the multiple components listed. We also consider the incompleteness of the catalogue. We estimate the angular two-point correlation function $w(\theta)$, the variance $\Psi_2$, and skewness $\Psi_3$ of the distribution for the various sub-samples chosen on different criteria. Both $w(\theta)$ and $\Psi_2$ show power-law behaviour with an amplitude corresponding a spatial correlation length of $r_0 \sim 10 h^{-1}$Mpc. We detect significant skewness in the distribution, the first such detection in radio surveys. This skewness is found to be related to the variance through $\Psi_3=S_3(\Psi_2)^{\alpha}$, with $\alpha=1.9\pm 0.1$, consistent with the non-linear gravitational growth of perturbations from primordial Gaussian initial conditions. We show that the amplitude of variance and skewness are consistent with realistic models of galaxy clustering.Comment: 13 pages, 21 inline figures, to appear in MNRA

The X-ray Cluster Dipole

We estimate the dipole of the whole sky X-ray flux-limited sample of Abell/ACO clusters (XBACs) and compare it to the optical Abell/ACO cluster dipole. The X-ray cluster dipole is well aligned ($\le 25^{\circ}$) with the CMB dipole, while it follows closely the radial profile of its optical cluster counterpart although its amplitude is $\sim 10 - 30$ per cent lower. In view of the fact that the the XBACs sample is not affected by the volume incompleteness and the projection effects that are known to exist at some level in the optical parent Abell/ACO cluster catalogue, our present results confirm the previous optical cluster dipole analysis that there are significant contributions to the Local Group motion from large distances ($\sim 160h^{-1}$Mpc). In order to assess the expected contribution to the X-ray cluster dipole from a purely X-ray selected sample we compare the dipoles of the XBACs and the Brightest Cluster Sample (Ebeling et al. 1997a) in their overlap region. The resulting dipoles are in mutual good aggreement with an indication that the XBACs sample slightly underestimates the full X-ray dipole (by $\le 5$ per cent) while the Virgo cluster contributes about 10 - 15 per cent to the overall X-ray cluster dipole. Using linear perturbation theory to relate the X-ray cluster dipole to the Local group peculiar velocity we estimate the density parameter to be $\beta_{c_{x}} \simeq 0.24 \pm 0.05$.Comment: 16 pages, latex, + 4 ps figures, submitted to Ap

AUTOMATED MORPHOLOGICAL CLASSIFICATION OF APM GALAXIES BY SUPERVISED ARTIFICIAL NEURAL NETWORKS

We train Artificial Neural Networks to classify galaxies based solely on the morphology of the galaxy images as they appear on blue survey plates. The images are reduced and morphological features such as bulge size and the number of arms are extracted, all in a fully automated manner. The galaxy sample was first classified by 6 independent experts. We use several definitions for the mean type of each galaxy, based on those classifications. We then train and test the network on these features. We find that the rms error of the network classifications, as compared with the mean types of the expert classifications, is 1.8 Revised Hubble Types. This is comparable to the overall rms dispersion between the experts. This result is robust and almost completely independent of the network architecture used.Comment: The full paper contains 25 pages, and includes 22 figures. It is available at ftp://ftp.ast.cam.ac.uk/pub/hn/apm2.ps . The table in the appendix is available on request from [email protected]. Mon. Not. R. Astr. Soc., in pres

The Dipole Anisotropy of the First All-Sky X-ray Cluster Sample

We combine the recently published CIZA galaxy cluster catalogue with the XBACs cluster sample to produce the first all-sky catalogue of X-ray clusters in order to examine the origins of the Local Group's peculiar velocity without the use of reconstruction methods to fill the traditional Zone of Avoidance. The advantages of this approach are (i) X-ray emitting clusters tend to trace the deepest potential wells and therefore have the greatest effect on the dynamics of the Local Group and (ii) our all-sky sample provides data for nearly a quarter of the sky that is largely incomplete in optical cluster catalogues. We find that the direction of the Local Group's peculiar velocity is well aligned with the CMB as early as the Great Attractor region 40 h^-1 Mpc away, but that the amplitude of its dipole motion is largely set between 140 and 160 h^-1 Mpc. Unlike previous studies using galaxy samples, we find that without Virgo included, roughly ~70% of our dipole signal comes from mass concentrations at large distances (>60 h^-1 Mpc) and does not flatten, indicating isotropy in the cluster distribution, until at least 160 h^-1 Mpc. We also present a detailed discussion of our dipole profile, linking observed features to the structures and superclusters that produce them. We find that most of the dipole signal can be attributed to the Shapley supercluster centered at about 150 h^-1 Mpc and a handful of very massive individual clusters, some of which are newly discovered and lie well in the Zone of Avoidance.Comment: 15 Pages, 9 Figures. Accepted by Ap

Measuring the Mach number of the Universe via the Sunyaev-Zeldovich effect

We introduce a new statistic to measure more accurately the cosmic sound speed of clusters of galaxies at different redshifts. This statistic is evaluated by cross-correlating cosmic microwave background (CMB) fluctuations caused by the Sunyaev-Zel'dovich effect from observed clusters of galaxies with their redshifts. When clusters are distributed in redshift bins of narrow width, one could measure the mean squared cluster peculiar velocity with an error \sigma_{C_S^2}\lsim (300{\rm km/s})^2. This can be done around z>0.3 with clusters of flux above 200 mJy which will be detected by PLANCK, coupled with high resolution microwave images to eliminate the cosmological part of the CMB fluctuations. The latter can be achieved with observations by the planned ALMA array or the NSF South Pole telescope and other surveys. By measuring the cosmic sound speed and the bulk flow in, e.g., 4 spheres of ~ 100h^{-1}Mpc at z=0.3, we could have a direct measurement of the matter density 0.21<\Omega_m<0.47 at 95 % confidence level.Comment: Ap.J.Letters, submitte

Combining cosmological datasets: hyperparameters and Bayesian evidence

A method is presented for performing joint analyses of cosmological datasets, in which the weight assigned to each dataset is determined directly by it own statistical properties. The weights are considered in a Bayesian context as a set of hyperparameters, which are then marginalised over in order to recover the posterior distribution as a function only of the cosmological parameters of interest. In the case of a Gaussian likelihood function, this marginalisation may be performed analytically. Calculation of the Bayesian evidence for the data, with and without the introduction of hyperparameters, enables a direct determination of whether the data warrant the introduction of weights into the analysis; this generalises the standard likelihood ratio approach to model comparison. The method is illustrated by application to the classic toy problem of fitting a straight line to a set of data. A cosmological illustration of the technique is also presented, in which the latest measurements of the cosmic microwave background power spectrum are used to infer constraints on cosmological parameters.Comment: 12 pages, 6 figures, submitted to MNRA

Bayesian `Hyper-Parameters' Approach to Joint Estimation: The Hubble Constant from CMB Measurements

Recently several studies have jointly analysed data from different cosmological probes with the motivation of estimating cosmological parameters. Here we generalise this procedure to take into account the relative weights of various probes. This is done by including in the joint \chi^2 function a set of `Hyper-Parameters', which are dealt with using Bayesian considerations. The resulting algorithm (in the case of uniform priors on the log of the Hyper-Parameters) is very simple: instead of minimising \sum \chi_j^2 (where \chi_j^2 is per data set j) we propose to minimise \sum N_j \ln (\chi_j^2) (where N_j is the number of data points per data set j). We illustrate the method by estimating the Hubble constant H_0 from different sets of recent CMB experiments (including Saskatoon, Python V, MSAM1, TOCO and Boomerang).Comment: submitted to MNRAS, 6 pages, Latex, with 3 figures embedde