Weak gravitational flexion

Flexion is the significant third-order weak gravitational lensing effect responsible for the weakly skewed and arc-like appearance of lensed galaxies. Here we demonstrate how flexion measurements can be used to measure galaxy halo density profiles and large-scale structure on non-linear scales, via galaxy–galaxy lensing, dark matter mapping and cosmic flexion correlation functions. We describe the origin of gravitational flexion, and discuss its four components, two of which are first described here. We also introduce an efficient complex formalism for all orders of lensing distortion. We proceed to examine the flexion predictions for galaxy–galaxy lensing, examining isothermal sphere and Navarro–Frenk–White (NFW) profiles and both circularly symmetric and elliptical cases. We show that in combination with shear we can precisely measure galaxy masses and NFW halo concentrations. We also show how flexion measurements can be used to reconstruct mass maps in two-dimensional projection on the sky, and in three dimensions in combination with redshift data. Finally, we examine the predictions for cosmic flexion, including convergence–flexion cross-correlations, and we find that the signal is an effective probe of structure on non-linear scales.     

Peaks in the cosmological density field: sensitivity to initial power spectrum, redshift distortions and galaxy halo occupation

We investigate the number density of maxima in the cosmological galaxy density field smoothed with a filter as a probe of clustering. In previous work it has been shown that this statistic is closely related to the slope of the linear power spectrum, even when the directly measured power spectrum is non-linear. In the present paper we investigate the sensitivity of the peak number density to various models with differing power spectra, including rolling index models, cosmologies with massive neutrinos and different baryon densities. We find that rolling index models which have given an improved fit to CMB/LSS (cosmic microwave background/large scale structure) data yield a ∼10 per cent difference in peak density compared to the scale invariant case. Models with 0.3 eV neutrinos have effects of similar magnitude and it should be possible to constrain them with data from current galaxy redshift surveys. Baryon oscillations in the power spectrum also give rise to distinctive features in the peak density. These are preserved without modification when measured from the peak density in fully non-linear N -body simulations. Using the simulations, we also investigate how the peak density is modified in the presence of redshift distortions. Redshift distortions cause a suppression of the number of peaks, largely due to fingers of God overlapping in redshift space. We find that this effect can be modelled by using a modification of the input power spectrum. We also study the results when the simulation density field is traced by galaxies obtained by populating haloes with a halo occupation distribution consistent with observations. The peak number density is consistent with that in the dark matter for filter scales  >4  h ⁻¹ Mpc  , for which we find good agreement with the linear theory predictions. In a companion paper we analyse data from the 2dF Galaxy Redshift Survey.     

Projected bispectrum in spherical harmonics and its application to angular galaxy catalogues

We present a theoretical and exact analysis of the bispectrum of projected galaxy catalogues. The result can be generalized to evaluate the projection in spherical harmonics of any 3D bispectrum and therefore has applications to cosmic microwave background and gravitational lensing studies.
By expanding the 2D distribution of galaxies on the sky in spherical harmonics, we show how the three-point function of the coefficients can be used in principle to determine the bias parameter of the galaxy sample. If this can be achieved, it would allow a lifting of the degeneracy between the bias and the matter density parameter of the Universe, which occurs in linear analysis of 3D galaxy catalogues. In previous papers, we have shown how a similar analysis can be done in three dimensions, and we show here through an error analysis and by implementing the method on a simulated projected catalogue that ongoing three-dimensional galaxy redshift surveys (even with all the additional uncertainties introduced by partial sky coverage, redshift-space distortions and smaller numbers) will do far better than all-sky projected catalogues with similar selection function.     

Source–lens clustering effects on the skewness of the lensing convergence

The correlation between source galaxies and lensing potentials causes a systematic effect on measurements of cosmic shear statistics, known as the source–lens clustering (SLC) effect. The SLC effect on the skewness of lensing convergence, S ₃, is examined using a non-linear semi-analytic approach and is checked against numerical simulations. The semi-analytic calculations have been performed in a wide variety of generic models for the redshift distribution of source galaxies and power-law models for the bias parameter between the galaxy and dark matter distributions. The semi-analytic predictions are tested successfully against numerical simulations. We find the relative amplitude of the SLC effect on S ₃ to be of the order of  5–40  per cent. It depends significantly on the redshift distribution of sources and on the way in which the bias parameter evolves. We discuss possible measurement strategies to minimize the SLC effects.     

The luminosity function around isolated spiral galaxies

We determine the companion galaxy luminosity function (LF) for regions around isolated spiral galaxies. If we assume that any excess in the galaxy number counts in the vicinity of a spiral galaxy is due to galaxies at the same distance, then a system LF can be determined from the variation of excess numbers with apparent magnitude. By studying the excess over many field 'centre' galaxies, a good statistical accuracy can be obtained for the companion galaxy LF. Since redshift information is not required for the faint galaxies, it is possible to sample further down the LF as compared with redshift surveys. For 23 primary galaxies of known redshift, we find a dwarf satellite Schechter LF with a characteristic magnitude M _V *( D )≃−19 and a faint-end slope α=−1.7, down to M_V =−14 ( H ₀=50 km s⁻¹ Mpc⁻¹).     

Predicting spectral features in galaxy spectra from broad-band photometry

We explore the prospects of predicting emission-line features present in galaxy spectra given broad-band photometry alone. There is a general consent that colours, and spectral features, most notably the 4000 Å break, can predict many properties of galaxies, including star formation rates and hence they could infer some of the line properties. We argue that these techniques have great prospects in helping us understand line emission in extragalactic objects and might speed up future galaxy redshift surveys if they are to target emission-line objects only. We use two independent methods, Artificial Neural Networks (based on the ANNz code) and Locally Weighted Regression (LWR), to retrieve correlations present in the colour N -dimensional space and to predict the equivalent widths present in the corresponding spectra. We also investigate how well it is possible to separate galaxies with and without lines from broad-band photometry only. We find, unsurprisingly, that recombination lines can be well predicted by galaxy colours. However, among collisional lines some can and some cannot be predicted well from galaxy colours alone, without any further redshift information. We also use our techniques to estimate how much information contained in spectral diagnostic diagrams can be recovered from broad-band photometry alone. We find that it is possible to classify active galactic nuclei and star formation objects relatively well using colours only. We suggest that this technique could be used to considerably improve redshift surveys such as the upcoming Fibre Multi Object Spectrograph (FMOS) survey and the planned Wide Field Multi Object Spectrograph (WFMOS) survey.     

Tracing the nature of dark energy with galaxy distribution

Dynamical dark energy (DE) is a viable alternative to the cosmological constant. Constructing tests to discriminate between Λ and dynamical DE models is difficult, however, because the differences are not large. In this paper we explore tests based on the galaxy mass function, the void probability function (VPF), and the number of galaxy clusters. At high z , the number density of clusters shows large differences between DE models, but geometrical factors reduce the differences substantially. We find that detecting a model dependence in the cluster redshift distribution is a significant challenge. We show that the galaxy redshift distribution is potentially a more sensitive characteristic. We do this by populating dark matter haloes in N -body simulations with galaxies using well-tested halo occupation distributions. We also estimate the VPF and find that samples with the same angular surface density of galaxies, in different models, exhibition almost model-independent VPF which therefore cannot be used as a test for DE. Once again, geometry and cosmic evolution compensate each other. By comparing VPFs for samples with fixed galaxy mass limits, we find measurable differences.     

The non-linear redshift-space power spectrum of galaxies

We study the power spectrum of galaxies in redshift space, with third-order perturbation theory to include corrections that are absent in linear theory. We assume a local bias for the galaxies: i.e., the galaxy density is sampled from some local function of the underlying mass distribution. We find that the effect of the non-linear bias in real space is to introduce two new features: first, there is a contribution to the power which is constant with wavenumber, whose nature we reveal as essentially a shot-noise term. In principle this contribution can mask the primordial power spectrum, and could limit the accuracy with which the latter might be measured on very large scales. Secondly, the effect of second- and third-order bias is to modify the effective bias (defined as the square root of the ratio of galaxy power spectrum to matter power spectrum). The effective bias is almost scale-independent over a wide range of scales. These general conclusions also hold in redshift space. In addition, we have investigated the distortion of the power spectrum by peculiar velocities, which may be used to constrain the density of the Universe. We look at the quadrupole-to-monopole ratio, and find that higher order terms can mimic linear theory bias, but the bias implied is neither the linear bias, nor the effective bias referred to above. We test the theory with biased N -body simulations, and find excellent agreement in both real and redshift space, providing the local biasing is applied on a scale whose fractional rms density fluctuations are < 0.5.     

Morphological redshift estimates for galaxy clusters in a Sunyaev–Zel'dovich effect survey

We develop a new method to estimate the redshift of galaxy clusters through resolved images of the Sunyaev–Zel'dovich effect (SZE). Our method is based on morphological observables which can be measured by actual and future SZE experiments. We test the method with a set of high-resolution hydrodynamical simulations of galaxy clusters at different redshifts. Our method combines the observables in a principal component analysis. After calibrating the method with an independent redshift estimation for some of the clusters, we show – using a Bayesian approach – how the method can give an estimate of the redshift of the galaxy clusters. Although the error bars given by the morphological redshift estimation are large, it should be useful for future SZE surveys where thousands of clusters are expected to be detected; a first preselection of the high-redshift candidates could be done using our proposed morphological redshift estimator. Although not considered in this work, our method should also be useful to give an estimate of the redshift of clusters in X-ray and optical surveys.     

The three-dimensional power spectrum of dark and luminous matter from the VIRMOS-DESCART cosmic shear survey

We present the first optimal power spectrum estimation and three-dimensional deprojections for the dark and luminous matter and their cross-correlations. The results are obtained using a new optimal fast estimator, deprojected using minimum variance and Singular Value Decomposition (SVD) techniques. We show the resulting 3D power spectra for dark matter and galaxies, and their covariance for the VIRMOS-DESCART weak lensing shear and galaxy data. The survey is most sensitive to non-linear scales   k _NL∼ 1 h Mpc⁻¹  . On these scales, our 3D power spectrum of dark matter is in good agreement with the RCS 3D power spectrum found by Tegmark & Zaldarriaga. Our galaxy power is similar to that found by the 2MASS survey, and larger than that of SDSS, APM and RCS, consistent with the expected difference in galaxy population.
We find an average bias   b = 1.24 ± 0.18  for the I -selected galaxies, and a cross-correlation coefficient   r = 0.75 ± 0.23  . Together with the power spectra, these results optimally encode the entire two point information about dark matter and galaxies, including galaxy–galaxy lensing. We address some of the implications regarding galaxy haloes and mass-to-light ratios. The best-fitting 'halo' parameter   h ≡ r / b = 0.57 ± 0.16  , suggesting that dynamical masses estimated using galaxies systematically underestimate total mass.
Ongoing surveys, such as the Canada–France–Hawaii Telescope Legacy Survey, will significantly improve on the dynamic range, and future photometric redshift catalogues will allow tomography along the same principles.     

Photometric redshifts with surface brightness priors

We use galaxy surface brightness as prior information to improve photometric redshift (photo- z ) estimation. We apply our template-based photo- z method to imaging data from the ground-based VVDS survey and the space-based GOODS field from HST , and use spectroscopic redshifts to test our photometric redshifts for different galaxy types and redshifts. We find that the surface brightness prior eliminates a large fraction of outliers by lifting the degeneracy between the Lyman and 4000-Å breaks. Bias and scatter are improved by about a factor of 2 with the prior in each redshift bin in the range  0.4 < z < 1.3  , for both the ground and space data. Ongoing and planned surveys from the ground and space will benefit, provided that care is taken in measurements of galaxy sizes and in the application of the prior. We discuss the image quality and signal-to-noise ratio requirements that enable the surface brightness prior to be successfully applied.     

The effect of primordial non-Gaussianity on the topology of large-scale structure

We study the effect of primordial non-Gaussianity on the development of large-scale cosmic structure using high-resolution N -body simulations. In particular, we focus on the topological properties of the 'cosmic web', quantitatively characterized by the Minkowski functionals (MFs), for models with quadratic non-linearities with different values of the usual non-Gaussianity parameter f _NL. In the weakly non-linear regime (the amplitude of mass density fluctuations σ₀ < 0.1), we find that analytic formulae derived from perturbation theory agree with the numerical results within a few per cent of the amplitude of each MF when | f _NL| < 1000. In the non-linear regime, the detailed behaviour of the MFs as functions of threshold density deviates more strongly from the analytical curves, while the overall amplitude of the primordial non-Gaussian effect remains comparable to the perturbative prediction. When smaller-scale information is included, the influence of primordial non-Gaussianity becomes increasingly significant statistically due to decreasing sample variance. We find that the effect of the primordial non-Gaussianity with  | f _NL| = 50  is comparable to the sample variance of mass density fields with a volume of 0.125( h ⁻¹ Gpc)³ when they are smoothed by Gaussian filter at a scale of 5  h ⁻¹ Mpc. The detectability of this effect in actual galaxy surveys will strongly depend on residual uncertainties in cosmological parameters and galaxy biasing.     

Large-scale bias in the Universe — II. Redshift-space bispectrum

The determination of the density parameter Ω₀ from the large-scale distribution of galaxies is one of the major goals of modern cosmology. However, if galaxies are biased tracers of the underlying mass distribution, linear perturbation theory leads to a degeneracy between Ω₀ and the linear bias parameter b , and the density parameter cannot be estimated. In Matarrese, Verde &38; Heavens we developed a method based on second-order perturbation theory to use the bispectrum to lift this degeneracy by measuring the bias parameter in an Ω₀-independent way. The formalism was developed assuming that one has perfect information on the positions of galaxies in three dimensions. In galaxy redshift surveys, the three-dimensional information is imperfect, because of the contaminating effects of peculiar velocities, and the resulting clustering pattern in redshift space is distorted. In this paper we combine second-order perturbation theory with a model for collapsed, virialized structures, to extend the method to redshift space, and demonstrate that the method should be successful in determining with reasonable accuracy the bias parameter from state-of-the-art surveys such as the Anglo-Australian 2 degree Field Survey and the Sloan Digital Sky Survey.     

Recovering physical parameters from galaxy spectra using MOPED

We derive physical parameters of galaxies from their observed spectra using MOPED, the optimized data compression algorithm of Heavens, Jimenez & Lahav. Here we concentrate on parametrizing galaxy properties, and apply the method to the NGC galaxies in Kennicutt's spectral atlas. We focus on deriving the star formation history, metallicity and dust content of galaxies. The method is very fast, taking a few seconds of CPU time to estimate ∼17 parameters, and is therefore specially suited to studying large data sets, such as the Anglo-Australian two-degree-field (2dF) galaxy survey and the Sloan Digital Sky Survey (SDSS). Without the power of MOPED, the recovery of star formation histories in these surveys would be impractical. In Kennicutt's atlas, we find that for the spheroidals a small recent burst of star formation is required to provide the best fit to the spectrum. There is clearly a need for theoretical stellar atmospheric models with spectral resolution better than 1 Å if we are to extract all the rich information that large redshift surveys contain in their galaxy spectra.     

Features in the primordial power spectrum: constraints from the cosmic microwave background and the limitation of the 2dF and SDSS redshift surveys to detect them

We allow a more general (step-function) form of the primordial power spectrum than the usual featureless power-law Harrison–Zeldovich (with spectral index   n =1)  power spectrum, and fit it to the latest cosmic microwave background data sets. Although the best-fitting initial power spectrum can differ significantly from the power-law shape, and contains a dip at scales   k ∼0.003  h  Mpc^-1  , we find that  Ω_m≈0.24  , consistent with previous analyses that assume power-law initial fluctuations. We also explore the feasibility of the early releases of the 2dF and Sloan Digital Sky Survey (SDSS) galaxy redshifts surveys to see these features, and we find that even if features exist in the primordial power spectrum, they are washed out by the window functions of the redshift surveys on scales   k <0.03  h  Mpc^-1  .     

Probing the gravity-induced bias with weak lensing: test of analytical results against simulations

Future weak lensing surveys will directly probe the density fluctuation in the Universe. Recent studies have shown how the statistics of the weak lensing convergence field is related to the statistics of collapsed objects. Extending earlier analytical results on the probability distribution function of the convergence field, we show that the bias associated with the convergence field can be directly related to the bias associated with the statistics of underlying overdense objects. This will provide us with a direct method to study the gravity-induced bias in galaxy clustering. Based on our analytical results, which use the hierarchical Ansatz for non-linear clustering, we study how such a bias depends on the smoothing angle and the source redshift. We compare our analytical results with ray-tracing experiments through N -body simulations of four different realistic cosmological scenarios, and find a very good match. Our study shows that the bias in the convergence map strongly depends on the background geometry and hence can help us in distinguishing different cosmological models in addition to improving our understanding of the gravity-induced bias in galaxy clustering.     

Galaxy properties derived with spectral energy distribution fitting in the Hawaii-Hubble Deep Field-North

We compile multi-wavelength data from ultraviolet to infrared(IR) bands as well as redshift and source-type information, for a large sample of 178 341 sources in the Hawaii-Hubble Deep Field-North field. A total of 145 635 sources among the full sample are classified/treated as galaxies and have redshift information available. We derive physical properties for these sources utilizing the spectral energy distribution fitting code CIGALE that is based on Bayesian analysis. Through various consistency and robustness checks, we find that our stellar-mass and star-formation rate(SFR) estimates are reliable, which is mainly due to two facts. Firstly, we adopt the most up-to-date and accurate redshifts and point spread functionmatched photometry; and secondly, we make sensible parameter choices with the CIGALE code and take into account the influences of mid-IR/far-IR data, star-formation history models, and AGN contribution. We release our catalog of galaxy properties publicly(including, e.g., redshift, stellar mass, SFR, age, metallicity, dust attenuation). It is the largest of its kind in this field and should facilitate future relevant studies on the formation and evolution of galaxies.