Cosmological systematics beyond nuisance parameters: form-filling functions

In the absence of any compelling physical model, cosmological systematics are often misrepresented as statistical effects and the approach of marginalizing over extra nuisance systematic parameters is used to gauge the effect of the systematic. In this article, we argue that such an approach is risky at best since the key choice of function can have a large effect on the resultant cosmological errors.
As an alternative we present a functional form-filling technique in which an unknown, residual, systematic is treated as such. Since the underlying function is unknown, we evaluate the effect of every functional form allowed by the information available (either a hard boundary or some data). Using a simple toy model, we introduce the formalism of functional form filling. We show that parameter errors can be dramatically affected by the choice of function in the case of marginalizing over a systematic, but that in contrast the functional form-filling approach is independent of the choice of basis set.
We then apply the technique to cosmic shear shape measurement systematics and show that a shear calibration bias of  | m ( z )| ≲ 10⁻³ (1 + z )^0.7  is required for a future all-sky photometric survey to yield unbiased cosmological parameter constraints to per cent accuracy.
A module associated with the work in this paper is available through the open source icosmo code available at http://www.icosmo.org .     

Photometric redshifts for weak lensing tomography from space: the role of optical and near infrared photometry

We study in detail the photometric redshift requirements needed for tomographic weak gravitational lensing in order to measure accurately the dark energy equation of state. In particular, we examine how ground-based photometry  ( u , g , r , i , z , y )  can be complemented by space-based near-infrared (near-IR) photometry  ( J , H )  , e.g. onboard the planned DUNE satellite. Using realistic photometric redshift simulations and an artificial neural network photo- z method we evaluate the figure of merit for the dark energy parameters  ( w ₀, w _a )  . We consider a DUNE -like broad optical filter supplemented with ground-based multiband optical data from surveys like the Dark Energy Survey, Pan-STARRS and LSST. We show that the dark energy figure of merit would be improved by a factor of 1.3–1.7 if IR filters are added onboard DUNE . Furthermore we show that with IR data catastrophic photo- z outliers can be removed effectively. There is an interplay between the choice of filters, the magnitude limits and the removal of outliers. We draw attention to the dependence of the results on the galaxy formation scenarios encoded into the mock galaxies, e.g. the galaxy reddening. For example, very deep u -band data could be as effective as the IR. We also find that about  10⁵–10⁶  spectroscopic redshifts are needed for calibration of the full survey.     

Comparison of the ENEAR peculiar velocities with the PSCz gravity field

We present a comparison between the peculiar velocity field measured from the ENEAR all-sky D _n– σ catalogue and that derived from the galaxy distribution of the IRAS Point Source Catalog Redshift Survey (PSC z ). The analysis is based on a modal expansion of these data in redshift space by means of spherical harmonics and Bessel functions. The effective smoothing scale of the expansion is almost linear with redshift reaching 1500 km s⁻¹ at 3000 km s⁻¹. The general flow patterns in the filtered ENEAR and PSC z velocity fields agree well within 6000 km s⁻¹, assuming a linear biasing relation between the mass and the PSC z galaxies. The comparison allows us to determine the parameter     where Ω is the cosmological density parameter and b is the linear biasing factor. A likelihood analysis of the ENEAR and PSC z modes yields     in good agreement with values obtained from Tully–Fisher surveys.     

Revisiting the parametrization of equation of state of dark energy via SNIa data

In this paper, we revisit the parametrizations of the equation of state of dark energy and point out that comparing merely the  χ²  of different fittings may not be optimal for choosing the 'best' parametrization. Another figure of merit for evaluating different parametrizations based on the area of the   w ( z ) − z   band is proposed. In light of the analysis of some two-parameter parametrizations and models based on available SNIa data, the area of   w ( z ) − z   band seems to be a good figure of merit, especially in the situation that the value of  χ²_min  for different parametrizations are very close. Therefore, we argue that both the area of the   w ( z ) − z   band and  χ²_min  should be synthetically considered for choosing a better parametrization of dark energy in the future experiments.     

MegaZ-LRG: a photometric redshift catalogue of one million SDSS luminous red galaxies

We describe the construction of MegaZ-LRG, a photometric redshift catalogue of over one million luminous red galaxies (LRGs) in the redshift range  0.4 < z < 0.7  with limiting magnitude   i < 20  . The catalogue is selected from the imaging data of the Sloan Digital Sky Survey (SDSS) Data Release 4. The 2dF-SDSS LRG and Quasar (2SLAQ) spectroscopic redshift catalogue of 13 000 intermediate-redshift LRGs provides a photometric redshift training set, allowing use of ann z, a neural network-based photometric-redshift estimator. The rms photometric redshift accuracy obtained for an evaluation set selected from the 2SLAQ sample is  σ _z = 0.049  averaged over all galaxies, and  σ _z = 0.040  for a brighter subsample  ( i < 19.0)  . The catalogue is expected to contain ∼5 per cent stellar contamination. The ann z code is used to compute a refined star/galaxy probability based on a range of photometric parameters; this allows the contamination fraction to be reduced to 2 per cent with negligible loss of genuine galaxies. The MegaZ-LRG catalogue is publicly available on the World Wide Web from http://www.2slaq.info .     

Smoothing supernova data to reconstruct the expansion history of the Universe and its age

We propose a non-parametric method of smoothing supernova data over redshift using a Gaussian kernel in order to reconstruct important cosmological quantities including   H ( z )  and   w ( z )  in a model-independent manner. This method is shown to be successful in discriminating between different models of dark energy when the quality of data is commensurate with that expected from the future Supernova Acceleration Probe ( SNAP ). We find that the Hubble parameter is especially well determined and useful for this purpose. The look-back time of the Universe may also be determined to a very high degree of accuracy (≲0.2 per cent) using this method. By refining the method, it is also possible to obtain reasonable bounds on the equation of state of dark energy. We explore a new diagnostic of dark energy – the ' w -probe'– which can be calculated from the first derivative of the data. We find that this diagnostic is reconstructed extremely accurately for different reconstruction methods even if Ω_{0 m} is marginalized over. The w -probe can be used to successfully distinguish between Λ cold dark matter and other models of dark energy to a high degree of accuracy.     

Modelling the number counts of early-type galaxies by pure luminosity evolution

In this paper, we explore the plausible luminosity evolution of early-type galaxies in different cosmological models by constructing a set of pure luminosity evolution (PLE) models via the choices of the star-formation rate (SFR) parameters and formation redshift z _f of galaxies, with the observational constraints derived from the Hubble Space Telescope ( HST  ) morphological number counts for elliptical and S0 galaxies of the Medium Deep Survey (MDS) and the Hubble Deep Field (HDF). We find that the number counts of early-type galaxies can be explained by the pure luminosity evolution models, without invoking exotic scenarios such as merging or introducing an additional population, but the evolution should be nearly passive, with a high z _f assumed. The conclusion is valid in all of the three cosmological models we adopt in this paper. We also present the redshift distributions for three bins of observed magnitudes in the F814w passband, to show the redshift at which the objects that dominate the counts at a given magnitude may be found. The predictions of the redshift distribution of 22.5 <  b _j  < 24.0 are also presented for comparison with future data.     

Constraints on perfect fluid and scalar field dark energy models from future redshift surveys

We discuss the constraints that future photometric and spectroscopic redshift surveys can put on dark energy through the baryon oscillations of the power spectrum. We model the dark energy either with a perfect fluid or a scalar field and take into account the information contained in the linear growth function. We show that the growth function helps to break the degeneracy in the dark energy parameters and reduce the errors on   w ₀, w ₁  roughly by 30 per cent, making more appealing multicolour surveys based on photometric redshifts. We find that a 200-deg² spectroscopic survey reaching   z ≈ 3  can constrain   w ₀, w ₁  to within  Δ w ₀= 0.21, Δ w ₁= 0.26  , to  Δ w ₀= 0.39, Δ w ₁= 0.54  using photometric redshifts with an absolute uncertainty of 0.02, and to  Δ w ₀= 0.43, Δ w ₁= 0.66  with an uncertainty of 0.04. In the scalar field case, we show that the slope n of the inverse power-law potential for dark energy can be constrained to  Δ n = 0.26  (spectroscopic redshifts) or  Δ n = 0.40  (photometric redshifts), i.e. better than with future ground-based supernovae surveys or cosmic microwave background data.     

Recent arrival of faint cluster galaxies on the red sequence: luminosity functions from 119 deg2 of CFHTLS

The global star formation rate has decreased significantly since   z ∼ 1  , for reasons that are not well understood. Red-sequence galaxies, dominating in galaxy clusters, represent the population that have had their star formation shut off, and may therefore be the key to this problem. In this work, we select 127 rich galaxy clusters at  0.17 ≤ z ≤ 0.36  , from 119 deg² of the Canada–France–Hawaii Telescope Legacy Survey (CFHTLS) optical imaging data, and construct the r '-band red-sequence luminosity functions (LFs). We show that the faint end of the LF is very sensitive to how red-sequence galaxies are selected, and an optimal way to minimize the contamination from the blue cloud is to mirror galaxies on the redder side of the colour–magnitude relation. The LFs of our sample have a significant inflexion centred at     , suggesting a mixture of two populations. Combining our survey with low-redshift samples constructed from the Sloan Digital Sky Survey, we show that there is no strong evolution of the faint end of the LF (or the red-sequence dwarf-to-giant ratio) over the redshift range  0.2 ≲ z ≲ 0.4  , but from   z ∼ 0.2  to ∼0 the relative number of red-sequence dwarf galaxies has increased by a factor of ∼3, implying a significant build-up of the faint end of the cluster red sequence over the last 2.5 Gyr.     

Compact groups in theory and practice – III. Compact groups of galaxies in the Sixth Data Release of the Sloan Digital Sky Survey

We present the largest publicly available catalogue of compact groups (CGs) of galaxies identified using the original selection criteria of Hickson, selected from the Sixth Data Release of the Sloan Digital Sky Survey (SDSS DR6). We identify 2297 CGs down to a limiting magnitude of   r = 18 (∼0.24 groups  deg⁻²), and 74 791 CGs down to a limiting magnitude of   r = 21 (∼6.7 groups  deg⁻²). This represents 0.9 per cent of all galaxies in the SDSS DR6 at these magnitude levels. Contamination due to gross photometric errors has been removed from the bright sample of groups, and we estimate it is present in the large sample at the 14 per cent level. Spectroscopic information is available for 4131 galaxies in the bright catalogue (43 per cent completeness), and we find that the median redshift of these groups is   z _med= 0.09  . The median line-of-sight (LOS) velocity dispersion within the CGs from the bright catalogue is  σ_LOS≃ 230 km s⁻¹  , and their typical intergalactic separations are of the order of 50–100 kpc. We show that the fraction of groups with interloping galaxies identified as members is in good agreement with the predictions from our previous study of a mock galaxy catalogue, and we demonstrate how to select CGs such that the interloper fraction is well defined and minimized. This observational data set is ideal for large statistical studies of CGs, the role of environment on galaxy evolution and the effect of galaxy interactions in determining galaxy morphology.     

Probing quintessence: reconstruction and parameter estimation from supernovae

We explore the prospects for using future supernova observations to probe the dark energy. We focus on quintessence, an evolving scalar field that has been suggested as a candidate for the dark energy. After simulating the observations that would be expected from the proposed SuperNova / Acceleration Probe satellite ( SNAP ), we investigate two methods for extracting information concerning quintessence from such data. First, by expanding the quintessence equation of state as   w _Q ( z ) = w _Q (0) −α ln(1 + z )  , to fit the data, it is possible to reconstruct the quintessence potential for a wide range of smoothly varying potentials. Secondly, it will be possible to test the basic properties of the dark energy by constraining the parameters  Ω _Q , w _Q   and α. We show that it may be possible, for example, to distinguish between quintessence and the cosmological constant in this way. Furthermore, when supernova data are combined with other planned cosmological observations, the precision of reconstructions and parameter constraints is significantly improved, allowing a wider range of dark energy models to be distinguished.     

Decorrelating the power spectrum of galaxies

We show how to decorrelate the (pre-whitened) power spectrum measured from a galaxy survey into a set of high-resolution uncorrelated band-powers. The treatment includes non-linearity, but not redshift distortions. Amongst the infinitely many possible decorrelation matrices, the square root of the Fisher matrix, or a scaled version thereof, offers a particularly good choice, in the sense that the band-power windows are narrow, approximately symmetric, and well-behaved in the presence of noise. We use this method to compute band-power windows for, and the information content of, the Sloan Digital Sky Survey, the Las Campanas Redshift Survey, and the IRAS 1.2-Jy Survey.     

On the onset of stochasticity in Λ cold dark matter cosmological simulations

The onset of stochasticity is measured in Λ cold dark matter cosmological simulations using a set of classical observables. It is quantified as the local derivative of the logarithm of the dispersion of a given observable (within a set of different simulations differing weakly through their initial realization), with respect to the cosmic growth factor. In an Eulerian framework, it is shown here that chaos appears at small scales, where dynamic is non-linear, while it vanishes at larger scales, allowing the computation of a critical transition scale corresponding to  ∼3.5 Mpc  h ⁻¹  . This picture is confirmed by Lagrangian measurements which show that the distribution of substructures within clusters is partially sensitive to initial conditions, with a critical mass upper bound scaling roughly like the perturbation's amplitude to the power 0.15. The corresponding characteristic mass,   M _crit= 2 10¹³ M_⊙  , is roughly of the order of the critical mass of non-linearities at   z = 1  and accounts for the decoupling induced by the dark energy triggered acceleration.
The sensitivity to detailed initial conditions spills to some of the overall physical properties of the host halo (spin and velocity dispersion tensor orientation) while other 'global' properties are quite robust and show no chaos (mass, spin parameter, connexity and centre-of-mass position). This apparent discrepancy may reflect the fact that quantities which are integrals over particles rapidly average out details of difference in orbits, while the other observables are more sensitive to the detailed environment of forming haloes and reflect the non-linear scale coupling characterizing the environments of haloes.     

On the theory of magnetar QPOs

We examine the effect of inhomogeneous re-ionization on the galaxy power spectrum and the consequences for probing dark energy. To model feedback during re-ionization, we apply an ansatz setting the galaxy overdensity proportional to the underlying ionization field. Thus, inhomogeneous re-ionization may leave an imprint in the galaxy power spectrum. We evolve this imprint to low redshift and use the Fisher-matrix formalism to assess the effect on parameter estimation. We show that a combination of low-redshift  ( z = 0.3)  and high-redshift  ( z = 3)  galaxy surveys can constrain the size of cosmological H  ii regions during re-ionization. This imprint can also cause confusion when using baryon oscillations or other features of the galaxy power spectrum to probe the dark energy. We show that when bubbles are large, and hence detectable, our ability to constrain w can be degraded by up to 50 per cent. When bubbles are small, the imprint has little or no effect on measuring dark energy parameters.     

Galaxies under the cosmic microscope: resolved spectroscopy and new constraints on the z= 1 Tully–Fisher relation

We exploit the gravitational potential of massive cluster lenses to probe the emission-line properties of six   z = 1  galaxies which appear as highly magnified luminous arcs. Using the Gemini Multi-Object Spectrograph (GMOS) integral field spectrograph together with detailed cluster lens models, we reconstruct the intrinsic morphologies and two-dimensional velocity fields in these galaxies on scales corresponds to ∼0.5 kpc (unlensed) at   z = 1  . Four of the galaxies have stable disc-like kinematics, whilst the other two resemble interacting or starburst galaxies. These galaxies lie close to the mean rest-frame I -band Tully–Fisher relation for nearby spirals suggesting a clear preference for hierarchical growth of structure. In the rest-frame B band, the observations suggest  0.5 ± 0.3 mag  of brightening, consistent with increased star-formation activity at   z = 1  . However, the galaxies with stable disc kinematics have more slowly rising rotation curves than expected from galaxies with similar surface brightness in the local Universe. We suggest that this may arise because the distant galaxies have lower bulge masses than their local counterparts. Whilst this study is based on only six galaxies, the gain in flux and in spatial resolution achieved via gravitational magnification provides a much more detailed view of the high-redshift Universe than that possible with conventional surveys.     

Estimating the redshift distribution of photometric galaxy samples – II. Applications and tests of a new method

In Lima et al. we presented a new method for estimating the redshift distribution,   N ( z )  , of a photometric galaxy sample, using photometric observables and weighted sampling from a spectroscopic subsample of the data. In this paper, we extend this method and explore various applications of it, using both simulations and real data from the Sloan Digital Sky Survey (SDSS). In addition to estimating the redshift distribution for an entire sample, the weighting method enables accurate estimates of the redshift probability distribution,   p ( z )  , for each galaxy in a photometric sample. Use of   p ( z )  in cosmological analyses can substantially reduce biases associated with traditional photometric redshifts, in which a single redshift estimate is associated with each galaxy. The weighting procedure also naturally indicates which galaxies in the photometric sample are expected to have accurate redshift estimates, namely those that lie in regions of photometric-observable space that are well sampled by the spectroscopic subsample. In addition to providing a method that has some advantages over standard photo- z estimates, the weights method can also be used in conjunction with photo- z estimates e.g. by providing improved estimation of   N ( z )  via deconvolution of   N ( z _phot)  and improved estimates of photo- z scatter and bias. We present a publicly available   p ( z )  catalogue for ∼78 million SDSS DR7 galaxies.     

Cosmological implications of the PSCz PDF and its moments

We compare the probability density function (PDF) and its low-order moments (variance and skewness) of the smoothed IRAS Point Source Catalogue Redshift Survey (PSC z ) galaxy density field and of the corresponding simulated PSC z look-alikes, generated from N -body simulations of six different dark matter models: four structure-normalized with     and     , one COBE -normalized, and the old standard cold dark matter model. The galaxy distributions are smoothed with a Gaussian window at three different smoothing scales,     , 10 and 15  h ⁻¹ Mpc. We find that the simulation PSC z look-alike PDFs are sensitive only to the normalization of the power spectrum, probably owing to the shape similarity of the simulated galaxy power spectrum on the relevant scales. We find that the only models that are consistent, at a high significance level, with the observed PSC z PDF are models with a relatively low power spectrum normalization     . From the phenomenologically derived σ ₈–moments relation, fitted from the simulation data, we find that the PSC z moments suggest     .     

On the least action principle in cosmology

Given the present distribution of mass tracing objects in an expanding universe, we develop and test a fast method for recovering their past orbits using the least action principle. In this method, termed FAM for fast action minimization, the orbits are expanded in a set of orthogonal time basis functions satisfying the appropriate boundary conditions at the initial and final times. The conjugate gradient method is applied to locate the extremum of the action in the space of the expansion coefficients of the orbits. The treecode gravity solver routine is used for computing the gravitational field appearing in the action and the potential field appearing in the gradient of the action. The time integration of the Lagrangian is done using Gaussian quadratures. FAM allows us to increase the number of galaxies over previous numerical action principle implementations by more than one order of magnitude. For example, orbits for the 15 000 IRAS PSC z galaxies can be recovered in 12 000 CPU seconds on a 400-MHz DEC-Alpha machine. FAM can recover the present peculiar velocities of particles and the initial fluctuations field. It successfully recovers the flow field down to cluster scales, where deviations of the flow from the Zel'dovich solution are significant. We also show how to recover orbits from the present distribution of objects in redshift space by direct minimization of a modified action, without iterating the solution between real and redshift spaces.     

The H i opacity of the intergalactic medium at redshifts 1.6 < z < 3.2

We use high-quality echelle spectra of 24 quasi-stellar objects to provide a calibrated measurement of the total amount of Lyα forest absorption (DA) over the redshift range  2.2 < z < 3.2  . Our measurement of DA excludes absorption from metal lines or the Lyα lines of Lyman-limit systems and damped Lyα systems. We use artificial spectra with realistic flux calibration errors to show that we are able to place continuum levels that are accurate to better than 1 per cent. When we combine our results with our previous results between  1.6 < z < 2.2  , we find that the redshift evolution of DA is well described over  1.6 < z < 3.2  as   A (1 + z )^γ  , where   A = 0.0062  and  γ= 2.75  . We detect no significant deviations from a smooth power-law evolution over the redshift range studied. We find less H  i absorption than expected at   z = 3  , implying that the ultraviolet background is  ∼40  per cent higher than expected. Our data appears to be consistent with an H  i ionization rate of  Γ∼ 1.4 × 10⁻¹² s⁻¹  .     

Luminous red galaxy clustering at z≃ 0.7 – first results using AAOmega

We report on the AAT-AAOmega LRG Pilot observing run to establish the feasibility of a large spectroscopic survey using the new AAOmega instrument. We have selected luminous red galaxies (LRGs) using single epoch SDSS riz -photometry to   i < 20.5  and   z < 20.2  . We have observed in three fields including the COSMOS field and the COMBO-17 S11 field, obtaining a sample of ∼600 redshift   z ≳ 0.5  LRGs. Exposure times varied from 1–4 h to determine the minimum exposure for AAOmega to make an essentially complete LRG redshift survey in average conditions. We show that LRG redshifts to   i < 20.5  can be measured in ≈1.5 h exposures and present comparisons with 2SLAQ and COMBO-17 (photo)redshifts. Crucially, the riz selection coupled with the three to four times improved AAOmega throughput is shown to extend the LRG mean redshift from   z = 0.55  for 2SLAQ to   z = 0.681 ± 0.005  for riz -selected LRGs. This extended range is vital for maximizing the signal-to-noise ratio for the detection of the baryon acoustic oscillations (BAOs). Furthermore, we show that the amplitude of LRG clustering is   s ₀= 9.9 ± 0.7 h ⁻¹ Mpc  , as high as that seen in the 2SLAQ LRG Survey. Consistent results for this clustering amplitude are found from the projected and semi-projected correlation functions. This high amplitude is consistent with a long-lived population whose bias evolves as predicted by a simple 'high-peak' model. We conclude that a redshift survey of 360 000 LRGs over 3000 deg², with an effective volume some four times bigger than previously used to detect BAO with LRGs, is possible with AAOmega in 170 nights.