ALBERT

Description: We propose a new way of looking at the Baryon Acoustic Oscillation in the large-scale-structure clustering correlation function. We identify a scale s LP that has two fundamental features: its position is insensitive to non-linear gravity, redshift-space distortions and scale-dependent bias at the 0.5 per cent level; it is geometrical, i.e. independent of the power spectrum of the primordial density fluctuation parameters. These two properties together make s LP , called the ‘linear point’, an excellent cosmological standard ruler. The linear point is also appealing because it is easily identified irrespectively of how non-linearities distort the correlation function. Finally, the correlation function amplitude at s LP is similarly insensitive to non-linear corrections to within a few per cent. Hence, exploiting the particular baryon features in the correlation function, we propose three new estimators for growth measurements. A preliminary analysis of s LP in current data is encouraging.

Description: We compare the set of local galaxies having dynamically measured black holes with a large, unbiased sample of galaxies extracted from the Sloan Digital Sky Survey. We confirm earlier work showing that the majority of black hole hosts have significantly higher velocity dispersions than local galaxies of similar stellar mass. We use Monte Carlo simulations to illustrate the effect on black hole scaling relations if this bias arises from the requirement that the black hole sphere of influence must be resolved to measure black hole masses with spatially resolved kinematics. We find that this selection effect artificially increases the normalization of the M bh – relation by a factor of at least ~3; the bias for the M bh – M star relation is even larger. Our Monte Carlo simulations and analysis of the residuals from scaling relations both indicate that is more fundamental than M star or effective radius. In particular, the M bh – M star relation is mostly a consequence of the M bh – and – M star relations, and is heavily biased by up to a factor of 50 at small masses. This helps resolve the discrepancy between dynamically based black hole–galaxy scaling relations versus those of active galaxies. Our simulations also disfavour broad distributions of black hole masses at fixed . Correcting for this bias suggests that the calibration factor used to estimate black hole masses in active galaxies should be reduced to values of f vir  ~ 1. Black hole mass densities should also be proportionally smaller, perhaps implying significantly higher radiative efficiencies/black hole spins. Reducing black hole masses also reduces the gravitational wave signal expected from black hole mergers.

Description: Supermassive black hole–host galaxy relations are key to the computation of the expected gravitational wave background (GWB) in the pulsar timing array (PTA) frequency band. It has been recently pointed out that standard relations adopted in GWB computations are in fact biased-high. We show that when this selection bias is taken into account, the expected GWB in the PTA band is a factor of about 3 smaller than previously estimated. Compared to other scaling relations recently published in the literature, the median amplitude of the signal at f  = 1 yr –1 drops from 1.3  x  10 –15 to 4  x  10 –16 . Although this solves any potential tension between theoretical predictions and recent PTA limits without invoking other dynamical effects (such as stalling, eccentricity or strong coupling with the galactic environment), it also makes the GWB detection more challenging.

Description: We describe the luminosity function, based on Sérsic fits to the light profiles, of CMASS galaxies at z ~ 0.55. Compared to previous estimates, our Sérsic-based reductions imply more luminous, massive galaxies, consistent with the effects of Sérsic- rather than Petrosian or de Vaucouleur-based photometry on the Sloan Digital Sky Survey (SDSS) main galaxy sample at z ~ 0.1. This implies a significant revision of the high-mass end of the correlation between stellar and halo mass. Inferences about the evolution of the luminosity and stellar mass functions depend strongly on the assumed, and uncertain, k + e corrections. In turn, these depend on the assumed age of the population. Applying k + e corrections taken from fitting the models of Maraston et al. to the colours of both SDSS and CMASS galaxies, the evolution of the luminosity and stellar mass functions appears impressively passive, provided that the fits are required to return old ages. However, when matched in comoving number- or luminosity-density, the SDSS galaxies are less strongly clustered compared to their counterparts in CMASS. This rules out the passive evolution scenario, and, indeed, any minor merger scenarios which preserve the rank ordering in stellar mass of the population. Potential incompletenesses in the CMASS sample would further enhance this mismatch. Our analysis highlights the virtue of combining clustering measurements with number counts.

Description: Insight into a number of interesting questions in cosmology can be obtained by studying the first crossing distributions of physically motivated barriers by random walks with correlated steps: higher mass objects are associated with walks that cross the barrier in fewer steps. We write the first crossing distribution as a formal series, ordered by the number of times a walk upcrosses the barrier. Since the fraction of walks with many upcrossings is negligible if the walk has not taken many steps, the leading order term in this series is the most relevant for understanding the massive objects of most interest in cosmology. For walks associated with Gaussian random fields, this first term only requires knowledge of the bivariate distribution of the walk height and slope, and provides an excellent approximation to the first crossing distribution for all barriers and smoothing filters of current interest. We show that this simplicity survives when extending the approach to the case of non-Gaussian random fields. For non-Gaussian fields which are obtained by deterministic transformations of a Gaussian, the first crossing distribution is simply related to that for Gaussian walks crossing a suitably rescaled barrier. Our analysis shows that this is a useful way to think of the generic case as well. Although our study is motivated by the possibility that the primordial fluctuation field was non-Gaussian, our results are general. In particular, they do not assume the non-Gaussianity is small, so they may be viewed as the solution to an excursion set analysis of the late-time, non-linear fluctuation field rather than the initial one. They are also useful for models in which the barrier height is determined by quantities other than the initial density, since most other physically motivated variables (such as the shear) are usually stochastic and non-Gaussian. We use the Lognormal transformation to illustrate some of our arguments.

Description: We quantify the systematics in the size–luminosity relation of galaxies in the Sloan Digital Sky Survey main sample (i.e. at z  ~ 0.1) which arise from fitting different one- and two-component model profiles to the r -band images. For objects brighter than L * , fitting a single Sérsic profile to what is really a two-component SerExp system leads to biases: the half-light radius is increasingly overestimated as n of the fitted single component increases; it is also overestimated at B / T  ~ 0.6. For such objects, the assumption of a single Sérsic component is particularly misleading. However, the net effect on the R - L relation is small, except for the most luminous tail. We then study how this relation depends on morphology. Our analysis is one of the first to use Bayesian-classifier-derived weights, rather than hard cuts, to define morphology. For the R - L relation Es, S0s and Sas are early types, whereas Sbs and Scds are late, although S0s tend to be 15 per cent smaller than Es of the same luminosity, and faint Sbs are more than 25 per cent smaller than faint Scds. Neither the early- nor the late-type relations are pure power laws: both show significant curvature, which we quantify. This curvature confirms that two mass scales are special for both early- and late-type galaxies: M *  ~ 3 10 10 and 2 10 11 M . Also, although the R disc - L disc and R disc - M *disc relations of discs of disc-dominated galaxies run parallel to the corresponding relations for the total light in late types (i.e. they are significantly curved), R bulge - L bulge and R bulge - M *bulge for bulge-dominated systems show almost no curvature (i.e. unlike for the total light of early-type galaxies). Finally, the intrinsic scatter in the R - L relation decreases at large L and/or M * and should provide additional constraints on models of how the most massive galaxies formed.

Description: We describe a simple fully analytic model of the excursion set approach associated with two Gaussian random walks: the first walk represents the initial overdensity around a protohalo, and the second is a crude way of allowing for other factors which might influence halo formation. This model is richer than that based on a single walk, because it yields a distribution of heights at first crossing. We provide explicit expressions for the unconditional first crossing distribution which is usually used to model the halo mass function, the progenitor distributions from which merger rates are usually estimated and the conditional distributions from which correlations with environment are usually estimated. These latter exhibit perhaps the simplest form of what is often called non-local bias, and which we prefer to call stochastic bias, since the new bias effects arise from ‘hidden variables’ other than density, but these may still be defined locally. We provide explicit expressions for these new bias factors. We also provide formulae for the distribution of heights at first crossing in the unconditional and conditional cases. In contrast to the first crossing distribution, these are exact, even for moving barriers, and for walks with correlated steps. The conditional distributions yield predictions for the distribution of halo concentrations at fixed mass and formation redshift. They also exhibit assembly bias like effects, even when the steps in the walks themselves are uncorrelated. Our formulae show that without prior knowledge of the physical origin of the second walk, the naive estimate of the critical density required for halo formation which is based on the statistics of the first crossing distribution will be larger than that based on the statistical distribution of walk heights at first crossing; both will be biased low compared to the value associated with the physics. Finally, we show how the predictions are modified if we add the requirement that haloes form around peaks: these depend on whether the peaks constraint is applied to a combination of the overdensity and the other variable, or to the overdensity alone. Our results demonstrate the power of requiring models to reproduce not just halo counts but the distribution of overdensities at fixed protohalo mass as well.

Description: We present a new parallel implementation of the PINpointing Orbit Crossing-Collapsed HIerarchical Objects ( pinocchio ) algorithm, a quick tool, based on Lagrangian Perturbation Theory, for the hierarchical build-up of dark matter (DM) haloes in cosmological volumes. To assess its ability to predict halo correlations on large scales, we compare its results with those of an N -body simulation of a 3 h –1 Gpc box sampled with 2048 3 particles taken from the mice suite, matching the same seeds for the initial conditions. Thanks to the Fastest Fourier Transforms in the West (FFTW) libraries and to the relatively simple design, the code shows very good scaling properties. The CPU time required by pinocchio is a tiny fraction (~1/2000) of that required by the mice simulation. Varying some of pinocchio numerical parameters allows one to produce a universal mass function that lies in the range allowed by published fits, although it underestimates the mice mass function of Friends-of-Friends (FoF) haloes in the high-mass tail. We compare the matter–halo and the halo–halo power spectra with those of the mice simulation and find that these two-point statistics are well recovered on large scales. In particular, when catalogues are matched in number density, agreement within 10 per cent is achieved for the halo power spectrum. At scales k  〉 0.1 h Mpc –1 , the inaccuracy of the Zel’dovich approximation in locating halo positions causes an underestimate of the power spectrum that can be modelled as a Gaussian factor with a damping scale of d  = 3 h –1 Mpc at z  = 0, decreasing at higher redshift. Finally, a remarkable match is obtained for the reduced halo bispectrum, showing a good description of non-linear halo bias. Our results demonstrate the potential of pinocchio as an accurate and flexible tool for generating large ensembles of mock galaxy surveys, with interesting applications for the analysis of large galaxy redshift surveys.

Description: The simplest stochastic halo formation models assume that the traceless part of the shear field acts to increase the initial overdensity (or decrease the underdensity) that a protohalo (or protovoid) must have if it is to form by the present time. Equivalently, it is the difference between the overdensity and (the square root of the) shear that must be larger than a threshold value. To estimate the effect this has on halo abundances using the excursion set approach, we must solve for the first crossing distribution of a barrier of constant height by the random fluctuations of this difference, which is (even for Gaussian initial conditions) a non-Gaussian variate, since the shear is drawn from a $\chi ^2_5$ distribution. The correlation properties of such non-Gaussian walks are inherited from those of the density and the shear, and, since they are independent processes, the solution is in fact remarkably simple. We show that this provides an easy way to understand why earlier heuristic arguments about the nature of the solution worked so well. In addition to modelling haloes and voids, this potentially simplifies models of the abundance and spatial distribution of filaments and sheets in the cosmic web.