Abstract:
(Abridged). We present numerical simulations of isothermal, MHD, supersonic turbulence, designed to test various hypotheses frequently assumed in star formation(SF) theories. We consider three simulations, each with a different combination of physical size, rms sonic Mach number, and Jeans parameter, but chosen as to give the same value of the virial parameter and to conform with Larson's scaling relations. As in the non-magnetic case: we find no simultaneously subsonic and super-Jeans structures in our MHD simulations. We find that the fraction of small-scale super-Jeans structures increases when self gravity is turned on, and that the production of gravitationally unstable dense cores by turbulence alone is very low. This implies that self-gravity is in general necessary not only to induce the collapse of Jeans-unstable cores, but also to form them. We find that denser regions tend to have more negative values of the velocity divergence, implying a net inwards flow towards the regions' centers. We compare the results from our simulations with the predictions from the recent SF theories by Krumholz & McKee, Padoan & Nordlund, and Hennebelle & Chabrier, using the expressions recently provided by Federrath & Klessen. We find that none of these theories reproduces the dependence of the SFEff with Ms observed in our simulations in the MHD case. The SFEff predicted by the theories ranges between half and one order of magnitude larger than what we observe in the simulations in both the HD and the MHD cases. We conclude that the type of flow used in simulations like the ones presented here and assumed in recent SF theories, may not correctly represent the flow within actual clouds, and that theories that assume it does may be missing a fundamental aspect of the flow. We suggest that a more realistic regime may be that of hierarchical gravitational collapse.

Abstract:
If one wants to represent the galaxy number density at some point in terms of only the mass density at the same point, there appears the stochasticity in such a relation, which is referred to as ``stochastic bias''. The stochasticity is there because the galaxy number density is not merely a local function of a mass density field, but it is a nonlocal functional, instead. Thus, the phenomenological stochasticity of the bias should be accounted for by nonlocal features of galaxy formation processes. Based on mathematical arguments, we show that there are simple relations between biasing and nonlocality on linear scales of density fluctuations, and that the stochasticity in Fourier space does not exist on linear scales under a certain condition, even if the galaxy formation itself is a complex nonlinear and nonlocal precess. The stochasticity in real space, however, arise from the scale-dependence of bias parameter, $b$. As examples, we derive the stochastic bias parameters of simple nonlocal models of galaxy formation, i.e., the local Lagrangian bias models, the cooperative model, and the peak model. We show that the stochasticity in real space is also weak, except on the scales of nonlocality of the galaxy formation. Therefore, we do not have to worry too much about the stochasticity on linear scales, especially in Fourier space, even if we do not know the details of galaxy formation process.

Abstract:
We use semi-analytic models of galaxy formation combined with high resolution N-body simulations to make predictions for galaxy-dark matter correlations and apply them to galaxy-galaxy lensing. We analyze cross-correlation spectra between the dark matter and different galaxy samples selected by luminosity, color or star formation rate. We compare the predictions to the recent detection by SDSS. We show that the correlation amplitude and the mean tangential shear depend strongly on the luminosity of the sample on scales below 1 Mpc, reflecting the correlation between the galaxy luminosity and the halo mass. The cross-correlation cannot however be used to infer the halo profile directly because different halo masses dominate on different scales and because not all galaxies are at the centers of the corresponding halos. We compute the redshift evolution of the cross-correlation amplitude and compare it to those of galaxies and dark matter. We also compute the galaxy-dark matter correlation coefficient and show it is close to unity on scales above r > 1 Mpc for all considered galaxy types. This would allow one to extract the bias and the dark matter power spectrum on large scales from the galaxy and galaxy-dark matter correlations.

Abstract:
The VLT Multi Unit Spectroscopic Explorer (MUSE) integral-field spectrograph can detect Ly\alpha{} emitters (LAE) in the redshift range $2.8 \lesssim z \lesssim 6.7$ in a homogeneous way. Ongoing MUSE surveys will notably probe faint Ly\alpha{} sources that are usually missed by current narrow-band surveys. We provide quantitative predictions for a typical wedding-cake observing strategy with MUSE based on mock catalogs generated with a semi-analytic model of galaxy formation coupled to numerical Ly\alpha{} radiation transfer models in gas outflows. We expect $\approx$ 1500 bright LAEs ($F_{Ly\alpha}$ $\gtrsim$ $10^{-17}$ erg s$^{-1}$ cm$^{-2}$) in a typical Shallow Field (SF) survey carried over $\approx$ 100 arcmin$^2$, and $\approx$ 2,000 sources as faint as $10^{-18}$ erg s$^{-1}$ cm$^{-2}$ in a Medium-Deep Field (MDF) survey over 10 arcmin$^2$. In a typical Deep Field (DF) survey of 1 arcmin$^2$, we predict that $\approx$ 500 extremely faint LAEs ($F_{Ly\alpha}$ $\gtrsim$ $4 \times 10^{-19}$ erg s$^{-1}$ cm$^{-2}$) will be found. Our results suggest that faint Ly\alpha{} sources contribute significantly to the cosmic Ly\alpha{} luminosity and SFR budget. While the host halos of bright LAEs at z $\approx$ 3 and 6 have descendants with median masses of $2 \times 10^{12}$ and $5 \times 10^{13}$ $M_{\odot}$ respectively, the faintest sources detectable by MUSE at these redshifts are predicted to reside in halos which evolve into typical sub-$L^{*}$ and $L^{*}$ galaxy halos at z = 0. We expect typical DF and MDF surveys to uncover the building blocks of Milky Way-like objects, even probing the bulk of the stellar mass content of LAEs located in their progenitor halos at z $\approx$ 3.

Abstract:
Observationally confirming spatial homogeneity on sufficiently large cosmological scales is of importance to test one of the underpinning assumptions of cosmology, and is also imperative for correctly interpreting dark energy. A challenging aspect of this is that homogeneity must be probed inside our past lightcone, while observations take place on the lightcone. The star formation history (SFH) in the galaxy fossil record provides a novel way to do this. We calculate the SFH of stacked Luminous Red Galaxy (LRG) spectra obtained from the Sloan Digital Sky Survey. We divide the LRG sample into 12 equal area contiguous sky patches and 10 redshift slices (0.2 < z < 0.5), which correspond to 120 blocks of volume 0.04Gpc3. Using the SFH in a time period which samples the history of the Universe between look-back times 11.5 to 13.4 Gyrs as a proxy for homogeneity, we calculate the posterior distribution for the excess large-scale variance due to inhomogeneity, and find that the most likely solution is no extra variance at all. At 95% credibility, there is no evidence of deviations larger than 5.8%.

Abstract:
A semi-analytic model is proposed that couples the Press-Schechter formalism for the number of galaxies with a prescription for galaxy-galaxy interactions that enables to follow the evolution of galaxy morphologies along the Hubble sequence. Within this framework, we calculate the chemo-spectrophotometric evolution of galaxies to obtain spectral energy distributions. We find that such an approach is very successful in reproducing the statistical properties of galaxies as well as their time evolution. We are able to make predictions as a function of galaxy type: for clarity, we restrict ourselves to two categories of galaxies: early and late types that are identified with ellipticals and disks. In our model, irregulars are simply an early stage of galaxy formation. In particular, we obtain good matches for the galaxy counts and redshift distributions of sources from UV to submm wavelengths. We also reproduce the observed cosmic star formation history and the diffuse background radiation, and make predictions as to the epoch and wavelength at which the dust-shrouded star formation of spheroids begins to dominate over the star formation that occurs more quiescently in disks. A new prediction of our model is a rise in the FIR luminosity density with increasing redshift, peaking at about $z\sim 3$, and with a ratio to the local luminosity density $\rho_{L,\nu} (z = z_{peak})/ \rho_{L,\nu} (z = 0)$ about 10 times higher than that in the blue (B-band) which peaks near $z\sim 2$.

Abstract:
In this review, we describe our current understanding of cluster formation: from the general picture of collapse from initial density fluctuations in an expanding Universe to detailed simulations of cluster formation including the effects of galaxy formation. We outline both the areas in which highly accurate predictions of theoretical models can be obtained and areas where predictions are uncertain due to uncertain physics of galaxy formation and feedback. The former includes the description of the structural properties of the dark matter halos hosting cluster, their mass function and clustering properties. Their study provides a foundation for cosmological applications of clusters and for testing the fundamental assumptions of the standard model of structure formation. The latter includes the description of the total gas and stellar fractions, the thermodynamical and non-thermal processes in the intracluster plasma. Their study serves as a testing ground for galaxy formation models and plasma physics. In this context, we identify a suitable radial range where the observed thermal properties of the intra-cluster plasma exhibit the most regular behavior and thus can be used to define robust observational proxies for the total cluster mass. We put particular emphasis on examining assumptions and limitations of the widely used self-similar model of clusters. Finally, we discuss the formation of clusters in non-standard cosmological models, such as non-Gaussian models for the initial density field and models with modified gravity, along with prospects for testing these alternative scenarios with large cluster surveys in the near future.

Abstract:
We present the recently derived Wolf et al. (2009) mass estimator, which is applicable for spherical pressure-supported stellar systems spanning over ten orders of magnitude in luminosity, as a tool to test galaxy formation theories. We show that all of the Milky Way dwarf spheroidal galaxies (MW dSphs) are consistent with having formed within a halo of mass approximately 3 x 10^9 Msun in LCDM cosmology. The faintest MW dSphs seem to have formed in dark matter halos that are at least as massive as those of the brightest MW dSphs, despite the almost five orders of magnitude spread in luminosity. We expand our analysis to the full range of observed pressure-supported stellar systems and examine their half-light I-band mass-to-light ratios. The M/L vs. half-light mass M_1/2 relation for pressure-supported galaxies follows a U-shape, with a broad minimum near M/L ~ 3 that spans dwarf elliptical galaxies to normal ellipticals, a steep rise to M/L ~ 3,200 for ultra-faint dSphs, and a more shallow rise to M/L ~ 800 for galaxy cluster spheroids.

Abstract:
We present a set of predictions for weak lensing correlation functions in the context of modified gravity models, including a prescription for the impact of the nonlinear power spectrum regime in these models. We consider the DGP and f(R) models, together with dark energy models with the same expansion history. We use the requirement that gravity is close to GR on small scales to estimate the non-linear power for these models. We then calculate weak lensing statistics, showing their behaviour as a function of scale and redshift, and present predictions for measurement accuracy with future lensing surveys, taking into account cosmic variance and galaxy shape noise. We demonstrate the improved discriminatory power of weak lensing for testing modified gravities once the nonlinear power spectrum contribution has been included. We also examine the ability of future lensing surveys to constrain a parameterisation of the non-linear power spectrum, including sensitivity to the growth factor.

Abstract:
Accurate galaxy stellar masses are crucial to better understand the physical mechanisms driving the galaxy formation process. We use synthetic star formation and metal enrichment histories predicted by the {\sc galform} galaxy formation model to investigate the precision with which various colours $(m_{a}-m_{b})$ can alone be used as diagnostics of the stellar mass-to-light ratio. As an example, we find that, at $z=0$, the {\em intrinsic} (B$_{f435w}-$V$_{f606w}$) colour can be used to determine the intrinsic rest-frame $V$-band stellar mass-to-light ratio ($\log_{10}\Gamma_{V}=\log_{10}[(M/M_{\odot})/(L_{V}/L_{V\odot})]$) with a precision of $\sigma_{lg\Gamma}\simeq 0.06$ when the initial mass function and redshift are known beforehand. While the presence of dust, assuming a universal attenuation curve, can have a systematic effect on the inferred mass-to-light ratio using a single-colour relation, this is typically small as it is often possible to choose a colour for which the dust reddening vector is approximately aligned with the $(m_{a}-m_{b})-\log_{10}\Gamma_{V}$ relation. The precision with which the stellar mass-to-light ratio can be recovered using a single colour diagnostic rivals implementations of SED fitting using more information but in which simple parameterisations of the star formation and metal enrichment histories are assumed. To facilitate the wide use of these relations, we provide the optimal observer frame colour to estimate the stellar mass-to-light ratio, along with the associated parameters, as a function of redshift ($0