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Register a new userForward and backward galaxy evolution in comoving number density space
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Galaxy comoving number density is commonly used to forge progenitor/descendant links between observed galaxy populations at different epochs. However, this method breaks down in the presence of galaxy mergers, or when galaxies experience stochastic growth rates. We present a simple analytic framework to treat the physical processes that drive the evolution and diffusion of galaxies within comoving number density space. The evolution in mass rank order of a galaxy population with time is influenced by the galaxy coagulation rate and galaxy mass rank scatter rate. We quantify the relative contribution of these two effects to the mass rank order evolution. We show that galaxy coagulation is dominant at lower redshifts and stellar masses, while scattered growth rates dominate the mass rank evolution at higher redshifts and stellar masses. For a galaxy population at $10^{10} M_odot$, coagulation has been the dominant effect since $z=2.2$, but a galaxy population at $10^{11} M_odot$ was dominated by mass rank scatter until $z=0.6$. We show that although the forward and backward median number density evolution tracks are asymmetric, the backward median number density evolution can be obtained by convolving the descendant distribution function with progenitor relative abundances. We tabulate fits for the median number density evolution and scatter which can be applied to improve the way galaxy populations are linked in multi-epoch observational datasets.
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Studying the average properties of galaxies at a fixed comoving number density over a wide redshift range has become a popular observational method, because it may trace the evolution of galaxies statistically. We test this method by comparing the evolution of galaxies at fixed number density and by following individual galaxies through cosmic time (z=0-5) in cosmological, hydrodynamical simulations from OWLS. Comparing progenitors, descendants, and galaxies selected at fixed number density at each redshift, we find differences of up to a factor of three for galaxy and interstellar medium (ISM) masses. The difference is somewhat larger for black hole masses. The scatter in ISM mass increases significantly towards low redshift with all selection techniques. We use the fixed number density technique to study the assembly of dark matter, gas, stars, and black holes and the evolution in accretion and star formation rates. We find three different regimes for massive galaxies, consistent with observations: at high redshift the gas accretion rate dominates, at intermediate redshifts the star formation rate is the highest, and at low redshift galaxies grow mostly through mergers. Quiescent galaxies have much lower ISM masses (by definition) and much higher black hole masses, but the stellar and halo masses are fairly similar. Without active galactic nucleus (AGN) feedback, massive galaxies are dominated by star formation down to z=0 and most of their stellar mass growth occurs in the centre. With AGN feedback, stellar mass is only added to the outskirts of galaxies by mergers and they grow inside-out.
The cumulative comoving number-density of galaxies as a function of stellar mass or central velocity dispersion is commonly used to link galaxy populations across different epochs. By assuming that galaxies preserve their number-density in time, one can infer the evolution of their properties, such as masses, sizes, and morphologies. However, this assumption does not hold in the presence of galaxy mergers or when rank ordering is broken owing to variable stellar growth rates. We present an analysis of the evolving comoving number density of galaxy populations found in the Illustris cosmological hydrodynamical simulation focused on the redshift range $0leq z leq 3$. Our primary results are as follows: 1) The inferred average stellar mass evolution obtained via a constant comoving number density assumption is systematically biased compared to the merger tree results at the factor of $sim$2(4) level when tracking galaxies from redshift $z=0$ out to redshift $z=2(3)$; 2) The median number density evolution for galaxy populations tracked forward in time is shallower than for galaxy populations tracked backward in time; 3) A similar evolution in the median number density of tracked galaxy populations is found regardless of whether number density is assigned via stellar mass, stellar velocity dispersion, or dark matter halo mass; 4) Explicit tracking reveals a large diversity in galaxies assembly histories that cannot be captured by constant number-density analyses; 5) The significant scatter in galaxy linking methods is only marginally reduced by considering a number of additional physical and observable galaxy properties as realized in our simulation. We provide fits for the forward and backward median evolution in stellar mass and number density and discuss implications of our analysis for interpreting multi-epoch galaxy property observations.
The evolution of the number density of galaxies in the universe, and thus also the total number of galaxies, is a fundamental question with implications for a host of astrophysical problems including galaxy evolution and cosmology. However there has never been a detailed study of this important measurement, nor a clear path to answer it. To address this we use observed galaxy stellar mass functions up to $zsim8$ to determine how the number densities of galaxies changes as a function of time and mass limit. We show that the increase in the total number density of galaxies ($phi_{rm T}$), more massive than M$_{*} = 10^{6}$ M_0, decreases as $phi_{rm T} sim t^{-1}$, where $t$ is the age of the universe. We further show that this evolution turns-over and rather increases with time at higher mass lower limits of M$_{*}>10^{7}$ M_0. By using the M$_{*}=10^{6}$ M_0 lower limit we further show that the total number of galaxies in the universe up to $z = 8$ is $2.0^{+0.7}_{-0.6} times 10^{12}$ (two trillion), almost a factor of ten higher than would be seen in an all sky survey at Hubble Ultra-Deep Field depth. We discuss the implications for these results for galaxy evolution, as well as compare our results with the latest models of galaxy formation. These results also reveal that the cosmic background light in the optical and near-infrared likely arise from these unobserved faint galaxies. We also show how these results solve the question of why the sky at night is dark, otherwise known as Olbers paradox.
Preliminary but close to final results on the Z lineshape and Forward-Backward asymmetries from the four LEP experiments are presented. Combined values extracted from ALEPH. DELPHI, L3 and OPAL data recorded at energies around the Z pole are discussed.
A coupled forward-backward stochastic differential system (FBSDS) is formulated in spaces of fields for the incompressible Navier-Stokes equation in the whole space. It is shown to have a unique local solution, and further if either the Reynolds number is small or the dimension of the forward stochastic differential equation is equal to two, it can be shown to have a unique global solution. These results are shown with probabilistic arguments to imply the known existence and uniqueness results for the Navier-Stokes equation, and thus provide probabilistic formulas to the latter. Related results and the maximum principle are also addressed for partial differential equations (PDEs) of Burgers type. Moreover, from truncating the time interval of the above FBSDS, approximate solution is derived for the Navier-Stokes equation by a new class of FBSDSs and their associated PDEs; our probabilistic formula is also bridged to the probabilistic Lagrangian representations for the velocity field, given by Constantin and Iyer (Commun. Pure Appl. Math. 61: 330--345, 2008) and Zhang (Probab. Theory Relat. Fields 148: 305--332, 2010) ; finally, the solution of the Navier-Stokes equation is shown to be a critical point of controlled forward-backward stochastic differential equations.
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