Deriving effective models for multiscale systems via evolutionary GammaGamma-convergence

We discuss possible extensions of the recently established theory of evolutionary Gamma convergence for gradient systems to nonlinear dynamical systems obtained by perturbation of a gradient systems. Thus, it is possible to derive effective equations for pattern forming systems with multiple scales. Our applications include homogenization of reaction-diffusion systems, the justification of amplitude equations for Turing instabilities, and the limit from pure diffusion to reaction-diffusion. This is achieved by generalizing the Gamma-limit approaches based on the energy-dissipation principle or the evolutionary variational estimate

Implications for galaxy formation models from observations of globular clusters around ultradiffuse galaxies

We present an analysis of Hubble Space Telescope observations of globular clusters (GCs) in six ultradiffuse galaxies (UDGs) in the Coma cluster, a sample that represents UDGs with large effective radii (Re), and use the results to evaluate competing formation models. We eliminate two significant sources of systematic uncertainty in the determination of the number of GCs, NGC by using sufficiently deep observations that (i) reach the turnover of the globular cluster luminosity function (GCLF) and (ii) provide a sufficient number of GCs with which to measure the GC number radial distribution. We find that NGC for these galaxies is on average ∼ 20, which implies an average total mass, Mtotal, ∼ 1011 M⊙ when applying the relation between NGC and Mtotal. This value of NGC lies at the upper end of the range observed for dwarf galaxies of the same stellar mass and is roughly a factor of two larger than the mean. The GCLF, radial profile, and average colour are more consistent with those observed for dwarf galaxies than with those observed for the more massive (L*) galaxies, while both the radial and azimuthal GC distributions closely follow those of the stars in the host galaxy. Finally, we discuss why our observations, specifically the GC number and GC distribution around these six UDGs, pose challenges for several of the currently favoured UDG formation models

The Effects of Gas on Morphological Transformation in Mergers: Implications for Bulge and Disk Demographics

Transformation of disks into spheroids via mergers is a well-accepted element of galaxy formation models. However, recent simulations have shown that bulge formation is suppressed in increasingly gas-rich mergers. We investigate the global implications of these results in a cosmological framework, using independent approaches: empirical halo-occupation models (where galaxies are populated in halos according to observations) and semi-analytic models. In both, ignoring the effects of gas in mergers leads to the over-production of spheroids: low and intermediate-mass galaxies are predicted to be bulge-dominated (B/T~0.5 at <10^10 M_sun), with almost no bulgeless systems), even if they have avoided major mergers. Including the different physical behavior of gas in mergers immediately leads to a dramatic change: bulge formation is suppressed in low-mass galaxies, observed to be gas-rich (giving B/T~0.1 at <10^10 M_sun, with a number of bulgeless galaxies in good agreement with observations). Simulations and analytic models which neglect the similarity-breaking behavior of gas have difficulty reproducing the strong observed morphology-mass relation. However, the observed dependence of gas fractions on mass, combined with suppression of bulge formation in gas-rich mergers, naturally leads to the observed trends. Discrepancies between observations and models that ignore the role of gas increase with redshift; in models that treat gas properly, galaxies are predicted to be less bulge-dominated at high redshifts, in agreement with the observations. We discuss implications for the global bulge mass density and future observational tests.Comment: 14 pages, 11 figures, accepted to MNRAS (matched published version). A routine to return the galaxy merger rates discussed here is available at http://www.cfa.harvard.edu/~phopkins/Site/mergercalc.htm

A review of elliptical and disc galaxy structure, and modern scaling laws

A century ago, in 1911 and 1913, Plummer and then Reynolds introduced their models to describe the radial distribution of stars in `nebulae'. This article reviews the progress since then, providing both an historical perspective and a contemporary review of the stellar structure of bulges, discs and elliptical galaxies. The quantification of galaxy nuclei, such as central mass deficits and excess nuclear light, plus the structure of dark matter halos and cD galaxy envelopes, are discussed. Issues pertaining to spiral galaxies including dust, bulge-to-disc ratios, bulgeless galaxies, bars and the identification of pseudobulges are also reviewed. An array of modern scaling relations involving sizes, luminosities, surface brightnesses and stellar concentrations are presented, many of which are shown to be curved. These 'redshift zero' relations not only quantify the behavior and nature of galaxies in the Universe today, but are the modern benchmark for evolutionary studies of galaxies, whether based on observations, N-body-simulations or semi-analytical modelling. For example, it is shown that some of the recently discovered compact elliptical galaxies at 1.5 < z < 2.5 may be the bulges of modern disc galaxies.Comment: Condensed version (due to Contract) of an invited review article to appear in "Planets, Stars and Stellar Systems"(www.springer.com/astronomy/book/978-90-481-8818-5). 500+ references incl. many somewhat forgotten, pioneer papers. Original submission to Springer: 07-June-201

The Bulge/Disk Connection in Late-type Spirals

Recent ground-based photometric investigations suggest that central regions of late-type spirals are closely coupled to the inner disk and probably formed via secular evolution. Evidence presented in support of this model includes the predominance of exponential bulges, the correlation of bulge and disk scale lengths, blueness of the bulge and small differences between bulge and central disk colors, detection of spiral structure into the core, and rapid rotation. Recent HST observations show that our own bulge and that of M31, M32, and M33 probably harbor both an old and intermediate-age populations in agreement with models of early collapse of the spheroid plus gas transfer from the disk. Secular evolution provides a mechanism to build-up central regions in late-type spirals; mergers or accretion of small satellites could explain the brighter, kinematically distinct bulges of Sa's and SO's