A Characteristic Mass Scale in the Mass-Metallicity Relation of Galaxies

We study the shape of the gas-phase mass-metallicity relation (MZR) of a combined sample of present-day dwarf and high-mass star-forming galaxies using IZI, a Bayesian formalism for measuring chemical abundances presented in Blanc et al. 2015. We observe a characteristic stellar mass scale at $M_* \simeq 10^{9.5}$M$_{\odot}$, above which the ISM undergoes a sharp increase in its level of chemical enrichment. In the $10^{6}-10^{9.5}$M$_{\odot}$ range the MZR follows a shallow power-law ($Z\propto M^{\alpha}_*$) with slope $\alpha=0.14\pm0.08$. At approaching $M_* \simeq 10^{9.5}$M$_{\odot}$ the MZR steepens significantly, showing a slope of $\alpha=0.37\pm0.08$ in the $10^{9.5}-10^{10.5}$M$_{\odot}$ range, and a flattening towards a constant metallicity at higher stellar masses. This behavior is qualitatively different from results in the literature that show a single power-law MZR towards the low mass end. We thoroughly explore systematic uncertainties in our measurement, and show that the shape of the MZR is not induced by sample selection, aperture effects, a changing N/O abundance, the adopted methodology used to construct the MZR, secondary dependencies on star formation activity, nor diffuse ionized gas (DIG) contamination, but rather on differences in the method used to measure abundances. High resolution hydrodynamical simulations can qualitatively reproduce our result, and suggest a transition in the ability of galaxies to retain their metals for stellar masses above this threshold. The MZR characteristic mass scale also coincides with a transition in the scale height and clumpiness of cold gas disks, and a typical gas fraction below which the efficiency of star formation feedback for driving outflows is expected to decrease sharply.Comment: 24 pages, 11 figures, 4 tables, accepted for publication in Ap

The importance of preventive feedback: inference from observations of the stellar masses and metallicities of Milky Way dwarf galaxies

Dwarf galaxies are known to have remarkably low star formation efficiency due to strong feedback. Adopting the dwarf galaxies of the Milky Way as a laboratory, we explore a flexible semi-analytic galaxy formation model to understand how the feedback processes shape the satellite galaxies of the Milky Way. Using Markov-Chain Monte-Carlo, we exhaustively search a large parameter space of the model and rigorously show that the general wisdom of strong outflows as the primary feedback mechanism cannot simultaneously explain the stellar mass function and the mass--metallicity relation of the Milky Way satellites. An extended model that assumes that a fraction of baryons is prevented from collapsing into low-mass halos in the first place can be accurately constrained to simultaneously reproduce those observations. The inference suggests that two different physical mechanisms are needed to explain the two different data sets. In particular, moderate outflows with weak halo mass dependence are needed to explain the mass--metallicity relation, and prevention of baryons falling into shallow gravitational potentials of low-mass halos (e.g. "pre-heating") is needed to explain the low stellar mass fraction for a given subhalo mass.Comment: 14 pages, 4 figures, accepted for publication in Ap

The connection between the host halo and the satellite galaxies of the Milky Way

Many properties of the Milky Way's dark matter halo, including its mass assembly history, concentration, and subhalo population, remain poorly constrained. We explore the connection between these properties of the Milky Way and its satellite galaxy population, especially the implication of the presence of the Magellanic Clouds for the properties of the Milky Way halo. Using a suite of high-resolution $N$-body simulations of Milky Way-mass halos with a fixed final Mvir ~ 10^{12.1}Msun, we find that the presence of Magellanic Cloud-like satellites strongly correlates with the assembly history, concentration, and subhalo population of the host halo, such that Milky Way-mass systems with Magellanic Clouds have lower concentration, more rapid recent accretion, and more massive subhalos than typical halos of the same mass. Using a flexible semi-analytic galaxy formation model that is tuned to reproduce the stellar mass function of the classical dwarf galaxies of the Milky Way with Markov-Chain Monte-Carlo, we show that adopting host halos with different mass-assembly histories and concentrations can lead to different best-fit models for galaxy-formation physics, especially for the strength of feedback. These biases arise because the presence of the Magellanic Clouds boosts the overall population of high-mass subhalos, thus requiring a different stellar-mass-to-halo-mass ratio to match the data. These biases also lead to significant differences in the mass--metallicity relation, the kinematics of low-mass satellites, the number counts of small satellites associated with the Magellanic Clouds, and the stellar mass of Milky Way itself. Observations of these galaxy properties can thus provide useful constraints on the properties of the Milky Way halo.Comment: 20 pages, 12 figures, accepted for publication in ApJ. A new section on the effect of host halo mass-assembly history on the central galaxy stellar mass is adde

Every mapping class group is generated by 6 involutions

Let Mod_{g,b} denote the mapping class group of a surface of genus g with b punctures. Feng Luo asked in a recent preprint if there is a universal upper bound, independent of genus, for the number of torsion elements needed to generate Mod_{g,b}. We answer Luo's question by proving that 3 torsion elements suffice to generate Mod_{g,0}. We also prove the more delicate result that there is an upper bound, independent of genus, not only for the number of torsion elements needed to generate Mod_{g,b} but also for the order of those elements. In particular, our main result is that 6 involutions (i.e. orientation-preserving diffeomorphisms of order two) suffice to generate Mod_{g,b} for every genus g >= 3, b = 0, and g >= 4, b = 1.Comment: 15 pages, 7 figures; slightly improved main result; minor revisions. to appear in J. Al

Modelling solute transport in soil columns using advective-dispersive equations with fractional spatial derivatives

Solute transport in soils is commonly simulated with the advective–dispersive equation, or ADE. It has been reported that this model cannot take into account several important features of solute movement through soil. Recently, a new model has been suggested that results in a solute transport equation with fractional spatial derivatives, or FADE. We have assembled a database on published solute transport experiments in soil columns to test the new model. The FADE appears to be a useful generalization of the ADE. The order of the fractional differentiation reflects differences in physical conditions of the solute transport in soi

A Bayesian approach to the semi-analytic model of galaxy formation: methodology

We believe that a wide range of physical processes conspire to shape the observed galaxy population but we remain unsure of their detailed interactions. The semi-analytic model (SAM) of galaxy formation uses multi-dimensional parameterisations of the physical processes of galaxy formation and provides a tool to constrain these underlying physical interactions. Because of the high dimensionality, the parametric problem of galaxy formation may be profitably tackled with a Bayesian-inference based approach, which allows one to constrain theory with data in a statistically rigorous way. In this paper we develop a SAM in the framework of Bayesian inference. We show that, with a parallel implementation of an advanced Markov-Chain Monte-Carlo algorithm, it is now possible to rigorously sample the posterior distribution of the high-dimensional parameter space of typical SAMs. As an example, we characterise galaxy formation in the current $\Lambda$CDM cosmology using the stellar mass function of galaxies as an observational constraint. We find that the posterior probability distribution is both topologically complex and degenerate in some important model parameters, suggesting that thorough explorations of the parameter space are needed to understand the models. We also demonstrate that because of the model degeneracy, adopting a narrow prior strongly restricts the model. Therefore, the inferences based on SAMs are conditional to the model adopted. Using synthetic data to mimic systematic errors in the stellar mass function, we demonstrate that an accurate observational error model is essential to meaningful inference.Comment: revised version to match published article published in MNRA

Galaxy formation in the Planck cosmology - I. Matching the observed evolution of star formation rates, colours and stellar masses

We have updated the Munich galaxy formation model to the Planck first-year cosmology, while modifying the treatment of baryonic processes to reproduce recent data on the abundance and passive fractions of galaxies from z = 3 down to z = 0. Matching these more extensive and more precise observational results requires us to delay the reincorporation of wind ejecta, to lower the surface density threshold for turning cold gas into stars, to eliminate ram-pressure stripping in haloes less massive than ∼1014 M⊙, and to modify our model for radio mode feedback. These changes cure the most obvious failings of our previous models, namely the overly early formation of low-mass galaxies and the overly large fraction of them that are passive at late times. The new model is calibrated to reproduce the observed evolution both of the stellar mass function and of the distribution of star formation rate at each stellar mass. Massive galaxies (log M⋆/M⊙ ≥ 11.0) assemble most of their mass before z = 1 and are predominantly old and passive at z = 0, while lower mass galaxies assemble later and, for log M⋆/M⊙ ≤ 9.5, are still predominantly blue and star forming at z = 0. This phenomenological but physically based model allows the observations to be interpreted in terms of the efficiency of the various processes that control the formation and evolution of galaxies as a function of their stellar mass, gas content, environment and time

Convergence of Galaxy Properties with Merger Tree Temporal Resolution

Dark matter halo merger trees are now routinely extracted from cosmological simulations of structure formation. These trees are frequently used as inputs to semi-analytic models of galaxy formation to provide the backbone within which galaxy formation takes place. By necessity, these merger trees are constructed from a finite set of discrete "snapshots" of the N-body simulation and so have a limited temporal resolution. To date, there has been little consideration of how this temporal resolution affects the properties of galaxies formed within these trees. In particular, the question of how many snapshots are needed to achieve convergence in galaxy properties has not be answered. Therefore, we study the convergence in the stellar and total baryonic masses of galaxies, distribution of merger times, stellar mass functions and star formation rates in the Galacticus model of galaxy formation as a function of the number of "snapshot" times used to represent dark matter halo merger trees. When utilizing snapshots between z=20 and z=0, we find that at least 128 snapshots are required to achieve convergence to within 5% for galaxy masses. This convergence is obtained for mean quantities averaged over large samples of galaxies - significant variance for individual galaxies remains even when using very large numbers of snapshots. We find only weak dependence of the rate of convergence on the distribution of snapshots in time - snapshots spaced uniformly in the expansion factor, uniformly in the logarithm of expansion factor or uniformly in the logarithm of critical overdensity for collapse work equally well in almost all cases. We provide input parameters to Galacticus which allow this type of convergence study to be tuned to other simulations and to be carried out for other galaxy properties.Comment: 15 pages, 12 figures, submitted to MNRAS. Parameter files and plotting scripts available at http://www.ctcp.caltech.edu/galacticus/parameters/dmTreeConvergence.tar.bz2 and in the anciliary data stored with this arXiv submissio