Chemical evolution of ultra-faint dwarf galaxies in the self-consistently calculated IGIMF theory

The galaxy-wide stellar initial mass function (gwIMF) of a galaxy in dependence of its metallicity and star formation rate (SFR) can be calculated by the integrated galactic IMF (IGIMF) theory. Lacchin et al. (2019) apply the IGIMF theory for the first time to study the chemical evolution of the ultra-faint dwarf (UFD) satellite galaxies and failed to reproduce the data. Here, we find that the IGIMF theory is naturally consistent with the data. We apply the time-evolving gwIMF calculated at each timestep. The number of type Ia supernova explosions per unit stellar mass formed is renormalised according to the gwIMF. The chemical evolution of Bo\"otes I, one of the best observed UFD, is calculated. Our calculation suggests a mildly bottom-light and top-light gwIMF for Bo\"otes I, and that this UFD has the same gas-consumption timescale as other dwarfs but was quenched about 0.1 Gyr after formation, being consistent with independent estimations and similar to Dragonfly 44. The recovered best fitting input parameters in this work are not covered in the work of Lacchin et al. (2019), creating the discrepancy between our conclusions. In addition, a detailed discussion of uncertainties is presented addressing how the results of chemical evolution models depend on applied assumptions. This study demonstrates the power of the IGIMF theory in understanding the star-formation in extreme environments and shows that UDFs are a promising pathway to constrain the variation of the low-mass stellar IMF.Comment: 17 pages, 16 figures, accepted for publication in A&

Reinsurance Contracting with Adverse Selection and Moral Hazard: Theory and Evidence

This dissertation includes two essays on adverse selection and moral hazard problems in reinsurance markets. The first essay builds a competitive principal-agent model that considers adverse selection and moral hazard jointly, and characterizes graphically various forms of separating Nash equilibria. In the second essay, we use panel data on U.S. property liability reinsurance for the period 1995-2000 to test for the existence of adverse selection and moral hazard. We find that (1) adverse selection is present in private passenger auto liability reinsurance market and homeowners reinsurance market, but not in product liability reinsurance market; (2) residual moral hazard does not exist in all the three largest lines of reinsurance, but is present in overall reinsurance markets; and (3) moral hazard is present in the product liability reinsurance market, but not in the other two lines of reinsurance

Sensitivity Analysis for Iceberg Geometry Shape in Ship-Iceberg Collision in View of Different Material Models

The increasing marine activities in Arctic area have brought growing interest in ship-iceberg collision study. The purpose of this paper is to study the iceberg geometry shape effect on the collision process. In order to estimate the sensitivity parameter, five different geometry iceberg models and two iceberg material models are adopted in the analysis. The FEM numerical simulation is used to predict the scenario and the related responses. The simulation results including energy dissipation and impact force are investigated and compared. It is shown that the collision process and energy dissipation are more sensitive to iceberg local shape than other factors when the elastic-plastic iceberg material model is applied. The blunt iceberg models act rigidly while the sharp ones crush easily during the simulation process. With respect to the crushable foam iceberg material model, the iceberg geometry has relatively small influence on the collision process. The spherical iceberg model shows the most rigidity for both iceberg material models and should be paid the most attention for ice-resist design for ships

The star formation timescale of elliptical galaxies -- Fitting [Mg/Fe] and total metallicity simultaneously

The alpha element to iron peak element ratio, for example [Mg/Fe], is a commonly applied indicator of the galaxy star formation timescale (SFT) since the two groups of elements are mainly produced by different types of supernovae that explode over different timescales. However, it is insufficient to consider only [Mg/Fe] when estimating the SFT. The [Mg/Fe] yield of a stellar population depends on its metallicity. Therefore, it is possible for galaxies with different SFTs and at the same time different total metallicity to have the same [Mg/Fe]. This effect has not been properly taken into consideration in previous studies. In this study, we assume the galaxy-wide stellar initial mass function (gwIMF) to be canonical and invariant. We demonstrate that our computation code reproduces the SFT estimations of previous studies where only the [Mg/Fe] observational constraint is applied. We then demonstrate that once both metallicity and [Mg/Fe] observations are considered, a more severe "downsizing relation" is required. This means that either low-mass ellipticals have longer SFTs (> 4 Gyr for galaxies with mass below $10^{10}$ M$_\odot$) or massive ellipticals have shorter SFTs ($\approx 200$ Myr for galaxies more massive than $10^{11}$ M$_\odot$) than previously thought. This modification increases the difficulty in reconciling such SFTs with other observational constraints. We show that applying different stellar yield modifications does not relieve this formation timescale problem. The quite unrealistically short SFT required by [Mg/Fe] and total metallicity would be prolonged if a variable stellar gwIMF were assumed. Since a systematically varying gwIMF has been suggested by various observations this could present a natural solution to this problem.Comment: 9 pages, 7 figures, A&A, in press. Version 2 added reference