On the Bail-Out Optimal Dividend Problem

This paper studies the optimal dividend problem with capital injection under the constraint that the cumulative dividend strategy is absolutely continuous. We consider an open problem of the general spectrally negative case and derive the optimal solution explicitly using the fluctuation identities of the refracted-reflected L\'evy process. The optimal strategy as well as the value function are concisely written in terms of the scale function. Numerical results are also provided to confirm the analytical conclusions.Comment: To appear in Journal of Optimization Theory and Applications. Keywords: stochastic control, scale functions, refracted-reflected L\'evy processes, bail-out dividend proble

The Carnegie-Irvine Galaxy Survey. V. Statistical study of bars and buckled bars

Simulations have shown that bars are subject to a vertical buckling instability that transforms thin bars into boxy or peanut-shaped structures, but the physical conditions necessary for buckling to occur are not fully understood. We use the large sample of local disk galaxies in the Carnegie-Irvine Galaxy Survey to examine the incidence of bars and buckled bars across the Hubble sequence. Depending on the disk inclination angle ($i$), a buckled bar reveals itself as either a boxy/peanut-shaped bulge (at high $i$) or as a barlens structure (at low $i$). We visually identify bars, boxy/peanut-shaped bulges, and barlenses, and examine the dependence of bar and buckled bar fractions on host galaxy properties, including Hubble type, stellar mass, color, and gas mass fraction. We find that the barred and unbarred disks show similar distributions in these physical parameters. The bar fraction is higher (70\%--80\%) in late-type disks with low stellar mass ($M_{*} < 10^{10.5}\, M_{\odot}$) and high gas mass ratio. In contrast, the buckled bar fraction increases to 80\% toward massive and early-type disks ($M_{*} > 10^{10.5}\, M_{\odot}$), and decreases with higher gas mass ratio. These results suggest that bars are more difficult to grow in massive disks that are dynamically hotter than low-mass disks. However, once a bar forms, it can easily buckle in the massive disks, where a deeper potential can sustain the vertical resonant orbits. We also find a probable buckling bar candidate (ESO 506$-$G004) that could provide further clues to understand the timescale of the buckling process.Comment: 9 pages, 7 figures, 2 tables. Accepted for publication in The Astrophysical Journa

The Carnegie-Irvine Galaxy Survey. III. The Three-Component Structure of Nearby Elliptical Galaxies

Motivated by recent developments in our understanding of the formation and evolution of massive galaxies, we explore the detailed photometric structure of a representative sample of 94 bright, nearby elliptical galaxies, using high-quality optical images from the Carnegie-Irvine Galaxy Survey. The sample spans a range of environments and stellar masses, from M* = 10^{10.2} to 10^{12.0} solar mass. We exploit the unique capabilities of two-dimensional image decomposition to explore the possibility that local elliptical galaxies may contain photometrically distinct substructure that can shed light on their evolutionary history. Compared with the traditional one-dimensional approach, these two-dimensional models are capable of consistently recovering the surface brightness distribution and the systematic radial variation of geometric information at the same time. Contrary to conventional perception, we find that the global light distribution of the majority (>75%) of elliptical galaxies is not well described by a single Sersic function. Instead, we propose that local elliptical galaxies generically contain three subcomponents: a compact (R_e < 1 kpc) inner component with luminosity fraction f ~ 0.1-0.15; an intermediate-scale (R_e ~ 2.5 kpc) middle component with f ~ 0.2-0.25; and a dominant (f = 0.6), extended (R_e ~ 10 kpc) outer envelope. All subcomponents have average Sersic indices n ~ 1-2, significantly lower than the values typically obtained from single-component fits. The individual subcomponents follow well-defined photometric scaling relations and the stellar mass-size relation. We discuss the physical nature of the substructures and their implications for the formation of massive elliptical galaxies.Comment: To appear in The Astrophysical Journal; 36 pages, 2 tables, 38 figures; For the full resolution version, see: http://users.obs.carnegiescience.edu/shuang/PaperIII.pdf ; For the atlas of all selected models, see http://users.obs.carnegiescience.edu/shuang/AppendixE.pd

The Carnegie-Irvine Galaxy Survey. IV. A Method to Determine the Average Mass Ratio of Mergers That Built Massive Elliptical Galaxies

Many recent observations and numerical simulations suggest that nearby massive, early-type galaxies were formed through a "two-phase" process. In the proposed second phase, the extended stellar envelope was accumulated through many dry mergers. However, details of the past merger history of present-day ellipticals, such as the typical merger mass ratio, are difficult to constrain observationally. Within the context and assumptions of the two-phase formation scenario, we propose a straightforward method, using photometric data alone, to estimate the average mass ratio of mergers that contributed to the build-up of massive elliptical galaxies. We study a sample of nearby massive elliptical galaxies selected from the Carnegie-Irvine Galaxy Survey, using two-dimensional analysis to decompose their light distribution into an inner, denser component plus an extended, outer envelope, each having a different optical color. The combination of these two substructures accurately recovers the negative color gradient exhibited by the galaxy as whole. The color difference between the two components ( ~ 0.10 mag; ~ 0.14 mag), based on the slope of the M_stellar-color relation for nearby early-type galaxies, can be translated into an estimate of the average mass ratio of the mergers. The rough estimate, 1:5 to 1:10, is consistent with the expectation of the two-phase formation scenario, suggesting that minor mergers were largely responsible for building up to the outer stellar envelope of present-day massive ellipticals. With the help of accurate photometry, large sample size, and more choices of colors promised by ongoing and future surveys, the approach proposed here can reveal more insights into the growth of massive galaxies during the last few Gyr.Comment: Accepted by ApJ; 20 pages, 11 figures, 1 table; The high resolution figures and the full table can be downloaded from here: https://github.com/dr-guangtou/cgs_colorgra