We present new mid- to far-infrared images of the two dwarf compact elliptical galaxies that are satellites of M31, NGC 185 and NGC 147, obtained with the Spitzer Space Telescope. Spitzers high sensitivity and spatial resolution enable us for the fir
st time to look directly into the detailed spatial structure and properties of the dust in these systems. The images of NGC 185 at 8 and 24 micron display a mixed morphology characterized by a shell-like diffuse emission region surrounding a central concentration of more intense infrared emission. The lower resolution images at longer wavelengths show the same spatial distribution within the central 50 but beyond this radius, the 160 micron emission is more extended than that at 24 and 70micron. On the other hand, the dwarf galaxy NGC 147 located only a small distance away from NGC 185 shows no significant infrared emission beyond 24 micron and therefore its diffuse infrared emission is mainly stellar in origin. For NGC 185, the derived dust mass based on the best fit to the spectral energy distribution is 1.9e3 Msol, implying a gas mass of ~3.0e5 Msol. These values are in agreement with those previously estimated from infrared as well as from CO and HI observations and are consistent with the predicted mass return from dying stars based on the last burst of star formation ~1.0e9 yr ago. Based on the 70 to 160micron flux density ratio, we estimate a temperature for the dust of ~17K. For NGC 147, we obtain an upper limit for the dust mass of 4.5e2 Msol at 160 micron (assuming a temperature of ~20K), a value consistent with the previous upper limit derived using ISO observations of this galaxy. In the case of NGC 185, we also present full 5-38 micron low-resolution (R~100) spectra of the main emission regions.
SONYC -- Substellar Objects in Nearby Young Clusters -- is a survey program to investigate the frequency and properties of substellar objects with masses down to a few times that of Jupiter in nearby star-forming regions. Here we present the first re
sults from SONYC observations of NGC1333, a ~1Myr old cluster in the Perseus star-forming complex. We have carried out extremely deep optical and near-infrared imaging in four bands (i, z, J, K) using Suprime-Cam and MOIRCS instruments at the Subaru telescope. The survey covers 0.25sqdeg and reaches completeness limits of 24.7mag in the i-band and 20.8mag in the J-band. We select 196 candidates with colors as expected for young, very low-mass objects. Follow-up multi-object spectroscopy with MOIRCS is presented for 53 objects. We confirm 19 objects as likely brown dwarfs in NGC1333, seven of them previously known. For 11 of them, we confirm the presence of disks based on Spitzer/IRAC photometry. The effective temperatures for the brown dwarf sample range from 2500K to 3000K, which translates to masses of ~0.015 to 0.1Ms. For comparison, the completeness limit of our survey translates to mass limits of 0.004Ms for Av<~5mag or 0.008Ms for Av<~ 10mag. Compared with other star-forming regions, NGC1333 shows an overabundance of brown dwarfs relative to low-mass stars, by a factor of 2-5. On the other hand, NGC1333 has a deficit of planetary-mass objects: Based on the surveys in SOrionis, the ONC and Cha I, the expected number of planetary-mass objects in NGC1333 is 8-10, but we find none. It is plausible that our survey has detected the minimum mass limit for star formation in this particular cluster, at around 0.012-0.02Ms. If confirmed, our findings point to significant regional/environmental differences in the number of brown dwarfs and the minimum mass of the IMF. (abridged)
We examine the stability of a standing shock wave within a spherical accretion flow onto a gravitating star, in the context of core-collapse supernova explosions. Our focus is on the effect of nuclear dissociation below the shock on the linear growth
, and non-linear saturation, of non-radial oscillations of the shocked fluid. We combine two-dimensional, time-dependent hydrodynamic simulations using FLASH2.5 with a solution to the linear eigenvalue problem, and demonstrate the consistency of the two approaches. Previous studies of this `Standing Accretion Shock Instability (SASI) have focused either on zero-energy accretion flows without nuclear dissociation, or made use of a detailed finite-temperature nuclear equation of state and included strong neutrino heating. Our main goal in this and subsequent papers is to introduce equations of state of increasing complexity, in order to isolate the various competing effects. In this work we employ an ideal gas equation of state with a constant rate of nuclear dissociation below the shock, and do not include neutrino heating. We find that a negative Bernoulli parameter below the shock significantly lowers the real frequency, growth rate, and saturation amplitude of the SASI. A decrease in the adiabatic index has similar effects. The non-linear development of the instability is characterized by an expansion of the shock driven by turbulent kinetic energy at nearly constant internal energy. Our results also provide further insight into the instability mechanism: the rate of growth of a particular mode is fastest when the radial advection time from the shock to the accretor overlaps with the period of a standing lateral sound wave. The fastest-growing mode can therefore be modified by nuclear dissociation.
Let $H(p)$ be the set of 2-bridge knots $K$ whose group $G$ is mapped onto a non-trivial free product, $Z/2 * Z/p$, $p$ being odd. Then there is an algebraic integer $s_0$ such that for any $K$ in $H(p)$, $G$ has a parabolic representation $rho$ into
$SL(2, Z[s_0]) subset SL(2,C)$. Let $Delta(t)$ be the twisted Alexander polynomial associated to $rho$. Then we prove that for any $K$ in $H(p)$, $Delta(1)=-2s_0^{-1}$ and $Delta(-1)=-2s_0^{-1}mu^2$, where $s_0^{-1}, mu in Z[s_0]$. The number $mu$ can be recursively evaluated.
Modular decomposition is fundamental for many important problems in algorithmic graph theory including transitive orientation, the recognition of several classes of graphs, and certain combinatorial optimization problems. Accordingly, there has been
a drive towards a practical, linear-time algorithm for the problem. Despite considerable effort, such an algorithm has remained elusive. The linear-time algorithms to date are impractical and of mainly theoretical interest. In this paper we present the first simple, linear-time algorithm to compute the modular decomposition tree of an undirected graph. The breakthrough comes by combining the best elements of two different approaches to the problem.
