We present 3.6 and 4.5 micron Spitzer IRAC imaging over 0.77 square degrees at the Virgo cluster core for the purpose of understanding the formation mechanisms of the low surface brightness intracluster light features. Instrumental and astrophysical
backgrounds that are hundreds of times higher than the signal were carefully characterized and removed. We examine both intracluster light plumes as well as the outer halo of the giant elliptical M87. For two intracluster light plumes, we use optical colors to constrain their ages to be greater than 3 & 5 Gyr, respectively. Upper limits on the IRAC fluxes constrain the upper limits to the masses, and optical detections constrain the lower limits to the masses. In this first measurement of mass of intracluster light plumes we find masses in the range of 5.5 x 10^8 - 4.5 x 10^9 and 2.1 x 10^8 - 1.5 x 10^9 solar masses for the two plumes for which we have coverage. Given their expected short lifetimes, and a constant production rate for these types of streams, integrated over Virgos lifetime, they can account for the total ICL content of the cluster implying that we do not need to invoke ICL formation mechanisms other than gravitational mechanisms leading to bright plumes. We also examined the outer halo of the giant elliptical M87. The color profile from the inner to outer halo of M87 (160 Kpc) is consistent with either a flat or optically blue gradient, where a blue gradient could be due to younger or lower metallicity stars at larger radii. The similarity of the age predicted by both the infrared and optical colors (> few Gyr) indicates that the optical measurements are not strongly affected by dust extinction.
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural `projection of a well studied l
inear program for exact dynamic programming. Such programs restrict attention to approximations that are lower bounds to the optimal cost-to-go function. Our program--the `smoothed approximate linear program--is distinct from such approaches and relaxes the restriction to lower bounding approximations in an appropriate fashion while remaining computationally tractable. Doing so appears to have several advantages: First, we demonstrate substantially superior bounds on the quality of approximation to the optimal cost-to-go function afforded by our approach. Second, experiments with our approach on a challenging problem (the game of Tetris) show that the approach outperforms the existing LP approach (which has previously been shown to be competitive with several ADP algorithms) by an order of magnitude.
Spitzer MIPS images in the Bootes field of the NOAO Deep Wide-Field Survey have revealed a class of extremely dust obscured galaxy (DOG) at z~2. The DOGs are defined by very red optical to mid-IR (observed-frame) colors, R - [24 um] > 14 mag, i.e. f_
v (24 um) / f_v (R) > 1000. They are Ultra-Luminous Infrared Galaxies with L_8-1000 um > 10^12 -10^14 L_sun, but typically have very faint optical (rest-frame UV) fluxes. We imaged three DOGs with the Keck Laser Guide Star Adaptive Optics (LGSAO) system, obtaining ~0.06 resolution in the K-band. One system was dominated by a point source, while the other two were clearly resolved. Of the resolved sources, one can be modeled as a exponential disk system. The other is consistent with a de Vaucouleurs profile typical of elliptical galaxies. The non-parametric measures of their concentration and asymmetry, show the DOGs to be both compact and smooth. The AO images rule out double nuclei with separations of greater than 0.1 (< 1 kpc at z=2), making it unlikely that ongoing major mergers (mass ratios of 1/3 and greater) are triggering the high IR luminosities. By contrast, high resolution images of z~2 SCUBA sources tend to show multiple components and a higher degree of asymmetry. We compare near-IR morphologies of the DOGs with a set of z=1 luminous infrared galaxies (LIRGs; L_IR ~ 10^11 L_sun) imaged with Keck LGSAO by the Center for Adaptive Optics Treasury Survey. The DOGs in our sample have significantly smaller effective radii, ~1/4 the size of the z=1 LIRGs, and tend towards higher concentrations. The small sizes and high concentrations may help explain the globally obscured rest-frame blue-to-UV emission of the DOGs.
We explore the relationships between the Polycyclic Aromatic Hydrocarbon (PAH) feature strengths, mid-infrared continuum luminosities, far-infrared spectral slopes, optical spectroscopic classifications, and silicate optical depths within a sample of
107 ULIRGs observed with the Infrared Spectrograph on the Spitzer Space Telescope. The detected 6.2 micron PAH equivalent widths (EQWs) in the sample span more than two orders of magnitude (0.006-0.8 micron), and ULIRGs with HII-like optical spectra or steep far-infrared spectral slopes (S_{25} / S_{60} < 0.2) typically have 6.2 micron PAH EQWs that are half that of lower-luminosity starbursts. A significant fraction (~40-60%) of HII-like, LINER-like, and cold ULIRGs have very weak PAH EQWs. Many of these ULIRGs also have large (tau_{9.7} > 2.3) silicate optical depths. The far-infrared spectral slope is strongly correlated with PAH EQW, but not with silicate optical depth. In addition, the PAH EQW decreases with increasing rest-frame 24 micron luminosity. We argue that this trend results primarily from dilution of the PAH EQW by continuum emission from dust heated by a compact central source, probably an AGN. High luminosity, high-redshift sources studied with Spitzer appear to have a much larger range in PAH EQW than seen in local ULIRGs, which is consistent with extremely luminous starburst systems being absent at low redshift, but present at early epochs.
