Photometry Results for the Globular Clusters M10 and M12: Extinction Maps, Color-Magnitude Diagrams, and Variable Star Candidates

We report on photometry results of the equatorial globular clusters (GCs) M10 and M12. These two clusters are part of our sample of GCs which we are probing for the existence of photometrically varying eclipsing binary stars. During the search for binaries in M10 and M12, we discovered the signature of differential reddening across the fields of the clusters. The effect is stronger for M10 than for M12. Using our previously described dereddening technique, we create differential extinction maps for the clusters which dramatically improve the appearance of the color-magnitude diagrams (CMDs). Comparison of our maps with the dust emissivity maps of Schlegel, Finkbeiner, & Davis (SFD) shows good agreement in terms of spatial extinction features. Several methods of adding an E_{V-I} zero point to our differential maps are presented of which isochrone fitting proved to be the most successful. Our E_{V-I} values fall within the range of widely varying literature values. More specifically, our reddening zero point estimate for M12 agrees well with the SFD estimate, whereas the one for M10 falls below the SFD value. Our search for variable stars in the clusters produced a total of five variables: three in M10 and two in M12. The M10 variables include a binary system of the W Ursa Majoris (W UMa) type, a background RR Lyrae star, and an SX Phoenicis pulsator, none of which is physically associated with M10. M12's variables are two W UMa binaries, one of which is most likely a member of the cluster. We present the phased photometry lightcurves for the variable stars, estimate their distances, and show their locations in the fields and the CMDs of the GCs.Comment: 22 pages, 21 figures, to be published in AJ October 2002. For a higher-resolution version of this paper, please visit http://www.astro.lsa.umich.edu/~kaspar/M10_M12_photometry.ps.gz (gzipped postscript) or http://www.astro.lsa.umich.edu/~kaspar/M10_M12_photometry.pdf (pdf file

The fraction of BL Lac objects in groups of galaxies

Context: BL Lac objects are a rare class of active galactic nuclei that typically show featureless optical spectra that make it difficult to estimate the redshift. A novel method for estimating the redshift of BL Lac objects has recently been proposed which assumes that these objects typically reside in groups of galaxies. Aims: The aim of this work is to estimate the fraction of BL Lac objects that reside in groups of galaxies. Methods: We use a sample of groups (M12 catalogue) selected by applying a friends-of-friends algorithm in the SDSS DR12. Galaxies in the M12 sample were cross-correlated with the sample of blazars in the BZCAT. Results: We found that 121 galaxies in the M12 catalogue are blazars in the BZCAT sample, all but one are BL Lac objects, and a large fraction are classified as BL Lac-galaxy dominated. Analysing the fraction of galaxies in groups as a function of redshift we have estimated a correction factor that takes into account the typical incompleteness of the catalogues based on the friends-of-friends algorithm. Once this factor was applied to the sample of BL Lac objects with a counterpart in the M12 catalogue, we found that the percentage of BL Lac objects in groups is $\gtrsim 67 \pm 8\%$. Conclusions: The high rate of BL Lac objects in groups found in this work strongly supports a recent method that has successfully estimated the redshift of BL Lac objects with featureless spectra.Comment: Accepted for publication in Astronomy and Astrophysics (Letter

Multiple Access Channels with Combined Cooperation and Partial Cribbing

In this paper we study the multiple access channel (MAC) with combined cooperation and partial cribbing and characterize its capacity region. Cooperation means that the two encoders send a message to one another via a rate-limited link prior to transmission, while partial cribbing means that each of the two encoders obtains a deterministic function of the other encoder's output with or without delay. Prior work in this field dealt separately with cooperation and partial cribbing. However, by combining these two methods we can achieve significantly higher rates. Remarkably, the capacity region does not require an additional auxiliary random variable (RV) since the purpose of both cooperation and partial cribbing is to generate a common message between the encoders. In the proof we combine methods of block Markov coding, backward decoding, double rate-splitting, and joint typicality decoding. Furthermore, we present the Gaussian MAC with combined one-sided cooperation and quantized cribbing. For this model, we give an achievability scheme that shows how many cooperation or quantization bits are required in order to achieve a Gaussian MAC with full cooperation/cribbing capacity region. After establishing our main results, we consider two cases where only one auxiliary RV is needed. The first is a rate distortion dual setting for the MAC with a common message, a private message and combined cooperation and cribbing. The second is a state-dependent MAC with cooperation, where the state is known at a partially cribbing encoder and at the decoder. However, there are cases where more than one auxiliary RV is needed, e.g., when the cooperation and cribbing are not used for the same purposes. We present a MAC with an action-dependent state, where the action is based on the cooperation but not on the cribbing. Therefore, in this case more than one auxiliary RV is needed

Mind the Gap: Tightening the Mass-Richness Relation with Magnitude Gaps

We investigate the potential to improve optical tracers of cluster mass by exploiting measurements of the magnitude gap, m12, defined as the difference between the r-band absolute magnitude of the two brightest cluster members. We find that in a mock sample of galaxy groups and clusters constructed from the Bolshoi simulation, the scatter about the mass-richness relation decreases by 15-20% when magnitude gap information is included. A similar trend is evident in a volume-limited, spectroscopic sample of galaxy groups observed in the Sloan Digital Sky Survey (SDSS). We find that SDSS groups with small magnitude gaps are richer than large-gap groups at fixed values of the one-dimensional velocity dispersion among group members sigma_v, which we use as a mass proxy. We demonstrate explicitly that m12 contains information about cluster mass that supplements the information provided by group richness and the luminosity of the brightest cluster galaxy, L_bcg. In so doing, we show that the luminosities of the members of a group with richness N are inconsistent with the distribution of luminosities that results from N random draws from the global galaxy luminosity function. As the cosmological constraining power of galaxy clusters is limited by the precision in cluster mass determination, our findings suggest a new way to improve the cosmological constraints derived from galaxy clusters.Comment: references adde