A Bivariate Measure of Redundant Information

We define a measure of redundant information based on projections in the space of probability distributions. Redundant information between random variables is information that is shared between those variables. But in contrast to mutual information, redundant information denotes information that is shared about the outcome of a third variable. Formalizing this concept, and being able to measure it, is required for the non-negative decomposition of mutual information into redundant and synergistic information. Previous attempts to formalize redundant or synergistic information struggle to capture some desired properties. We introduce a new formalism for redundant information and prove that it satisfies all the properties necessary outlined in earlier work, as well as an additional criterion that we propose to be necessary to capture redundancy. We also demonstrate the behaviour of this new measure for several examples, compare it to previous measures and apply it to the decomposition of transfer entropy.Comment: 16 pages, 15 figures, 1 table, added citation to Griffith et al 2012, Maurer et al 199

IDCS J1426.5+3508: Cosmological implications of a massive, strong lensing cluster at Z = 1.75

The galaxy cluster IDCS J1426.5+3508 at z = 1.75 is the most massive galaxy cluster yet discovered at z > 1.4 and the first cluster at this epoch for which the Sunyaev-Zel'Dovich effect has been observed. In this paper we report on the discovery with HST imaging of a giant arc associated with this cluster. The curvature of the arc suggests that the lensing mass is nearly coincident with the brightest cluster galaxy, and the color is consistent with the arc being a star-forming galaxy. We compare the constraint on M200 based upon strong lensing with Sunyaev-Zel'Dovich results, finding that the two are consistent if the redshift of the arc is z > 3. Finally, we explore the cosmological implications of this system, considering the likelihood of the existence of a strongly lensing galaxy cluster at this epoch in an LCDM universe. While the existence of the cluster itself can potentially be accomodated if one considers the entire volume covered at this redshift by all current high-redshift cluster surveys, the existence of this strongly lensed galaxy greatly exacerbates the long-standing giant arc problem. For standard LCDM structure formation and observed background field galaxy counts this lens system should not exist. Specifically, there should be no giant arcs in the entire sky as bright in F814W as the observed arc for clusters at z \geq 1.75, and only \sim 0.3 as bright in F160W as the observed arc. If we relax the redshift constraint to consider all clusters at z \geq 1.5, the expected number of giant arcs rises to \sim15 in F160W, but the number of giant arcs of this brightness in F814W remains zero. These arc statistic results are independent of the mass of IDCS J1426.5+3508. We consider possible explanations for this discrepancy.Comment: 7 pages, 4 figures, Accepted to The Astrophysical Journa

IRAC Observations of M81

IRAC images of M81 show three distinct morphological constituents: a smooth distribution of evolved stars with bulge, disk, and spiral arm components; a clumpy distribution of dust emission tracing the spiral arms; and a pointlike nuclear source. The bulge stellar colors are consistent with M-type giants, and the disk colors are consistent with a slightly younger population. The dust emission generally follows the blue and ultraviolet emission, but there are large areas that have dust emission without ultraviolet and smaller areas with ultraviolet but little dust emission. The former are presumably caused by extinction, and the latter may be due to cavities in the gas and dust created by supernova explosions. The nucleus appears fainter at 8 um than expected from ground-based 10 um observations made four years ago.Comment: ApJS in press (Spitzer special issue); 15 pages, 3 figures. Changes: unused references removed, numbers and labels in Table 1 change

Bostonia: The Boston University Alumni Magazine. Volume 32

Founded in 1900, Bostonia magazine is Boston University's main alumni publication, which covers alumni and student life, as well as university activities, events, and programs

Clustering of red galaxies around the z=1.53 quasar 3C270.1

In the paradigm of hierarchical galaxy formation, luminous radio galaxies mark mass assembly peaks that should contain clusters of galaxies. Observations of the z=1.53 quasar 3C270.1 with the Spitzer Space Telescope at 3.6-24 micron and with the 6.5-m MMT in the z'- and Y-bands allow detection of potential cluster members via photometric redshifts. Compared with nearby control fields, there is an excess of 11 extremely red objects (EROs) at 1.33 < z_phot < 1.73, consistent with a proto-cluster around the quasar. The spectral energy distributions (SEDs) of 3/4 of the EROs are better fitted with passive elliptical galaxies than withdust-reddened starbursts, and of four sources well-detected on an archival HST snapshot image, all have undisturbed morphologies. However, one ERO, not covered by the HST image, is a double source with 0.8" separation on the z' image and a marginal (2sigma) 24 micron detection indicating a dust-enshrouded starburst. The EROs are more luminous than L* (H = -23.6 AB mag at z=1.5).Comment: 12 pages, 7 figures, accepted by Ap

Ultracool Field Brown Dwarf Candidates Selected at 4.5 microns

We have identified a sample of cool field brown dwarf candidates using IRAC data from the Spitzer Deep, Wide-Field Survey (SDWFS). The candidates were selected from 400,000 SDWFS sources with [4.5] <= 18.5 mag and required to have [3.6]-[4.5] >= 1.5 and [4.5] - [8.0] <= 2.0 on the Vega system. The first color requirement selects objects redder than all but a handful of presently known brown dwarfs with spectral classes later than T7, while the second eliminates 14 probable reddened AGN. Optical detection of 4 of the remaining 18 sources implies they are likely also AGN, leaving 14 brown dwarf candidates. For two of the brightest candidates (SDWFS J143524.44+335334.6 and SDWFS J143222.82+323746.5), the spectral energy distributions including near-infrared detections suggest a spectral class of ~ T8. The proper motion is < 0.25 "/yr, consistent with expectations for a luminosity inferred distance of >70 pc. The reddest brown dwarf candidate (SDWFS J143356.62+351849.2) has [3.6] - [4.5]=2.24 and H - [4.5] > 5.7, redder than any published brown dwarf in these colors, and may be the first example of the elusive Y-dwarf spectral class. Models from Burrows et al. (2003) predict larger numbers of cool brown dwarfs should be found for a Chabrier (2003) mass function. Suppressing the model [4.5] flux by a factor of two, as indicated by previous work, brings the Burrows models and observations into reasonable agreement. The recently launched Wide-field Infrared Survey Explorer (WISE) will probe a volume ~40x larger and should find hundreds of brown dwarfs cooler than T7.Comment: 13 pages, 6 figures, accepted for publication in the June 2010 issue of The Astronomical Journa

The Formation of Massive Cluster Galaxies

We present composite 3.6 and 4.5 micron luminosity functions for cluster galaxies measured from the Spitzer Deep, Wide-Field Survey (SDWFS) for 0.3<z<2. We compare the evolution of m* for these luminosity functions to models for passively evolving stellar populations to constrain the primary epoch of star formation in massive cluster galaxies. At low redshifts (z < 1.3) our results agree well with models with no mass assembly and passively evolving stellar populations with a luminosity-weighted mean formation redshift zf=2.4 assuming a Kroupa initial mass function (IMF). We conduct a thorough investigation of systematic biases that might influence our results, and estimate systematic uncertainites of Delta zf=(+0.16-0.18) (model normalization), Delta zf=(+0.40-0.05) (alpha), and Delta zf=(+0.30-0.45) (choice of stellar population model). For a Salpeter type IMF, the typical formation epoch is thus strongly constrained to be z ~2-3. Higher formation redshifts can only be made consistent with the data if one permits an evolving IMF that is bottom-light at high redshift, as suggested by van Dokkum et al 2008. At high redshift (z > 1.3) we also witness a statistically significant (>5sigma) disagreement between the measured luminosity function and the continuation of the passive evolution model from lower redshifts. After considering potential systematic biases that might influence our highest redshift data points, we interpret the observed deviation as potential evidence for ongoing mass assembly at this epoch.Comment: 17 pages, 14 figures, accepted for publication in Ap

Spitzer Photometry of WISE-Selected Brown Dwarf and Hyper-Luminous Infrared Galaxy Candidates

We present Spitzer 3.6 and 4.5 $\mu$m photometry and positions for a sample of 1510 brown dwarf candidates identified by the WISE all-sky survey. Of these, 166 have been spectroscopically classified as objects with spectral types M(1), L(7), T(146), and Y(12); Sixteen other objects are non-(sub)stellar in nature. The remainder are most likely distant L and T dwarfs lacking spectroscopic verification, other Y dwarf candidates still awaiting follow-up, and assorted other objects whose Spitzer photometry reveals them to be background sources. We present a catalog of Spitzer photometry for all astrophysical sources identified in these fields and use this catalog to identify 7 fainter (4.5 $\mu$m $\sim$ 17.0 mag) brown dwarf candidates, which are possibly wide-field companions to the original WISE sources. To test this hypothesis, we use a sample of 919 Spitzer observations around WISE-selected high-redshift hyper-luminous infrared galaxy (HyLIRG) candidates. For this control sample we find another 6 brown dwarf candidates, suggesting that the 7 companion candidates are not physically associated. In fact, only one of these 7 Spitzer brown dwarf candidates has a photometric distance estimate consistent with being a companion to the WISE brown dwarf candidate. Other than this there is no evidence for any widely separated ($>$ 20 AU) ultra-cool binaries. As an adjunct to this paper, we make available a source catalog of $\sim$ 7.33 $\times 10^5$ objects detected in all of these Spitzer follow-up fields for use by the astronomical community. The complete catalog includes the Spitzer 3.6 and 4.5 $\mu$m photometry, along with positionally matched $B$ and $R$ photometry from USNO-B; $J$, $H$, and $K_s$ photometry from 2MASS; and $W1$, $W2$, $W3$, and $W4$ photometry from the WISE all-sky catalog

Assembly of the Red Sequence in Infrared-Selected Galaxy Clusters from the IRAC Shallow Cluster Survey

We present results for the assembly and star formation histories of massive (~L*) red sequence galaxies in 11 spectroscopically confirmed, infrared-selected galaxy clusters at 1.0 < z < 1.5, the precursors to present-day massive clusters with M ~ 10^15 M_sun. Using rest-frame optical photometry, we investigate evolution in the color and scatter of the red sequence galaxy population, comparing with models of possible star formation histories. In contrast to studies of central cluster galaxies at lower redshift (z < 1), these data are clearly inconsistent with the continued evolution of stars formed and assembled primarily at a single, much-earlier time. Specifically, we find that the colors of massive cluster galaxies at z = 1.5 imply that the bulk of star formation occurred at z ~ 3, whereas by z = 1 their colors imply formation at z ~ 2; therefore these galaxies exhibit approximately the same luminosity-weighted stellar age at 1 < z < 1.5. This likely reflects star formation that occurs over an extended period, the effects of significant progenitor bias, or both. Our results generally indicate that massive cluster galaxy populations began forming a significant mass of stars at z >~ 4, contained some red spheroids by z ~ 1.5, and were actively assembling much of their final mass during 1 < z < 2 in the form of younger stars. Qualitatively, the slopes of the cluster color-magnitude relations are consistent with no significant evolution relative to local clusters.Comment: 24 pages, 9 figures, accepted to Ap