Deep 1.1 mm-wavelength imaging of the GOODS-S field by AzTEC/ASTE - I. Source catalogue and number counts

[Abridged] We present the first results from a 1.1 mm confusion-limited map of the GOODS-S field taken with AzTEC on the ASTE telescope. We imaged a 270 sq. arcmin field to a 1\sigma depth of 0.48 - 0.73 mJy/beam, making this one of the deepest blank-field surveys at mm-wavelengths ever achieved. Although our GOODS-S map is extremely confused, we demonstrate that our source identification and number counts analyses are robust, and the techniques discussed in this paper are relevant for other deeply confused surveys. We find a total of 41 dusty starburst galaxies with S/N >= 3.5 within this uniformly covered region, where only two are expected to be false detections. We derive the 1.1mm number counts from this field using both a "P(d)" analysis and a semi-Bayesian technique, and find that both methods give consistent results. Our data are well-fit by a Schechter function model with (S', N(3mJy), \alpha) = (1.30+0.19 mJy, 160+27 (mJy/deg^2)^(-1), -2.0). Given the depth of this survey, we put the first tight constraints on the 1.1 mm number counts at S(1.1mm) = 0.5 mJy, and we find evidence that the faint-end of the number counts at S(850\mu m) < 2.0 mJy from various SCUBA surveys towards lensing clusters are biased high. In contrast to the 870 \mu m survey of this field with the LABOCA camera, we find no apparent under-density of sources compared to previous surveys at 1.1 mm. Additionally, we find a significant number of SMGs not identified in the LABOCA catalogue. We find that in contrast to observations at wavelengths < 500 \mu m, MIPS 24 \mu m sources do not resolve the total energy density in the cosmic infrared background at 1.1 mm, demonstrating that a population of z > 3 dust-obscured galaxies that are unaccounted for at these shorter wavelengths potentially contribute to a large fraction (~2/3) of the infrared background at 1.1 mm.Comment: 21 pages, 9 figures. Accepted to MNRAS

On the Clustering of Sub-millimeter Galaxies

We measure the angular two-point correlation function of sub-millimeter galaxies (SMGs) from 1.1-millimeter imaging of the COSMOS field with the AzTEC camera and ASTE 10-meter telescope. These data yields one of the largest contiguous samples of SMGs to date, covering an area of 0.72 degrees^2 down to a 1.26 mJy/beam (1-sigma) limit, including 189 (328) sources with S/N greater than 3.5 (3). We can only set upper limits to the correlation length r_0, modeling the correlation function as a power-law with pre-assigned slope. Assuming existing redshift distributions, we derive 68.3% confidence level upper limits of r_0 < 6-8 h^-1 Mpc at 3.7 mJy, and r_0 < 11-12 h^-1 Mpc at 4.2 mJy. Although consistent with most previous estimates, these upper limits imply that the real r_0 is likely smaller. This casts doubts on the robustness of claims that SMGs are characterized by significantly stronger spatial clustering, (and thus larger mass), than differently selected galaxies at high-redshift. Using Monte Carlo simulations we show that even strongly clustered distributions of galaxies can appear unclustered when sampled with limited sensitivity and coarse angular resolution common to current sub-millimeter surveys. The simulations, however, also show that unclustered distributions can appear strongly clustered under these circumstances. From the simulations, we predict that at our survey depth, a mapped area of two degrees^2 is needed to reconstruct the correlation function, assuming smaller beam sizes of future surveys (e.g. the Large Millimeter Telescope's 6" beam size). At present, robust measures of the clustering strength of bright SMGs appear to be below the reach of most observations.Comment: 23 pages, 8 figures, accepted for publication in The Astrophysical Journa

Constructing Carmichael numbers through improved subset-product algorithms

We have constructed a Carmichael number with 10,333,229,505 prime factors, and have also constructed Carmichael numbers with k prime factors for every k between 3 and 19,565,220. These computations are the product of implementations of two new algorithms for the subset product problem that exploit the non-uniform distribution of primes p with the property that p-1 divides a highly composite \Lambda.Comment: Table 1 fixed; previously the last 30 digits and number of digits were calculated incorrectl

Origins of the extragalactic background at 1mm from a combined analysis of the AzTEC and MAMBO data in GOODS-N

We present a study of the cosmic infrared background, which is a measure of the dust obscured activity in all galaxies in the Universe. We venture to isolate the galaxies responsible for the background at 1mm; with spectroscopic and photometric redshifts we constrain the redshift distribution of these galaxies. We create a deep 1.16mm map (sigma ~ 0.5mJy) by combining the AzTEC 1.1mm and MAMBO 1.2mm datasets in GOODS-N. This combined map contains 41 secure detections, 13 of which are new. By averaging the 1.16mm flux densities of individually undetected galaxies with 24um flux densities > 25uJy, we resolve 31--45 per cent of the 1.16mm background. Repeating our analysis on the SCUBA 850um map, we resolve a higher percentage (40--64 per cent) of the 850um background. A majority of the background resolved (attributed to individual galaxies) at both wavelengths comes from galaxies at z > 1.3. If the ratio of the resolved submillimeter to millimeter background is applied to a reasonable scenario for the origins of the unresolved submillimeter background, 60--88 per cent of the total 1.16mm background comes from galaxies at z > 1.3.Comment: 12 pages, 10 figures. Accepted by MNRAS. The combined map is publicly available at http://www.astro.umass.edu/~pope/goodsn_mm

The Madisonian Standard for Conceptualizing American Citizenship

American political development was fashioned by a social contract. More specifically, the American republic evolved through the Madisonian social contract, an agreement premised on James Madison’s intention that deliberative citizenship would collaborate with decentralized government in order to advance the public good. This paper identifies the problem with the Madisonian contract today, that the relationship between citizens and government, or rather, Congress, is one that is infused with antagonism and a record high level of distrust. This present-day characterization of the broken relationship between citizens and Congress is symptomatic of a deteriorated Madisonian contract. Public opinion polls cast the illusion that a broken Congress is responsible for the deterioration of Madison’s contract. However, through an assessment of polling data along with an examination of the exceptional nature of citizenship in America, this paper reasons that the dwindling of the Madisonian contract is due to a decline in thick deliberative citizenship. In addition to diagnosing the current state of Madison’s contract, this paper compares remedies to cure the problem of a thinly engaged citizenry in the hope to rewrite the terms of the Madisonian contract within the contours of American political development

Activities in the Mathematics Classroom that Promote Mathematical Fluency

Mathematics, in and of itself, is a language— reading notations, writing solutions, and communicating explanations. The importance of developing mathematical fluency is frequently overshadowed by an emphasis on implementation of memorized formulas in mathematics classrooms. The National Council of Teachers of Mathematics (NCTM) has recognized the relevance of using mathematics as a language as early as 1989 and promotes learning to communicate mathematically as a major goal for students. Hufferd-Ackles, Fuson, and Sherin (2004) recognize the importance of a math-talk community in the classrooms to encourage students’ understanding of mathematics. This self-study focuses on the advantages of writing, reading, and speaking mathematics in students’ learning. It is conducted the study in two Algebra II classes at a rural high school in Central Illinois. Different activities, students’ work, and analyzed personal reflective journals are content analyzed to draw conclusions on the ways these instructional activities promote mathematical fluency and mathematical understanding