Math and Democracy

Math and Democracy is a math class containing topics such as voting theory, weighted voting, apportionment, and gerrymandering. It was first designed by Erika Ward for math master’s students, mostly educators, but then adapted separately by both Erika Ward and Kim Roth for a general audience of undergraduates. The course contains materials that can be explored in mathematics classes from those for non-majors through graduate students. As such, it serves students from all majors and allows for discussion of fairness, racial justice, and politics while exploring mathematics that non-major students might not otherwise encounter. This article serves as a guide to resources and activities for teaching similar courses and also as a call to talk about issues of race and justice in the math classroom

Extranuclear X-ray Emission in the Edge-on Seyfert Galaxy NGC 2992

We found several extranuclear (r >~ 3") X-ray nebulae within 40" (6.3 kpc at 32.5 Mpc) of the nucleus of the Seyfert galaxy NGC 2992. The net X-ray luminosity from the extranuclear sources is ~2-3 E39 erg/s (0.3-8.0 keV). The X-ray core itself (r <~ 1") is positioned at 9:45:41.95 -14:19:34.8 (J2000) and has a remarkably simple power-law spectrum with photon index Gamma=1.86 and Nh=7E21 /cm2. The near-nuclear (3" <~ r <~ 18") Chandra spectrum is best modelled by three components: (1) a direct AGN component with Gamma fixed at 1.86, (2) cold Compton reflection of the AGN component, and (3) a 0.5 keV low-abundance (Z < 0.03 Zsolar) "thermal plasma," with ~10% of the flux of either of the first two components. The X-ray luminosity of the 3rd component (the "soft excess") is ~1.4E40 erg/s, or ~5X that of all of the detected extranuclear X-ray sources. We suggest that most (~75-80%) of the soft excess emission originates from 1" < r < 3", which is not imaged in our observation due to severe CCD pile-up. We also require the cold reflector to be positioned at least 1" (158 pc) from the nucleus, since there is no reflection component in the X-ray core spectrum. Much of the extranuclear X-ray emission is coincident with radio structures (nuclear radio bubbles and large-scale radio features), and its soft X-ray luminosity is generally consistent with luminosities expected from a starburst-driven wind (with the starburst scaled from L_FIR). However, the AGN in NGC 2992 seems equally likely to power the galactic wind in that object. Furthermore, AGN photoionization and photoexcitation processes could dominate the soft excess, especially the \~75-80% which is not imaged by our observations.Comment: 34 pages AASTEX, 9 (low-res) PS figures, ApJ, in press. For full-resolution postscript file, visit http://www.pha.jhu.edu/~colbert/n2992_chandra.ps.g

Performance of a multi-disciplinary emergency department observation protocol for acetaminophen overdose.

The availability of 20-h N-acetylcysteine (NAC) infusion for low-risk acetaminophen (APAP) overdose enabled our center to implement an Emergency Department observation unit (OU) protocol as an alternative to hospitalization. Our objective was to evaluate our early experience with this protocol. This retrospective cohort study included all patients treated for low-risk APAP overdose in our academic hospital between 2006 and 2011. Cases were identified using OU and pharmacy records. Successful OU discharge was defined as disposition with no inpatient admission. Differences in medians with 95 % confidence intervals were used for comparisons. One hundred ninety-six patients received NAC for APAP overdose with a mean age of 35 years (SD 14); 73 % were white, and 43 % were male. Twenty (10 %) received care in the OU; 3/20(15 %) met criteria for inclusion in the OU protocol and 13/20(65 %) were discharged successfully. Out of the 196 patients, 10 met criteria for inclusion in the OU protocol but instead received care in the inpatient setting. The median total length of stay from presentation to ED discharge was 41 h for all patients treated in the OU, compared to 68 h for ten patients who met criteria for inclusion in the OU protocol but who were admitted (difference 27 h, 95 % CI 18-72 h). ED observation for APAP overdose can be a viable alternative to inpatient admission. Most patients were successfully discharged from the OU. This evaluation identified both over- and under-utilization of the OU. OU treatment resulted in shorter median length of stay than inpatient admission

ALMA Discovery of a Disk around the Planetary-Mass Companion Sr 12 C

We report an Atacama Large Millimeter/submillimeter Array 0.88 mm (Band 7) continuum detection of the accretion disk around SR 12 c, an ∼11 M Jup planetary-mass companion (PMC) orbiting its host binary at 980 au. This is the first submillimeter detection of a circumplanetary disk around a wide PMC. The disk has a flux density of 127 ± 14 μJy and is not resolved by the ∼0.″1 beam, so the dust disk radius is likely less than 5 au and can be much smaller if the dust continuum is optically thick. If, however, the dust emission is optically thin, then the SR 12 c disk has a comparable dust mass to the circumplanetary disk around PDS 70 c but is about five times lower than that of the ∼12 M Jup free-floating OTS 44. This suggests that disks around bound and unbound planetary-mass objects can span a wide range of masses. The gas mass estimated with an accretion rate of 10-11 M ⊙ yr-1 implies a gas-to-dust ratio higher than 100. If cloud absorption is not significant, a nondetection of 12CO(3-2) implies a compact gas disk around SR 12 c. Future sensitive observations may detect more PMC disks at 0.88 mm flux densities of ≲ 100 μJy

The LEECH Exoplanet Imaging Survey: Limits on Planet Occurrence Rates Under Conservative Assumptions

We present the results of the largest $L^{\prime}$ ($3.8~\mu$m) direct imaging survey for exoplanets to date, the Large Binocular Telescope Interferometer (LBTI) Exozodi Exoplanet Common Hunt (LEECH). We observed 98 stars with spectral types from B to M. Cool planets emit a larger share of their flux in $L^{\prime}$ compared to shorter wavelengths, affording LEECH an advantage in detecting low-mass, old, and cold-start giant planets. We emphasize proximity over youth in our target selection, probing physical separations smaller than other direct imaging surveys. For FGK stars, LEECH outperforms many previous studies, placing tighter constraints on the hot-start planet occurrence frequency interior to $\sim20$ au. For less luminous, cold-start planets, LEECH provides the best constraints on giant-planet frequency interior to $\sim20$ au around FGK stars. Direct imaging survey results depend sensitively on both the choice of evolutionary model (e.g., hot- or cold-start) and assumptions (explicit or implicit) about the shape of the underlying planet distribution, in particular its radial extent. Artificially low limits on the planet occurrence frequency can be derived when the shape of the planet distribution is assumed to extend to very large separations, well beyond typical protoplanetary dust-disk radii ($\lesssim50$ au), and when hot-start models are used exclusively. We place a conservative upper limit on the planet occurrence frequency using cold-start models and planetary population distributions that do not extend beyond typical protoplanetary dust-disk radii. We find that $\lesssim90\%$ of FGK systems can host a 7 to 10 $M_{\mathrm{Jup}}$ planet from 5 to 50 au. This limit leaves open the possibility that planets in this range are common.Comment: 31 pages, 13 figures, accepted to A

The Peculiar Debris Disk of HD 111520 as Resolved by the Gemini Planet Imager

Using the Gemini Planet Imager (GPI), we have resolved the circumstellar debris disk around HD 111520 at a projected range of ~30-100 AU in both total and polarized $H$-band intensity. The disk is seen edge-on at a position angle of ~165$^{\circ}$ along the spine of emission. A slight inclination or asymmetric warping are covariant and alters the interpretation of the observed disk emission. We employ 3 point spread function (PSF) subtraction methods to reduce the stellar glare and instrumental artifacts to confirm that there is a roughly 2:1 brightness asymmetry between the NW and SE extension. This specific feature makes HD 111520 the most extreme examples of asymmetric debris disks observed in scattered light among similar highly inclined systems, such as HD 15115 and HD 106906. We further identify a tentative localized brightness enhancement and scale height enhancement associated with the disk at ~40 AU away from the star on the SE extension. We also find that the fractional polarization rises from 10 to 40% from 0.5" to 0.8" from the star. The combination of large brightness asymmetry and symmetric polarization fraction leads us to believe that an azimuthal dust density variation is causing the observed asymmetry.Comment: 9 pages, 8 Figures, 1 table, Accepted to Ap