Discovery of Blue Luminescence in the Red Rectangle: Possible Fluorescence from Neutral Polycyclic Aromatic Hydrocarbon Molecules?

Here we report our discovery of a band of blue luminescence (BL) in the Red Rectangle (RR) nebula. This enigmatic proto-planetary nebula is also one of the brightest known sources of extended red emission as well as of unidentified infra-red (UIR) band emissions. The spectrum of this newly discovered BL is most likely fluorescence from small neutral polycyclic aromatic hydrocarbon (PAH) molecules. PAH molecules are thought to be widely present in many interstellar and circumstellar environments in our galaxy as well as in other galaxies, and are considered likely carriers of the UIR-band emission. However, no specific PAH molecule has yet been identified in a source outside the solar system, as the set of mid-infra-red emission features attributed to these molecules between the wavelengths of 3.3 micron and 16.4 micron is largely insensitive to molecular sizes. In contrast, near-UV/blue fluorescence of PAHs is more specific as to size, structure, and charge state of a PAH molecule. If the carriers of this near-UV/blue fluorescence are PAHs, they are most likely neutral PAH molecules consisting of 3-4 aromatic rings such as anthracene (C14H10) and pyrene (C16H10). These small PAHs would then be the largest molecules specifically identified in the interstellar medium.Comment: 4 pages, 4 figures, Accepted for publication in ApJL (LaTeX, uses emulateapj.sty

Lensing Properties of Cored Galaxy Models

A method is developed to evaluate the magnifications of the images of galaxies with lensing potentials stratified on similar concentric ellipses. A simple contour integral is provided which enables the sums of the magnifications of even parity or odd parity or the central image to be easily calculated. The sums for pairs of images vary considerably with source position, while the signed sums can be remarkably uniform inside the tangential caustic in the absence of naked cusps. For a family of models in which the potential is a power-law of the elliptic radius, the number of visible images is found as a function of flattening, external shear and core radius. The magnification of the central image depends on the core radius and the slope of the potential. For typical source and lens redshifts, the missing central image leads to strong constraints; the mass distribution in the lensing galaxy must be nearly cusped, and the cusp must be isothermal or stronger. This is in accord with the cuspy cores seen in high resolution photometry of nearby, massive, early-type galaxies, which typically have the surface density falling like distance^{-1.3} outside a break radius of a few hundred parsecs. Cuspy cores by themselves can provide an explanation of the missing central images. Dark matter at large radii may alter the slope of the projected density; provided the slope remains isothermal or steeper and the break radius remains small, then the central image remains unobservable. The sensitivity of the radio maps must be increased fifty-fold to find the central images in abundance.Comment: 42 pages, 11 figures, ApJ in pres

Analytic Time Delays and H_0 Estimates for Gravitational Lenses

We study gravitational lens time delays for a general family of lensing potentials, which includes the popular singular isothermal elliptical potential and singular isothermal elliptical density distribution but allows general angular structure. Using a novel approach, we show that the time delay can be cast in a very simple form, depending only on the observed image positions. Including an external shear changes the time delay proportional to the shear strength, and varying the radial profile of the potential changes the time delay approximately linearly. These analytic results can be used to obtain simple estimates of the time delay and the Hubble constant in observed gravitational lenses. The naive estimates for four of five time delay lenses show surprising agreement with each other and with local measurements of H_0; the complicated Q 0957+561 system is the only outlier. The agreement suggests that it is reasonable to use simple isothermal lens models to infer H_0, although it is still important to check this conclusion by examining detailed models and by measuring more lensing time delays.Comment: 16 pages with 2 embedded figures; submitted to Ap

Benefit Plan Design and Prescription Drug Utilization Among Asthmatics: Do Patient Copayments Matter?

Objective: The ratio of controller to reliever medication use has been proposed as a measure of treatment quality for asthma patients. In this study we examine the effects of plan level mean out-of-pocket asthma medication patient copayments and other features of benefit plan design on the use of controller medications alone, controller and reliever medications (combination therapy), and reliever medications alone. Methods: 1995-2000 MarketScan claims data were used to construct plan-level out-of-pocket copayment and physician/practice prescriber preference variables for asthma medications. Separate multinomial logit models were estimated for patients in fee-for-service (FFS) and non-FFS plans relating benefit plan design features, physician/practice prescribing preferences, patient demographics, patient comorbidities and county-level income variables to patient-level asthma treatment patterns. Results: We find that the controller reliever ratio rose steadily over 1995-2000, along with out-of-pocket payments for asthma medications, which rose more for controllers than for relievers. However, after controlling for other variables, plan level mean out-of-pocket copayments were not found to have a statistically significant influence upon patient-level asthma treatment patterns. On the other hand, physician practice prescribing patterns strongly influenced patient level treatment patterns. Conclusions: There is no strong statistical evidence that higher levels of out-of-pocket copayments for prescription drugs influence asthma treatment patterns. However, physician/practice prescribing preferences influence patient treatment.

Quantization of Two-Dimensional Gravity with Dynamical Torsion

We consider two-dimensional gravity with dynamical torsion in the Batalin - Vilkovisky and Batalin - Lavrov - Tyutin formalisms of gauge theories quantization as well as in the background field method.Comment: 12 pages, LaTe

Correlated Binomial Models and Correlation Structures

We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional probabilities. The beta-binomial distribution is derived by a strong symmetric assumption on the conditional correlations. Our derivation clarifies the 'correlation' structure of the beta-binomial distribution. It is also possible to study the correlation structures of other probability distributions of exchangeable (homogeneous) correlated Bernoulli random variables. We study some distribution functions and discuss their behaviors in terms of their correlation structures.Comment: 12 pages, 7 figure