Femtolens Imaging of a Quasar Central Engine Using a Dwarf Star Telescope

We show that it is possible to image the structure of a distant quasar on scales of $\sim 1\,$AU by constructing a telescope which uses a nearby dwarf star as its ``primary lens'' together with a satellite-borne ``secondary''. The image produced by the primary is magnified by $\sim 10^5$ in one direction but is contracted by 0.5 in the other, and therefore contains highly degenerate one-dimensional information about the two-dimensional source. We discuss various methods for extracting information about the second dimension including ``femtolens interferometry'' where one measures the interference between different parts of the one-dimensional image with each other. Assuming that the satellite could be dispatched to a position along a star-quasar line of sight at a distance $r$ from the Sun, the nearest available dwarf-star primary is likely to be at \sim 15\,\pc\,(r/40\,\rm AU)^{-2}. The secondary should consist of a one-dimensional array of mirrors extending $\sim 700\,$m to achieve 1 AU resolution, or $\sim 100\,$m to achieve 4 AU resolution.Comment: 12 pages including 3 embedded figure

The Ratio of Total to Selective Extinction Toward Baade's Window

We measure the ratio of total to selective extinction, R_{VI}=A_V/E(V-I), toward Baade's Window by comparing the VIK colors of 132 Baade's Window G and K giants from Tiede, Frogel, & Terndrup with the solar-neighborhood (V-I),(V-K) relation from Bessell & Brett. We find R_{VI}=2.283 +/- 0.016, and show that our measurement has no significant dependence on stellar type from G0 to K4. Adjusting the Paczynski et al. determination of the centroid of the dereddened Baade's Window clump for this revised value of $R_{VI}$, we find I_{0,RC}=14.43 and (V-I)_{0,RC}=1.058. This implies a distance to the Baade's Window clump of d_{BW} = 8.63 +/- 0.16 kpc, where the error bar takes account of statistical but not systematic uncertainties.Comment: 8 pages, 1 figure, submitted to Ap

Near mean-field behavior in the generalized Burridge-Knopoff earthquake model with variable range stress transfer

Simple models of earthquake faults are important for understanding the mechanisms for their observed behavior in nature, such as Gutenberg-Richter scaling. Because of the importance of long-range interactions in an elastic medium, we generalize the Burridge-Knopoff slider-block model to include variable range stress transfer. We find that the Burridge-Knopoff model with long-range stress transfer exhibits qualitatively different behavior than the corresponding long-range cellular automata models and the usual Burridge-Knopoff model with nearest-neighbor stress transfer, depending on how quickly the friction force weakens with increasing velocity. Extensive simulations of quasiperiodic characteristic events, mode-switching phenomena, ergodicity, and waiting-time distributions are also discussed. Our results are consistent with the existence of a mean-field critical point and have important implications for our understanding of earthquakes and other driven dissipative systems.Comment: 24 pages 12 figures, revised version for Phys. Rev.

Studying Wrongful Convictions: Learning from Social Science

There has been an explosion of legal scholarship on wrongful convictions in the last decade, reflecting a growing concern about the problem of actual innocence in the criminal justice system. Yet criminal law and procedure scholars have engaged in relatively little dialogue or collaboration on this topic with criminologists. In this article, we use the empirical study of wrongful convictions to illustrate what criminological approaches—or, more broadly, social science methods—can teach legal scholars. After briefly examining the history of wrongful conviction scholarship, we discuss the limits of the (primarily) narrative methodology of legal scholarship on wrongful convictions. We argue that social scientific methods allow for more precise and accurate depictions of the multifactorial and complex nature of causation in wrongful conviction cases. In the main body of this article, we discuss and illustrate several social science approaches to the study of wrongful conviction: aggregated case studies, matched comparison samples, and path analysis. We argue these methods would help criminal law and procedure scholars to better understand the causes, characteristics, and consequences of wrongful convictions than a purely narrative approach. Finally, we offer concluding thoughts about improving the dialogue between criminal law and criminology on the subject of wrongful conviction

Anomaluos RR Lyrae (V-I)_0 colors in Baade's Window

We compare (V-I)_0-(V-K)_0 color-color and (V-I)_0-log P period-color diagrams for Baade's Window and local RRab Lyrae stars. We find that for a fixed log P the Baade's Window RR Lyrae stars are ~0.17 magnitudes redder in (V-I)_0 than the local RR Lyrae stars. We also show that there is no such effect observed in (V-K)_0. We argue that an extinction misestimate towards Baade's Window is not a plausible explanation of the discrepancy. Unlike Baade's Window RR Lyrae stars, the local ones follow a black-body color-color relation and are well approximated by theoretical models. We test two parameters, metallicity and surface gravity, and find that their effects are too small to explain the (V-I)_0 discrepancy between the two groups of stars. We do not provide any explanation for the anomalous (V-I)_0 behavior of the Baade's Window RR Lyrae stars. We note that a similar effect for clump giant stars has been recently reported by Paczynski and we caution that RR Lyrae stars and clump giants, often used as standard candles, can be subject to the same type of systematics.Comment: 10 pages, 7 figures, submitted to Ap

Early-type Stars: Most Favorable Targets for Astrometrically Detectable Planets in the Habitable Zone

Early-type stars appear to be a difficult place to look for planets astrometrically. First, they are relatively heavy, and for fixed planetary mass the astrometric signal falls inversely as the stellar mass. Second, they are relatively rare (and so tend to be more distant), and for fixed orbital separation the astrometric signal falls inversely as the distance. Nevertheless, because early-type stars are relatively more luminous, their habitable zones are at larger semi-major axis. Since astrometric signal scales directly as orbital size, this gives early-type stars a strong advantage, which more than compensates for the other two factors. Using the Hipparcos catalog, we show that early-type stars constitute the majority of viable targets for astrometric searches for planets in the habitable zone. We contrast this characteristic to transit searches, which are primarily sensitive to habitable planets around late-type stars.Comment: Submitted to ApJ Letters, 8 pages including 2 figure

Imaging a Quasar Accretion Disk with Microlensing

We show how analysis of a quasar high-magnification microlensing event may be used to construct a map of the frequency-dependent surface brightness of the quasar accretion disk. The same procedure also allows determination of the disk inclination angle, the black hole mass (modulo the caustic velocity), and possibly the black hole spin. This method depends on the validity of one assumption: that the optical and ultraviolet continuum of the quasar is produced on the surface of an azimuthally symmetric, flat equatorial disk, whose gas follows prograde circular orbits in a Kerr spacetime (and plunges inside the marginally stable orbit). Given this assumption, we advocate using a variant of first-order linear regularization to invert multi-frequency microlensing lightcurves to obtain the disk surface brightness as a function of radius and frequency. The other parameters can be found by minimizing chi-square in a fashion consistent with the regularized solution for the surface brightness. We present simulations for a disk model appropriate to the Einstein Cross quasar, an object uniquely well-suited to this approach. These simulations confirm that the surface brightness can be reconstructed quite well near its peak, and that there are no systematic errors in determining the other model parameters. We also discuss the observational requirements for successful implementation of this technique.Comment: accepted to ApJ for publicatio

MOA-2011-BLG-293Lb: First Microlensing Planet possibly in the Habitable Zone

We used Keck adaptive optics observations to identify the first planet discovered by microlensing to lie in or near the habitable zone, i.e., at projected separation $r_\perp=1.1\pm 0.1\,$AU from its $M_{L}=0.86\pm 0.06\,M_\odot$ host, being the highest microlensing mass definitely identified. The planet has a mass $m_p = 4.8\pm 0.3\,M_{\rm Jup}$, and could in principle have habitable moons. This is also the first planet to be identified as being in the Galactic bulge with good confidence: $D_L=7.72\pm 0.44$ kpc. The planet/host masses and distance were previously not known, but only estimated using Bayesian priors based on a Galactic model (Yee et al. 2012). These estimates had suggested that the planet might be a super-Jupiter orbiting an M dwarf, a very rare class of planets. We obtained high-resolution $JHK$ images using Keck adaptive optics to detect the lens and so test this hypothesis. We clearly detect light from a G dwarf at the position of the event, and exclude all interpretations other than that this is the lens with high confidence (95%), using a new astrometric technique. The calibrated magnitude of the planet host star is $H_{L}=19.16\pm 0.13$. We infer the following probabilities for the three possible orbital configurations of the gas giant planet: 53% to be in the habitable zone, 35% to be near the habitable zone, and 12% to be beyond the snow line, depending on the atmospherical conditions and the uncertainties on the semimajor axis.Comment: Accepted by ApJ, 21 pages, 4 figure