2-D Radiative Transfer in Protostellar Envelopes: II. An Evolutionary Sequence

We present model spectral energy distributions, colors, polarization, and images for an evolutionary sequence of a low-mass protostar from the early collapse stage (Class 0) to the remnant disk stage (Class III). We find a substantial overlap in colors and SEDs between protostars embedded in envelopes (Class 0-I) and T Tauri disks (Class II), especially at mid-IR wavelengths. Edge-on Class I-II sources show double-peaked spectral energy distributions, with a short-wavelength hump due to scattered light and the long-wavelength hump due to thermal emission. These are the bluest sources in mid-IR color-color diagrams. Since Class 0 and I sources are diffuse, the size of the aperture over which fluxes are integrated has a substantial effect on the computed colors, with larger aperture results showing significantly bluer colors. This causes overlap in color-color diagrams between all evolutionary states, especially in the mid-IR. However the near-IR polarization of the Class 0 sources is much higher than the Class I-II sources, providing a means to separate these evolutionary states. We varied the grain properties in the circumstellar envelope, allowing for larger grains in the disk midplane and smaller in the envelope. We find that grain growth in disks of Class I sources can be detected at wavelengths greater than 100 $\mu$m. Our image calculations predict that the diffuse emission from edge-on Class I and II sources should be detectable in the mid-IR with the Space Infrared Telescope Facility (SIRTF) in nearby star forming regions (out to several hundred parsecs).Comment: A version with high-resolution images is available at http://www.astro.wisc.edu/glimpse/glimpsepubs.htm

Mind the gap: A review and recommendations for statistically evaluating Dual Systems models of adolescent risk behavior

According to Dual Systems models (Casey et al., 2008; Luna and Wright, 2016; Steinberg, 2008), a rapidly-developing socioemotional system and gradually-developing cognitive control system characterize adolescent brain development. The imbalance hypothesis forwarded by Dual Systems models posits that the magnitude of the imbalance between these two developing systems should predict the propensity for engaging in a variety of risk behaviors. The current integrative review argues that the excitement generated by the imbalance hypothesis and its implications for explaining adolescent risk behaviors has not been meet with equal efforts to rigorously test this hypothesis. The goal of the current review is to help guide the field to consider appropriate and rigorous methods of testing the imbalance hypothesis. First, we review the analytic approaches that have been used to test the imbalance hypothesis and outline statistical and conceptual limitations of these approaches. Next, we discuss the utility of two longitudinal analytic approaches (Latent Difference Scores and Growth Mixture Modeling) for testing the imbalance hypothesis. We utilize data from a large community adolescent sample to illustrate each approach and argue that Latent Difference Scores and Growth Mixture Modeling approaches enhance the specificity and precision with which the imbalance hypothesis is evaluated

Families of Graphs With Chromatic Zeros Lying on Circles

We define an infinite set of families of graphs, which we call $p$-wheels and denote $(Wh)^{(p)}_n$, that generalize the wheel ($p=1$) and biwheel ($p=2$) graphs. The chromatic polynomial for $(Wh)^{(p)}_n$ is calculated, and remarkably simple properties of the chromatic zeros are found: (i) the real zeros occur at $q=0,1,...p+1$ for $n-p$ even and $q=0,1,...p+2$ for $n-p$ odd; and (ii) the complex zeros all lie, equally spaced, on the unit circle $|q-(p+1)|=1$ in the complex $q$ plane. In the $n \to \infty$ limit, the zeros on this circle merge to form a boundary curve separating two regions where the limiting function $W(\{(Wh)^{(p)}\},q)$ is analytic, viz., the exterior and interior of the above circle. Connections with statistical mechanics are noted.Comment: 8 pages, Late

Coupling Non-Gravitational Fields with Simplicial Spacetimes

The inclusion of source terms in discrete gravity is a long-standing problem. Providing a consistent coupling of source to the lattice in Regge Calculus (RC) yields a robust unstructured spacetime mesh applicable to both numerical relativity and quantum gravity. RC provides a particularly insightful approach to this problem with its purely geometric representation of spacetime. The simplicial building blocks of RC enable us to represent all matter and fields in a coordinate-free manner. We provide an interpretation of RC as a discrete exterior calculus framework into which non-gravitational fields naturally couple with the simplicial lattice. Using this approach we obtain a consistent mapping of the continuum action for non-gravitational fields to the Regge lattice. In this paper we apply this framework to scalar, vector and tensor fields. In particular we reconstruct the lattice action for (1) the scalar field, (2) Maxwell field tensor and (3) Dirac particles. The straightforward application of our discretization techniques to these three fields demonstrates a universal implementation of coupling source to the lattice in Regge calculus.Comment: 10 pages, no figures, Latex, fixed typos and minor corrections

Determining the Contribution of Epidermal Cell Shape to Petal Wettability Using Isogenic Antirrhinum Lines

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

2-D Radiative Transfer in Protostellar Envelopes: I. Effects of Geometry on Class I Sources

We present 2-D radiation transfer models of Class I Protostars and show the effect of including more realistic geometries on the resulting spectral energy distributions and images. We begin with a rotationally flattened infalling envelope as our comparison model, and add a flared disk and bipolar cavity. The disk affects the spectral energy distribution most strongly at edge-on inclinations, causing a broad dip at about 10 um (independent of the silicate feature) due to high extinction and low scattering albedo in this wavelength region. The bipolar cavities allow more direct stellar+disk radiation to emerge into polar directions, and more scattering radiation to emerge into all directions. The wavelength-integrated flux, often interpreted as luminosity, varies with viewing angle, with pole-on viewing angles seeing 2-4 times as much flux as edge-on, depending on geometry. Thus, observational estimates of luminosity should take into account the inclination of a source. The envelopes with cavities are significantly bluer in near-IR and mid-IR color-color plots than those without cavities. Using 1-D models to interpret Class I sources with bipolar cavities would lead to an underestimate of envelope mass and an overestimate of the implied evolutionary state. We compute images at near-, mid-, and far-IR wavelengths. We find that the mid-IR colors and images are sensitive to scattering albedo, and that the flared disk shadows the midplane on large size scales at all wavelengths plotted. Finally, our models produce polarization spectra which can be used to diagnose dust properties, such as albedo variations due to grain growth. Our results of polarization across the 3.1 um ice feature agree well with observations for ice mantles covering 5% of the radius of the grains.Comment: Accepted for publication in ApJ, 37 pages, 13 figures (several figures reduced in quality; find original version at http://gemelli.colorado.edu/~bwhitney/preprints.html

Spanning Trees on Graphs and Lattices in d Dimensions

The problem of enumerating spanning trees on graphs and lattices is considered. We obtain bounds on the number of spanning trees $N_{ST}$ and establish inequalities relating the numbers of spanning trees of different graphs or lattices. A general formulation is presented for the enumeration of spanning trees on lattices in $d\geq 2$ dimensions, and is applied to the hypercubic, body-centered cubic, face-centered cubic, and specific planar lattices including the kagom\'e, diced, 4-8-8 (bathroom-tile), Union Jack, and 3-12-12 lattices. This leads to closed-form expressions for $N_{ST}$ for these lattices of finite sizes. We prove a theorem concerning the classes of graphs and lattices ${\cal L}$ with the property that $N_{ST} \sim \exp(nz_{\cal L})$ as the number of vertices $n \to \infty$, where $z_{\cal L}$ is a finite nonzero constant. This includes the bulk limit of lattices in any spatial dimension, and also sections of lattices whose lengths in some dimensions go to infinity while others are finite. We evaluate $z_{\cal L}$ exactly for the lattices we considered, and discuss the dependence of $z_{\cal L}$ on d and the lattice coordination number. We also establish a relation connecting $z_{\cal L}$ to the free energy of the critical Ising model for planar lattices ${\cal L}$.Comment: 28 pages, latex, 1 postscript figure, J. Phys. A, in pres

High-resolution Near-Infrared Images and Models of the Circumstellar Disk in HH 30

We present Hubble Space Telescope (HST) Near-Infrared Camera and Multi-object Spectrometer (NICMOS) observations of the reflection nebulosity associated with the T Tauri star HH 30. The images show the scattered light pattern characteristic of a highly inclined, optically thick disk with a prominent dustlane whose width decreases with increasing wavelength. The reflected nebulosity exhibits a lateral asymmetry in the upper lobe on the opposite side to that reported in previously published Wide Field Planetary Camera 2 (WFPC2) images. The radiation transfer model which most closely reproduces the data has a flared accretion disk with dust grains larger than standard interstellar medium grains by a factor of approximately 2.1. A single hotspot on the stellar surface provides the necessary asymmetry to fit the images and is consistent with previous modeling of the light curve and images. Photometric analysis results in an estimated extinction of Av>~80; however, since the photometry measures only scattered light rather than direct stellar flux, this a lower limit. The radiative transfer models require an extinction of Av = 7,900.Comment: Accepted for publication in Ap.