Freshly Formed Dust in the Cassiopeia A Supernova Remnant as Revealed by the Spitzer Space Telescope

We performed Spitzer Infrared Spectrograph mapping observations covering nearly the entire extent of the Cassiopeia A supernova remnant (SNR), producing mid-infrared (5.5-35 micron) spectra every 5-10". Gas lines of Ar, Ne, O, Si, S and Fe, and dust continua were strong for most positions. We identify three distinct ejecta dust populations based on their continuum shapes. The dominant dust continuum shape exhibits a strong peak at 21 micron. A line-free map of 21 micron-peak dust made from the 19-23 micron range closely resembles the [Ar II], [O IV], and [Ne II] ejecta-line maps implying that dust is freshly formed in the ejecta. Spectral fitting implies the presence of SiO2, Mg protosilicates, and FeO grains in these regions. The second dust type exhibits a rising continuum up to 21 micron and then flattens thereafter. This ``weak 21 micron'' dust is likely composed of Al2O3 and C grains. The third dust continuum shape is featureless with a gently rising spectrum and is likely composed of MgSiO3 and either Al2O3 or Fe grains. Using the least massive composition for each of the three dust classes yields a total mass of 0.02 Msun. Using the most-massive composition yields a total mass of 0.054 Msun. The primary uncertainty in the total dust mass stems from the selection of the dust composition necessary for fitting the featureless dust as well as 70 micron flux. The freshly formed dust mass derived from Cas A is sufficient from SNe to explain the lower limit on the dust masses in high redshift galaxies.Comment: 8 figures: Accepted for the publication in Ap

Vertex corrections in localized and extended systems

Within many-body perturbation theory we apply vertex corrections to various closed-shell atoms and to jellium, using a local approximation for the vertex consistent with starting the many-body perturbation theory from a DFT-LDA Green's function. The vertex appears in two places -- in the screened Coulomb interaction, W, and in the self-energy, \Sigma -- and we obtain a systematic discrimination of these two effects by turning the vertex in \Sigma on and off. We also make comparisons to standard GW results within the usual random-phase approximation (RPA), which omits the vertex from both. When a vertex is included for closed-shell atoms, both ground-state and excited-state properties demonstrate only limited improvements over standard GW. For jellium we observe marked improvement in the quasiparticle band width when the vertex is included only in W, whereas turning on the vertex in \Sigma leads to an unphysical quasiparticle dispersion and work function. A simple analysis suggests why implementation of the vertex only in W is a valid way to improve quasiparticle energy calculations, while the vertex in \Sigma is unphysical, and points the way to development of improved vertices for ab initio electronic structure calculations.Comment: 8 Pages, 6 Figures. Updated with quasiparticle neon results, extended conclusions and references section. Minor changes: Updated references, minor improvement

The Three-Dimensional Structure of Interior Ejecta in Cassiopeia A at High Spectral Resolution

We used the Spitzer Space Telescope's Infrared Spectrograph to create a high resolution spectral map of the central region of the Cassiopeia A supernova remnant, allowing us to make a Doppler reconstruction of its 3D structure. The ejecta responsible for this emission have not yet encountered the remnant's reverse shock or the circumstellar medium, making it an ideal laboratory for exploring the dynamics of the supernova explosion itself. We observe that the O, Si, and S ejecta can form both sheet-like structures as well as filaments. Si and O, which come from different nucleosynthetic layers of the star, are observed to be coincident in velocity space in some regions, and separated by 500 km/s or more in others. Ejecta traveling toward us are, on average, ~900 km/s slower than the material traveling away from us. We compare our observations to recent supernova explosion models and find that no single model can simultaneously reproduce all the observed features. However, models of different supernova explosions can collectively produce the observed geometries and structures of the interior emission. We use the results from the models to address the conditions during the supernova explosion, concentrating on asymmetries in the shock structure. We also predict that the back surface of Cassiopeia A will begin brightening in ~30 years, and the front surface in ~100 years.Comment: 35 pages, 16 figures, accepted to Ap

The Lillie Mae: A Capital Investment Project In Riverboat Restoration

This case involves a proposed capital investment project. It was written for use in an introductory business finance course to present students a capital budgeting scenario involving elements of both an expansion project and a replacement project that is more complex than the usual textbook problems. It also provides students an exercise in the application of standard spreadsheet software to a common analytical problem in corporate finance, namely, a proposed capital expenditure

Time Variability in the X-ray Nebula Powered by Pulsar B1509-58

We use new and archival Chandra and ROSAT data to study the time variability of the X-ray emission from the pulsar wind nebula (PWN) powered by PSR B1509-58 on timescales of one week to twelve years. There is variability in the size, number, and brightness of compact knots appearing within 20" of the pulsar, with at least one knot showing a possible outflow velocity of ~0.6c (assuming a distance to the source of 5.2 kpc). The transient nature of these knots may indicate that they are produced by turbulence in the flows surrounding the pulsar. A previously identified prominent jet extending 12 pc to the southeast of the pulsar increased in brightness by 30% over 9 years; apparent outflow of material along this jet is observed with a velocity of ~0.5c. However, outflow alone cannot account for the changes in the jet on such short timescales. Magnetohydrodynamic sausage or kink instabilities are feasible explanations for the jet variability with timescale of ~1.3-2 years. An arc structure, located 30"-45" north of the pulsar, shows transverse structural variations and appears to have moved inward with a velocity of ~0.03c over three years. The overall structure and brightness of the diffuse PWN exterior to this arc and excluding the jet has remained the same over the twelve year span. The photon indices of the diffuse PWN and possibly the jet steepen with increasing radius, likely indicating synchrotron cooling at X-ray energies.Comment: accepted to ApJ, 14 pages, 8 figure

The Lillie Mae: A Capital Investment Project In Riverboat Restoration

This case involves a proposed capital investment project.  It was written for use in an introductory business finance course to present students a capital budgeting scenario involving elements of both an expansion project and a replacement project that is more complex than the usual textbook problems.  It also provides students an exercise in the application of standard spreadsheet software to a common analytical problem in corporate finance, namely, a proposed capital expenditure

A Paradox Within The Time Value Of Money: A Critical Thinking Exercise For Finance Students

This study presents a paradox within the time value of money (TVM), namely, that the interest-principal sequence embedded in the payment stream of an amortized loan is exactly the opposite of the interest-principal sequence implicit in the present value of a matching annuity.  We examine this inverse sequence, both mathematically and intuitively, and argue that it provides an excellent exercise for finance students to explore, both to enhance their critical thinking skills as well as to strengthen their understanding of TVM concepts.  Additionally, such an exercise will involve them actively in the learning process, as mandated by AACSB International’s Eligibility Procedures and Standards for Business Accreditation

Coherent States Formulation of Polymer Field Theory

We introduce a stable and efficient complex Langevin (CL) scheme to enable the first numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards' well known auxiliary-field (AF) framework, the CS formulation does not contain an embedded non-linear, non-local functional of the auxiliary fields, and the action of the field theory has a fully explicit, finite-order and semi-local polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.Comment: 14pages 8 figure

Mapping the spectral index of Cassiopeia A : evidence for flattening from radio to infrared

Funding: The work of VD is supported by a grant from the NWO graduate programme/GRAPPA-PhD programme. JVHS acknowledges support from the STFC grant ST/R000824/1.Synchrotron radiation from supernova remnants is caused by electrons accelerated through diffusive shock acceleration (DSA). The standard DSA theory predicts an electron spectral index of p = 2, corresponding to a radio spectral index of α = −0.5. An extension of DSA theory predicts that the accelerated particles change the shock structure, resulting in a spectrum that is steeper than p > 2 (α < −0.5) at low energies and flattens with energy. For Cassiopeia A, a synchrotron spectral flattening was previously reported for a small part of the remnant in the mid-infrared regime. Here, we present new measurements for spectral flattening using archival radio (4.72 GHz) and mid-infrared (3.6 μm) data, and we produce a complete spectral index map to investigate the spatial variations within the remnant. We compare this to measurements of the radio spectral index from L-band (1.285 GHz) and C-band (4.64 GHz) maps. Our result shows overall spectral flattening across the remnant (αR-IR ∼ −0.5 to −0.7), to be compared with the radio spectral index of αR = −0.77. The flattest values coincide with the locations of most recent particle acceleration. In addition to overall flattening, we detect a relatively steeper region in the south-east of the remnant (αR-IR ∼ −0.67). We explore whether these locally steeper spectra could be the result of synchrotron cooling, which provides constraints on the local magnetic field strengths and the age of the plasma, suggesting B ≲ 2 mG for an age of 100 yr, and even B ≲ 1 mG using the age of Cas A, in agreement with other estimates.Publisher PDFPeer reviewe