Controlling Stocks and Flows to Promote Quality: The Environment, With Applications to Physical and Human Capital

Our analysis melds two traditional approaches to promoting quality. The first is restoring the stock of quality. The second is curbing its flow of deterioration. Although both approaches are widely used in real world settings, analytic models have tended to focus on one strategy or the other. We consider a class of problems, which we call SFQ' problems, in which both stocks and flows can be controlled to promote quality. We develop our results in the context of environmental quality, drawing on real-world examples from atomic wastes to zebra mussels. But the lessons are general, and we show how they apply to promoting the quality of both physical and human capital. We first study optimal policies in the limiting cases when only abatement or restoration is possible. We then focus on the full SFQ world, where both approaches can be used. We show that the optimal policy employs both instruments. Moreover, when combined optimally, neither strategy takes the form it would in the absence of the other.

An X-ray upper limit on the presence of a Neutron Star for the Small Magellanic Cloud and Supernova Remnant 1E0102.2-7219

We present Chandra X-ray Observatory archival observations of the supernova remnant 1E0102.2-7219, a young Oxygen-rich remnant in the Small Magellanic Cloud. Combining 28 ObsIDs for 324 ks of total exposure time, we present an ACIS image with an unprecedented signal-to-noise ratio (mean S/N ~ sqrt(S) ~6; maximum S/N > 35) . We search within the remnant, using the source detection software {\sc wavdetect}, for point sources which may indicate a compact object. Despite finding numerous detections of high significance in both broad and narrow band images of the remnant, we are unable to satisfactorily distinguish whether these detections correspond to emission from a compact object. We also present upper limits to the luminosity of an obscured compact stellar object which were derived from an analysis of spectra extracted from the high signal-to-noise image. We are able to further constrain the characteristics of a potential neutron star for this remnant with the results of the analysis presented here, though we cannot confirm the existence of such an object for this remnant.Comment: Accepted to the Astrophysical Journa

Evidence for Proportionate Partition Between the Magnetic Field and Hot Gas in Turbulent Cassiopeia A

We present a deep X-ray observation of the young Galactic supernova remnant Cas A, acquired with the ROSAT High Resolution Imager. This high dynamic range (232 ks) image reveals low-surface-brightness X-ray structure, which appears qualitatively similar to corresponding radio features. We consider the correlation between the X-ray and radio morphologies and its physical implications. After correcting for the inhomogeneous absorption across the remnant, we performed a point by point (4" resolution) surface brightness comparison between the X-ray and radio images. We find a strong (r = 0.75) log-log correlation, implying an overall relationship of $\log(\Sigma_{_{\rm X-ray}}) \propto (2.21\pm0.05) \times \log(\Sigma_{_{\rm radio}})$. This is consistent with proportionate partition (and possibly equipartition) between the local magnetic field and the hot gas --- implying that Cas A's plasma is fully turbulent and continuously amplifying the magnetic field.Comment: 8 pages with embedded bitmapped figures, Accepted by ApJ Letters 5/1/9

Spatial identification of the overionized plasma in W49B

Recent Suzaku X-ray observations of the ejecta-dominated supernova remnant W49B have shown that in the global spectrum there is a clear indication for the presence of overionized plasma whose physical origin is still under debate. In order to ascertain the physical origin of such a rapidly cooling plasma, we focus on the study of its spatial localization within the X-ray emitting ejecta. We confirm the presence of a saw-edged excess (interpreted as a strong radiative recombination continuum) in the global spectrum above 8 keV, emerging above the ionization-equilibrium model. We produce a hardness ratio map to determine where the plasma is overionized and we perform a spectral analysis of the regions with and without strong overionization. We find that the overionized plasma is localized in the center of the remnant and in its western jet, while it is not detected in the bright eastern jet, where the expansion of the ejecta is hampered by their interaction with a dense interstellar cloud. The location of overionized plasma suggests that the inner ejecta are rapidly cooling by expansion, unlike the outer ejecta, for which expansion is hampered by interstellar clouds seen in H2Comment: Accepted for publication as a Letter in Astronomy and Astrophysics

The Optimal Management of Environmental Quality with Stock and Flow Controls

We characterize environmental quality as a stock, and its rate of deterioration as a flow. We consider a class of problems, which we call "SFQ" problems, in which both stocks and flows can be controlled to promote the quality of a resource stock. Abatement (curbing the flow) and restoration (restoring the stock) are interdependent tools in such problems. Under the optimal policy, periodic restoration complements positive but variable abatement that partly stems the quality decline. The preferred balance between the two strategies depends on environmental and economic factors. If flows are low enough, or if abatement is sufficiently inexpensive relative to restoration, optimal abatement may be sufficiently intense to offset the expected deterioration and produce an equilibrium in expectation. When deterioration is more rapid or more variable, when abatement is more expensive, or when restoration is less costly, the optimal policy relies more on restoration. We apply the analysis to the restoration of an endangered species, and show how it could illuminate a range of other problems in the environmental arena. But the lessons are general, and we briefly discuss how they apply to the management of both physical and human capital stocks.

A Broadband X-Ray Study of the Supernova Remnant 3C 397

We present an X-ray study of the radio bright supernova remnant (SNR) 3C 397 with ROSAT, ASCA, and RXTE. A central X-ray spot seen with the ROSAT High-Resolution Imager hints at the presence of a pulsar-powered component, and gives this SNR a composite X-ray morphology. Combined ROSAT and ASCA imaging show that the remnant is highly asymmetric, with its hard X-ray emission peaking at the western lobe. The spectrum of 3C 397 is heavily absorbed, and dominated by thermal emission with emission lines evident from Mg, Si, S, Ar and Fe. Single-component models fail to describe the spectrum, and at least two components are required. We use a set of non-equilibrium ionization (NEI) models (Borkowski et al. in preparation). The temperatures from the soft and hard components are 0.2 keV and 1.6 keV respectively. The corresponding ionization time-scales $n_0 t$ ($n_0$ being the pre-shock hydrogen density) are 6 $\times 10^{12}$ cm$^{-3}$ s and 6 $\times$ 10$^{10}$ cm$^{-3}$ s, respectively. The spectrum obtained with the Proportional Counter Array (PCA) of RXTE is contaminated by emission from the Galactic ridge, with only $\sim$ 15% of the count rate originating from 3C 397 in the 5-15 keV range. The PCA spectrum allowed us to confirm the thermal nature of the hard X-ray emission. A third component originating from a pulsar-driven component is possible, but the contamination of the source signal by the Galactic ridge did not allow us to find pulsations from any hidden pulsar. We discuss the X-ray spectrum in the light of two scenarios: a young ejecta-dominated remnant of a core-collapse SN, and a middle-aged SNR expanding in a dense ISM. Spatially resolved spectroscopy (with CHANDRA and XMM) is needed to differentiate between the two scenarios, and address the nature of the mysterious radio-quiet X-ray hot spot.Comment: 21 pages including 8 figures and 5 tables. Accepted for publication in the Astrophysical journa

Metastatic meningioma: positron emission tomography CT imaging findings

The imaging findings of a case of metastasing meningioma are described. The case illustrates a number of rare and interesting features. The patient presented with haemoptysis 22 years after the initial resection of an intracranial meningioma. CT demonstrated heterogeneous masses with avid peripheral enhancement without central enhancement. Blood supply to the larger lesion was partially from small feeding vessels from the inferior pulmonary vein. These findings correlate with a previously published case in which there was avid uptake of fluoro-18-deoxyglucose peripherally with lesser uptake centrally. The diagnosis of metastasing meningioma was confirmed on percutaneous lung tissue biopsy

Metastatic meningioma: positron emission tomography CT imaging findings

The imaging findings of a case of metastasing meningioma are described. The case illustrates a number of rare and interesting features. The patient presented with haemoptysis 22 years after the initial resection of an intracranial meningioma. CT demonstrated heterogeneous masses with avid peripheral enhancement without central enhancement. Blood supply to the larger lesion was partially from small feeding vessels from the inferior pulmonary vein. These findings correlate with a previously published case in which there was avid uptake of fluoro-18-deoxyglucose peripherally with lesser uptake centrally. The diagnosis of metastasing meningioma was confirmed on percutaneous lung tissue biopsy