The Proper Motion of the Central Compact Object RX J0822-4300 in the Supernova Remnant Puppis A

Using the High Resolution Camera (HRC) aboard the Chandra X-ray Observatory, we have re-examined the proper motion of the central compact object RX J0822-4300 in the supernova remnant Puppis A. New data from 2010 August, combined with three archival data sets from as early as 1999 December, provide a baseline of 3886 days (more than 10 1/2 years) to perform the measurement. Correlating the four positions of RX J0822-4300 measured in each data set implies a projected proper motion of mu 71 \pm 12 masy. For a distance of 2 kpc this proper motion is equivalent to a recoil velocity of 672 \pm 115 km/s. The position angle is found to be 244 \pm 11 degrees. Both the magnitude and direction of the proper motion are in agreement with RX J0822-4300 originating near the optical expansion center of the supernova remnant. For a displacement of 371 \pm 31 arcsec between its birth place and today's position we deduce an age of (5.2 \pm 1.0) 10^3 yrs for RX J0822-4300. The age inferred from the neutron star proper motion and filament motions can be considered as two independent measurements of the same quantity. They average to 4450 \pm 750 yrs for the age of the supernova remnant Puppis A.Comment: Accepted for publication in the Astrophysical Journa

Direct Measurement of Neutron-Star Recoil in the Oxygen-Rich Supernova Remnant Puppis A

A sequence of three Chandra X-ray Observatory High Resolution Camera images taken over a span of five years reveals arc-second-scale displacement of RX J0822-4300, the stellar remnant (presumably a neutron star) near the center of the Puppis A supernova remnant. We measure its proper motion to be 0.165+/-0.025 arcsec/yr toward the west-southwest. At a distance of 2 kpc, this corresponds to a transverse space velocity of ~1600 km/s. The space velocity is consistent with the explosion center inferred from proper motions of the oxygen-rich optical filaments, and confirms the idea that Puppis A resulted from an asymmetric explosion accompanied by a kick that imparted roughly 3*10^49 ergs of kinetic energy (some 3 percent of the kinetic energy for a typical supernova) to the stellar remnant. We discuss constraints on core-collapse supernova models that have been proposed to explain neutron star kick velocities

Optimal dynamic scale and structure of a multi-pollution economy

We analyze the optimal dynamic scale and structure of a two-sectoreconomy, where each sector produces one consumption good and one specific pollutant. Both pollutants accumulate at di_erent rates to stocks which damage the natural environment. This acts as a dynamic driving force for the economy. Our analysis shows that along the optimal time-path (i) the overall scale of economic activity may be less than maximal; (ii) the time scale of economic dynamics (change of scale and structure) is mainly determined by the lifetime of pollutants, their harmfulness and the discount rate; and (iii) the optimal control of economic scale and structure may be non-monotonic. These results raise important questions about the optimal design of environmental policies.- Ökonomie , Ökologie , Emission , Wertpapieremission, dynamic economy-environment interaction , multi-pollutant emissions , non-monotonic control , optimal scale , stock pollutio

Optimal dynamic scale and structure of a multi-pollution economy

We analyze the optimal dynamic scale and structure of a two-sector-economy, where each sector produces one consumption good and one specific pollutant. Both pollutants accumulate at different rates to stocks that damage the natural environment, which acts as a dynamic driving force for the economy. Our analysis shows that along the optimal time-path (i) the overall scale of economic activity may be less than maximal, (ii) the time-scale of structural change is mainly determined by the longer-lived pollutant, (iii) the optimal control of emissions may be non-monotonic. In particular the last result raises important questions about the design of optimal environmental policies

The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices

This paper proposes scalable and fast algorithms for solving the Robust PCA problem, namely recovering a low-rank matrix with an unknown fraction of its entries being arbitrarily corrupted. This problem arises in many applications, such as image processing, web data ranking, and bioinformatic data analysis. It was recently shown that under surprisingly broad conditions, the Robust PCA problem can be exactly solved via convex optimization that minimizes a combination of the nuclear norm and the $\ell^1$-norm . In this paper, we apply the method of augmented Lagrange multipliers (ALM) to solve this convex program. As the objective function is non-smooth, we show how to extend the classical analysis of ALM to such new objective functions and prove the optimality of the proposed algorithms and characterize their convergence rate. Empirically, the proposed new algorithms can be more than five times faster than the previous state-of-the-art algorithms for Robust PCA, such as the accelerated proximal gradient (APG) algorithm. Moreover, the new algorithms achieve higher precision, yet being less storage/memory demanding. We also show that the ALM technique can be used to solve the (related but somewhat simpler) matrix completion problem and obtain rather promising results too. We further prove the necessary and sufficient condition for the inexact ALM to converge globally. Matlab code of all algorithms discussed are available at http://perception.csl.illinois.edu/matrix-rank/home.htmlComment: Please cite "Zhouchen Lin, Risheng Liu, and Zhixun Su, Linearized Alternating Direction Method with Adaptive Penalty for Low Rank Representation, NIPS 2011." (available at arXiv:1109.0367) instead for a more general method called Linearized Alternating Direction Method This manuscript first appeared as University of Illinois at Urbana-Champaign technical report #UILU-ENG-09-2215 in October 2009 Zhouchen Lin, Risheng Liu, and Zhixun Su, Linearized Alternating Direction Method with Adaptive Penalty for Low Rank Representation, NIPS 2011. (available at http://arxiv.org/abs/1109.0367