High Energy Emission from Supernova Remnants

This paper discusses several aspects of current research on high energy emission from supernova remnants, covering the following main topics: 1) The recent evidence for magnetic field amplification near supernova remnant shocks, which makes that cosmic rays are more efficiently accelerated than previously thought. 2) The evidence that ions and electrons in some remnants have very different temperatures, and only equilibrate through Coulomb interactions. 3) The evidence that the explosion that created Cas A was asymmetric, and seems to have involved a jet/counter jet structure. And finally, 4), I will argue that the unremarkable properties of supernova remnants associated with magnetars candidates, suggest that magnetars are not formed from rapidly (P ~ 1 ms) rotating proto-neutron stars, but that it is more likely that they are formed from massive progenitors stars with high magnetic fields.Comment: Invited review, to be published in the proceedings of IAUS230: "Populations of High Energy Sources in Galaxies", 14-19 August 2005, Dublin, Eds E.J.A. Meurs and G. Fabbian

Non-thermal X-ray Emission from Supernova Remnants

Recent studies of narrow, X-ray synchrotron radiating filaments surrounding young supernova remnants indicate that magnetic fields strengths are relatively high, B ~ 0.1 mG, or even higher, and that diffusion is close to the Bohm limit. I illustrate this using Cas A as an example. Also older remnants such as RCW 86 appear to emit X-ray synchrotron radiation, but the emission is more diffuse, and not always confined to a region close to the shock front. I argue that for RCW 86 the magnetic field is likely to be low (B ~ 17 microGauss), and at the location where the shell emits X-ray synchrotron radiation the shock velocity is much higher than the average shock velocity of ~600 km/s.Comment: To be published in the proceedings of the "International Symposium on High Energy Gamma-Ray Astronomy" (Gamma-2004), Heidelberg, edited by F.A. Aharonian and H. Voelk (AIP, NY). This preprint version contains 13 pages, 5 figures (4 in color

Supernova Remnants as the Sources of Galactic Cosmic Rays

The origin of cosmic rays holds still many mysteries hundred years after they were first discovered. Supernova remnants have for long been the most likely sources of Galactic cosmic rays. I discuss here some recent evidence that suggests that supernova remnants can indeed efficiently accelerate cosmic rays. For this conference devoted to the Astronomical Institute Utrecht I put the emphasis on work that was done in my group, but placed in a broader context: efficient cosmic-ray acceleration and the im- plications for cosmic-ray escape, synchrotron radiation and the evidence for magnetic- field amplification, potential X-ray synchrotron emission from cosmic-ray precursors, and I conclude with the implications of cosmic-ray escape for a Type Ia remnant like Tycho and a core-collapse remnant like Cas A.Comment: Proceedings of the Meeting "370 years of astronomy in Utrecht", Noordwijkerhout, The Netherlands, April 2-5, 2012 (ASPCS Conference Series

Ramsey Waits: A Computational Study on General Equilibrium Pricing of Derivative Securities

This paper analyses the accuracy of replicating portfolio methods in predicting asset prices. In a two-period, general equilibrium model with incomplete financial markets and heterogeneous agents, a computational study is conducted under various distributional assumptions. We focus on the price of a call option on an underlying risky asset. There is evidence that the value of the (approximate) replicating portfolio is a good approximation for the general equilibrium price for CRRA preferences, but not for CARA preferences. Furthermore, there is strong evidence that the introduction of the call option reduces market incompleteness and that the price of the underlying asset is unchanged. There is, however, inconclusive evidence on whether the availability of the option increases agents' welfare.Asset pricing, general equilibrium, incomplete markets

A critical shock Mach number for particle acceleration in the absence of pre-existing cosmic rays: M=5M=\sqrt 5

It is shown that, under some generic assumptions, shocks cannot accelerate particles unless the overall shock Mach number exceeds a critical value M > sqrt(5). The reason is that for M <= sqrt(5) the work done to compress the flow in a particle precursor requires more enthalpy flux than the system can sustain. This lower limit applies to situations without significant magnetic field pressure. In case that the magnetic field pressure dominates the pressure in the unshocked medium, i.e. for low plasma beta, the resistivity of the magnetic field makes it even more difficult to fulfil the energetic requirements for the formation of shock with an accelerated particle precursor and associated compression of the upstream plasma. We illustrate the effects of magnetic fields for the extreme situation of a purely perpendicular magnetic field configuration with plasma beta = 0, which gives a minimum Mach number of M = 5/2. The situation becomes more complex, if we incorporate the effects of pre-existing cosmic rays, indicating that the additional degree of freedom allows for less strict Mach number limits on acceleration. We discuss the implications of this result for low Mach number shock acceleration as found in solar system shocks, and shocks in clusters of galaxies.Comment: Accepted for publication in the Astrophysical Journal. 14 pages, 10 figures. (Minor corrections wrt last version.

Ramsey Waits: A Theory of Non-Exclusive Real Options with First-Mover Advantages

This paper analyses the exercise decision of non-exclusive real options in a two-player setting. A general model of non-exclusive real options, allowing the underlying asset to follow any strong Markov process is developed, thus extending the existing literature, which is mainly based on one-dimensional geometric Brownian motion. For games with a first-mover advantage it is proved that an equilibrium with the rent-equalisation property exists. As an example, a duopoly where two firms can adopt a new technology, whose profitability follows a two-dimensional, correlated geometric Brownian motion is studied.Timing games, real options, rent equalisation, technology adoption

Evolution of Conjectures in Cournot Oligopoly

This paper considers a dynamic market where a fixed number of firms engages in Cournot oligopoly.  Firms choose the output level based on their assessment of the competitors' reaction to their output choice.  This is parameterized using an approach reminiscent of conjectural variations.  On a second level firms adapt their conjectural variation by imitating the most successful firm.  Simulations suggest that in the long-run the Walrasian, Cournot-Nash and cartel equilibria survive.  The theory of nearly-complete decomposability is used to show that the Walrasian equilibrium is approximately the only stochastically stable state.

Asymmetric Type-Ia supernova origin of W49B as revealed from spatially resolved X-ray spectroscopic study

The origin of the asymmetric supernova remnant (SNR) W49B has been a matter of debate: is it produced by a rare jet-driven core-collapse supernova, or by a normal supernova that is strongly shaped by its dense environment? Aiming to uncover the explosion mechanism and origin of the asymmetric, centrally filled X-ray morphology of W49B, we have performed spatially resolved X-ray spectroscopy and a search for potential point sources. We report new candidate point sources inside W49B. The Chandra X-ray spectra from W49B are well-characterized by two-temperature gas components ($\sim 0.27$ keV + 0.6--2.2 keV). The hot component gas shows a large temperature gradient from the northeast to the southwest and is over-ionized in most regions with recombination timescales of 1--$10\times 10^{11}$ cm$^{-3}$ s. The Fe element shows strong lateral distribution in the SNR east, while the distribution of Si, S, Ar, Ca is relatively smooth and nearly axially symmetric. Asymmetric Type-Ia explosion of a Chandrasekhar-mass white dwarf well-explains the abundance ratios and metal distribution of W49B, whereas a jet-driven explosion and normal core-collapse models fail to describe the abundance ratios and large masses of iron-group elements. A model based on a multi-spot ignition of the white dwarf can explain the observed high $M_{\rm Mn}/M_{\rm Cr}$ value (0.8--2.2). The bar-like morphology is mainly due to a density enhancement in the center, given the good spatial correlation between gas density and X-ray brightness. The recombination ages and the Sedov age consistently suggest a revised SNR age of 5--6 kyr. This study suggests that despite the presence of candidate point sources projected within the boundary of this SNR, W49B is likely a Type-Ia SNR, which suggests that Type-Ia supernovae can also result in mixed-morphology SNRs.Comment: 15 pages, 10 figures, 2 tables; accepted for publication in A&