The jets of the Vela pulsar

Chandra observations of the Vela pulsar-wind nebula (PWN) have revealed a jet in the direction of the pulsar's proper motion, and a counter-jet in the opposite direction, embedded in diffuse nebular emission. The jet consists of a bright, 8''-long inner jet, between the pulsar and the outer arc, and a dim, curved outer jet that extends up to 100'' in approximately the same direction. From the analysis of thirteen Chandra observations spread over about 2.5 years we found that this outer jet shows particularly strong variability, changing its shape and brightness. We observed bright blobs in the outer jet moving away from the pulsar with apparent speeds (0.3-0.6)c and fading on time-scales of days to weeks. The spectrum of the outer jet fits a power-law model with a photon index of 1.3\pm0.1. The X-ray emission of the outer jet can be interpreted as synchrotron radiation of ultrarelativistic electrons/positrons. This interpretation allows one to estimate the magnetic field, ~100 microGauss, maximum energy of X-ray emitting electrons, ~2\times 10^{14} eV, and energy injection rate, ~8\times 10^{33} erg/s, for the outer jet. In the summed PWN image we see a dim, 2'-long outer counter-jet, which also shows a power-law spectrum with photon ined of 1.2-1.5. Southwest of the jet/counter-jet an extended region of diffuse emission is seen. Relativistic particles responsible for this radiation are apparently supplied by the outer jet.Comment: 4 pages, including 1 figure, accepted for publication in New Astronomy Reviews; proceedings of the conference "The Physics of Relativistic Jets in the CHANDRA and XMM Era", 23-27 September 2002, Bologna. The full resolution versions of the images shown in the fugure are avaliable at http://www.astro.psu.edu/users/green/vela_jet_proc/vela_jet_proc.htm

Differential Geometry of Hydrodynamic Vlasov Equations

We consider hydrodynamic chains in $(1+1)$ dimensions which are Hamiltonian with respect to the Kupershmidt-Manin Poisson bracket. These systems can be derived from single $(2+1)$ equations, here called hydrodynamic Vlasov equations, under the map $A^n =\int_{-\infty}^\infty p^n f dp.$ For these equations an analogue of the Dubrovin-Novikov Hamiltonian structure is constructed. The Vlasov formalism allows us to describe objects like the Haantjes tensor for such a chain in a much more compact and computable way. We prove that the necessary conditions found by Ferapontov and Marshall in (arXiv:nlin.SI/0505013) for the integrability of these hydrodynamic chains are also sufficient.Comment: 24 page

Shifts of finite type with nearly full entropy

For any fixed alphabet A, the maximum topological entropy of a Z^d subshift with alphabet A is obviously log |A|. We study the class of nearest neighbor Z^d shifts of finite type which have topological entropy very close to this maximum, and show that they have many useful properties. Specifically, we prove that for any d, there exists beta_d such that for any nearest neighbor Z^d shift of finite type X with alphabet A for which log |A| - h(X) < beta_d, X has a unique measure of maximal entropy. Our values of beta_d decay polynomially (like O(d^(-17))), and we prove that the sequence must decay at least polynomially (like d^(-0.25+o(1))). We also show some other desirable properties for such X, for instance that the topological entropy of X is computable and that the unique m.m.e. is isomorphic to a Bernoulli measure. Though there are other sufficient conditions in the literature which guarantee a unique measure of maximal entropy for Z^d shifts of finite type, this is (to our knowledge) the first such condition which makes no reference to the specific adjacency rules of individual letters of the alphabet.Comment: 33 pages, accepted by Proceedings of the London Mathematical Societ