Herschel and Spitzer observations of slowly rotating, nearby isolated neutron stars

Supernova fallback disks around neutron stars have been discussed to influence the evolution of the diverse neutron star populations. Slowly rotating neutron stars are most promising to find such disks. Searching for the cold and warm debris of old fallback disks, we carried out Herschel PACS (70 $\mu$m, 160 $\mu$m) and Spitzer IRAC (3.6 $\mu$m, 4.5 $\mu$m) observations of eight slowly rotating ($P\approx 3 - 11$ s) nearby ($<1$ kpc) isolated neutron stars. Herschel detected 160 $\mu$m emission ($>5\sigma$) at locations consistent with the positions of the neutron stars RX J0806.4-4123 and RX J2143.0+0654. No other significant infrared emission was detected from the eight neutron stars. We estimate probabilities of 63%, 33% and 3% that, respectively, none, one, or both Herschel PACS 160 $\mu$m detections are unrelated excess sources due to background source confusion or an interstellar cirrus. If the 160 $\mu$m emission is indeed related to cold (10 K to 22 K) dust around the neutron stars, this dust is absorbing and re-emitting $\sim 10$% to $\sim 20$% of the neutron stars' X-rays. Such high efficiencies would be at least three orders of magnitude larger than the efficiencies of debris disks around nondegenerate stars. While thin dusty disks around the neutron stars can be excluded as counterparts of the 160 $\mu$m emission, dusty asteroid belts constitute a viable option.Comment: 22 pages, 26 Figures, 5 tables; accepted for publication in ApJ

Generalized hydrodynamic reductions of the kinetic equation for a soliton gas

We derive generalized multiflow hydrodynamic reductions of the nonlocal kinetic equation for a soliton gas and investigate their structure. These reductions not only provide further insight into the properties of the new kinetic equation but also could prove to be representatives of a novel class of integrable systems of hydrodynamic type beyond the conventional semi-Hamiltonian framework

Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity

We examine the completeness of bi-orthogonal sets of eigenfunctions for non-Hermitian Hamiltonians possessing a spectral singularity. The correct resolutions of identity are constructed for delta like and smooth potentials. Their form and the contribution of a spectral singularity depend on the class of functions employed for physical states. With this specification there is no obstruction to completeness originating from a spectral singularity.Comment: 25 pages, more refs adde