Extremely flat and inverted radio spectra as observed in galactic nuclei and BL Lac sources are still a challenge for fast particle acceleration models. Continuous acceleration by electric fields in reconnection regions can result in almost constant particle distributions and thereby in inverted synchrotron spectra independent from the details of the injected spectrum. These spectra are calculated from a spatially averaged diffusion transport equation in momentum space that includes systematic momentum gains and losses as well as finite particle escape lifetimes.

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We develop a model for the infrared, optical, and soft X-ray emission of the Crab pulsar in terms of anisotropic synchrotron emission by relativistic particles in an outer gap scenario with a single energy distribution N(c) P c~2. It is shown that such a distribution is naturally produced in an efficient pair cascade and that the energy of the primary particles is limited by synchrotron radiation to c D 107. It is further shown that this synchrotron model is able to reproduce the spectral shape between the infrared and soft X-rays and also the corresponding luminosities. In particular, the long-standing problem of the rapid spectral decline toward infrared frequencies is understandable as emission at very small pitch angles from low-energy particles with c D 102. Finally, we show that the scaling of our synchrotron model explains the observed correlation between the X-ray luminosity and the spin-down luminosity of the neutron star found by Becker & L X D 10~3L sdTrumper.

We discuss the origin of the observed strong poloidal fields Bz in the central regions of galaxies which have gaseous rings. In the context of galactic disk dynamo models only weak poloidal fields but strong toroidal fields result (Bϕ > Bz). Therefore we tie the strength of the poloidal fields to the central activity and apply known and tested ideas rigorously. A battery process on galactic scales is discussed which ensures the existence of a large scale magnetic field in the inner galactic region. The frozen-in field may be amplified by compression and turbulent stretching; the resulting field is poloidal. The central activity provides a nonaxisymmetric flow field which, just as the α – ω dynamo produces mostly Bϕ > Bz, can produce Bz ≥ Bϕ. This model explains the structure and strength of the magnetic field in star-burst galaxies like M82 (Lesch et al., 1989).

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