We analyze Faraday rotation and depolarization of extragalactic radio point sources in the direction of the inner Galactic plane to determine the outer scale and amplitude of the rotation measure power spectrum. Structure functions of rotation measur
e show lower amplitudes than expected when extrapolating electron density fluctuations to large scales assuming a Kolmogorov spectral index. This implies an outer scale of those fluctuations on the order of a parsec, much smaller than commonly assumed. Analysis of partial depolarization of point sources independently indicates a small outer scale of a Kolmogorov power spectrum. In the Galaxys spiral arms, no rotation measure fluctuations on scales above a few parsecs are measured. In the interarm regions fluctuations on larger scales than in spiral arms are present, and show power law behavior with a shallow spectrum. These results suggest that in the spiral arms stellar sources such as stellar winds or protostellar outflows dominate the energy injection for the turbulent energy cascade on parsec scales, while in the interarm regions supernova and super bubble explosions are the main sources of energy on scales on the order of 100 parsecs.
Hard X-Ray bremsstrahlung continuum spectra, such as from solar flares, are commonly described in terms of power-law fits, either to the photon spectra themselves or to the electron spectra responsible for them. In applications various approximate re
lations between electron and photon spectral indices are often used for energies both above and below electron low-energy cutoffs. We examine the form of the exact relationships in various situations, and for various cross-sections, showing that empirical relations sometimes used can be highly misleading and consider how to improve fitting procedures. We obtain expressions for photon spectra from single, double and truncated power-law electron spectra for a variety of cross-sections and for the thin and thick target models and simple analytic expressions for the Bethe-Heitler cases. We show that above a low-energy cutoff the Kramers and Bethe-Heitler results match reasonably well with results for exact cross-sections up to energies around 100 keV; that below the low-energy cutoff, Kramers and other constant spectral index forms commonly used are very poor approximations to accurate results; but that our analytical forms are a very good match. Analytical forms of the Bethe-Heitler photon spectra from general power-law electron spectra are an excellent match to exact results for both thin and thick targets and they enable much faster spectral fitting than evaluation of the full spectral integrations.
