Mathematics
Scientific paper
Oct 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986ap%26ss.126..313n&link_type=abstract
Astrophysics and Space Science (ISSN 0004-640X), vol. 126, no. 2, Oct. 1986, p. 313-327.
Mathematics
1
Coefficients, Particle Energy, Relativistic Particles, Spherical Harmonics, Transformations (Mathematics), Compton Effect, Relativistic Velocity
Scientific paper
A general frame transformation on spherical-harmonic coefficients of differential particle intensity has been derived to terms of second order. The transformation is valid for relativistic particles as well, and it demonstrates explicitly how each transformed harmonic depends on a subset of the original harmonic coefficients. The differential mean intensity and streaming in a spacecraft frame are expressed in terms of the quantities in the comoving frame. A general expression for the first-order Compton Getting vector anisotropy, which is characteristically not aligned with the transformation velocity, is also derived. The new transformation is shown to simplify a current emthod for determining the directional intensity in a comoving frame.
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