By Kenneth R. Lang
This ebook is intended to be a reference resource for the basic formulae of astrophysics. anyplace attainable, the unique resource of the fabric being awarded is referenced including references to more moderen transformations and functions.
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Additional info for Astrophysical Formulae: A Compendium for the Physicist and Astrophysicist
33. 13. Polarization of Plane Waves-The Stokes Parameters If the propagation direction of a harmonie plane wave is the z axis of a Cartesian co ordinate system, the components of the electric field vector are Ex al cos(wt-k' r+6 1 ) = Ev = a2 cos(wt-k' r+6 2 ) (1-66) Ez = 0, and where a l and a 2 are scalar amplitudes, w is the harmonie frequency, t is the time variable, k is the wave vector, r is the vector radius, and 6 1 and 62 are arbitrary phases. It follows directly from Eqs. (1-66) that Ex and Ey are related by (1-67) where 6 =6 2 -6 1 , Eq.
Are, respectively, the dielectric constant and the magnetic permeability. Eqs. (1-57) are wave equations for electromagnetic waves which propagate with the velocity (1-58) v=cj~. 10 Continuum Radiation Of special interest is the harmonie solution to Eq. (1-57) for whieh E = Eo exp [i(k· r -w t)] , (1-59) where t is the time variable and the harmonie frequeney, w, is related to the propagation or wave veetor, k, by 2rc w k=-s=-ns, A (1-60) C where ). is the wavelength, s is the direetion of wave propagation whieh is perpendieular to E, and n is the index of refraetion.
K. CONKLlN, and the other data are from KELLERMANN (1966), HJELLMING, and CHURCHWELL (1969), TERZIAN and PARRISH (1970), KELLERMANN, PAULlNY-TOTH, and WILLIAMS (1969), and KELLERMANN er al. = 2 or 3, and the total luminosity, L, of the source is given by +~y~~ Jvadv, V2 L=4nr 2 (1 v, (1-182) Synchrotron Radiation in a Plasma 39 where r=ez/H o is the metric distance to the source, Ho is the Hubble constant, z is the redshift, Sv, is the source flux density measured at some reference frequency, vr ' and v1 and v2 are the lower and upper cutotT frequencies beyond which the source radiation is negligible.