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Calculate the terminal velocity 0 attained by such a cloud under radiation and gravitational forces alone, if it starts from rest a distance R from the object. Show that C. A minimum value for K may be estimated for pure hydrogen as that due to Thomson scattering off free electrons, when the hydrogen is completely ionized. 65 X cm'. The mass scattering coefficient is therefore >a,/rn,, where mH = mass of hydrogen atom. 25x 103'erg s-' (M/M,), where M, 3mass of sun = 2 x 1033g. This is called the Eddington limit.
1 19b) This equation is also sometimes called the radiative diffusion equation. Given the temperature structure of the medium, that is, B ( r ) , one can solve this equation for J and thus also determine S from Eq. 95). Then the ) be problem is essentially solved, because the full intensity field 1 ( ~ , pcan found by formal solution of Eq. 1 16). 44 Fundimmtah of Radiatiw T m f e r An interesting form of Eq. 1 19b) can be derived in the case when z does not depend on depth. Let us define the new optical depth scale [cf.
55) is positive. At any frequency the effect of increasing temperature is to increase B,(T). Also note B,+O as T-0 and B,+m as T-00. d-Wien Displacement Law. 88 X 10" Hz deg-l. 56b) Thus the peak frequency of the blackbody law shifts linearly with temperature; this is known as the Wien displacement law. 290 cm deg. 57) This is also known as the Wien displacement law. 57) are very reasonable. By dimensional analysis, one could have argued that the blackbody radiation spectrum should peak at energy -kT, since k T is the only quantity with dimensions of energy one can form from k, T,h,c.