Volume 549, January 2013
|Number of page(s)||1|
|Section||Numerical methods and codes|
|Published online||12 December 2012|
Time-dependent radiative transfer with PHOENIX (Corrigendum)
1 Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany
2 Departamento de Astronomía, Universidad de Guanajuato, Apartado Postal 144, 36000 Guanajuato, Mexico
3 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, 440 W Brooks, Rm 100, Norman, OK 73019-2061 USA
Key words: supernovae: general / radiative transfer / methods: numerical / errata, addenda
The equation of radiative transfer is given by: where λ∞/λ = γ(1 + βμ) is the Doppler factor (Baron et al. 2012). In the original work the transformation of the time-dependent term from frequency space to wavelength space was neglected. Thus, our discussion of Eqs. (24)–(27) should read:
For an implementation of the time dependence in the radiative transfer itself, the spherical symmetric special relativistic radiative transfer equation (SSRTE) for expanding atmospheres (Hauschildt & Baron 1999) is extended so that the additional time-dependent term is given by (24)where is the velocity in units of the speed of light c and γ = (1 − β2) − 1/2 is the usual Lorentz factor. Here, I is the intensity, μ the cosine of the angle between the radial direction and the propagation vector of the light. Using the notation of Hauschildt & Baron (2004), the comoving frame SSRTE with the additional time-dependent term is given by (25)where η is the emissivity and χ the extinction coefficient. The wavelength is represented by λ. The additional time-dependent coefficient is given by (26)Along the characteristics the equation has the form (27)where ds is a line element along a (curved) characteristic and Il() is the specific intensity along the characteristic at point s ≥ 0 (s = 0 denotes the beginning of the characteristic). For a definition of the other coefficients see Hauschildt & Baron (2004).
For the tests presented in this paper, the error is small, since the velocities considered were less than 10% of the speed of light, but it will affect the results at the 10% level. We have tested that the correction does not materially alter our conclusions.
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© ESO, 2012
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