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Erratum
This article is an erratum for:
[https://doi.org/10.1051/0004-6361/200810982]


Issue
A&A
Volume 549, January 2013
Article Number C1
Number of page(s) 1
Section Numerical methods and codes
DOI https://doi.org/10.1051/0004-6361/200810982e
Published online 12 December 2012

4. Time-dependent radiative transfer

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.

References

  1. Baron, E., Hauschildt, P. H., Chen, B., & Knop, S. 2012, A&A, 548, A67 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  2. Hauschildt, P. H., & Baron, E. 1999, J. Comp. Appl. Math., 109, 41 [NASA ADS] [CrossRef] [Google Scholar]
  3. Hauschildt, P. H., & Baron, E. 2004, A&A, 417, 317 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]

© ESO, 2012

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