Abstract
Radiative accelerations are one of the most important drivers of diffusion in stars. They are first introduced in this chapter using a simple physical interpretation of the interaction between outflowing photons and the various atomic species present, leading to a first evaluation. The reader is then led through the various degrees of approximations, progressing from the contribution of individual lines of one atomic state to the total radiative acceleration of an atomic species. This in particular involves giving proper weight to contributions from various ionization states as well as an evaluation of the detailed sharing of photon momentum between atom and electron during ionization. Applications to stellar evolution calculations are shown and references to approximate expressions are given to allow easier calculations.
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Notes
- 1.
In this chapter, the word ion designates charged atoms as well as the neutral state of atoms.
- 2.
No magnetic field is considered in this chapter.
- 3.
In this chapter, A i designates ion i of atomic species A. In other chapters A i designates atomic species i.
- 4.
Radiative acceleration must not be confused with radiation pressure: the radiative acceleration of a given ion is a vector proportional to the gradient of a partial radiation pressure; the sum of properly weighted radiative accelerations over all ions and electrons is equal to the gradient of the usual radiation pressure (see for instance Eqs. (2)–(6) of Watson 1971).
- 5.
They are assumed to lead to an external force.
- 6.
In this chapter many expressions representing radiative accelerations are defined without the rad subscript to alleviate writing.
- 7.
Following Seaton (1997), one may argue that the f ion should not be applied to autoionization resonances which often dominate photoionization in non-hydrogenic cases.
- 8.
Notice that the neutral state (i = 0) cannot have any momentum from b-f interactions (g bf, 0 = 0), except if ions with negative charge are considered. They are usually neglected.
- 9.
In stellar physics, the region between the atmosphere and the core is usually called envelope. In other astrophysical contexts, this same expression can also designate circumstellar regions or atmospheric extensions.
- 10.
As discussed by Alecian (1994).
- 11.
Note that this definition is the reverse of the one of Gonzalez et al. (1995).
- 12.
As is the case for Proffitt et al. (1999).
- 13.
Adopted by Gonzalez et al. (1995).
- 14.
Giving the diffusion velocity (\(v_{D_{i}}\)) of ions individually.
- 15.
Since, in stellar evolution calculations using these data banks, the chemical composition changes continuously mainly because of atomic diffusion, interpolation must be carried out in (T,N e ) space rather than in (T, ρ) or (T, R) space. See § 2.2 of Turcotte et al. (1998b).
- 16.
Discussed in detail by LeBlanc et al. (2000).
- 17.
The dashed lines give the correction factors calculated assuming that the momentum from absorption lines ending with a value of n equal to that of the fundamental plus 1 is spent in that state of ionization. The full line was calculated assuming that only the momentum from lines ending with a value of n equal to that of the fundamental is spent in that state of ionization.
- 18.
See the discussion in Richer et al. (1998).
- 19.
- 20.
The method has been improved by Alecian and Artru (1990), and applied to isoelectronic sequences.
- 21.
They called this approximation SVP which stands for Single Valued Parameter.
- 22.
http://gradsvp.obspm.fr. In these tables parameters \(\alpha _{A_{i}}\), \(a_{A_{i}}\) and \(\beta _{A_{i}}\) are adjusted by means of comparisons with the results of Seaton’s interpolation method. The same adjustments have been used for Parametric curves in Fig. 3.3, this is why they are closer to the Interpolation curves than to the others.
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Michaud, G., Alecian, G., Richer, J. (2015). Radiative Accelerations. In: Atomic Diffusion in Stars. Astronomy and Astrophysics Library. Springer, Cham. https://doi.org/10.1007/978-3-319-19854-5_3
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