Opacities and Atomic Diffusion
Abstract
:1. Introduction
2. Stellar Opacities
2.1. Definitions
2.2. Implementation in Stellar Evolution Codes
2.3. Asteroseismic Constraints on Opacities
3. Atomic Diffusion
3.1. Main Ingredients to Be Included in Evaluating This Physical Process
3.2. Radiative Acceleration
- −
- Atomic transition approach. This method consists of calculating explicitly the integral of Equation (6) over the transition probability profile for each atomic transition that is considered to make a significant contribution to the acceleration. Note that momentum acquired by bound–free transitions of ion i have to be attributed to . This method is most often used for atmospheres [45,46], and no more for interiors after large atomic or opacity data banks became available. With no surprise, this method is the most CPU time-consuming. However, it is, in principle, the most precise one as much as atomic data are accurate and complete.
- −
- Opacity sampling in stellar evolution. Here, the radiative acceleration is computed using Equation (7), the method was developed by Richer et al. (1998) [10] and was based on the OPAL database. One of the difficulties of this method is that calculation is performed on a fixed frequency grid, which is most often equally spaced in u, which needs to pay particular attention to the grid resolution. On another hand, this method applies to average atoms (with averaged ionization degree). Notice also that there is a limited number of elements in the databases (mostly elements lighter than Fe), generally elements contributing to the Rosseland average. This implies that studies needing to consider the atomic diffusion of these missing elements cannot be addressed.
- −
- Interpolation method. This method was proposed by M. Seaton in 1997 [47]. He was the initiator and the main architect of the Opacity Project (OP). The OP project first consists of computing ab initio numerically a large number of atomic transitions for many metals (presently lighter than iron). From these atomic data, the OP team computes tables of opacities (Rosseland average, monochromatic opacities of each element), and the numerical codes allowing interpolation from these tables for any chemical composition and position inside the stars. Since all the necessary data for radiative accelerations are already in the OP database, M. Seaton understood the potential importance of also providing radiative accelerations. He therefore added the codes to compute them with interpolations (as performed for opacities) in a specific table of a function built from Equation (7). This method is accurate and fast compared to the previous ones since all the necessary tables are already computed by the OP team. The method is easy to implement in existing codes. The limit of this method, as previously, is imposed by the list of elements in the database.
- −
- Semi-analytic or parametric approximation. The SVP (Single-Valued Parameters) method gives radiative accelerations in stellar interiors without having to explicitly handle large amounts of atomic data or opacity tables. A preliminary version was first proposed by G. Alecian (1985) [48]. In developing Equation (6), one obtains an expression where the atomic data and the concentration of the considered element are mixed, with a non-linear dependence on the concentration. In the SVP approximation, radiative acceleration has an analytic expression where atomic data and concentration are separated. Finally, the part depending on atomic data (which does not change when the concentration changes) may be obtained through pre-calculated small tables with only six parameters per ion [49,50,51]. This method is the less accurate one; however, it allows very fast computation ( time faster the Seaton’s interpolation) and was checked to be accurate enough for modeling stellar evolution [52]. The numerical code and the small table of parameters are provided online [51] presently for 16 elements (more elements should be added in a near future), but when needed for other elements they may be calculated by the user following [49], provided that atomic data are available.
3.3. Atomic Diffusion and Magnetic Fields
3.4. Competition with Macroscopic Motions
- −
- Meridional Circulation. This process is directly linked to star rotation. It is a large-scale motion that transports matter between the pole and the equator and may go deep inside the star. It is stronger as rotation is faster, and according to the efficiency of the kinetic momentum extraction, this could be why chemically peculiar stars are slow rotators. In slow-rotating stars (with types A V or B V), it is believed that meridional circulation is too weak to prevent the gravitational settling of He; Therefore, this diffusion produces the under-abundance of the element. The consequence is that the superficial He convection zone may disappear, and then external layers become stable enough for diffusion.
- −
- Turbulence. This is of course the most trivial mixing process since it involves small scales and advective motions. E. Schatzman (1969) [53] proposed to model its effect as a diffusive term. Therefore, he introduced the turbulent diffusion coefficient that leads to modify Equation (5) by writing the pure diffusive term as instead of . is assumed to be the same for all elements. In the case of perfect mixing, it should be infinite, and zero in a perfectly stable medium. Actually, this coefficient is difficult to estimate. Generally, it is parametrized in the modeling to ensure a soft transition between a mixing and a stable zone, see for instance [54].
- −
- Convection. Convection is a very common process in stars and has an important role in models, including atomic diffusion. One may say that it is at the basis of our definition of what we call normal stars. In the absence of convection, possibly all slowly rotating stars would have been more or less like chemically peculiar stars, i.e., with a large variety of superficial chemical compositions. If one limits ourselves to the usual convection determined by the Schwarzschild criterion, models including diffusion are strongly constrained by the precise positions of convection zones (CZ). Inside a CZ, the matter is assumed well-mixed (homogeneous abundances); however, its chemical composition is affected by how abundances are stratified by diffusion in the radiative zone just below. This chemical composition is supposed to reflect (with some dilution depending on the mass of the CZ) the composition of the last stable layers before it. Therefore, the parametrization of is crucial since it determines the real position of the bottom of the mixing zone. In ApBp stars, the superficial CZ is assumed non-existent or very small. Therefore, diffusion is extremely efficient directly in the atmosphere, hence producing spectacular abundance anomalies.
- −
- Mass loss. This is not a mixing process, but its effect on abundance anomalies may be comparable. In models including atomic diffusion, mass loss is a global outflow of matter. Assuming that it is permanent, stationary, and the star spherical, without magnetic fields, it is modeled as a constant flux of matter (a wind) determined by a unique parameter: the rate of mass loss. At a given radius r with matter density inside a star of mass , it is easy with the assumptions to determine the velocity of the flow to be . It appears that this velocity may be comparable, at certain depths, to that of diffusion in A- and B-type main sequence stars. If the rate of mass loss is too great (e.g., greater than about solar mass per year), the mass loss flux brings in new material from deeper parts of the star faster than diffusion can change the local composition, thus preventing abundance stratification. In particular, it is believed that the CP stars phenomenon does not extend to stars hotter than about because of their strong mass loss. Several studies show that the CP star phenomenon is better reproduced by models if atomic diffusion is combined with mass loss rates around – solar mass per year see for instance [55,56].
4. Stratification of Abundances across the Star
Horizontal-Branch, and More Evolved Stars
5. The Opacity as Vector of Coupling between Transport Processes
6. Radiatively Driven Winds
7. Discussion and Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
1 | A group of main-sequence magnetic and chemically peculiar stars (CP stars) of type A. |
2 | Slowly Pulsating B-type stars. |
3 | Groups of main-sequence CP stars of types A and late B, showing the strongest abundance anomalies in their atmospheres. In these stars, some elements are underabundant, but most heavy metals are overabundant by several orders of magnitude with respect to solar abundances: for instance Fe may be time overabundant, Hg up to time! |
4 | Group of main-sequence CP stars of type A, with milder abundance anomalies than the groups previously mentioned. |
5 | Electric field is due to the relative diffusion of protons and electrons due to the gradient of the total pressure, it was introduced by [44]. |
6 | We are speaking about local line profile (not the observed one), i.e., the absorption profile of the net radiation flux at radius r (even in optically thick depth), and at the absorption frequency. Below atmosphere, due to an increase in the collisional broadening of transition probability profile, saturation of lines decreases, and Zeeman splitting has much less effect on radiative acceleration. |
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Type of Table | Group | Status | Ref. |
---|---|---|---|
Rosseland mean | OP | Public 1 | [2] |
- | OPAL | Public 2 | [3] |
- | OPAS | Public 3 | [4,5] |
- | OPLIB | Public 4 | [6] |
- | SCO-RCG | In progress | [7] |
low T | Whichita | Public 5 | [8] |
- | ÆSOPUS | Public 6 | [9] |
Monochromatic cross-sections | OP | Public 1 | [2] |
- | OPAL | Not public | [3,10] |
- | SCO-RCG | In progress | [7,11] |
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Alecian, G.; Deal, M. Opacities and Atomic Diffusion. Galaxies 2023, 11, 62. https://doi.org/10.3390/galaxies11030062
Alecian G, Deal M. Opacities and Atomic Diffusion. Galaxies. 2023; 11(3):62. https://doi.org/10.3390/galaxies11030062
Chicago/Turabian StyleAlecian, Georges, and Morgan Deal. 2023. "Opacities and Atomic Diffusion" Galaxies 11, no. 3: 62. https://doi.org/10.3390/galaxies11030062