Overview of kap module ====================== .. toctree:: :maxdepth: 1 :hidden: defaults interface The opacity values returned by the ``kap`` module combine opacity data from many sources. The most important opacity-related MESA options select which opacity sources to use and control the location of the blends between them. The total opacity is the appropriately combined radiative opacity :math:`\kappa_{\rm rad}` and the conductive opacity :math:`\kappa_{\rm cond}`: .. math:: \frac{1}{\kappa} = \frac{1}{\kappa_{\rm rad}} + \frac{1}{\kappa_{\rm cond}} ~. Radiative Opacities ------------------- The radiative opacity is the Rosseland mean opacity. The opacity depends on the temperature, density, and composition. A set of opacity tables consists of a collection of individual opacity tables, each at a different composition. Each individual table is tabulated in :math:`\log T` and in :math:`\log R \equiv \log \rho - 3 \log T + 18` (cgs). For tables that assume a fixed metal distribution, the composition can be encoded via the variables :math:`(X, Z)`. Tables assume a particular metal abundance pattern (usually scaled solar). Some opacity table sets include additional parameters in order to allow the metal abundance pattern (often the CNO abundances) to vary. Such variation naturally occurs in the stellar core during helium burning (and beyond) and in the stellar envelope as a result of dredge-up processes. .. note:: The value of the option :ref:`kap/defaults:Zbase` provides the reference metallicity necessary to calculate element variations (e.g., carbon and oxygen enhancement) from the composition of a cell. The default opacity configuration requires this value to be specified. Physically, this usually corresponds to the initial metallicity of the star. In MESA, separate opacity table sets are used for high and low temperature. In the intermediate region, both opacities are evaluated and blended. The location of this blend is controlled with the options :ref:`kap/defaults:kap_blend_logT_upper_bdy` and :ref:`kap/defaults:kap_blend_logT_lower_bdy`. ------------------------------------------------ High temperature :math:`(T \gtrsim 10^4\,\rm K)` ------------------------------------------------ The OPAL tables (|OPAL|) with fixed metal distributions are called Type 1 and cover the region :math:`0.0 \leq X \leq 1-Z` and :math:`0.0\leq Z \leq 0.1`. The Opacity Project (OP; |OP|) are also available. Type 1 tables from The Los Alamos OPLIB database (OPLIB; |OPLIB|) are also available, and cover the region :math:`0.0 \leq X \leq 1-Z` and :math:`0.0\leq Z \leq 0.2`. The set of tables to be used are selected by the option :ref:`kap/defaults:kap_file_prefix`. A direct comparison between the Type 1 format of OPAL/OP tables and the OPLIB tables are shown in the figure below taken from Figure 1 in `Farag et al. 2024 `_. Further comparisons between OP/OPAL/OPLIB can be found in `Farag et al. 2024 `_. .. figure:: type1_format.png :alt: kap blends in solar-like compositions Location of each Type-1 opacity table in the :math:`X–Z` plane (left panel) and the log :math:`T` – log :math:`R` plane (right panel). Orange circles mark the location of the 126 OPAL Type-1 tables (Rogers & Iglesias 1992). Blue circles mark the location of the new 1194 Type-1 opacity tables (Farag et al. 2024). Additionally, there is support for the OPAL Type 2 tables that allow for varying amounts of C and O beyond that accounted for by :math:`Z`; these are needed during helium burning and beyond. These have a range :math:`0.0 \leq X \leq 0.7`, :math:`0.0\leq Z\leq0.1`. The set of tables to be used are selected by the option :ref:`kap/defaults:kap_CO_prefix`. Type 2 tables on by default (see :ref:`kap/defaults:use_Type2_opacities`) and The blends between these table sets occur based on hydrogen fraction (see :ref:`kap/defaults:kap_Type2_full_off_X` and :ref:`kap/defaults:kap_Type2_full_on_X` and ) and metal enhancement (controlled by :ref:`kap/defaults:kap_Type2_full_off_dZ` and :ref:`kap/defaults:kap_Type2_full_on_dZ`). ------------------------------------------------- Low temperature :math:`(T \lesssim 10^4\,\rm K)` ------------------------------------------------- Low temperature opacities are selected with the option :ref:`kap/defaults:kap_lowT_prefix`. Tables based on the work of |Fergusson| include the effects of molecules and grains and cover the range :math:`2.7 \le \log T \le 4.5` and :math:`-8 \le \log R \le 1`. Tables based on the work of |Freedman| include the effects of molecules and cover the range :math:`1.88 \le \log T \le 4.5` and :math:`-8 \le \log R \le 9`. The table set was privately communicated by R. S. Freedman in 2011. Unlike other opacity sources, this is a 1D sequence of tables in :math:`Z` as opposed to a 2D grid of :math:`(X,Z)` values. (The assumed H/He abundances scale with :math:`Z`.) Tables from ÆSOPUS (|AESOPUS|) include variation factors for the CNO isotopes. The opacity is evaluated using the global value of :math:`Z_{\rm base}` and the local (cell) values of :math:`(X, X_{\rm C}, X_{\rm N}, X_{\rm O})`. The ÆSOPUS tables are provided at a set of reference metalicites. In order to interpolate to the provided :math:`Z_{\rm base}`, the opacity is evaluated at an appropriate subset of these reference values (and then interpolated). For each such :math:`Z_{\rm ref}`, the ÆSOPUS composition parameters .. math:: \begin{eqnarray*} f_{\rm CO} = \log(X_{\rm C}/X_{\rm O}) - f_{\rm CO, ref} \\ f_{\rm C} = \log(X_{\rm C}/Z_{\rm ref}) - f_{\rm C, ref} \\ f_{\rm N} = \log(X_{\rm N}/Z_{\rm ref}) - f_{\rm N, ref} \\ \end{eqnarray*} are calculated, the opacities evaluated the tables with bracketing compositions, and the resulting opacities linearly interpolated. (Note that this means that the interpolation in :math:`Z` occurs at fixed :math:`X` and :math:`f_{\rm CO}`, but not at fixed :math:`f_{\rm C}` or :math:`f_{\rm N}`.) ------------------ Compton Scattering ------------------ At sufficiently high temperature :math:`(T \gtrsim 10^8\,\rm K)`, the opacity will be dominated by Compton scattering. MESA calculates the opacity of Compton scattering using the prescription of |P17|. Near the high-:math:`T` and low-:math:`R` edges of the high temperature opacity tables, MESA smoothly blends the tabulated opacity values with the Compton scattering values. The location of these blends is not user-controllable. Conductive Opacities -------------------- The conductive opacity :math:`(\kappa_{\rm cond})` is given by the thermal conductivity :math:`(K)` appropriately recast such that the heat transfer equation resembles the form of the equation used in radiative diffusion (e.g., HKT Section 4.5). This implies .. math:: \kappa_{\rm cond} = \frac{16 \sigma_{\rm SB} T^3}{\rho K} ~. The thermal conductivities used in MESA are an extended version of the results of |Cassisi| privately communicated by A.Y. Potekhin. They are tabulated for a set of :math:`1 \le \bar{Z} \le 60`. Each table spans :math:`-6 \le \log(\rho/\rm g\,cm^{-3}) \le 11.50` and :math:`3 \le \log(T/\rm K) \le 10`. For H and He in the regime of moderate coupling and moderate degeneracy, the additional correction formulae of |B20| are applied. .. |P17| replace:: `Poutanen (2017) `__ .. |B20| replace:: `Blouin et al. (2020) `__ .. |Fergusson| replace:: `Ferguson et al. (2005) `__ .. |Freedman| replace:: `Freedman et al. (2008) `__ .. |AESOPUS| replace:: `Marigo & Aringer 2009 `__ .. |OPAL| replace:: Iglesias & Rogers `1993 `__, `1996 `__ .. |OP| replace:: `Seaton 2005 `__ .. |OPLIB| replace:: `Colgan 2016 `__ .. |Cassisi| replace:: `Cassisi et al. (2007) `__