|
| 1 | +Overview of colors module |
| 2 | +========================= |
| 3 | + |
| 4 | +XXX TODO XXX |
| 5 | + |
| 6 | +The opacity values returned by the ``kap`` module combine opacity |
| 7 | +data from many sources. The most important opacity-related MESA |
| 8 | +options select which opacity sources to use and control the location |
| 9 | +of the blends between them. The total opacity is the appropriately |
| 10 | +combined radiative opacity :math:`\kappa_{\rm rad}` and the conductive |
| 11 | +opacity :math:`\kappa_{\rm cond}`: |
| 12 | + |
| 13 | +.. math:: |
| 14 | +
|
| 15 | + \frac{1}{\kappa} = \frac{1}{\kappa_{\rm rad}} + \frac{1}{\kappa_{\rm cond}} ~. |
| 16 | +
|
| 17 | +
|
| 18 | +Radiative Opacities |
| 19 | +------------------- |
| 20 | + |
| 21 | +The radiative opacity is the Rosseland mean opacity. The opacity |
| 22 | +depends on the temperature, density, and composition. A set of |
| 23 | +opacity tables consists of a collection of individual opacity tables, |
| 24 | +each at a different composition. Each individual table is |
| 25 | +tabulated in :math:`\log T` and in :math:`\log R \equiv \log \rho - 3 |
| 26 | +\log T + 18` (cgs). |
| 27 | + |
| 28 | +For tables that assume a fixed metal distribution, the composition can |
| 29 | +be encoded via the variables :math:`(X, Z)`. Tables assume a |
| 30 | +particular metal abundance pattern (usually scaled solar). Some opacity |
| 31 | +table sets include additional parameters in order to allow the metal |
| 32 | +abundance pattern (often the CNO abundances) to vary. Such |
| 33 | +variation naturally occurs in the stellar core during helium burning |
| 34 | +(and beyond) and in the stellar envelope as a result of dredge-up |
| 35 | +processes. |
| 36 | + |
| 37 | + |
| 38 | +.. note:: |
| 39 | + |
| 40 | + The value of the option :ref:`kap/defaults:Zbase` provides the reference |
| 41 | + metallicity necessary to calculate element variations (e.g., carbon |
| 42 | + and oxygen enhancement) from the composition of a cell. The |
| 43 | + default opacity configuration requires this value to be specified. |
| 44 | + Physically, this usually corresponds to the initial metallicity of |
| 45 | + the star. |
| 46 | + |
| 47 | + |
| 48 | +In MESA, separate opacity table sets are used for high and low |
| 49 | +temperature. In the intermediate region, both opacities are evaluated |
| 50 | +and blended. The location of this blend is controlled with the |
| 51 | +options :ref:`kap/defaults:kap_blend_logT_upper_bdy` and |
| 52 | +:ref:`kap/defaults:kap_blend_logT_lower_bdy`. |
| 53 | + |
| 54 | + |
| 55 | + |
| 56 | +------------------------------------------------ |
| 57 | +High temperature :math:`(T \gtrsim 10^4\,\rm K)` |
| 58 | +------------------------------------------------ |
| 59 | + |
| 60 | +The OPAL tables (|OPAL|) with fixed metal distributions are called |
| 61 | +Type 1 and cover the region :math:`0.0 \leq X \leq 1-Z` and |
| 62 | +:math:`0.0\leq Z \leq 0.1`. The Opacity Project |
| 63 | +(OP; |OP|) are also available. Type 1 tables from The Los Alamos |
| 64 | +OPLIB database (OPLIB; |OPLIB|) are also available, and cover the |
| 65 | +region :math:`0.0 \leq X \leq 1-Z` and |
| 66 | +:math:`0.0\leq Z \leq 0.2`. The set of tables to be used are |
| 67 | +selected by the option :ref:`kap/defaults:kap_file_prefix`. |
| 68 | + |
| 69 | +A direct comparison between the Type 1 format of OPAL/OP tables and |
| 70 | +the OPLIB tables are shown in the figure below |
| 71 | +taken from Figure 1 in `Farag et al. 2024 <https://doi.org/10.3847/1538-4357/ad4355>`_. Further comparisons |
| 72 | +between OP/OPAL/OPLIB can be found in `Farag et al. 2024 <https://doi.org/10.3847/1538-4357/ad4355>`_. |
| 73 | + |
| 74 | + |
| 75 | +.. figure:: type1_format.png |
| 76 | + :alt: kap blends in solar-like compositions |
| 77 | + |
| 78 | + Location of each Type-1 opacity table in the :math:`X–Z` plane (left panel) and the |
| 79 | + log:math:`T`–log:math:`R` plane (right panel). Orange circles mark the location of |
| 80 | + the 126 OPAL Type-1 tables (Rogers & Iglesias 1992). Blue circles |
| 81 | + mark the location of the new 1194 Type-1 opacity tables (Farag et al. 2024). |
| 82 | + |
| 83 | +Additionally, there is support for the OPAL Type 2 tables that allow |
| 84 | +for varying amounts of C and O beyond that accounted for by :math:`Z`; |
| 85 | +these are needed during helium burning and beyond. These have a range |
| 86 | +:math:`0.0 \leq X \leq 0.7`, :math:`0.0\leq Z\leq0.1`. The set of |
| 87 | +tables to be used are selected by the option :ref:`kap/defaults:kap_CO_prefix`. |
| 88 | + |
| 89 | +Type 2 tables on by default (see :ref:`kap/defaults:use_Type2_opacities`) and The |
| 90 | +blends between these table sets occur based on hydrogen fraction |
| 91 | +(see :ref:`kap/defaults:kap_Type2_full_off_X` and :ref:`kap/defaults:kap_Type2_full_on_X` and ) |
| 92 | +and metal enhancement (controlled by :ref:`kap/defaults:kap_Type2_full_off_dZ` and |
| 93 | +:ref:`kap/defaults:kap_Type2_full_on_dZ`). |
| 94 | + |
| 95 | + |
| 96 | +------------------------------------------------- |
| 97 | +Low temperature :math:`(T \lesssim 10^4\,\rm K)` |
| 98 | +------------------------------------------------- |
| 99 | + |
| 100 | +Low temperature opacities are selected with the option |
| 101 | +:ref:`kap/defaults:kap_lowT_prefix`. |
| 102 | + |
| 103 | +Tables based on the work of |Fergusson| include the effects of |
| 104 | +molecules and grains and cover the range |
| 105 | +:math:`2.7 \le \log T \le 4.5` and :math:`-8 \le \log R \le 1`. |
| 106 | + |
| 107 | +Tables based on the work of |Freedman| include the effects of |
| 108 | +molecules and cover the range :math:`1.88 \le \log T \le 4.5` and |
| 109 | +:math:`-8 \le \log R \le 9`. The table set was privately communicated |
| 110 | +by R. S. Freedman in 2011. Unlike other opacity sources, this is a 1D |
| 111 | +sequence of tables in :math:`Z` as opposed to a 2D grid of |
| 112 | +:math:`(X,Z)` values. (The assumed H/He abundances scale with |
| 113 | +:math:`Z`.) |
| 114 | + |
| 115 | + |
| 116 | +Tables from ÆSOPUS (|AESOPUS|) include variation factors for the CNO |
| 117 | +isotopes. The opacity is evaluated using the global value of |
| 118 | +:math:`Z_{\rm base}` and the local (cell) values of :math:`(X, X_{\rm |
| 119 | +C}, X_{\rm N}, X_{\rm O})`. |
| 120 | + |
| 121 | +The ÆSOPUS tables are provided at a set of reference metalicites. In |
| 122 | +order to interpolate to the provided :math:`Z_{\rm base}`, the opacity |
| 123 | +is evaluated at an appropriate subset of these reference values (and |
| 124 | +then interpolated). For each such :math:`Z_{\rm ref}`, the ÆSOPUS |
| 125 | +composition parameters |
| 126 | + |
| 127 | +.. math:: |
| 128 | +
|
| 129 | + \begin{eqnarray*} |
| 130 | + f_{\rm CO} = \log(X_{\rm C}/X_{\rm O}) - f_{\rm CO, ref} \\ |
| 131 | + f_{\rm C} = \log(X_{\rm C}/Z_{\rm ref}) - f_{\rm C, ref} \\ |
| 132 | + f_{\rm N} = \log(X_{\rm N}/Z_{\rm ref}) - f_{\rm N, ref} \\ |
| 133 | + \end{eqnarray*} |
| 134 | +
|
| 135 | +are calculated, the opacities evaluated the tables with bracketing |
| 136 | +compositions, and the resulting opacities linearly interpolated. |
| 137 | +(Note that this means that the interpolation in :math:`Z` occurs at |
| 138 | +fixed :math:`X` and :math:`f_{\rm CO}`, but not at fixed :math:`f_{\rm |
| 139 | +C}` or :math:`f_{\rm N}`.) |
| 140 | + |
| 141 | +------------------ |
| 142 | +Compton Scattering |
| 143 | +------------------ |
| 144 | + |
| 145 | +At sufficiently high temperature :math:`(T \gtrsim 10^8\,\rm K)`, the |
| 146 | +opacity will be dominated by Compton scattering. MESA calculates the |
| 147 | +opacity of Compton scattering using the prescription of |P17|. Near the |
| 148 | +high-:math:`T` and low-:math:`R` edges of the high temperature opacity |
| 149 | +tables, MESA smoothly blends the tabulated opacity values with the |
| 150 | +Compton scattering values. The location of these blends is not |
| 151 | +user-controllable. |
| 152 | + |
| 153 | +Conductive Opacities |
| 154 | +-------------------- |
| 155 | + |
| 156 | +The conductive opacity :math:`(\kappa_{\rm cond})` is given by the |
| 157 | +thermal conductivity :math:`(K)` appropriately recast such that the heat |
| 158 | +transfer equation resembles the form of the equation used in radiative |
| 159 | +diffusion (e.g., HKT Section 4.5). This implies |
| 160 | + |
| 161 | +.. math:: |
| 162 | +
|
| 163 | + \kappa_{\rm cond} = \frac{16 \sigma_{\rm SB} T^3}{\rho K} ~. |
| 164 | +
|
| 165 | +The thermal conductivities used in MESA are an extended version of the |
| 166 | +results of |Cassisi| privately communicated by A.Y. Potekhin. They |
| 167 | +are tabulated for a set of :math:`1 \le \bar{Z} \le 60`. Each table |
| 168 | +spans :math:`-6 \le \log(\rho/\rm g\,cm^{-3}) \le 11.50` and :math:`3 |
| 169 | +\le \log(T/\rm K) \le 10`. |
| 170 | + |
| 171 | +For H and He in the regime of moderate coupling and moderate |
| 172 | +degeneracy, the additional correction formulae of |B20| are applied. |
| 173 | + |
| 174 | +.. |P17| replace:: `Poutanen (2017) <https://ui.adsabs.harvard.edu/abs/2017ApJ...835..119P/abstract>`__ |
| 175 | + |
| 176 | +.. |B20| replace:: `Blouin et al. (2020) <https://ui.adsabs.harvard.edu/abs/2020ApJ...899...46B/abstract>`__ |
| 177 | + |
| 178 | +.. |Fergusson| replace:: `Ferguson et al. (2005) <https://ui.adsabs.harvard.edu/abs/2005ApJ...623..585F/abstract>`__ |
| 179 | + |
| 180 | +.. |Freedman| replace:: `Freedman et al. (2008) <https://ui.adsabs.harvard.edu/abs/2008ApJS..174..504F/abstract>`__ |
| 181 | + |
| 182 | +.. |AESOPUS| replace:: `Marigo & Aringer 2009 <https://ui.adsabs.harvard.edu/abs/2009A%26A...508.1539M/abstract>`__ |
| 183 | + |
| 184 | +.. |OPAL| replace:: Iglesias & Rogers `1993 <https://ui.adsabs.harvard.edu/abs/1993ApJ...412..752I/abstract>`__, `1996 <https://ui.adsabs.harvard.edu/abs/1996ApJ...464..943I/abstract>`__ |
| 185 | + |
| 186 | +.. |OP| replace:: `Seaton 2005 <https://ui.adsabs.harvard.edu/abs/2005MNRAS.362L...1S/abstract>`__ |
| 187 | + |
| 188 | +.. |OPLIB| replace:: `Colgan 2016 <https://ui.adsabs.harvard.edu/abs/2016ApJ...817..116C/abstract>`__ |
| 189 | + |
| 190 | +.. |Cassisi| replace:: `Cassisi et al. (2007) <https://ui.adsabs.harvard.edu/abs/2007ApJ...661.1094C/abstract>`__ |
| 191 | + |
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