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# Solar models
These are models discussed in J. Christensen-Dalsgaard:
<a href='https://arxiv.org/abs/2007.06488'><i>Solar structure and evolution</i></a>
(see Tables 1 and 5 of the paper), to be published by
<i>Living Reviews in Solar Physics</i>.
The model names are linked to ASCII files of the model structure, in the
so-called GONG format.
The structure of the files is described in
<a href='file-format.pdf'><i>File format for the GONG solar model project</i></a>.
<table style="width:100%">
<thead align="left">
<tr style="left-align">
<th style="left-align">Model</th>
<th>Age</th>
<th>R</th>
<th>L</th>
<th>Opacity</th>
<th>Surface</th>
<th>Surface</th>
<th>Other changes </th>
</tr>
<tr>
<th></th>
<th>(Gyr)</th>
<th>(1.e10 cm)</th>
<th>(1.e33 erg/s)</th>
<th>tables</th>
<th>opacity</th>
<th>comp.</th>
<th>(see caption) </th>
</tr>
</thead>
<tr>
<td><a href='models/fgong_S_d_02c.txt?raw=true'>S</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>- </td>
</tr>
<tr>
<td><a href='models/fgong_Age_d_06c.txt?raw=true'>Age</a></td>
<td>4.57</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>- </td>
</tr>
<tr>
<td><a href='models/fgong_R_s_d_05c.txt?raw=true'>R_s</a></td>
<td>4.60</td>
<td>6.95508</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>- </td>
</tr>
<tr>
<td><a href='models/fgong_L_s_d_41c.txt?raw=true'>L_s</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.828</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>- </td>
</tr>
<tr>
<td><a href='models/fgong_Opc_7_0_d_15c.txt?raw=true'>Opc_7_0</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>EOS Liv05 </td>
</tr>
<tr>
<td><a href='models/fgong_Opc_6_5_d_16c.txt?raw=true'>Opc_6_5</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>Local delta log kappa </td>
</tr>
<tr>
<td><a href='models/fgong_OPAL96_d_07c.txt?raw=true'>OPAL96</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>Local delta log kappa </td>
</tr>
<tr>
<td><a href='models/fgong_OP05_d_36c.txt?raw=true'>OP05</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL96</td>
<td>Kur91</td>
<td>GN93</td>
<td>- </td>
</tr>
<tr>
<td><a href='models/fgong_GS98_d_37c.txt?raw=true'>GS98</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL96</td>
<td>Fer05</td>
<td>GN93</td>
<td>Surf. opac. </td>
</tr>
<tr>
<td><a href='models/fgong_Liv05_d_40c.txt?raw=true'>Liv05</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL96</td>
<td>Fer05</td>
<td>GS98</td>
<td>- </td>
</tr>
<tr>
<td><a href='models/fgong_Surf_opac_d_35c.txt?raw=true'>Surf_opac</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OP05</td>
<td>Fer05</td>
<td>GS98</td>
<td>- </td>
</tr>
<tr>
<td><a href='models/fgong_CM_d_24c.txt?raw=true'>CM</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>CM conv. </td>
</tr>
<tr>
<td><a href='models/fgong_Adelb11_d_34c.txt?raw=true'>Adelb11</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>EnGen. Adelberger </td>
</tr>
<tr>
<td><a href='models/fgong_NACRE_d_39c.txt?raw=true'>NACRE</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>EnGen. NACRE </td>
</tr>
<tr>
<td><a href='models/fgong_3He_eql_d_02c_eq.txt?raw=true'>3He_eql</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>3He nucl. eql. </td>
</tr>
<tr>
<td><a href='models/fgong_No_el_scrn_d_20c.txt?raw=true'>No_el_scrn</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>no electr. screen. </td>
</tr>
<tr>
<td><a href='models/fgong_Dc_d_17c.txt?raw=true'>Dc</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>Change diff. </td>
</tr>
<tr>
<td><a href='models/fgong_DVc_d_18c.txt?raw=true'>DVc</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>Change diff., settl. </td>
</tr>
<tr>
<td><a href='models/fgong_No_diff_03c.txt?raw=true'>No_diff</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL96</td>
<td>Alex94</td>
<td>GN93</td>
<td>No diffusion </td>
</tr>
<tr>
<td><a href='models/fgong_AGS05_d_21c.txt?raw=true'>AGS05</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL96</td>
<td>Fer05</td>
<td>AGS05 </td>
<td>- </td>
</tr>
<tr>
<td><a href='models/fgong_AGSS09_d_22c.txt?raw=true'>AGSS09</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL96</td>
<td>Fer05</td>
<td>AGSS09 </td>
<td>- </td>
</tr>
</table>
## Parameters of solar models.
- Age, R and L are for the model of the present Sun.
- `OPAL92`, `OPAL96` and `OP05` refer to the opacity tables by
<a href='https://doi.org/10.1086/191659'>Rogers and Iglesias (1992)</a>,
<a href='https://doi.org/10.1086/175539'>Iglesias and Rogers (1996)</a> and
<a href='https://doi.org/10.1111/j.1365-2966.2005.08991.x'>Badnell et al. (2005)</a>,
respectively, while `Kur91`, `Alex94` and `Fer05` indicate low-temperature opacities from
<a href='https://doi.org/10.1007/978-94-011-3554-2_42'>Kurucz (1991)</a>,
<a href='https://doi.org/10.1086/175039'>Alexander and Ferguson (1994)</a> and
<a href='https://doi.org/10.1086/428642'>Ferguson et al. (2005)</a>.
- The heavy-element abundance used in the opacities are `GN93`
(Grevesse and Noels 1993),
<a href='https://doi.org/10.1007/978-94-011-4820-7_15'>(Grevesse and Sauval 1998)</a>,
`AGS05` <a href='https://doi.org/10.1051/0004-6361:20041951'>(Asplund et al. 2005)</a> or
`AGSS09` <a href='https://doi.org/10.1146/annurev.astro.46.060407.145222'>(Asplund et al. 2009)</a>.
- The default equation of state is the
<a href='https://doi.org/10.1086/176705'>Rogers et al. (1996)</a>
implementation of the
OPAL formulation, while Model `Liv05` used the
<a href='https://doi.org/10.1086/341894'>Rogers and Nayfonov (2002)</a>
version.
- In Models `Opc_7_0` and `Opc_6_5` localized increases in opacity
were included, at respectively log T_kappa = 7.0 and 6.5.
- Model `CM` replaced the mixing-length treatment of convection
(Bohm-Vitense 1958) by an emulation of the
<a href='https://doi.org/10.1086/169815'>Canuto and Mazzitelli (1991)</a>
formulation.
- The default set of nuclear-reaction parameters is based on
<a href='https://doi.org/10.1103/revmodphys.67.781'>Bahcal and Pinsonneault (1995)</a>,
while Models `Adelb11` and `NACRE` used, respectively,
the set from
<a href='https://doi.org/10.1103/RevModPhys.83.195'>Adelberger et al. (2011)</a>
and the NACRE set
<a href='https://doi.org.10.1016/S0375-9474(99)00030-5'>(Angulo et al. 1999)</a>
with an updated 14N + 1H reaction
<a href='https://doi.org/10.1016/j.physletb.2004.03.092'>(Formicola et al. 2004)</a>.
- In Model `3He_eql` the 3He abundance was assumed to be always in nuclear equilibrium, while Model `No_el_scrn` neglected electron screening.
- In Model `Dc` the diffusion coefficient D_i was increased by a factor 1.2, while in Model `DVc`
both D_i and V_i were increased by this factor.
- Finally diffusion and settling were neglected in Model `No_diff`.<p><p>
<!--
Values or other aspects differing from Model~S are shown as {\bf bold}.
-->
For convenience, all models have been collected in
<a href=fgong_combined.zip>a zip file</a>.
Here the file names have the structure<p>
fgong_name_file-ID.txt<p>
where 'name' is the model name used above and 'file-ID' identifies the
internal file name used in the modelling.
# Oscillation frequencies
Oscillation frequencies have been computed for the models listed above, for
frequencies between the lower (gravity-wave) and upper (acoustic) cut-off
frequencies (see Unno et al. 1989; <i>Non-radial oscillations of stars</i>,
for details).
They are linked in the copy below of the above table.
The structure of the files is described in
<a href='frequency_format.pdf'><i>Format for frequency comparison</i></a>.
<p><p>
<table style="width:100%">
<thead align="left">
<tr style="left-align">
<th style="left-align">Model</th>
<th>Age</th>
<th>R</th>
<th>L</th>
<th>Opacity</th>
<th>Surface</th>
<th>Surface</th>
<th>Other changes </th>
</tr>
<tr>
<th></th>
<th>(Gyr)</th>
<th>(1.e10 cm)</th>
<th>(1.e33 erg/s)</th>
<th>tables</th>
<th>opacity</th>
<th>comp.</th>
<th>(see caption) </th>
</tr>
</thead>
<tr>
<td><a href='frequencies/fobs_S_d_02c.txt?raw=true'>S</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>- </td>
</tr>
<tr>
<td><a href='frequencies/fobs_Age_d_06c.txt?raw=true'>Age</a></td>
<td>4.57</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>- </td>
</tr>
<tr>
<td><a href='frequencies/fobs_R_s_d_05c.txt?raw=true'>R_s</a></td>
<td>4.60</td>
<td>6.95508</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>- </td>
</tr>
<tr>
<td><a href='frequencies/fobs_L_s_d_41c.txt?raw=true'>L_s</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.828</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>- </td>
</tr>
<tr>
<td><a href='frequencies/fobs_Opc_7_0_d_15c.txt?raw=true'>Opc_7_0</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>EOS Liv05 </td>
</tr>
<tr>
<td><a href='frequencies/fobs_Opc_6_5_d_16c.txt?raw=true'>Opc_6_5</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>Local delta log kappa </td>
</tr>
<tr>
<td><a href='frequencies/fobs_OPAL96_d_07c.txt?raw=true'>OPAL96</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>Local delta log kappa </td>
</tr>
<tr>
<td><a href='frequencies/fobs_OP05_d_36c.txt?raw=true'>OP05</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL96</td>
<td>Kur91</td>
<td>GN93</td>
<td>- </td>
</tr>
<tr>
<td><a href='frequencies/fobs_GS98_d_37c.txt?raw=true'>GS98</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL96</td>
<td>Fer05</td>
<td>GN93</td>
<td>Surf. opac. </td>
</tr>
<tr>
<td><a href='frequencies/fobs_Liv05_d_40c.txt?raw=true'>Liv05</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL96</td>
<td>Fer05</td>
<td>GS98</td>
<td>- </td>
</tr>
<tr>
<td><a href='frequencies/fobs_Surf_opac_d_35c.txt?raw=true'>Surf_opac</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OP05</td>
<td>Fer05</td>
<td>GS98</td>
<td>- </td>
</tr>
<tr>
<td><a href='frequencies/fobs_CM_d_24c.txt?raw=true'>CM</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>CM conv. </td>
</tr>
<tr>
<td><a href='frequencies/fobs_Adelb11_d_34c.txt?raw=true'>Adelb11</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>EnGen. Adelberger </td>
</tr>
<tr>
<td><a href='frequencies/fobs_NACRE_d_39c.txt?raw=true'>NACRE</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>EnGen. NACRE </td>
</tr>
<tr>
<td><a href='frequencies/fobs_3He_eql_d_02c_eq.txt?raw=true'>3He_eql</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>3He nucl. eql. </td>
</tr>
<tr>
<td><a href='frequencies/fobs_No_el_scrn_d_20c.txt?raw=true'>No_el_scrn</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>no electr. screen. </td>
</tr>
<tr>
<td><a href='frequencies/fobs_Dc_d_17c.txt?raw=true'>Dc</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>Change diff. </td>
</tr>
<tr>
<td><a href='frequencies/fobs_DVc_d_18c.txt?raw=true'>DVc</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL92</td>
<td>Kur91</td>
<td>GN93</td>
<td>Change diff., settl. </td>
</tr>
<tr>
<td><a href='frequencies/fobs_No_diff_03c.txt?raw=true'>No_diff</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL96</td>
<td>Alex94</td>
<td>GN93</td>
<td>No diffusion </td>
</tr>
<tr>
<td><a href='frequencies/fobs_AGS05_d_21c.txt?raw=true'>AGS05</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL96</td>
<td>Fer05</td>
<td>AGS05 </td>
<td>- </td>
</tr>
<tr>
<td><a href='frequencies/fobs_AGSS09_d_22c.txt?raw=true'>AGSS09</a></td>
<td>4.60</td>
<td>6.9599</td>
<td>3.846</td>
<td>OPAL96</td>
<td>Fer05</td>
<td>AGSS09 </td>
<td>- </td>
</tr>
</table>
<p><p>
For convenience, all models have been collected in
<a href=fobs_combined.zip>a zip file</a>.
The file names use the same convection as the model file names provided above,
with 'fobs' instead of 'fgong'
<hr>
Last updated
Thursday 15 February 2021
by Jørgen Christensen-Dalsgaard