Detail Files
Detail files store spatial quantities, such as eigenfunctions and
differential inertias, for an individual solution (mode, tidal
response, etc.) found during a run. The specific data written to
detail files are controlled by the detail_item_list
parameters of the &ad_output
and &nad_output
namelist
groups (gyre adiabatic and non-adiabatic calculations,
respectively) and the &tides_output
namelist group
(gyre_tides calculations). These parameters specify the
items to be written, via a comma-separated list.
The following subsections describe the items that may appear in
detail_item_list
, grouped together by functional area. For
each item, the corresponding math symbol is given (if there is one),
together with the datatype, and a brief description. Units (where
applicable) are indicated in brackets [].
Solution Data
Item |
Symbol |
Datatype |
Description |
---|---|---|---|
|
\(N\) |
integer |
number of spatial grid points |
|
\(\omega\) |
complex |
dimensionless eigenfrequency (gyre) or forcing frequency (gyre_tides) |
|
\(x\) |
real( |
independent variable \(x = r/R\) |
|
\(\Delta x_{\rm min}\) |
real |
minimum spacing of spatial grid |
|
\(\Delta x_{\rm max}\) |
real |
maximum spacing of spatial grid |
|
\(\Delta x_{\rm rms}\) |
real |
root-mean-square spacing of spatial grid |
|
\(x_{\rm ref}\) |
real |
fractional radius of reference location |
|
\(y_{1}\) |
complex( |
dependent variable |
|
\(y_{2}\) |
complex( |
dependent variable |
|
\(y_{3}\) |
complex( |
dependent variable |
|
\(y_{4}\) |
complex( |
dependent variable |
|
\(y_{5}\) |
complex( |
dependent variable |
|
\(y_{6}\) |
complex( |
dependent variable |
The definitions of the dependent variables \(\{y_{1},\ldots,y_{6}\}\) are provided in the Oscillation Equations chapter (for gyre) and in the Tidal Equations chapter (for gyre_tides).
Observables
Item |
Symbol |
Datatype |
Description |
---|---|---|---|
|
— |
complex |
dimensioned frequency; units and reference frame controlled by
|
|
— |
string |
|
|
— |
string |
|
|
\(f_{T}\) |
real |
Effective temperature perturbation amplitude; evaluated using eqn. 5 of Dupret et al. (2003) |
|
\(f_{\rm g}\) |
real |
Effective gravity perturbation amplitude; evaluated using eqn. 6 of Dupret et al. (2003) |
|
\(\psi_{T}\) |
real |
Effective temperature perturbation phase; evaluated using eqn. 5 of Dupret et al. (2003) |
|
\(\psi_{\rm g}\) |
real |
Effective gravity perturbation phase; evaluated using eqn. 6 of Dupret et al. (2003) |
Classification & Validation
Item |
Symbol |
Datatype |
Description |
---|---|---|---|
|
— |
integer |
unique mode index |
|
\(\ell\) |
integer |
harmonic degree |
|
\(\ell_{\rm i}\) |
complex |
effective harmonic degree at inner boundary |
|
\(m\) |
integer |
azimuthal order |
|
\(\np\) |
integer |
acoustic-wave winding number |
|
\(\ng\) |
integer |
gravity-wave winding number |
|
\(\npg\) |
integer |
radial order within the Eckart-Scuflaire-Osaki-Takata scheme (see Takata, 2006b) |
|
\(\omega_{\rm int}\) |
complex |
dimensionless eigenfrequency; evaluated as omega_{rm int} = sqrt{zeta/E} |
|
\(\sderiv{\zeta}{x}\) |
complex( |
dimensionless frequency weight function; controlled by |
|
\(\zeta\) |
complex |
integral of \(\sderiv{\zeta}{x}\) with respect to \(x\) |
|
\(\mathcal{Y}_{1}\) |
complex( |
primary eigenfunction for Takata classification; evaluated using a rescaled eqn. 69 of Takata (2006b) |
|
\(\mathcal{Y}_{2}\) |
complex( |
secondary eigenfunction for Takata classification; evaluated using a rescaled eqn. 70 of Takata (2006b) |
|
\(I_{0}\) |
complex( |
first integral for radial modes; evaluated using eqn. 42 of Takata (2006a) |
|
\(I_{1}\) |
complex( |
first integral for dipole modes; evaluated using eqn. 43 of Takata (2006a) |
|
\(\varpi\) |
integer( |
propagation type; \(\varpi = 1\) in acoustic-wave regions, \(\varpi=-1\) in gravity-wave regions, and \(\varpi=0\) in evanescent regions |
Perturbations
Item |
Symbol |
Datatype |
Description |
---|---|---|---|
|
\(\txi_{r,{\rm ref}}\) |
complex |
radial displacement perturbation at reference location [\(R\)] |
|
\(\txi_{\rm h,ref}\) |
complex |
radial displacement perturbation at reference location [\(R\)] |
|
\(\tPhi'_{\rm ref}\) |
complex |
Eulerian potential perturbation at reference location [\(GM/R\)] |
|
\((\sderiv{\tPhi'}{x})_{\rm ref}\) |
complex |
Eulerian potential gradient perturbation at reference location [\(GM/R^{2}\)] |
|
\(\delta\tS_{\rm ref}\) |
complex |
Lagrangian specific entropy perturbation at reference location [\(R\)] |
|
\(\delta\tL_{\rm R,ref}\) |
complex |
Lagrangian radiative luminosity perturbation at reference location [\(L\)] |
|
\(\txir\) |
complex( |
radial displacement perturbation [\(R\)] |
|
\(\txih\) |
complex( |
radial displacement perturbation [\(R\)] |
|
\(\tPhi'\) |
complex( |
Eulerian potential perturbation [\(GM/R\)] |
|
\(\sderiv{\tPhi'}{x}\) |
complex( |
Eulerian potential gradient perturbation [\(GM/R^{2}\)] |
|
\(\delta\tS\) |
complex( |
Lagrangian specific entropy perturbation [\(\cP\)] |
|
\(\delta\tLrad\) |
complex( |
Lagrangian radiative luminosity perturbation [\(L\)] |
|
\(\tP'\) |
complex( |
Eulerian total pressure perturbation [\(P\)] |
|
\(\trho'\) |
complex( |
Eulerian density perturbation [\(\rho\)] |
|
\(\tT'\) |
complex( |
Eulerian temperature perturbation [\(T\)] |
|
\(\delta\tP\) |
complex( |
Lagrangian total pressure perturbation [\(P\)] |
|
\(\delta\trho\) |
complex( |
Lagrangian density perturbation [\(\rho\)] |
|
\(\delta\tT\) |
complex( |
Lagrangian temperature perturbation [\(T\)] |
Energetics & Transport
Item |
Symbol |
Datatype |
Description |
---|---|---|---|
|
\(\eta\) |
real |
normalized growth rate \(\eta\); evaluated using expression in text of page 1186 of Stellingwerf (1978) |
|
\(E\) |
real |
mode inertia [\(M R^{2}\)]; evaluated by integrating \(\sderiv{E}{x}\) |
|
\(E_{\rm p}\) |
real |
acoustic mode inertia [\(M R^{2}\)]; evaluated by integrating \(\sderiv{E}{x}\) where \(\varpi=1\) |
|
\(E_{\rm g}\) |
real |
gravity mode inertia [\(M R^{2}\)]; evaluated by integrating \(\sderiv{E}{x}\) in regions where \(\varpi=-1\) |
|
\(E_{\rm norm}\) |
real |
normalized inertia; evaluation controlled by |
|
real |
ratio of mode inertias inertia inside/outside reference location |
|
|
\(H\) |
real |
mode energy [\(G M^{2}/R\)]; evaluated as \(\frac{1}{2} \omega^{2} E\) |
|
\(W\) |
real |
mode work [\(G M^{2}/R\)]; evaluated by integrating \(\sderiv{W}{x}\) |
|
\(W_{\epsilon}\) |
real |
mode work [\(G M^{2}/R\)]; evaluated by integrating \(\sderiv{W_{\epsilon}}{x}\) |
|
\(\tau_{\rm ss}\) |
real |
steady-state torque [\(G M^{2}/R\)]; evaluated by integrating \(\sderiv{\tau_{\rm ss}}{x}\) |
|
\(\tau_{\rm tr}\) |
real |
steady-state torque [\(G M^{2}/R\)]; evaluated by integrating \(\sderiv{\tau_{\rm tr}}{x}\) |
|
\(\sderiv{E}{x}\) |
real( |
differential inertia [\(M R^{2}\)]; evaluated using eqn. 3.139 of Aerts et al. (2010) |
|
\(\sderiv{W}{x}\) |
real( |
differential work [\(GM^{2}/R\)]; evaluated using eqn. 25.9 of Unno et al. (1989) |
|
\(\sderiv{W_{\epsilon}}{x}\) |
real( |
differential nuclear work [\(GM^{2}/R\)]; evaluated using eqn. 25.9 of Unno et al. (1989) |
|
\(\sderiv{\tau_{\rm ss}}{x}\) |
real( |
steady-state differential torque [G M^{2}/R] |
|
\(\sderiv{\tau_{\rm tr}}{x}\) |
real( |
transient differential torque [G M^{2}/R] |
|
\(\alpha_{0}\) |
real( |
excitation coefficient; evaluated using eqn. 26.10 of Unno et al. (1989) |
|
\(\alpha_{1}\) |
real( |
excitation coefficient; evaluated using eqn. 26.12 of Unno et al. (1989) |
Rotation
Item |
Symbol |
Datatype |
Description |
---|---|---|---|
|
\(\Omega_{\rm ref}\) |
real |
rotation angular frequency at reference location[\(\sqrt{GM/R^{3}}\)] |
|
\(\Omega\) |
real( |
rotation angular frequency [\(\sqrt{GM/R^{3}}\)] |
|
\(\delta \omega\) |
real |
dimensionless first-order rotational splitting; evaluated using eqn. 3.355 of Aerts et al. (2010) |
|
— |
real |
dimensioned first-order rotational splitting; units and reference frame controlled by
|
|
\(\beta\) |
real |
rotation splitting coefficient; evaluated by integrating \(\sderiv{\beta}{x}\) |
|
\(\sderiv{\beta}{x}\) |
complex( |
unnormalized rotation splitting kernel; evaluated using eqn. 3.357 of Aerts et al. (2010) |
|
\(\lambda\) |
complex( |
tidal equation eigenvalue |
Stellar Structure
Item |
Symbol |
Datatype |
Description |
---|---|---|---|
|
\(M\) |
real |
stellar mass [\(\gram\)] |
|
\(R\) |
real |
stellar radius [\(\cm\)] |
|
\(L\) |
real |
stellar luminosity [\(\erg\,\second^{-1}\)] |
|
\(\Delta \nu\) |
real |
asymptotic p-mode large frequency separation [\(\sqrt{GM/R^{3}}\)] |
|
\((\Delta P)^{-1}\) |
real |
asymptotic g-mode inverse period separation [\(\sqrt{GM/R^{3}}\)] |
|
\(V_2\) |
real( |
structure coefficient; defined in Structure Coefficients section |
|
\(A^{*}\) |
real( |
structure coefficient; defined in Structure Coefficients section |
|
\(U\) |
real( |
structure coefficient; defined in Structure Coefficients section |
|
\(c_{1}\) |
real( |
structure coefficient; defined in Structure Coefficients section |
|
\(\Gammi\) |
real( |
adiabatic exponent; defined in Linearized Equations section |
|
\(\nabla\) |
real( |
temperature gradient; defined in Structure Coefficients section Dimensionless Formulation section |
|
\(\nabad\) |
real( |
adiabatic temperature gradient; defined in Linearized Equations section |
|
\(\dnabad\) |
real( |
derivative of adiabatic temperature gradient |
|
\(\upsT\) |
real( |
thermodynamic coefficient; defined in Linearized Equations section |
|
\(\clum\) |
real( |
structure coefficient; defined in Structure Coefficients section |
|
\(\crad\) |
real( |
structure coefficient; defined in Structure Coefficients section |
|
\(\cthn\) |
real( |
structure coefficient; defined in Structure Coefficients section |
|
\(\cthk\) |
real( |
structure coefficient; defined in Structure Coefficients section |
|
\(\ceps\) |
real( |
structure coefficient; defined in Structure Coefficients section |
|
\(\kaprho\) |
real( |
opacity partial; defined in Linearized Equations section |
|
\(\kapT\) |
real( |
opacity partial; defined in Linearized Equations section |
|
\(\epsrho\) |
real( |
nuclear energy generation partial; defined in Linearized Equations section |
|
\(\epsT\) |
real( |
nuclear energy generation partial; defined in Linearized Equations section |
|
\(M_r\) |
real( |
interior mass [\(\gram\)] |
|
\(P\) |
real( |
total pressure [\(\barye\)] |
|
\(\rho\) |
real( |
density [\(\gram\,\cm^{-3}\)] |
|
\(T\) |
real( |
temperature [\(\kelvin\)] |
Tidal Response
Note that these items are available only when using gyre_tides.
Item |
Symbol |
Datatype |
Description |
---|---|---|---|
|
\(k\) |
integer |
Fourier harmonic |
|
\(\tPsi'_{\rm ref}\) |
complex |
Eulerian total potential perturbation at reference location [\(GM/R\)] |
|
\(\tPhi_{\rm T, ref}\) |
real |
tidal potential at reference location [\(GM/R\)] |
|
\(\tPsi'\) |
complex( |
Eulerian total potential perturbation [\(GM/R\)] |
|
\(\tPhi_{{\rm T}}\) |
real( |
tidal potential [\(GM/R\)] |
|
\(\Omega_{\rm orb}\) |
real |
orbital angular frequency; units and reference frame controlled by
|
|
\(q\) |
real |
ratio of secondary mass to primary mass |
|
\(e\) |
real |
orbital eccentricity |
|
\(R/a\) |
real |
ratio of primary radius to orbital semi-major axis |
|
\(\cbar_{\ell,m,k}\) |
real |
tidal expansion coefficient; see eqn. A1 of Sun et al. (2023) |
|
\(\Gbar^{(1)}_{\ell,m,k}\) |
real |
secular orbital evolution coefficient; equivalent to \(G^{(1)}_{\ell,m,-k}\) (see Willems et al., 2003) |
|
\(\Gbar^{(2)}_{\ell,m,k}\) |
real |
secular orbital evolution coefficient; equivalent to \(G^{(2)}_{\ell,m,-k}\) (see Willems et al., 2003) |
|
\(\Gbar^{(3)}_{\ell,m,k}\) |
real |
secular orbital evolution coefficient; equivalent to \(G^{(3)}_{\ell,m,-k}\) (see Willems et al., 2003) |
|
\(\Gbar^{(4)}_{\ell,m,k}\) |
real |
secular orbital evolution coefficient; equivalent to \(G^{(4)}_{\ell,m,-k}\) (see Willems et al., 2003) |
Footnotes