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	\(N\)	integer	number of spatial grid points
omega	\(\omega\)	complex	dimensionless eigenfrequency (gyre) or forcing frequency (gyre_tides)
x	\(x\)	real(n)	independent variable \(x = r/R\)
dx_min	\(\Delta x_{\rm min}\)	real	minimum spacing of spatial grid
dx_max	\(\Delta x_{\rm max}\)	real	maximum spacing of spatial grid
dx_rms	\(\Delta x_{\rm rms}\)	real	root-mean-square spacing of spatial grid
x_ref	\(x_{\rm ref}\)	real	fractional radius of reference location
y_1	\(y_{1}\)	complex(n)	dependent variable
y_2	\(y_{2}\)	complex(n)	dependent variable
y_3	\(y_{3}\)	complex(n)	dependent variable
y_4	\(y_{4}\)	complex(n)	dependent variable
y_5	\(y_{5}\)	complex(n)	dependent variable
y_6	\(y_{6}\)	complex(n)	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
freq	—	complex	dimensioned frequency; units and reference frame controlled by freq_units and freq_frame parameters
freq_units	—	string	freq_units parameter
freq_frame	—	string	freq_frame parameter
f_T	\(f_{T}\)	real	Effective temperature perturbation amplitude; evaluated using eqn. 5 of Dupret et al. (2003)
f_g	\(f_{\rm g}\)	real	Effective gravity perturbation amplitude; evaluated using eqn. 6 of Dupret et al. (2003)
psi_T	\(\psi_{T}\)	real	Effective temperature perturbation phase; evaluated using eqn. 5 of Dupret et al. (2003)
f_g	\(\psi_{\rm g}\)	real	Effective gravity perturbation phase; evaluated using eqn. 6 of Dupret et al. (2003)

Classification & Validation

Item	Symbol	Datatype	Description
id	—	integer	unique mode index
l	\(\ell\)	integer	harmonic degree
l_i	\(\ell_{\rm i}\)	complex	effective harmonic degree at inner boundary
m	\(m\)	integer	azimuthal order
n_p	\(\np\)	integer	acoustic-wave winding number
n_g	\(\ng\)	integer	gravity-wave winding number
n_pg	\(\npg\)	integer	radial order within the Eckart-Scuflaire-Osaki-Takata scheme (see Takata, 2006b)
omega_int	\(\omega_{\rm int}\)	complex	dimensionless eigenfrequency; evaluated as omega_{rm int} = sqrt{zeta/E}
dzeta_dx	\(\sderiv{\zeta}{x}\)	complex(n)	dimensionless frequency weight function; controlled by zeta_scheme parameter
zeta	\(\zeta\)	complex	integral of \(\sderiv{\zeta}{x}\) with respect to \(x\)
Yt_1	\(\mathcal{Y}_{1}\)	complex(n)	primary eigenfunction for Takata classification; evaluated using a rescaled eqn. 69 of Takata (2006b)
Yt_2	\(\mathcal{Y}_{2}\)	complex(n)	secondary eigenfunction for Takata classification; evaluated using a rescaled eqn. 70 of Takata (2006b)
I_0	\(I_{0}\)	complex(n)	first integral for radial modes; evaluated using eqn. 42 of Takata (2006a)
I_1	\(I_{1}\)	complex(n)	first integral for dipole modes; evaluated using eqn. 43 of Takata (2006a)
prop_type	\(\varpi\)	integer(n)	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
xi_r_ref	\(\txi_{r,{\rm ref}}\)	complex	radial displacement perturbation at reference location [\(R\)]
xi_h_ref	\(\txi_{\rm h,ref}\)	complex	radial displacement perturbation at reference location [\(R\)]
eul_Phi_ref	\(\tPhi'_{\rm ref}\)	complex	Eulerian potential perturbation at reference location [\(GM/R\)]
deul_Phi_ref	\((\sderiv{\tPhi'}{x})_{\rm ref}\)	complex	Eulerian potential gradient perturbation at reference location [\(GM/R^{2}\)]
lag_S_ref	\(\delta\tS_{\rm ref}\)	complex	Lagrangian specific entropy perturbation at reference location [\(R\)]
lag_L_ref	\(\delta\tL_{\rm R,ref}\)	complex	Lagrangian radiative luminosity perturbation at reference location [\(L\)]
xi_r	\(\txir\)	complex(n)	radial displacement perturbation [\(R\)]
xi_h	\(\txih\)	complex(n)	radial displacement perturbation [\(R\)]
eul_Phi	\(\tPhi'\)	complex(n)	Eulerian potential perturbation [\(GM/R\)]
deul_Phi	\(\sderiv{\tPhi'}{x}\)	complex(n)	Eulerian potential gradient perturbation [\(GM/R^{2}\)]
lag_S	\(\delta\tS\)	complex(n)	Lagrangian specific entropy perturbation [\(\cP\)]
lag_L	\(\delta\tLrad\)	complex(n)	Lagrangian radiative luminosity perturbation [\(L\)]
eul_P	\(\tP'\)	complex(n)	Eulerian total pressure perturbation [\(P\)]
eul_rho	\(\trho'\)	complex(n)	Eulerian density perturbation [\(\rho\)]
eul_T	\(\tT'\)	complex(n)	Eulerian temperature perturbation [\(T\)]
lag_P	\(\delta\tP\)	complex(n)	Lagrangian total pressure perturbation [\(P\)]
lag_rho	\(\delta\trho\)	complex(n)	Lagrangian density perturbation [\(\rho\)]
lag_T	\(\delta\tT\)	complex(n)	Lagrangian temperature perturbation [\(T\)]

Energetics & Transport

Item	Symbol	Datatype	Description
eta	\(\eta\)	real	normalized growth rate \(\eta\); evaluated using expression in text of page 1186 of Stellingwerf (1978)
E	\(E\)	real	mode inertia [\(M R^{2}\)]; evaluated by integrating \(\sderiv{E}{x}\)
E_p	\(E_{\rm p}\)	real	acoustic mode inertia [\(M R^{2}\)]; evaluated by integrating \(\sderiv{E}{x}\) where \(\varpi=1\)
E_g	\(E_{\rm g}\)	real	gravity mode inertia [\(M R^{2}\)]; evaluated by integrating \(\sderiv{E}{x}\) in regions where \(\varpi=-1\)
E_norm	\(E_{\rm norm}\)	real	normalized inertia; evaluation controlled by inertia_norm parameter
E_ratio		real	ratio of mode inertias inertia inside/outside reference location
H	\(H\)	real	mode energy [\(G M^{2}/R\)]; evaluated as \(\frac{1}{2} \omega^{2} E\)
W	\(W\)	real	mode work [\(G M^{2}/R\)]; evaluated by integrating \(\sderiv{W}{x}\)
W_eps	\(W_{\epsilon}\)	real	mode work [\(G M^{2}/R\)]; evaluated by integrating \(\sderiv{W_{\epsilon}}{x}\)
tau_ss	\(\tau_{\rm ss}\)	real	steady-state torque [\(G M^{2}/R\)]; evaluated by integrating \(\sderiv{\tau_{\rm ss}}{x}\)
tau_tr	\(\tau_{\rm tr}\)	real	steady-state torque [\(G M^{2}/R\)]; evaluated by integrating \(\sderiv{\tau_{\rm tr}}{x}\)
dE_dx	\(\sderiv{E}{x}\)	real(n)	differential inertia [\(M R^{2}\)]; evaluated using eqn. 3.139 of Aerts et al. (2010)
dW_dx[1]	\(\sderiv{W}{x}\)	real(n)	differential work [\(GM^{2}/R\)]; evaluated using eqn. 25.9 of Unno et al. (1989)
dW_eps_dx[1]	\(\sderiv{W_{\epsilon}}{x}\)	real(n)	differential nuclear work [\(GM^{2}/R\)]; evaluated using eqn. 25.9 of Unno et al. (1989)
dtau_ss_dx	\(\sderiv{\tau_{\rm ss}}{x}\)	real(n)	steady-state differential torque [G M^{2}/R]
dtau_tr_dx	\(\sderiv{\tau_{\rm tr}}{x}\)	real(n)	transient differential torque [G M^{2}/R]
alpha_0	\(\alpha_{0}\)	real(n)	excitation coefficient; evaluated using eqn. 26.10 of Unno et al. (1989)
alpha_1	\(\alpha_{1}\)	real(n)	excitation coefficient; evaluated using eqn. 26.12 of Unno et al. (1989)

Rotation

Item	Symbol	Datatype	Description
Omega_rot_ref	\(\Omega_{\rm ref}\)	real	rotation angular frequency at reference location[\(\sqrt{GM/R^{3}}\)]
Omega_rot	\(\Omega\)	real(n)	rotation angular frequency [\(\sqrt{GM/R^{3}}\)]
domega_rot	\(\delta \omega\)	real	dimensionless first-order rotational splitting; evaluated using eqn. 3.355 of Aerts et al. (2010)
dfreq_rot	—	real	dimensioned first-order rotational splitting; units and reference frame controlled by freq_units and freq_frame parameters
beta	\(\beta\)	real	rotation splitting coefficient; evaluated by integrating \(\sderiv{\beta}{x}\)
dbeta_dx	\(\sderiv{\beta}{x}\)	complex(n)	unnormalized rotation splitting kernel; evaluated using eqn. 3.357 of Aerts et al. (2010)
lambda	\(\lambda\)	complex(n)	tidal equation eigenvalue

Stellar Structure

Item	Symbol	Datatype	Description
M_star[2]	\(M\)	real	stellar mass [\(\gram\)]
R_star[2]	\(R\)	real	stellar radius [\(\cm\)]
L_star[2]	\(L\)	real	stellar luminosity [\(\erg\,\second^{-1}\)]
Delta_p	\(\Delta \nu\)	real	asymptotic p-mode large frequency separation [\(\sqrt{GM/R^{3}}\)]
Delta_g	\((\Delta P)^{-1}\)	real	asymptotic g-mode inverse period separation [\(\sqrt{GM/R^{3}}\)]
V_2	\(V_2\)	real(n)	structure coefficient; defined in Structure Coefficients section
As	\(A^{*}\)	real(n)	structure coefficient; defined in Structure Coefficients section
U	\(U\)	real(n)	structure coefficient; defined in Structure Coefficients section
c_1	\(c_{1}\)	real(n)	structure coefficient; defined in Structure Coefficients section
Gamma_1	\(\Gammi\)	real(n)	adiabatic exponent; defined in Linearized Equations section
nabla[1]	\(\nabla\)	real(n)	temperature gradient; defined in Structure Coefficients section Dimensionless Formulation section
nabla_ad[1]	\(\nabad\)	real(n)	adiabatic temperature gradient; defined in Linearized Equations section
dnabla_ad[1]	\(\dnabad\)	real(n)	derivative of adiabatic temperature gradient
upsilon_T[1]	\(\upsT\)	real(n)	thermodynamic coefficient; defined in Linearized Equations section
c_lum[1]	\(\clum\)	real(n)	structure coefficient; defined in Structure Coefficients section
c_rad[1]	\(\crad\)	real(n)	structure coefficient; defined in Structure Coefficients section
c_thn[1]	\(\cthn\)	real(n)	structure coefficient; defined in Structure Coefficients section
c_thk[1]	\(\cthk\)	real(n)	structure coefficient; defined in Structure Coefficients section
c_eps[1]	\(\ceps\)	real(n)	structure coefficient; defined in Structure Coefficients section
kap_rho[1]	\(\kaprho\)	real(n)	opacity partial; defined in Linearized Equations section
kap_T[1]	\(\kapT\)	real(n)	opacity partial; defined in Linearized Equations section
eps_rho[1]	\(\epsrho\)	real(n)	nuclear energy generation partial; defined in Linearized Equations section
eps_T[1]	\(\epsT\)	real(n)	nuclear energy generation partial; defined in Linearized Equations section
M_r[2]	\(M_r\)	real(n)	interior mass [\(\gram\)]
P[2]	\(P\)	real(n)	total pressure [\(\barye\)]
rho[2]	\(\rho\)	real(n)	density [\(\gram\,\cm^{-3}\)]
T[2]	\(T\)	real(n)	temperature [\(\kelvin\)]

Tidal Response

Note that these items are available only when using gyre_tides.

Item	Symbol	Datatype	Description
k	\(k\)	integer	Fourier harmonic
eul_Psi_ref	\(\tPsi'_{\rm ref}\)	complex	Eulerian total potential perturbation at reference location [\(GM/R\)]
Phi_T_ref	\(\tPhi_{\rm T, ref}\)	real	tidal potential at reference location [\(GM/R\)]
eul_Psi	\(\tPsi'\)	complex(n)	Eulerian total potential perturbation [\(GM/R\)]
Phi_T	\(\tPhi_{{\rm T}}\)	real(n)	tidal potential [\(GM/R\)]
Omega_orb	\(\Omega_{\rm orb}\)	real	orbital angular frequency; units and reference frame controlled by freq_units and freq_frame parameters
q	\(q\)	real	ratio of secondary mass to primary mass
e	\(e\)	real	orbital eccentricity
R_a	\(R/a\)	real	ratio of primary radius to orbital semi-major axis
cbar	\(\cbar_{\ell,m,k}\)	real	tidal expansion coefficient; see eqn. A1 of Sun et al. (2023)
Gbar_1	\(\Gbar^{(1)}_{\ell,m,k}\)	real	secular orbital evolution coefficient; equivalent to \(G^{(1)}_{\ell,m,-k}\) (see Willems et al., 2003)
Gbar_2	\(\Gbar^{(2)}_{\ell,m,k}\)	real	secular orbital evolution coefficient; equivalent to \(G^{(2)}_{\ell,m,-k}\) (see Willems et al., 2003)
Gbar_3	\(\Gbar^{(3)}_{\ell,m,k}\)	real	secular orbital evolution coefficient; equivalent to \(G^{(3)}_{\ell,m,-k}\) (see Willems et al., 2003)
Gbar_4	\(\Gbar^{(4)}_{\ell,m,k}\)	real	secular orbital evolution coefficient; equivalent to \(G^{(4)}_{\ell,m,-k}\) (see Willems et al., 2003)

Footnotes

[1] (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)

This option is available only for stellar models with N capability

[2] (1,2,3,4,5,6,7)

This option is available only for stellar models with D capability