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 \(x = r/R\)

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

x_ref

\(x_{\rm ref}\)

real

fractional radius of reference location

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_dx1

\(\sderiv{W}{x}\)

real(n)

differential work [\(GM^{2}/R\)]; evaluated using eqn. 25.9 of Unno et al. (1989)

dW_eps_dx1

\(\sderiv{W_{\epsilon}}{x}\)

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_star2

\(M\)

real

stellar mass [\(\gram\)]

R_star2

\(R\)

real

stellar radius [\(\cm\)]

L_star2

\(L\)

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

nabla1

\(\nabla\)

real(n)

temperature gradient; defined in Structure Coefficients section Dimensionless Formulation section

nabla_ad1

\(\nabad\)

real(n)

adiabatic temperature gradient; defined in Linearized Equations section

dnabla_ad1

\(\dnabad\)

real(n)

derivative of adiabatic temperature gradient

upsilon_T1

\(\upsT\)

real(n)

thermodynamic coefficient; defined in Linearized Equations section

c_lum1

\(\clum\)

real(n)

structure coefficient; defined in Structure Coefficients section

c_rad1

\(\crad\)

real(n)

structure coefficient; defined in Structure Coefficients section

c_thn1

\(\cthn\)

real(n)

structure coefficient; defined in Structure Coefficients section

c_thk1

\(\cthk\)

real(n)

structure coefficient; defined in Structure Coefficients section

c_eps1

\(\ceps\)

real(n)

structure coefficient; defined in Structure Coefficients section

kap_rho1

\(\kaprho\)

real(n)

opacity partial; defined in Linearized Equations section

kap_T1

\(\kapT\)

real(n)

opacity partial; defined in Linearized Equations section

eps_rho1

\(\epsrho\)

real(n)

nuclear energy generation partial; defined in Linearized Equations section

eps_T1

\(\epsT\)

real(n)

nuclear energy generation partial; defined in Linearized Equations section

M_r2

\(M_r\)

real(n)

interior mass [\(\gram\)]

P2

\(P\)

real(n)

total pressure [\(\barye\)]

rho2

\(\rho\)

real(n)

density [\(\gram\,\cm^{-3}\)]

T2

\(T\)

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