Exploring the probing power of γ Dor’s inertial dip for core magnetism: The case of a toroidal field

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Volume 701 (September 2025)

A&A, 701 (2025) A253

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Table B.1.

Meaning of the symbols used throughout this work.

	Physical background quantities
$B_{0}^{φ}$ $\mathrm{\boldsymbol{B}}_{0}^{\varphi}$	Background toroidal magnetic field
V₀	Background velocity field
$\bar{ρ}$ $\bar{\rho}$	Background density
$\bar{P}$ $\bar{P}$	Background gaseous pressure
${\bar{P}}_{M}$ $\bar{P}_{\mathrm{M}}$	Background magnetic pressure
N	Brunt-Väisälä angular frequency
$\tilde{S}$ $\tilde{S}$	Lamb angular frequency modified by rotation
c_S	Sound speed
$\bar{g}$ $\bar{g}$	Local gravity acceleration

	Constants

𝒢	Gravitational constant
μ₀	Vacuum permeability
Γ₁	First adiabatic index
α	3^1/3Γ(2/3)/Γ(1/3)≈0.73

	Angular frequencies and related quantities

Ω_zone	Rotation rate of the considered zone
ω_A, zone	Alfvén angular frequency in the zone
σ_in	Wave angular frequency in an inertial frame
σ_zone	Wave angular frequency in an frame co-rotating with the zone
σ_M, zone	Wave magnetic angular frequency in a frame co-rotating with the zone
s_zone	Hydrodynamic spin parameter of the zone
s_M, zone	Magnetic spin parameter of the zone
ν_M, zone	Magnetic structural parameter of the zone
P_M	Modified magnetic period
P	Period in the frame co-rotating with the envelope
P_in	Period in an inertial frame
ΔP_M	Modified magnetic period-spacing
ΔP	Period-spacing in the frame co-rotating with the envelope
ΔP_in	Period-spacing in an inertial frame
α_rot	Differential rotation, Ω_env/Ω_core
Le_zone	Lehnert number of the considered zone, ω_A, zone/2Ω_zone
G_M	s_M, env = G_M(s_M, core)
u_zone	ν_M, zone = u_zone(s_M, zone)

	Angular structure quantities

l	Angular degree of the mode
m	Azimuthal order
k	l − \|m\| in a non-rotating star
μ	cos θ
$Θ_{k}^{m}$ $\Theta_{k}^{m}$	Hough function
$Λ_{k}^{m}$ $\Lambda_{k}^{m}$	Eigenvalue of the Laplace Tidal Equation
$P_{l}^{m}$ $P_{l}^{m}$	Legendre polynomial
${\tilde{P}}_{l}^{m}$ $\tilde{P}_{l}^{m}$	Normalised Legendre polynomial
$C_{l}^{m}$ $C_{l}^{m}$	$x (\frac{d}{d x} - \frac{m}{1 - x^{2}}) P_{l}^{m} (x)$ $x\left(\dfrac{\mathrm{d}}{\mathrm{d}x}-\dfrac{m}{1-x^{2}}\right)P_{l}^{m}(x)$
c_k, l	Geometrical factor
$F_{l}^{m}$ $F_{l}^{m}$	Phase function of pure inertial modes

	Parameters of the interaction (continuous N)

ϵ	Coupling parameter
V	Structure factor with solid-body rotation and no magnetism
V_M	Structure factor with solid-body rotation and uniform Alfvén frequency
V_M, ≠	Structure factor with bi-layer rotation and Alfvén frequency
Γ_M	Magnetic control parameter with uniform Lehnert number
Γ_M, ≠	Magnetic control parameter with bi-layer Lehnert number

	Magnetic fields estimate

B_ms	Estimate of the core magnetic field in a magnetostrophic regime
B_equi	Estimate of the core magnetic field in a equipartition regime
Ro	Rossby number
v_conv	Typical convective velocity given by the MLT
l_conv	Typical convective length scale given by the MLT
l_B	Typical length scale of magnetic field variation

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