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Table H.1
List of the symbols used throughout this work and their designations in order of introduction.
Symbol  Designation 


i  imaginary number 
ℜ  real part 
ℑ  imaginary part 
^{∗}  conjugate 
_{ ⊕ }  associated with the Earth 
_{ ♀ }  associated with Venus 
R_{ET}  planetary equatorial rotating frame 
X _{ E } , Y _{ E } , Z _{ E }  vectorial basis associated with R_{ET} 
r  radial coordinate 
θ  colatitude 
ϕ  east longitude 
δ  latitude/fluctuations 
e _{ r } , e _{ θ } , e _{ ϕ }  spherical vectorial basis 
t  time 
g  gravity 
Ω  planet spin vector 
Ω  angular velocity 
R  planet radius 
_{atm}  associated with the atmosphere 
_{gr}  associated with the ground 
R _{atm}  external radius of the atmosphere 
H _{atm}  typical thickness of the atmosphere 
M  molar mass of the atmosphere 
p  pressure 
ρ  density 
T  temperature 
p _{0}  background pressure distribution 
ρ _{0}  background density distribution 
T _{0}  background temperature distribution 
C _{0}  background molar concentration distribution 
Γ_{1}  adiabatic exponent 
N  BruntVäisälä frequency 
R_{GP}  perfect gas constant 
R_{s}  specific gas constant of the atmosphere 
U  gravitational tidal potential 
J  tidal heating power per unit mass 
V  tidal velocity field 
V _{ r } , V _{ θ } , V _{ ϕ }  components of V in spherical coordinates 
ξ  displacement vector 
ξ _{ r } , ξ _{ θ } , ξ _{ ϕ }  components of ξ in spherical coordinates 
δp  tidal pressure perturbation 
δρ  tidal density perturbation 
δT  tidal temperature perturbation 
c _{ s }  sound velocity 
κ  atmospheric parameter 
φ _{rad}  radiated power per unit mass 
σ _{0}  radiation frequency 
S  StefanBoltzmann constant 
ϵ _{ a }  effective molar attenuation coefficient 
f  any perturbed quantity 
σ  tidal frequency 
ν  spin parameter 
m  longitudinal degree 
y  pressure perturbation divided by ρ_{0} 
ξ _{ H }  horizontal displacement 
operator associated with θcomponents  
operator associated with ϕcomponents  
ℒ^{m,ν}  Laplace’s tidal operator 
n  meridional degree 
Hough functions  
eigenvalues of Laplace’s tidal equation  
components of J  
components of U  
components of ξ_{r}  
components of ξ_{θ}  
components of ξ_{ϕ}  
components of V_{r}  
components of V_{θ}  
components of V_{ϕ}  
components of δp  
components of δρ  
components of δT  
components of y  
A _{1} , A _{2} , A _{3}  coefficients of the equation r^{2}ξ_{r;n} 
B _{1} , B _{2} , B _{3}  coefficients of the equation y_{n} 
A,B,C  coefficients of the vertical structure 
equation  
ℱ  function of the variable change 
vertical wavenumber  
L _{V;n}  scale of variation 
ε _{s;n}  acoustic coefficient 
σ _{s;n}  acoustic frequency 
coefficients of polarization relations  
K _{curv}  curvature term in polarization relations 
linear operator associated with the vertical  
structure  
components of the operator  
associated with f  
X _{ n }  vector of the forcings 
Y _{ n }  vector of the response 
σ _{diff;n}  diffusive frequency 
G  gravitational constant 
l  degrees of Legendre polynomials 
associated Legendre functions  
normalized associated Legendre functions  
potential induced by the tidal response  
components of projected on the  
components of projected on the  
first component of  
second component of  
Love numbers for the gravitational potential  
coefficients of Kaula’s expansion  
density expansion coefficient for the perturbation  
projected on the  
components of  
weighting coefficients of modes in  
the expansion of the tidal torque  
M _{ S }  mass of the star 
a  semimajor axis 
ε  obliquity 
n _{orb}  mean motion 
σ _{SD}  semidiurnal tidal frequency 
U _{2,2,2,0,0}  semidiurnal gravitational tidal potential 
J _{2,2,2,0,0}  semidiurnal thermal forcing 
expansion function of the thermal forcing  
projected on P_{2}  
V  volumetric domain of the atmosphere 
tidal torque  
frequency components of the tidal torque  
Δϕ  phase lag of the tidal response 
_{H}  associated with the horizontal component 
_{V}  associated with the vertical component 
_{grav}  caused by the gravitational forcing 
_{therm}  caused by the thermal forcing 
torque due to the horizontal component  
torque due to the vertical component  
ℋ  factor in the expressions of the torque 
z  altitude 
x  altitude normalized by the pressure height scale 
x _{atm}  normalized upper boundary 
a _{RE;T}  local acceleration in the reference frame 
a _{ c }  centrifugal acceleration 
h _{ n }  equivalent depth 
h _{ c }  characteristic depth of the vertical wavenumber 
ς _{ n }  scale ratio in the vertical wavenumber 
Δ  discriminant in and 
A,B  functions generating the analytic solution 
coefficients of the upper boundary equation  
x _{crit}  typical damping depth 
parameters  
parametrized function of the analytic solution  
orbital period  
γ  lag angle 
dimensionless constant  
a,b  empirical parameters in the model of 
Correia et al. (2003)  
vertical wavenumber in CL70  
η  relative difference between and k_{CL;n} 
λ  wavelength of light 
I _{S;λ}  spectral radiance of the star 
I _{S}  blackbody stellar flux 
R _{S}  star radius 
T _{S}  surface temperature of the star 
d  starplanet distance 
c  speed of light in vacuum 
h  Planck constant 
k _{B}  Boltzmann constant 
A _{atm;λ}  albedo of the atmosphere for the wavelength λ 
I _{0;λ}  effective incident flux 
l  linear spatial coordinate 
^{inc}  caused by the incident flux 
^{ref}  caused by the reflected flux 
^{rad}  caused by the flux emitted by the surface 
C _{G}  molar concentration of an absorbing gas 
ε _{G;λ}  molar extinction density coefficient 
I _{ λ }  heat power flux 
J  heat power per unit volume 
τ _{ λ }  optical depth 
α _{ λ }  global absorption coefficient 
A _{gr;λ}  albedo of the ground for the wavelength λ 
T _{gr}  surface temperature 
ψ  angle to the starplanet direction 
I _{gr;BB}  blackbody emission of the ground 
ϵ _{gr}  emissivity of the ground 
ϵ _{atm}  emissivity of the atmosphere 
ϵ  effective emissivity of the ground 
T _{gr;0}  surface equilibrium temperature 
δ T _{gr}  surface temperature fluctuations 
transfer function of the ground  
Q _{atm}  diffusive power flux in the atmosphere 
Q _{gr}  diffusive power flux in the ground 
k _{atm}  thermal conductivity of the atmosphere 
k _{gr}  thermal conductivity of the ground 
K _{atm}  vertical turbulent thermal diffusivity 
K _{gr}  thermal diffusivity of the ground 
c _{atm}  thermal capacity of the atmosphere 
c _{gr}  thermal capacity of the ground 
skin thickness in the atmosphere  
skin thickness in the ground  
ς _{gr}  radiative impedance of the ground 
β _{atm}  thermal conductive capacity of the atmosphere 
β _{gr}  thermal conductive capacity of the ground 
σ _{bl}  typical frequency of the atmospheric boundary 
layer  
vertical damping coefficient in the boundary layer  
δ T _{bl}  temperature fluctuations in the boundary layer 
associated with visible light  
associated with the infrared  
N  number of points of the spatial discretization 
T  timescale of the spin evolution 
M  mass of the atmosphere 
χ  tidal frequency divided by the mean motion 
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