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Table B.1

Summary of variables.

Symbol Definition Equation

E total energy (1)
U internal energy (5)
W self gravitational energy (6)
T total kinetic energy (11)
Ts rotational kinetic energy (12)
T0 orbital kinetic energy (16)
Wi gravitational interaction energy (17)
n,   K polytropic index and temperature (3)
G gravitational constant
M mass of primary
R mean radius of the primary
P pressure
ρ density
ai principal axes of the ellipsoid
αi first order correction to ai (27)
r orbital distance
λi asymmetry factor  = (a3/ai)2/3
ρc central density (5)
scaling constant of the internal energy (5), (7)
scaling constant of the gravitational energy (6), (8)
ellipsoidal correction to the gravitational energy (6), (9)
Ai (10)
I principal moment of inertia (14), (30)
κ n dimensionless moment of inertia (13)
Ω orbital mean motion (16), (19)
Λ internal angular velocity of the fluid (12)
ω rotational angular velocity (15)
ξ1 dimensionless radius (see Chandrasekhar 1939) (7)
dimensionless density derivative (see Chandrasekhar 1939) (7)
I ij Inertia tensor (18)
δ ij Kronecker symbol
Δ (19)
gt (22)
R0 radius of the unperturbed spherical polytrope (24)
q n (25), (26)
μR  = GM′/r3 (25), (26)
(25), (26)
mean density
dimensionless angular velocity (31)
f oblateness (36)
J2 quadrupolar gravitational moment (37)
k2 Love number (half the apsidal motion constant) (42)
L   stellar luminosity out of transit (48)
δ L   stellar luminosity variation in transit (48)
δ relative transit depth (48)
Rtr transit radius (48)
η non spherical contribution to the transit depth (49)

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