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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