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Table 2
Parameters used in modeling.
| Symbol | Quantity |
|
|
|
| t | time |
| 2τ | transit duration, or gap duration |
| T | observation duration |
| I(t) | star luminosity, power output |
| IT(ν) | Fourier transform of star luminosity |
| I 0 | star luminosity average |
| S(ν) | power spectrum of I(t) |
| L | distance from Earth |
| S | star radius |
| s | planet radius |
|
planet surface vector |
| r | planet-star distance |
|
planet position vector |
| a | orbit semimajor axis |
| ϵ | orbit eccentricity |
| ω | orbital angular frequency, mean motion |
| ωt | orbital phase angle, mean anomaly |
| ν | frequency variable; true anomaly (in Appendix B) |
| λ | eccentric anomaly |
| Ω | rotational/spin angular frequency |
|
rotation/spin axis |
| β | obliquity, tilt angle of rotation axis |
| α | polar cap extension angle from north pole |
| b, c | inner ring radius, outer ring radius |
 , ℛ |
ring transmitivity, ring- or ocean reflectivity |
| M I | ice cap/continent (albedo) map |
| M L | liquid lake/ocean surface map |
|
|
|
| (x,y,z) | various rectangular coordinates |
| (ρ,ν,z) | cylindrical coordinates in inertial frame i, j, k |
| (s,μ,ν) | radius, polar and azimuth angle in inertial frame |
| (s,ϑ,ϕ) | radius, polar and azimuth angle in rotating frame |
|
|
|
| θ | inclination, (polar) observation angle |
| θ = 0 | observation is face-on (orbital plane) |
|
observation is edge-on (orbital plane) |
| φ | azimuthal observation angle |
| ωt = φ | phase at inferior conjunction |
| F(t) | planet luminosity |
| FT(ν) | Fourier transform of planet luminosity |
| f(t) | light curve, normalized to 1 for a mirror ball |
|
Fourier coefficient for light curve |
| g(ν,t) | pattern function, planet map integrated over z |
|
Fourier coefficient for pattern function |
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