Table D.1.
Prior distributions for emcee parameters.
| Parameter | Boundary | Dist. |
|---|---|---|
| aring, outer | aring, outer > 0 | Uniform |
| aring, inner | 0 < aring, inner < (aring, outer − wouter) | Uniform |
| i | 0° ≤i < 90° | Uniform |
| ϕa | 0° ≤ϕ ≤ 180° | Uniform |
| wouter | 0 < wouter < aring, outer | Uniform |
| winner | 0 < winner < aring, inner | Uniform |
| Touter | 0 < Tinner < 1 | Uniform |
| Tinner | 0 < Tinner < 1 | Uniform |
| yring | yring ≥ 0 | Uniform |
| v | v > 0 | Uniform |
| t0b | 58000 ≤ t0 ≤ 64000 | Uniform |
Notes.
Although technically ϕ has a range of 0° ≤ϕ ≤ 360°, the ring system, which due to having a value for i is drawn as an ellipse, has a rotational symmetry when it is rotated 180°, making evaluating for only the 1st and 2nd quadrant sufficient.
Intuitively, t0 cannot be passed before the start of the dip. Because there are two dips and the second dip is longer than the first, it is safe to say that it will also not be passed before the start of the second dip, hence the lower boundary. The upper boundary is also intuitively should not be lower than the predicted tend. To be on the safe side, it is set to a much higher value than tend so that a good amount of values when t0 > tend can also be accommodated in the MCMC.
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