Glass Pearl Player wrote:It also states the Period as P=41.4 days. This is much shorter than the stated phase shift of 185 days
You're making the same mistake Wyrm did: the star's period is not the same as the phase shift between the star and whatever knot of gas is nearby. However, you've nailed the paper and that the ambiguity needs to be resolved. If I read it right, they took many measurements of dust objects around the star, each with a whole range of possible N values. The correct distance corresponds to the set of {N_i} which are consistent. Another way to do it is to check variations in the star's luminosity among different periods and see how long it takes the nebula to reflect them.
Your method is a little bit dissatisfying because it relies on other types of measurements, rather than concluding based only on reflection measurements.
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You're incorrect in your magnitude calculations - the 185 days is the phase difference, not the period.
Spoiler
Of course the magnitude calculation is incorrect — it produces an absolute magnitude too big to be believable. Therefore, the period is shorter than 185 days. The phase difference is part of an equivalence class separated by multiples of the period. So if the period is 10 days, a 185 day phase difference would be equivalent to a 5 day phase difference. However, if the period is 100 days, a 185 day phase difference is equivalent to an 80 day phase difference. That makes a 16 fold difference in the distance calculations.
I guess what I'm saying is that you need to confirm that this is indeed the least phase difference and this Cepheid is a really bright fucker, or that I'm right that you pulled a fast one with the phases, making us believe that the distance to the knot is 185 light days distance when it is in fact much closer.
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