How to compute for Distance Modulus' uncertainty/ies? This is rather a short question. As we know of;
Distance Modulus (DM) $\mu = 5 \log d - 5$
If $d = 168_{-14.9}^{+27.5}$ pc ($3\sigma$ value), how can I possibly compute for $\mu$'s uncertainty?
P.S. Perhaps I need to multiply those $\pm$ values to a 'some constant'(?)
Thanks a lot and clear skies.
You can just use these upper and lower bounds to create an upper/lower bound for the distance modulus. The lower bound is $168-14.9 = 153.1$, and the upper bound is $168+27.5 = 195.5.$ You can calculate the distance moduli for these values to get upper and lower bounds:
$$5\log(153.1) - 5 = 5.924876 \\ 5\log(195.5) - 5 = 6.455734$$
Then we calculate the distance modulus of the base value: $$5\log(168) - 5 = 6.126546$$
To get the deviations, we just subtract the distance moduli from the original. Therefore, your distance modulus is equal to $6.126546_{- 0.20167}^{+0.329188} \text{ pc.}$ I hope this helps. If there are any issues with my answer, please notify me.