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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.

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  • $\begingroup$ Can't you just use the upper and lower bounds of distance to calculate upper and lower bounds to distance modulus? And BTW, distance modulus is $5\log d - 5$. $\endgroup$
    – ProfRob
    Commented Mar 22, 2021 at 8:29
  • $\begingroup$ @ProfRob That seems applicable. ^^ Let me check. $\endgroup$
    – CGHA
    Commented Mar 22, 2021 at 8:42

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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.

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    $\begingroup$ The units of distance modulus are "mag". It is incorrect to quote more than 3 Sig figs in the result or more than 2 in the error bars. $\endgroup$
    – ProfRob
    Commented Mar 22, 2021 at 19:53
  • $\begingroup$ Alright. Thanks a lot :) $\endgroup$
    – CGHA
    Commented Mar 26, 2021 at 7:12

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