3
$\begingroup$

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.

$\endgroup$
2
  • $\begingroup$ 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 Mar 22 at 8:29
  • $\begingroup$ @ProfRob That seems applicable. ^^ Let me check. $\endgroup$ – CGHA Mar 22 at 8:42
3
$\begingroup$

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.

$\endgroup$
2
  • 1
    $\begingroup$ 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 Mar 22 at 19:53
  • $\begingroup$ Alright. Thanks a lot :) $\endgroup$ – CGHA Mar 26 at 7:12

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.