How to convert $K_S$ magnitude to $M_K$

My question is how do I convert a magnitude $$K_S$$, from a system like 2MASS, to $$M_K$$, and what are the differences. A use of this $$M_K$$ can be seen on Delfosse et al. (2000) in the $$\log(M/M\odot) - M_K$$ can be found. In the end I want to be able to use a $$K_S$$, and other possible parameters to derive the mass of the star.

Delfosse et al. (2000) - Delfosse, X., Forveille, T., Ségransan, D., et al. 2000, A&A, 364, 217

• Can you provide the equations / formulas which define $K_S$ and $M_K$ ? – Carl Witthoft Sep 16 '19 at 18:19
• $K_S$ is defined as the magnitude in the K band in the 2MASS system I believe. There are others like $K_{CIT}$ from other systems that can be related by equations as in Carpenter, J. M. 2001, AJ, 121, 2851. $M_K$ seems to also be a absolute magnitude in the K band, but I do not know why (if) they are different and how are related. – T. Silva Sep 16 '19 at 18:30
• As in general with any apparent vs absolute magnitude, you will need a distance or distance modulus – astrosnapper Sep 17 '19 at 10:08
• I have the parallaxes, but the relation $M=m+5(\log_{10} (p)+1)$ doesn't give good results. What leads me to doubt what $K_S$ or $M_K$ really are. – T. Silva Sep 18 '19 at 2:31

Since this seems to be a kind of niche question I will answer and leave some comments for future souls with the same problem.

To whom it may interest that may be searching for the same problem. The solution is the basic $$M = m + 5( \log (parallax) + 1)$$. Parallax in arcsec.

The reason I'm going with K instead of V is due to a more independent relationships with the stellar metallicity

Parallaxes can be from catalogues like Hipparcus or Gaia.

If anyone is searching and gets here with the goal of using $$M_K$$ in the $$\log (M / M_\odot) - M_K$$ relation from Delfosse et al. (2000) keep in mind that in the paper the $$\log$$ relation is in $$\log_{10}$$ !!

Delfosse et al. uses "Johnson-Cousins-CIT", for that I followed equation (12) on Carpenter, J. M. 2001, AJ, 121, 2851.

If you want the $$\log g$$ I recommend the relation in:

Bean, J. L., Sneden, C., Hauschildt, P. H., Johns-Krull, C. M. and Benedict, G. F. (2006), ‘Ac- curate m dwarf metallicities from spectral synthesis: A critical test of model atmospheres’, The Astrophysical Journal 652(2), 1604.