# 9. Scaling of the Total Metallicity¶

VICE quantifies the total metallicity by mass of both gas and stars in VICE according to:

$Z = Z_\odot \frac{\sum_i Z_i}{\sum_i Z_{i,\odot}}$

where the summation is taken over all elements tracked by the simulation. This is motivated by numerical artifacts that would be introduced into metallicity dependent quantities when only a small number of elements are being simulated. For example, if there are only three elements in a simulation and they are all near the solar abundance, this scaling ensures that metallicity dependent yields will behave as if the metallicity is near solar, as opposed to the much lower total metallicity of only three elements.

This is where the user’s adopted solar metallicity $$Z_\odot$$ enters in their simulations. Because the element-by-element breakdown of the solar composition $$Z_{i,\odot}$$ is taken from Asplund et al. (2009) 1, we recommend adopting $$Z_\odot = 0.014$$ from their findings for a self-consistent scaling.

The total logarithmic metallicity $$[M/H]$$ relative to the sun is then evaluated according to:

$[M/H] = \log_{10}\left(\frac{Z}{Z_\odot}\right) = \log_{10}\left(\sum_i Z_i\right) - \log_{10}\left(\sum_i Z_{i,\odot}\right)$

Note

These quantities are not recorded with outputs in order to minimize write-out time when the number of elements is high. Instead, history and tracer objects evaluate these equations automatically for gas and stars, respectively.

1

Asplund et al. (2009), ARA&A, 47, 481