### Converting given metallicities to log(O/H)+12 Benjamin Metha
• 1
• 26 Jun '19

Hi team,

My name is Benjamin Metha. I'm a masters student currently studying at the University of Melbourne, and I'm currently making use of Illustris TNG to investigate population statistics for gamma ray burst host galaxies.

In TNG's 2017 paper The evolution of the mass-metallicity relation in IllustrisTNG, a method for converting the metallicity values available as Illustris data products (in particular, the star formation rate weighted metallicity) into log(O/H)+12 values is mentioned, but not described. I tried to convert the primordial solar metallicity (0.0127 according to http://www.tng-project.org/data/docs/specifications/) into a log(O/H)+12 value assuming that Oxygen is 35% of the metal mass, and got a value of 8.44.

This seems slightly lower than values of solar metallicity quoted in the literature, which seem to be around 8.7-8.9 - corresponding to a difference by a factor of around 2.5. I just wanted to confirm that these numbers match yours, and I'm not doing anything drastically wrong. If it helps, my program is as follows:

``````def to_log12(z):
# Assume that oxygen is 35% of the metal mass
oxy_mass_frac = 0.35*z
n_oxy_frac = oxy_mass_frac/16.0
logOH = np.log10(n_oxy_frac)
return logOH + 12
``````

Benji Paul Torrey
• 1
• 27 Jun '19

Hi Benji,

I think you're more-or-less doing things right here. Though, for the calculation you provide, you're calculating Log(O/M_total) + 12 = Log( 0.35 x 0.0127 / 16) + 12 = 8.44, but should instead be using Log(O/H) + 12 = Log( 0.35 x 0.0127 / (0.74 * 16) ) + 12 = 8.57 to account for Hydrogen only being ~74% of the total mass.

This is ~0.1 dex lower than the measured present day photosphere Oxygen abundances which come in the mid-to-high mid 8.6 range in http://articles.adsabs.harvard.edu/pdf/2005ASPC..336...25A (8.66) or https://www.annualreviews.org/doi/pdf/10.1146/annurev.astro.46.060407.145222 (8.69). Any offset here could be caused by the 35% Oxygen assumed fraction being a bit low (raising this to 40-45% removes the tension) or a low assumed solar metallicity for Illustris (though, this would have to be raised to ~ 0.018 to reconcile the difference). In either case, the normalization of galactic metallicity measurements are known to be very uncertain, and so we aimed to not take the overall metallicity normalization too seriously (and hopefully the text reflected this).

In your analysis, I might encourage using directly the Oxygen-to-Hydrogen abundances which should remove this uncertainty and is almost equivalently simple.

Best,
Paul Torrey

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