Metallicity - Calculation

Calculation

The metallicity of the Sun is approximately 1.8 percent by mass. For other stars, the metallicity is often expressed as "", which represents the logarithm of the ratio of a star's iron abundance compared to that of the Sun (iron is not the most abundant heavy element, but it is among the easiest to measure with spectral data in the visible spectrum). The formula for the logarithm is expressed thus:

where and are the number of iron and hydrogen atoms per unit of volume respectively. The unit often used for metallicity is the "dex" which is a (now-deprecated) contraction of decimal exponent. By this formulation, stars with a higher metallicity than the Sun have a positive logarithmic value, while those with a lower metallicity than the Sun have a negative value. The logarithm is based on powers of ten; stars with a value of +1 have ten times the metallicity of the Sun (101). Conversely, those with a value of −1 have one tenth (10 −1), while those with −2 have a hundredth (10−2), and so on. Young Population I stars have significantly higher iron-to-hydrogen ratios than older Population II stars. Primordial Population III stars are estimated to have a metallicity of less than −6.0, that is, less than a millionth of the abundance of iron which is found in the Sun.

This same sort of notation is used to express differences in the individual elements from the solar proportion. For example, the notation "" represents the difference in the logarithm of the star's oxygen abundance compared to that of the Sun and the logarithm of the star's iron abundance compared to the Sun:

The point of this notation is that if a mass of gas is diluted with pure hydrogen, then its value will decrease (since there are fewer iron atoms per hydrogen atom after the dilution), but for all other elements X, the ratios will remain unchanged. By contrast, if a mass of gas is polluted with some amount of pure oxygen, then its will remain unchanged but its ratio will increase. In general, a given stellar nucleosynthetic process alters the proportions of only a few elements or isotopes, so a star or gas sample with nonzero values may be showing the signature of particular nuclear processes.