Notes C

1st Week: Introduction to Nuclear Physics & Abundance Determination in Astrophysics C

Abundancies

Several related quantities for measuring the abundances of the various elements exist in astrophysics. The first, and most obvious, is simply the number of particles of a given species $i$ divided by the total number of particles in a given volume, that is, the particle abundance:

$X_{i}={\frac {n_{i}}{\sum _{j}{n_{j}}}}$

The relative abundance $\epsilon _{i}$ of a species $i$ is also sometimes given. It's the log of the number of particles divided by the number of hydrogen particles in the volume, with a constant added to make negative values unlikely.

$\epsilon _{i}=\log _{10}({\frac {n_{i}}{n_{H}}})+12$

Finally if we're interested in the portion of the mass made up by a given element, we can calculate the mass fraction:

$X_{i}={\frac {n_{i}m_{i}}{\rho }}$

We might also be interested in the number of electrons (or protons) in the sample relative to all atomic particles, so we also define the electron abundance:

$Y_{e}={\frac {\sum {Z_{i}n_{i}}}{\sum {A_{i}n_{i}}}}$