Stephen St.Vincent - Emission Measure Calculation

Emission Measure Calculation
All calculations use Anders and Grevesse (1989) Standard Abundance Distribution

The ATOMDB definition of emission measure is

EM = &int n_en_HdV
We also have n_H = &rho / (n_i/n_H * m_H * &mu)
where &mu = 1.298, m_H=1.67x10^-24 g, and n_i/n_H &asymp 1 + n_He/n_H = 1.0974. The definition of n_e is n_e &asymp n_H + 2*n_He + 8*n_metals
Here I use a mean charge state of 8 for metals, 2 for helium, and 1 for hydrogen.
But n_i = A_i*n_H, so n_e &asymp n_H + 2*A_He*n_H + 8*A_metalsn_H
or
n_e &asymp n_H * (1 + 2*A_He + 8*A_metals)

A_He = 0.0974 from above. For A_metals, I simply sum the values of A for the 5 next most abundant elements: O, C, N, Ne, and Fe, giving a value of 0.0015. So the final expression for n_e is n_e &asymp &rho / (n_i/n_H * m_H * &mu) * (1 + 2*A_He + 8*A_metals)

So EM is then defined as EM = &int [&rho / (n_i/n_H * m_H * &mu)]^2 * (1 + 2*A_He + 8*A_metals) dV