Post-Processing Emission Line Maps

Use this program to get emission line maps from a fixed grid input. Maps produced can be from OI, OII, NI, NII, SII, or H-alpha. For the first five options, emission maps from the first five energy levels are possible.

Input for this program is the total number density of Hydrogen (nH_tot), the electron temperature (T), and the Hydrogen ionization fraction (Xh). The number density of electrons, ne, is assumed to be equal to the number density of ionized Hydrogen, n_HII, so ne ~ n_HII = nH_tot * Xh.

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OI, OII, NI, NII, SII

All S is assumed to be in the form of SII, and its number density, n_SII, is related to nH_tot through abundances: n_S/nH_tot = n_SII/nH_tot = 10^{(7.3 - 12)}, where 10^7.3 is the solar abundance of S, relative to a Hydrogen abundance of 10¹².

OI, OII, NI, and NII are determined via charge exchange

The percentage of each atom(or ion) (hereafter `species') in a given level is calculated assuming statistical equilibrium, such that the rate of collisionally exciting into a level is equal to the rate of collisionally de-exciting out of that level + the rate of radiatively decaying out of that level. e.g., for tranisitions between levels i & j: ni*ne*Cij = ne*Aji + nj*ne*Cji

• ni = number density of given species in level i (cm^-3*s^-1)
• ne = number density of electrons (we are only considering electron collisions) (cm^-3*s^-1)
• Cij = collision excitation rate coefficient (cm³/s)
• Aji = Einstein A coefficient for radiative decay from level j to level i (s^-1)
• Cji = collision de-excitation rate coefficient (cm³/s)

The emissivity for transition from level j to i is: J_ji = nj*hv_ji*Aji/(4Pi) (ergs/cm³/s/str)

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H-alpha

For H-alpha, radiative recombination and collisional excitation (from n=1 → 3) are considered.

Recombination:

j = n_HII*ne*hv_alpha*recom_coeff/(4Pi) = (ne²)*hv_alpha*recomb_coeff/(4Pi)

The recomb_coeff being used was from Pequignot et al, 1991, but I'm now using Verner & Ferland, 1996. Full hand-calc checks have not yet been completed, however.

Collisional Excitations:

j = n_HI*ne*hv_alpha*q13/(4Pi) ~ (nH_tot - ne)*ne*hv_alpha*q13/(4Pi)

The collision coefficient, q13 (since we're only looking at collisions from levels 1 to 3) = [(8.63*10^-6)*exp(-E13/kT)/(g*T^0.5)] * Gamma_13, where:

• 8.63*10^-6 comes from constants in the collisional cross-section as well as in the Maxwellian distribution of energies
• E13 is the energy from level 1 to 3 for Hydrogen (= 12.09 eV)
• g is the statistical weight of level 1 (= 2)
• Gamma_13 is a fit to the integration over collisiona strengths and energies.

Currently I'm switching from Giovanardi & Palla, 1989, fits for Gamma_13 to a combination of Callway et al '93 and Callaway, 1994. Again, hand-calcs not yet completed.

Total emissivity is the sum of the two j values.

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The emissivities are summed up along the line of sight and multiplied by cell length to get intensity maps.

More details yet to be added for all of this.