# ionic analysis.nebular

NAME · USAGE_ · DESCRIPTION · PARAMETERS · EXAMPLES · BUGS
REFERENCES · SEE_ALSO

## NAME

ionic -- Compute level populations, critical densities, line emissivities & ionic abundance

## USAGE

ionic atom spectrum

## DESCRIPTION

This task computes atomic energy-level populations, critical densities, and line emissivities for a nebular (i.e., low density) gas, within the N-level atom approximation, given the electron temperature (T_e) and density (N_e). The user specifies the name and the spectrum of the atom, the assumed values for T_e and N_e, and (optionally) the wavelength and relative flux of a particular emission line (or range of lines) of interest. The task output lists the level populations, critical densities, line emissivities, and optionally the ionic abundance relative to ionized hydrogen.

The critical density for a level "i" is defined as the density at which the collisional de-excitation rate balances the radiative transition rate:

```                          ___
\    A
/__   ij
j<i
N_crit(i) =  ----------
___
\   q
/__  ij
j!=i
```

In the low density limit the emissivity is proportional to the product N_e * N_ion, whereas for densities exceeding the critical density, the emissivity is proportional to N_ion. Thus, line emission in a nebula occurs most efficiently near the critical density.

Note that the output line emissivities are per unit ion density per unit electron density. That is, true volume emissivity is related to the output emissivities by:

```            4 * pi * j(true) = N_e * N_ion * j(output)
```

The emissivities are listed by atomic transition, as are the calculated wavelengths. If the wavelength of a particular line of interest and the observed line flux are also provided, the task will compute the ionic abundance, relative to ionized hydrogen, as:

```            N(X_i)    I(line)    j(H-beta)
------ = --------- * ---------
N(H+)    I(H-beta)    j(lines)
```

In this case the calculated wavelength is really the sum of all lines lying within a specified range of the wavelength of interest; that range is specified with the "wv_toler" parameter. The H-beta emissivity is derived from a formula by Aller (1984):

```    4 * PI * j(H-beta) = 1.387E-25 * N_e N_(H+) * T_4 ^(-0.983)
* dex (-0.0424/T_4),   erg/s/cm^3
```

Where T_4 = T_e / 10^4 K. This formula is accurate to within 4% for densities less than 10^6. The result of the abundance calculation is stored in the task parameter "result" for ease of use in CL scripts.

The available combinations of atoms and spectra are listed below:

```	 C I        C II       C III
N I        N II       N III     N IV
O I        O II       O III     O IV    O V
Ne III     Ne IV      Ne V      Ne VI
Na IV                 Na VI
Mg V                  Mg VII
Al II
Si II      Si III
S II       S III      S IV
Cl II      Cl III     Cl IV
Ar III     Ar IV      Ar V
K IV       K V
Ca V
```

A CAUTION ABOUT THE WAVELENGTHS: Please note that the wavelengths used throughout these help files are those commonly used in the astronomical literature. However, the wavelengths used in the program are derived from the published atomic data for each ion. These derived wavelengths are used partly for consistency with the models, and partly because there is as yet no good reference for ALL the wavelengths of all the ions used in these tasks. But be aware that there are differences with the accepted values (usually around +1 Angstroms). The wavelength discrepancy is only likely to cause confusion when using the "ionic" task to compute an ionic abundance from a particular line. In this case, be sure the "wave" or "wv_toler" parameters are set appropriately.

These wavelength discrepancies (in the fourth decimal place) are a reminder of the imperfections inherent in all the models from which the atomic data are derived, although the uncertainties in the cross-sections range from 5% to 50%.

## PARAMETERS

atom = "oxygen" [string]
Name of the atom, which is one of: carbon, nitrogen, oxygen, neon, sodium, magnesium, aluminum, silicon, sulfur, chlorine, argon, potassium, or calcium.
spectrum = [int]
Spectrum number of the atom, e.g. "3" for [O iii], "2" for [S ii], etc. Must lie in the range 1 <= spectrum <= 8.
(temperature = 10000.) [real]
Assumed nebular electron temperature, in Kelvins. Must lie in the range 500. <= T_e <= 1.e+5. (NB: some collision strengths in the literature are only given between 5000 K and 20,000 K, so use caution.)
(density = 1000.) [real]
Assumed nebular electron density, in units of 1/cm^3. Must lie in the range 1. <= N_e <= 1.E+8.
(wave = INDEF) [real]
Wavelength for a (semi-) forbidden line of interest, in Angstroms. When this and the "flxratio" parameter are specified, the ionic abundance relative to ionized hydrogen is calculated and stored in the "result" parameter.
(wv_toler = 1.0) [real]
Tolerance for "wave" parameter: all emission lines with wavelengths within "wv_toler" of "wave" will be included in the abundance calculation when both "wave" and "flxratio" are specified. This parameter can be used to calculate an accurate abundance even when the observed line flux is really a blend of two or more closely spaced lines. If the tolerance is zero, the "wave" parameter must match the calculated wavelength exactly, or the calculated abundance will be given as zero.
(flxratio = INDEF) [real]
Emission line flux, relative to I(H-beta) = 100. When this and the "wave" parameter are specified, the ionic abundance relative to ionized hydrogen is calculated and stored in the "result" parameter.
(result = INDEF) [real]
Ionic abundance relative to H+. Calculated only if the "flxratio" and "wave" parameters are both specified.
(verbose = yes) [boolean]
Print level populations and critical densities as well? The critical density for a level "i" is the density at which the collisional de-excitation rate from this upper level balances the radiative transition rate.
(at_data = at_data) [real]
Atomic reference data directory name.

## EXAMPLES

1. Find the level populations, critical densities, and line emissivities for the S+ ion, assuming an electron temperature of 9200 K and a density of 1500/cm^3.

```   cl> ionic sulfur 2 temper=9200 density=1500. verb+

# Volume Emissivities for: S^1+
T_e:   9200.0;  N_e: 1.500E3

# Level Populations - Critical Densities (/cm^3)

Level 1:   9.6E-1
Level 2: 1.200E-2       1.413E4
Level 3: 3.025E-2       1.551E3
Level 4: 4.481E-6       1.252E6
Level 5: 5.341E-6       1.678E6
Level 6: 1.16E-17      4.245E14
Level 7: 7.10E-18      1.798E14
Level 8: 3.37E-18      1.297E14

6730.87   # Wavelength
(2-->1)   # Upper->Lower Level
1.079E-20   # Volume Emissivity

6716.42   3148614.6
(3-->1)     (3-->2)
1.628E-20   4.262E-26

4076.35    10336.31    10370.36
(4-->1)     (4-->2)     (4-->3)
1.319E-21   8.096E-22   3.588E-22

4068.60    10286.63    10320.34   2139952.9
(5-->1)     (5-->2)     (5-->3)     (5-->4)
3.912E-21   8.321E-22   1.042E-21   3.405E-29

1259.52     1549.47     1550.23     1822.70     1824.25
(6-->1)     (6-->2)     (6-->3)     (6-->4)     (6-->5)
5.290E-24       INDEF       INDEF       INDEF       INDEF

1253.81     1540.84     1541.59     1810.77     1812.30   276663.44
(7-->1)     (7-->2)     (7-->3)     (7-->4)     (7-->5)     (7-->6)
3.294E-24       INDEF       INDEF       INDEF       INDEF       INDEF

1250.58     1535.97     1536.72     1804.05     1805.57   176289.11   485908.65
(8-->1)     (8-->2)     (8-->3)     (8-->4)     (8-->5)     (8-->6)     (8-->7)
1.581E-24       INDEF       INDEF       INDEF       INDEF       INDEF       INDEF

# H-beta Volume Emissivity:
1.354E-25 N(H+) * N(e-) ergs/s

Log10(x) =   1.194E0
```

2. Find the abundance of the O(+) ion, relative to ionized hydrogen. The observed flux in the [O ii] 3727.1 + 3729.8 AA emission line doublet (relative to I(H-beta) = 100) is provided, along with a wavelength tolerance large enough to accomodate both lines in the pair, to relate volume emissivities to ionic abundance.

```   cl> ionic oxygen 2 temper=1.e4 dens=1000. wave=3728 wv_tol=2.0 \
>>> flx=0.7 verb-

# Volume Emissivities for: O^1+
T_e:  10000.0; N_e:  1.000E3

3728.80   # Wavelength
(2-->1)   # Upper->Lower Level
1.156E-21   # Volume Emissivity

3726.05   5053057.1
(3-->1)     (3-->2)
1.670E-21   8.995E-28

2470.33     7319.50     7330.12
(4-->1)     (4-->2)     (4-->3)
6.706E-23   4.297E-23   2.312E-23

2470.21     7318.44     7329.06   50761421.3
(5-->1)     (5-->2)     (5-->3)     (5-->4)
1.663E-23   1.374E-23   2.293E-23   5.383E-36

834.47     1075.05     1075.28     1260.13     1260.17
(6-->1)     (6-->2)     (6-->3)     (6-->4)     (6-->5)
2.002E-26       INDEF       INDEF       INDEF       INDEF

833.33     1073.17     1073.40     1257.55     1257.58   612745.10
(7-->1)     (7-->2)     (7-->3)     (7-->4)     (7-->5)     (7-->6)
1.306E-26       INDEF       INDEF       INDEF       INDEF       INDEF

832.76     1072.22     1072.45     1256.25     1256.28   407664.08   1218026.8
(8-->1)     (8-->2)     (8-->3)     (8-->4)     (8-->5)     (8-->6)     (8-->7)
6.456E-27       INDEF       INDEF       INDEF       INDEF       INDEF       INDEF

# H-beta Volume Emissivity:
1.258E-25 N(H+) * N(e-)  (erg/s)

Log10(x) =   1.000E0

Ionic Abundance: N(O^1+) / N(H+) =  3.116E-7
```

## BUGS

Extremely small volume emissivities, those less than about 1.E-36, are treated as INDEF.

## REFERENCES

The 5-level atom program, upon which this package is based, was originally written by M.M. DeRobertis, R. Dufour, and R. Hunt. This package was written by R.A. Shaw (STScI). A description was published by R.A. Shaw & R.J. Dufour (1994). Type "help nlevel" for additional information about the N-level atom approximation, and for references to the atomic parameters and the other literature references. Support for this software development was provided by the Astrophysics Data Program through NASA grant NAG5-1432, and through STScI internal research funds.