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nlevel analysis.nebular



nlevel -- Tasks for deriving T_e, N_e, and nebular ionic abundances


Some of the tasks in the `nebular' package are based upon the FIVEL program developed by De Robertis, Dufour & Hunt (1987). They can be used to calculate the physical conditions in a low density (nebular) gas given appropriate diagnostic emission line ratios; and line emissivities given appropriate emission line fluxes, the electron temeperature (T_e), and density (N_e). These tasks have been extended beyond the original FIVEL program to provide diagnostics from a greater set of ions and emission lines, most particularly those in the vacuum ultraviolet that are now available from the IUE and HST archives. In addition, more than 5 levels are now accomodated for most of the ions.

It should be noted that these routines are not intended as a full nebular photoionization model, such as G. Ferland's CLOUDY. Rather, they are intended for the fairly common instances where one has somewhat incomplete information about a complicated physical system (such as a narrow-line region in an active galactic nucleus), or somewhat more information about a physically simple system, such as a fairly evolved planetary nebula. In these cases it is useful to calculate nebular densities or temperatures from the traditional diagnostic line ratios, either to provide some resonable input parameters for a more complicated physical model, or to calculate ionic abundances (or other quantities) within some simplifying assumptions.

The physical basis for line emission from a photoionized nebula has been discussed in many excellent references and will not be repeated here. A detailed description of the methodology of this software, and the appropriate astrophysical problem domain, can be found in Shaw & Dufour (1995). A link to the on-line and PostSCript versions of this paper may be found on the Web page for the nebular package, at URL


Certain emission line ratios in five-level atoms are very useful as diagnostics of electron temperature or density. The p^2 and p^4 ions have ground state configurations such that some transitions from upper levels have very different excitation energies; ratios of the resulting emission lines can serve as very effective temperature indicators because they are insensitive to density. Conversely, in p^3 ions some transitions to the ground state have upper levels with nearly the same excitation energy. Ratios of these lines can serve as very effective density indicators because the level populations are quite insensitive to temperature. The available diagnostic line ratios for the FIVEL tasks are tabulated in the next section.

The ionic abundances, relative to H+, can be derived from the observed ratio of a forbidden line intensity relative to H-beta. Aller (1984) provides a convenient fitting formula for the H-beta emissivity which is accurate to within about 4% for densities less than about 10**6/cm^3. The formula:

  4(pi) j(H-beta) = 
		1.387E-25 N_e N(H+) t       dex(-0.0424/t)

in units of (erg/cm^3/s), is used within the nebular routines; here, t = T_e / 10^4 K. The H-beta emissivity is calculated for the same temperature as the specified ion, and the ionic abundance ratio is calculated from:

	        N(X )    I(line)    j(H-beta)
		----- = --------- * --------- 
		N(H+)   I(H-beta)    j(line)

where I(line)/I(H-beta) is the observed line ratio. Note that ALL of the line emissivities output by the "ionic" task are per unit ion density per unit electron density. That is, the true volume emissivity (j_true) is related to by:

          4 * pi * j(true) = N_e * N(X^i) * j(task) 

Any of the transitions for any of the ions can be used to derive the ionic abundance, but the strongest lines that are typically used in the nebular tasks are tabulated in the next section.

It should be noted that the nebular routines give line emissivities and diagnostic ratios for metastable-level magnetic dipole or electric quadrapole transitions under the assumption of pure statistical equilibrium and do not account for radiation transfer effects such as self-absorption in some levels. For some astrophysical situations such as giant H ii regions and AGNs, the optical depths of the ^3P multiplet levels of p^2 and p^4 ions such as [O iii], [N ii], and [Ne iii] can become significant, which will affect the observed far-infrared line strengths for such objects compared to the program predictions. While no nebular task currently makes use of N_e and T_e diagnostics from the far-infrared lines, one can make use of these lines with the "abund" task (see below) for low-density H II regions and planetary nebulae. However, caution is advised for such use on giant H II regions or dense, highly ionized planetary nebulae for which the optical depth in the ^3P levels could become important.


In order to calculate ionic abundances in a real nebula, it is necessary to know the electron temperature and density where the various ionic emissions are produced. In some physical contexts it makes sense to view the structure of a nebula an an "onion skin", where the ionization drops off radially from some central source of ionizing radiation, and T_e drops somewhat as N_e increases (on average) with distance. Different ions are found in spherical shells of various radii, depending on the ionization potential of the ion.

Two tasks in this package were designed to model nebulae in just this way, with 3 zones of low-, intermediate-, and high-ionization. The nebular physical parameters are derived within each zone by making simultaneous use of temperature- and density-sensitive line ratios from different ions with similar ionization potentials. The small dependence of the temperature indicators upon N_e, and of the density indicators upon T_e, is removed with an iterative technique and ultimately results in an average T_e and N_e within each zone.

The modelling tasks are layered upon the TABLES external package in order to provide a simple and powerful data structure and ancillary tools for access to the observed data and the derived results. The input tables may contain line fluxes for many nebulae and/or many regions within nebulae, one object/region per row. The flux(es) for a given emission line (usually, but not necessarily, given relative to I(H-beta)=100) are placed in separate columns. The tasks locate particular emission line fluxes and temeratures/ densities via names of specific columns in the input table(s). These columns have suggestive default names, but are entirely user-definable.

Since it is often difficult to provide a complete set of diagnostic line ratios (owing to limited signal-to-noise ratio, spectral resolution, wavelength coverage, etc., of the observed spectra) these tasks were designed to make use of whatever information is available, and to use reasonable defaults (e.g., T_e = 10,000 K, N_e = 1000/cm^3) when necessary. In particular, any emission line flux that is unavailable (e.g. the relevant line fluxes are INDEF, or the column name for that line flux is not found) is excluded from the calculations. If there are no valid diagnostic line fluxes available for a given ion, the result for that ion is INDEF.

The available diagnostic line ratios, the ionization potential of the associated ion, and the nebular ionization zone to which they are attributed, are listed by ion below. The line ratio is in the form I(wave1)/I(wave2), where "wave1" and "wave2" are in units of Angstroms; ratios involving sums of line strengths are given as I(wave1+wave2)/I(wave3+wave4). Diagnostics marked with an asterisk are not currently used in the 3-zone nebular model, described below.

            Table 1. Ions Included in NEBULAR

                        Ground   No. 
      Ion    Spectrum   Config  Levels  I.P.  Zone
      C(0)     C I        p^2     5	 0.0   Low
      C(+1)    C II       p^1     8     11.3   Low
      C(+2)    C III      s^2     5     24.4   Med  
      N(0)     N I        p^3     5      0.0   Low
      N(+1)    N II       p^2     6     14.5   Low
      N(+2)    N III      p^1     8     29.6   Med
      N(+3)    N IV	  s^2     5     47.4   Med
      O(0)     O I        p^4     5      0.0   Low
      O(+1)    O II       p^3     5     13.6   Low
      O(+2)    O III      P^2     6     35.1   Med 
      O(+3)    O IV       P^1     8     54.9   High
      O(+4)    O V	  s^2     5     77.4   High
     Ne(+2)   Ne III      p^4     5     41.1   Med
     Ne(+3)   Ne IV       P^3     5     63.5   High
     Ne(+4)   Ne V        P^2     6     97.0   High
     Ne(+5)   Ne VI       p^1     7    126.3   High 
     Na(+3)   Na IV       p^4     5     71.7   High
     Na(+5)   Na VI       p^2     5    138.4   High 
     Mg(+4)   Mg V        p^4     5    109.3   High 
     Mg(+6)   Mg VII      p^2     6    186.5   High
     Al(+1)   Al II       s^2     5      6.0   Low
     Si(+1)   Si II       p^1     7      8.2   Low
     Si(+2)   Si III      S^2     5     16.3   Low 
      S(+1)    S II       P^3     8     10.4   Low
      S(+2)    S III      p^2     5     23.4   Med
      S(+3)    S IV       p^1     5     35.0   Med
     Cl(+2)   Cl III      P^3     5     23.8   Med
     Cl(+3)   Cl IV       p^2     5     39.9   Med
     Ar(+2)   Ar III      p^4     5     27.6   Med
     Ar(+3)   Ar IV       P^3     5     40.9   Med
     Ar(+4)   Ar V        p^2     5     59.8   High
      K(+3)    K IV       p^4     5     46.0   Med
      K(+4)    K V        p^3     5     60.9   High 
     Ca(+4)   Ca V        p^4     5     67.0   High

         Table 2. Electron Density Diagnostics

     Spectrum       Line Ratio              Zone
       C ii]        I(2326) / I(2328)       Low  *
       C iii]       I(1907) / I(1909)       Med  
      [N i]         I(5198) / I(5200)       Low  *
       N iii]       I(1749) / I(1752)       Med  *
       N iv]        I(1483) / I(1487)       Med
      [O ii]        I(3726) / I(3729)       Low
       O iv]        I(1401) / I(1405)       High *
      [O v]         I(1214) / I(1218)       High
     [Ne iv]        I(2423) / I(2425)       High
     [Al ii]        I(2661) / I(2670)       Low
     [Si ii]        I(2335) / I(2345)       Low
      Si iii]       I(1883) / I(1892)       Low  *
      [S ii]        I(6716) / I(6731)       Low
      [S iv]        I(1406) / I(1417)       Med
     [Cl iii]       I(5517) / I(5537)       Med
     [Ar iv]        I(4711) / I(4740)       Med
      [K v]         I(6223) / I(6349)       High

        Table 3. Electron Temperature Diagnostics

     Spectrum       Line Ratio              Zone
      [C i]    I(9823+9849) / I(8728)        Low
      [N i]    I(5198+5200) / I(10397+10407) Low
      [N ii]   I(6548+6583) / I(5755)        Low
      [O i]    I(6300+6363) / I(5577)        Low
      [O ii]   I(3726+3729) / I(7320+7330)   Low
      [O iii]  I(4959+5007) / I(4363)        Med
     [Ne iii]  I(3869+3969) / I(3342)        Med
     [Ne iv]   I(2422+2425) / I(1601+1602)   High
     [Ne v]    I(3426+3346) / I(2975)        High
     [Na iv]   I(3242+3362) / I(2805)        High
     [Na vi]   I(2871+2970) / I(2569)        High
     [Mg v]    I(2783+2928) / I(2418)        High
     [Mg vii]  I(2506+2626) / I(2262)        High
     [Al ii]   I(2661+2670) / I(1671)        Low
      Si iii]  I(1883+1892) / I(1206)        Low  *
      [S ii]   I(6716+6731) / I(4068+4076)   Low
      [S iii]  I(9069+9532) / I(6312)        Med
     [Cl iii]  I(5517+5537) / I(3353+3343)   Med
     [Cl iv]   I(7530+8045) / I(5323)        Med  *
     [Ar iii]  I(7136+7751) / I(5192)        Med
     [Ar iv]   I(4711+4740) / I(2854+2868)   Med  *
     [Ar v]    I(6435+7006) / I(4626)        High
      [K iv]   I(6102+6796) / I(4511)        High
      [K v]    I(4123+4163) / I(2515+2495)   High
     [Ca v]    I(5309+6087) / I(3996)        High

The diagnostic line ratios are derived from the input line fluxes, corrected for interstellar reddening. The reddening corrected line flux "I" is derived from the input line flux "F" by:

	  I(line) = F(line) * dex {-c * f(lambda)}

where "c" is the extinction constant (i.e. the logarithmic extinction at H-beta, 4861 Ang), and "f(lambda)" is derived from one of a few possible extinction functions. The choices for Galactic extinction are: Savage & Mathis (1979), Cardelli, Clayton, & Mathis (1989), and the function of Kaler (1976), which is based on Whitford (1958). The choices for extra-Galactic extinction laws are Howarth (1983) for the LMC, and Prevot et al. (1984) for the SMC.

The abundance calculations in the 3-zone model are based upon the diagnostics appropriate for each ion, and are listed below in the "Ionization Zone" column. The emission lines that are actually used in the 3-zone model (which are generally also the strongest) can be found in the file nebular$atomic_data/, but most are also tabulated below (wavelengths are in Angstroms) by ion:

      Table 4. Line Fluxes Often Used for Ionic Abundances

        Ion    Spectrum    Lines Used             Zone
        C(0)    [C i]      9823 9849		   Low
        C(+1)    C ii]     2326+28		   Low
        C(+2)    C iii]    1907+09		   Med

        N(0)    [N i]      5198+5200		   Low
        N(+1)   [N ii]     5755, 6548, 6583 	   Low
        N(+2)    N iii]    1749+52		   Med
        N(+2)   [N iv]     1483+1487		   Med

        O(0)    [O i]      6300, 6363		   Low
        O(+1)   [O ii]     3726+29, 7320+30	   Low
        O(+2)   [O iii]    4363, 4959, 5007 	   Med
        O(+3)   [O iv]     1400+01+05+07	   High
        O(+4)   [O v]      1214+1218		   High

       Ne(+2)  [Ne iii]    3342, 3869, 3968 	   Med
       Ne(+3)  [Ne iv]     2423+25, 4724+25        High
       Ne(+4)  [Ne v]      2975, 3426, 3346 	   High

       Na(+3)  [Na iv]     2805, 3242, 3362 	   Med
       Na(+5)  [Na vi]     2569, 2871, 2970 	   High

       Mg(+4)  [Mg v]      2418, 2783, 2928 	   High
       Mg(+6)  [Mg vii]    2262, 2506, 2626 	   High

       Al(+1)  [Al ii]     1671, 2661+2670	   Low

       Si(+1)  [Si ii]     2335+45+51 		   Low
       Si(+2)   Si iii]    1206, 1883+92 	   Low

        S(+1)   [S ii]     4068+76, 6716+31 	   Low
        S(+2)   [S iii]    6312, 9069, 9532 	   Med
        S(+3)   [S iv]     1405+1406+1417 	   High

       Cl(+1)  [Cl ii]     3679, 5807, 9383	   Low
       Cl(+2)  [Cl iii]    3348, 5517+37	   Med
       Cl(+3)  [Cl iv]     5323, 7531, 8045	   Med

       Ar(+2)  [Ar iii]    5192, 7136, 7751 	   Med
       Ar(+3)  [Ar iv]     2854+68, 4711, 4740, 
                           7170			   Med
       Ar(+4)  [Ar v]      4626, 6435, 7006 	   High

        K(+3)   [K iv]     4511, 6102, 6796        High
        K(+4)   [K v]      2495, 2515, 4123, 4163  High

       Ca(+4)  [Ca v]      3996, 5309, 6087	   High

Note that some fluxes are really sums from closely spaced line pairs. The calculated ionic abundance is the weighted average of that derived from each of the emission lines for that ion.

A CAUTION ABOUT THE WAVELENGTHS: Please note that the wavelengths used throughout these help files are those commonly used in the astronomical literature. However, some of the wavelengths do not have particularly precisely measured values. References for the wavelengths used in this package may be found in the atomic data files in nebular$atomic_data. The wavelength uncertainties are 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.

A CAUTION ABOUT ACCURACIES: The ultimate accuracy of the line emissivities or ionic abundances calculated by this software is inherently limited by the accuracies in the published atomic data: the collision strengths (and their variation with temperature) and the oscillator strengths generally have accuracies of ~10%, although some are as high as 30%. We have endeavored to use the best, recent atomic data as of mid-1996. However, it is possible for this data to be updated easily by the user, if necessary. See the README file in nebular$data.


The atomic data for hydrogen were taken from Brocklehurst (1970, 1971); in particular, we adopt an empirical formula from Aller (1984) for the H-beta line emissivity. References for the other atomic data may be found by typing "help at_data".

The 5-level atom program was originally published by DeRobertis, Dufour & Hunt (1987). Although the nebular tasks are intended to provide all the functionality of their original "FIVEL" FORTRAN program, the code has been entirely re-engineered, and essentially all the atomic data have been updated since that code was published. These tasks also offer additional options and flexibility, including tasks for computing all available diagnostics at once within a simple physical context. Additional enhancements and a discussion of the scientific problem domain are described by Shaw & Dufour (1995). Support for this software development was provided from the NASA Astrophysics Data Program through grant NAG5-1432 to Space Telescope Science Institute, and supplemented by a grant from the STScI Director's Discretionary Research Fund.


Aller, 1984, "Physics of Thermal Gaseous Nebulae" (Dordrecht:D. Reidel)

Brocklehurst, 1970, MNRAS, 148, 417

Brocklehurst, 1971, MNRAS, 153, 471

Cardelli, Clayton & Mathis, 1989, ApJ, 345, 245

De Robertis, Dufour & Hunt, 1987, J. Roy. Astron. Soc. Canada, 81, 195

Hayes & Nussbaumer, 1984, A&A, 134, 193

Howarth, 1983, MNRAS, 203, 301

Kaler, 1976, ApJS, 31, 517

Osterbrock, D. 1989, "Astrophysics of Gaseous Nebulae and Active 
Galactic Nuclei" (Mill Valley:University Science Books)

Prevot, Lequeux, Maurice, Prevot & Rocca-Volmerange, 1984, A&A, 132, 389

Savage & Mathis, 1979, ARA&A, 17, 73

Shaw, & Dufour, 1995, PASP, 107, 896

Whitford, 1958, AJ, 63, 201



Type "help nebular opt=sys" for a general description of the tasks in the `nebular' package.

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