He-like Ion Line Emissivities for X-Ray Spectral Modeling


Helium-like energy level diagram for O VII (From Gabriel and Jordan 1969 MNRAS
    145, 241) Helium-like R-ratios vs n_e (Wolfson et al 1983 ApJ 269, 319)

(From Gabriel and Jordan 1969 MNRAS 145, 241; Wolfson et al 1983 ApJ 269, 319)

ERRATUM: October 26, 2016; We recently discovered an error in the photo-excitation coefficients table, he_photoex_modifier_chianti.fits, such that the energy-density scale was in error by a factor of two (due to inadvertent inclusion of the dilution factor). This made the critical flux for photoexciation too large by a factor of two, or conversely, the derived radius too small by a factor of sqrt(2). The fixed file is included distribution linked below.

Emissivity Modifier for He-like triplets

The He-like triplet lines which occur in the X-ray band from 4-42 A are powerful diagnostics of density or photoexcitation. The APED (Astrophysical Plasma Emission Database), however, only contains emissivities for low density.

To provide better support for more direct fitting and modeling within a data-analysis enviroment, we have

  • constructed tables of coefficients which parameterize the electron density dependence of the triplet lines' collisionally excited emissivities for a grid of temperatures, for several astrophysically important elements;
  • written an ISIS plasma model interface to define and apply "emissivity modifiers" for the atomic database (APED), which can be used directly in X-ray spectral modeling and fitting;
  • constructed similar coefficients tables using Chianti (Dere et al., 1997 A&AS, 125, 149; Dere et al., 2009, A&A 498, 915) emissivities;
  • constructed a coefficients table for photoexcitation-dominated triplet emission (also using Chianti) in which the independent parameter is photon energy density (further controlled by a dilution factor).

Stand-alone Use

While the coefficients tables are supported at a high level for plasma modeling and spectral fitting in ISIS, they can also be used independently since they contain all information required to evaluate the He-like emissivities as a function of temperature and density, in plasmas dominated either by collisional or photoelectric excitation. All that is required is the ability to read FITS binary tables.

The use of such tables allows direct access to density as a model parameter, as opposed to the common method of fitting triiplet line fluxes parametrically, then given the ratio of the forbidden to intercombination line fluxes (R = f/i), looking up the implied density from external sources.

Important Files

Files required to implement the emissivity modifiers within ISIS in conjunction with APED are a FITS file which tabulates emissivity modifier coefficients for He-like triplets, and an ISIS source code file which defines the modifier access and fit functions.
  • Technical notes, including detailed examples and FITS file specifications: he_modifier_technote.pdf
  • Coefficients data files:
    • Chianti-based density coefficients: he_modifier_chianti.fits
    • Chianti-based photoexcitation coefficients: he_photoex_modifier_chianti.fits
    • APEC-based density coefficients: he_modifier_apec.fits
  • The ISIS modifier model and function definitions: he_modifier.sl A Function reference is included with the source distribution (as on-line interactive help), and also here.
All are packaged together in this compressed tar file.


See INSTALL and Makefile in the distribution.


The following ISIS script gives a very simple example of model evaluation of the O VII triplet under high electron density, and then for photoexcitation.
  % Initialize:
  plasma( aped ) ;
  require( "he_modifier" );

  % Set up a model fit function:
  create_he_modifier( "hemod" );
  create_aped_fun( "xaped", default_plasma_state );

  fit_fun( "xaped(1, hemod(1))" );

  set_par( "xaped(1).temperature", 2.e6 );
  set_par( "hemod(1).O_log10_ndens", 12 );
  set_par( "xaped(1).vturb", 200 );

  % Evaluate, and plot; 1st, high n_e, then overplot low:
  use_thermal_profile;  % enable line broadening, for a nicer view:
  (wlo, whi) = linear_grid( 21.5, 22.2, 512 );
  f = eval_fun( wlo, whi ) ;

  label("Wavelength", "Flux", "O VII Triplet vs Density" );
  hplot( wlo, whi, f );
  set_par( "hemod(1).O_log10_ndens", 10 );
  ohplot( wlo, whi, eval_fun( wlo, whi ) );

  % Now the photoexcitation case:

  create_he_modifier( "photoex" ; photoex );

  fit_fun( "xaped( 1, photoex( 1; db_norm ) )" );

  set_par( "photoex(1).O_log10_unu", -13 ); % radiation field
  set_par( "photoex(1).O_r", 2 );

  label("Wavelength", "Flux", "O VII Triplet Photoexcitation" );
  hplot( wlo, whi, eval_fun( wlo, whi ) );
  set_par( "photoex(1).O_r", 10 );
  ohplot( wlo, whi, eval_fun( wlo, whi ) );
O VII triplet, at high and low number density O VII triplet, at high and low UV photon energy density.


Support for this work was provided by the National Aeronautics and Space Administration, Goddard Space Flight Center award NNX10AD41G to MIT through the Astrophysical Data Analysis Program. We also thank Dr. Randall Smith and Dr. Adam Foster for a pre-release version of APEC and for their help in production of a density-dependent emissivity database.

This page was last updated Oct 9, 2020 by David P. Huenemoerder. To comment on it or the material presented here, send email to dph@space.mit.edu.
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