The code SUMA
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                                                            2. PRESENTATION OF THE CODE

The SUMA code simulates the physical conditions of an emitting gaseous cloud under the coupled effect of photoionization from an external source and shocks assuming a plane-parallel geometry. Actually, the use of SUMA in case of spherical shells of gas is justified by large curvature radii ([26][27]). Two cases may be considered, corresponding to the photoionizing radiation flux reaching the gas on the same side or on the opposite side of the shock front. They are selected at the start of the calculations by the parameter str = 0 and str = 1, respectively.

 The main input parameters are those referring to the shock, as well as those characterizing the source of the ionizing radiation spectrum, those referring to dust, and the chemical abundances of He, C, N, O, Ne, Mg, Si, S, Cl, Ar and Fe, relative to H. The geometrical thickness of the nebula is also an input parameter in the matter-bound case and/or in case str = 1.

 Results regarding photoionization calculations have been compared with those obtained by other photoionization codes [31].

 The calculations start at the shock front where the gas is compressed and thermalized adiabatically, reaching the maximum temperature (T α Vs2, where Vs is the shock velocity) in the immediate post-shock region. In each slab compression is calculated by the Rankine- Hugoniot equations [32] for the conservation of mass, momentum, and energy. The downstream region is automatically cut in many plane-parallel slabs (up to 300) with different geometrical widths in order to account for the temperature gradient. Thus, the change of the physical conditions downstream from one slab to the next is minimal. If the primary ionizing radiation reaches the shock-front, the calculations stop when the electron temperature is as low as 200 K, if the nebula is radiation bound, or at a given value of the nebula geometric thickness, if it is matter bound. In the case where shock and photionization act on opposite sides of the nebula, the geometrical width of the nebula D is an input parameter. Diffuse radiation bridges the two sides, and the smaller D, more entangled are the effects of photoionization and shocks in the middle section of the cloud. In this case, a few iterations are necessary to consistently obtain the physical conditions downstream.


The ionizing radiation from an external source is characterized by its spectrum, which is calculated at 440 energies, from a few eV to KeV, depending on the object. Due to the radiative transfer, the radiation spectrum changes throughout the downstream slabs. Each slab contributes to the nebula optical depth. The calculations assume a steady state downstream.  In addition to the radiation from the primary source, the effect of the diffuse radiation created by the gas emission (line and continuum) is also taken into account [33], using about 240 energies to calculate the spectrum.


For each slab of gas, the ionic fractional abundances of each chemical element are obtained by solving the ionization equations. These equations account for the ionization mechanisms (photoionization by the primary and diffuse radiation, and collisional ionization) and recombination mechanisms (radiative, dielectronic recombinations) as well as, for charge transfer effects. The ionization equations are coupled to the energy equation [32], when collision processes dominate, and to the thermal balance equation if radiative processes dominate. This latter balances the heating of the gas due to the primary and diffuse radiations reaching the slab, and the cooling, due to recombinations and collisional excitation of the ions followed by line emission, as well as collisional ionizations and thermal bremsstrahlung. The coupled equations are solved for each slab, providing the physical conditions necessary for calculating the slab optical depth, as well as its line and continuum emissions. The slab contributions are integrated throughout the nebula.


The effect of dust within the gaseous nebula, characterized by the dust-to-gas ratio d/g and the initial grain radius, agr, is consistently taken into account. Dust and gas entering the shock front and downstream are coupled by the magnetic field. The grain radius can be reduced by sputtering depending on the shock velocity and on the gas density. The details of dust temperature calculations are given by [22][19]. The grains are heated by the primary and secondary radiation, and by gas collisional processes. When the dust-to-gas ratio is high, the mutual heating of dust and gas may accelerate the cooling rate of the gas, changing the line and continuum spectra emitted from the gas. The dust-to-gas ratios are constrained by the intensity of the continuum IR bump, and the relative abundances of the elements by the line ratios.