The structure of radiative shock waves

Abstract

Abstract. We considered the structure of steady-state plane-parallel radiative shock waves propagating through the partially ionized hydrogen gas of temperature T 1 = 3000 K and density 10 −12 g cm −3 ≤ ρ 1 ≤ 10 −9 g cm −3 . The upstream Mach numbers range within 6 ≤ M 1 ≤ 14. In frequency intervals of hydrogen lines the radiation field was treated using the transfer equation in the frame of the observer for the moving medium, whereas the continuum radiation was calculated for the static medium. Doppler shifts in Balmer emission lines of the radiation flux emerging from the upstream boundary of the shock wave model were found to be roughly one-third of the shock wave velocity: −δV ≈ 1 3 U 1 . The gas emitting the Balmer line radiation is located at the rear of the shock wave in the hydrogen recombination zone where the gas flow velocity in the frame of the observer is approximately one-half of the shock wave velocity: −V * ≈ 1 2 U 1 . The ratio of the Doppler shift to the gas flow velocity of δV/V * ≈ 0.7 results both from the small optical thickness of the shock wave in line frequencies and the anisotropy of the radiation field typical for the slab geometry. In the ambient gas with density of ρ 1 > ∼ 10 −11 g cm −3 the flux in the Hα frequency interval reveals the double structure of the profile. A weaker Hβ profile doubling was found for ρ 1 10 −10 g cm −3 and U 1 < ∼ 50 km s −1 . The unshifted redward component of the double profile is due to photodeexcitation accompanying the rapid growth of collisional ionization in the narrow layer in front of the discontinuous jump.

Emission lines and shock waves in RR Lyrae stars

“…This result is quite consitent with high resolution spectroscopic observations of the strong hydrogen emissions in Mira, W Virginis, and RV Tauri stars (see references in Fadeyev & Gillet 2004). The redshifted emission component, if we take the infalling motion of the high atmosphere into account, comes from photodeexcitations occurring in the radiative precursor just ahead of the discontinuous jump, while the gas producing the blueshifted emission component is located in the hydrogen recombination zone of the wake.…”

“…This width is several times smaller than those taking place in Mira, W Virginis, and RV Tauri stars (Fokin 1991). Fadeyev & Gillet (2004) found that the Doppler shift in Balmer emission lines is roughly one third of the shock front velocity V shock in the frame of the observer for gas densities of 10 −12 g cm ≤ ρ 1 ≤ 10 −9 gm cm. The upstream Mach numbers range within 6 ≤ M 1 ≤ 14 and a preshock temperature of T 1 = 3000 K,…”

“…One of the most remarkable results found by Fadeyev & Gillet (2004) is that the shock wave model reveals a double emission structure in Hα and Hβ profiles, whereas profiles of higher Balmer lines only exhibit the asymmetry. This result is quite consitent with high resolution spectroscopic observations of the strong hydrogen emissions in Mira, W Virginis, and RV Tauri stars (see references in Fadeyev & Gillet 2004).…”

“…All thermodynamical and dynamical processes occurring in the stellar envelope must be understood as a whole, along with the pulsation and the various spectral signatures observed. However, in the restrictive context of the steady-state, planeparallel approach, Fadeyev & Gillet (2004) considered a shock wave propagating through a homogeneous medium consisting solely of atomic hydrogen atoms with the five first bound levels and the continuum. They solved the transfer equation for the whole shock wave structure (precursor and wake) in the comoving frame for hydrogen lines, whereas the continuum radiation was calculated for the static medium to overcome the numerical instability arising at the velocity discontinuity.…”

“…Hydrogen emission lines are formed just after helium lines, in a slightly colder region of the shock wake. An example of the structure of the radiative shock wave occurring in radially pulsating stars is given by Fadeyev & Gillet (2004). The thickness of the hydrogen and helium emitting shell is less than a few kilometers when the unperturbed gas density is 10 −10 g cm −1 .…”