Radiative shocks in stellar atmospheres

There are about 200 billions of stars in our Galaxy. The temperature of the stellar ``surface'' is typically between 3000K and 20,000K depending on the star. Here ``surface'' refers to the gas layer from which the visible ($\lambda=5000$Å) continuum radiation emerges. This layer is called the photosphere. The numerous absorption lines which are observed in stellar spectra are produced in the atmosphere lying above the photosphere. It is composed in mass of 70% of hydrogen, 29.9% of helium and other elements do not exceed 0.1%. The atmosphere is relatively large, between 10 and 100% of the stellar radius i.e., a few million kilometers. Its density is low and ranges, from 10^-8 for the photosphere to 10^-15g/cm³ for the highest contributing line layers. Thus, a stellar atmosphere consists of a rarefied gas with a pressure between 10^-2 and 10^-13atm. Although the mass of the atmosphere is only 10^-6 times of that of the star, all informations that we obtain from stars come from their atmospheres.

  

Figure: Theoretical variations of stellar radii (in unit of solar radius) for the different mass zones versus time during several pulsation cycles for a pulsating star of type RR Lyrae. The deepest calculated mass layer for which the amplitude of oscillations is almost zero is at T=540,000K and $\rho=10^{-4}$g/cm³ and the highest calculated is at T=3700K and $\rho=10^{-15}$g/cm³. The stellar visible surface (T=7500K and $\rho=10^{-7}$g/cm³) is given by the discontinuity. The atmosphere is located above this layer [8].

During a very large fraction of the life of a star, its atmosphere is at the hydrostatic equilibrium. Nevertheless, gas motions such as convection which affects the whole stellar surface or small local hydrodynamic perturbations such as prominences or sunspots due to the magnetic activity of the star can be observed. The Sun is in this stable regime since 5 billions of years and for again a few billions of years. Thus, the Sun atmosphere does not undergo rapid and large hydrodynamical perturbations. During the stellar evolution, provoked by some changes of the thermonuclear reactions occurring in the stellar core, the atmosphere can become dynamically instable during a relatively short period. In this case, the highest subphotospheric layers together with the whole atmosphere are subjected to oscillations. These latter reach large amplitudes in the atmosphere (Fig.). During this phase of its evolution, which is between 1000 and a few million years, the star becomes a pulsating stars. Figure shows the variation of the radius of layers versus time for a pulsating star of the RR Lyrae type [8]. The stellar hydrodynamical model is represented by 90 mass layers. The phostophere is revealed by the almost sinuosidal discontinuity around a radius of 5 solar radii (1R$_{\odot}=700,000$km). This discontinuity is due to the hydrogen ionization which is close to the photosphere because the temperature of this latter is near 7500K. In the stellar interior the amplitude of oscillations rapidly decreases to the center of the star. It is almost equal to zero for layers at a temperature of 540,000K and a density of 10^-4g/cm³. The temperature of the highest atmospheric layer calculated with this model is 3700K which corresponds to a density of 10^-15g/cm³. It clearly appears that the amplitude of the highest layers is variable from one pulsation cycle (period of about 14hours) to the following.

The black zones visible above the photosphere reveal the presence of large compression regions which are due to the formation of shock waves propagating through the atmosphere. It is known now ([8], [9]) that there are three principal mechanisms responsible for formation of shock waves in pulsating atmospheres. The basic one is due to the steepening of a compressive wave propagating in the atmosphere with exponentially decreasing density (typically 6 orders of magnitude over the whole atmosphere). In these conditions, very strong shocks can be observed with Mach numbers up to 30. This means that the intensity of these hypersonic shocks is large enough to induce an appreciable ionization of the atmospheric gas. Consequently, the radiative energy produced by the shock passage is certainly not negligible and a coupling between the radiation and gas flows can be expected. This idea is well supported by the strong emission lines observed in the spectra of the most pulsating stars (for instance [4], [15]).