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2D effects in radiative shocks

Radiative shocks are characterised by the presence of an ionization front preceding the shock discontinuity. For instance this is the case for the region at the tip of bow shocks produced by high velocity (> 200 km/s) stellar YSO jets or in the case of accretion shocks (~ 500 km/s) at the surface of young stars. On earth, large-scale laser facilities allow to produce radiative shocks in millimetre-long tubes which are generally filled with high atomic mass gas, (e.g Xenon) at pressure of the order or a fraction of a bar. Both in space and in the laboratory these shock often have a nearly planar (2 D) geometry.

To make the problem more tractable one often assumes for astrophysical radiative shocks a 1D geometry,and stationarity. Experiments and associated simulations show however that we should be cautious when making such approximation. As shown for example in figure 1, the spatial extent of the shock has a strong impact on its structure, making the shock curve when its lateral radiative losses are significant, or equivalently when the section of the tube diminishes.

2DRS
Figure 1 instantaneous maps of the temperature in eV and longitudinal radiative flux in erg/s/cm2-3 g/cm3 and 300K) in a tube with square section 1.8 mm x 1.8 mm. The axis z=0 corresponds to the tube centre, whereas the position z=9 mm corresponds to one border of the cell. The shocks propagate from the top to the bottom. The optical mean free path is equal to the half of the tube section.

Simulations show also that the stationary limit is more rapidly obtained when the section of the tube or the opacity decrease, which induces an enhancement of the lateral radiative losses and thus of two-dimensional effects. In order to illustrate this point, we have computed the time needed to reach the stationary limit in a radiative shock propagating in a xenon filled shock tube, allowing for different radiative losses on the lateral tube boundaries.

Moreover, numerical simulations performed with the 2D radiative hydrodynamical code HERACLES by M. Gonzalez and E. Audit show that the radiative flux, which should theoretically emerge from an experimental shock tube varies with the angle of observation. This effect might have an important impact in the deduction of the stellar accretion rate from photometric observations in the case of the accretion through magnetospheric columns (figure 2)

AnisoFlux
Figure 2: Figure 2: Instantaneous radiative flux distribution versus the angle of observation for a shock propagating in xenon (0 longitudinal observation, before the shock discontinuity, &pi/2 perpendicular to the shock propagation and &pi behind the shock discontinuity).

Reference

"2D numerical study of the radiation influence on shock structure relevant to laboratory astrophysics",
M. González, E. Audit, C. Stehlé,
Astronomy and Astrophysics, 497, p27-34 (2009), arxiv.org/abs/0902.1645 Reprint

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