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tokens: luminosity wind that emanates from a stellar surface or a galaxy, the interaction between the wind supplying the energy and the ambient gas forms a ‘bubble’. This bubble consists of a forward shock that advances into the ambient gas, a reverse shock that travels back through the wind, and a contact discontinuity that separates the two shocked fluids (e.g. Castor, McCray Weaver 1975 ; Weaver et al. 1977 ; Fielding, Quataert Martizzi 2018 ); a self-similar solution describes the fluid properties between the forward shock and the contact discontinuity. When the shock generated from a supernova explosion or an expanding wind is young, the large temperatures and densities at the shock front imply that the effective adiabatic index γ of the multispecies fluid satisfies 4/3 ≲ γ ≲ 5/3. As the shock further expands and cools, however, the high-density regions near the shock front start to radiate efficiently, which reduces γ below the value of an ideal monatomic gas. On the other hand, the low-density material in the interior of the explosion remains hot, and the expanding blast wave is characterized by a thin, nearly isothermal shell that is in contact with a hot, pressurized interior (e.g. McKee Ostriker 1977 ; Shull McKee 1979 ; Blondin et al. 1998 ). Once the shock becomes radiative, it is no longer strictly correct to treat the fluid as adiabatic. However, it is reasonable to assume that the gas exhibits an increased degree of compressibility prior to radiating a significant amount of its total energy, during which time it is still approximately correct to use the self-similar scalings (derived under strict adiabaticity) for the relationship between the shock position and velocity, but with an appropriately reduced adiabatic index. At the very least, the self-similar solutions with a nearly isothermal equation of state describe the qualitative behaviour we expect at this stage – a nearly evacuated, extremely hot interior in contact with a thin shell that contains the majority of the mass (e.g. Fig. 1 ). Understanding the structure of these shocks therefore yields insight into the more general behaviour of radiative, thin shells formed from explosions and stellar and galactic winds. Figure 1. A comparison of the exact solution for the Sedov–Taylor blast wave (solid lines) and the analytical, leading-order solution in the quantity δ = (γ − 1)/(γ + 1) given by equation ( 13 ) (dashed lines) for the adiabatic indices γ and radial power-law indices n shown in the legend; recall that the ambient density follows the power-law decline ρ ∝ R − n , where R is the shock position. Solutions are plotted as functions of the standard Sedov–Taylor variable ξ = r / R ( t ), which is just the spherical radius at a given time normalized by the shock radius. The left, middle, and right columns show the radial velocity normalized by the shock velocity, the density normalized by the ambient density (and reduced by the factor δ), and the pressure normalized by the