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In air, transitioning from a local mach number ($M$) of $M > 1$ to $M < 1$ produces a shock. But $M$ is defined simply based on the velocity of an object relative to the local speed of sound. If a positron-electron gas is introduced into air, moving at supersonic speeds, will a shock be produced? The original air and injected gas species no long have similar masses, and I'm simply curious if a shock would be produced in such a scenario where the individual positrons and electrons may have significantly lower momentum than the gas particles, but are nevertheless moving faster than the local air's speed of sound.

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But M is defined simply based on the velocity of an object relative to the local speed of sound.

I think you are thinking about partial pressures (if not, you should be) because the speed of sound is defined as: $$ C_{s}^{2} = \frac{ \partial P }{ \partial \rho } $$ where $P = \sum_{s} P_{s}$ is the total gas pressure summed over all species $s$ and $\rho$ is the average mass density of the gas.

In Earth's atmosphere, there are unequal parts diatomic nitrogen, diatomic oxygen, carbon dioxide, argon, and lesser species. So yes, if Earth's atmosphere were entirely diatomic oxygen, the local speed of sound would be different from its current value (not to mention the atmosphere would be toxic to most life).

If a positron-electron gas is introduced into air, moving at supersonic speeds, will a shock be produced?

Yes, this could produce a shock wave if enough pair plasma (e.g., see this arXiv 1311.2605 paper for an example discussion) were injected into the system. The obvious initial response will be pair-annihilation but this releases gamma-rays that can quickly heat and ionize the surrounding neutral gas. If all of this happens quickly enough, even the injection of a non-moving (relative to neutral gas) cloud of pair plasma could generate a blast wave with an associated shock. There is a great xkcd article(?) about shock waves generated by fast moving plasmas and x-rays emitted ahead of the plasma.

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