Navigating storm fronts in space

The answer to your question depends strongly on the supernova rate in the galaxy. The Milky Way currently is not an active galaxy - the supermassive black hole at its center is relatively quiescent - and is not undergoing dramatic interactions with any of its neighbors. Energetic events like gamma-ray bursts and kilonovae are not expected to occur at high rates in our galaxy, either (one GRB every 100,000 to 1,000,000 years and one kilonova every 10,000 to 100,000 years). Therefore, we care mainly about the rates of core collapse supernovae.

This turns out to be much easier said than done. Thanks to uncertainties in stellar populations, dust and gas distributions, and other observational difficulties, we have yet to firmly constrain the supernova rate. Astronomers are confident about the order of magnitude - between 1 and 10 per century - but within that range, estimates vary dramatically. Typical measurements indicate values of 3-5 supernovae per century (see e.g. Hakobyan et al. 2011, so I'll go with that value.

Let's look at how a supernova shock wave - the entity we're concerned with - evolves over time. There are three phases to its life:

1. Free expansion. The shock has a roughly constant velocity (usually a few thousand kilometers per second) and therefore increases in radius linearly. This period lasts for about 500 years.
2. Blast wave phase/Sedov-Taylor phase. Now the shock undergoes adiabatic cooling, and begins to slow down. The velocity scales with time as $v(t)\propto t^{-3/5}$ and the radius scales as $r(t)\propto t^{2/5}$. The shock behaves like this for several tens of thousands of years.
3. Snowplow phase. Eventually, radiative losses become dominant and the Sedov-Taylor solution is no longer valid. A dense shell forms behind the shock, sweeping up matter in the interstellar medium as it expands. We have $v(t)\propto t^{-3/4}$ and $r(t)\propto t^{1/4}$, indicating that the shock is slowing down even quicker. We expect the snowplow phase to end after about one million years, when the speed of expansion drops to the speed of sound in the interstellar medium.

This is an approximation; there are a number of things that can cause some deviations from the model. For instance:

• Asymmetric ejecta would cause departure from a spherical remnant; this is important during the free expansion phase, where the swept-up matter is less massive than the ejecta from the explosion.
• Supernovae, especially those occurring in star formation regions, may exist inside superbubbles caused either by previous remnants or winds from massive stars. This, too, will have effects on the remnant's expansion.
• Pulsars may create pulsar wind nebulae, which produce complex interactions with the expanding shock waves.

Nevertheless, the normal expansion-blastwave-snowplow model is sufficient in the vast majority of cases. We're only looking for a simple approximation.

Our analysis indicates that the existing supernovae remnants in the galaxy should be less than about $\sim10^6$ years old (a conservative upper limit, I think). If they form at a rate of 3 per century, there should be about 30,000 still around - most currently in the snowplow phase, the longest of the three periods. Given that the galactic disk is about 100,000 light-years across, this comes out to a surface density of $3.82\times10^{-6}\text{ lyr}^{-2}$, and the nearest one should be, on average, about 500 light-years away.

Keep in mind, though, that these remnants are big. By the end of the snowplow phase, they may have radii of 100-200 light-years. That said, at that point in time, the shock waves are vanishing into the interstellar medium, and really aren't much of a threat. Earlier on in that phase, though, the shocks can be dangerous, with temperatures and densities in the expanding snowplow shells of $T\sim10^6\text{ K}$ and $n\sim10\text{ cm}^{-3}$ in the worst-case scenario (Cioffi et al. 1988). Interestingly enough, these properties make the shock similar to the solar wind as experienced at Earth's orbital radius.

We should expect to see cosmic ray and x-ray emission from the hot gas, especially during the Sedov-Taylor phase (see Vink 2012, which is actually a really good resource on supernova remnants in general), and I do imagine that this could pose a separate threat to any spacecraft in the vicinity. Turns out that if you heat up gas to $\sim10^7\text{ K}$ ($kT_e\sim1\text{ keV}$, for reference) and send shock waves through it, you get strong x-ray emission! The emission should take several forms:

• Thermal x-rays caused by free-free and bound-free emission in the optically thing plasma
• Line emission, both from collisional excitation and radioactivity
• Non-thermal emission, including x-ray synchrotron radiation and non-thermal bremsstrahlung

Fortunately for us, some of this strong emission should only occur in young supernova remnants - not those in the snowplow phase. That said, essentially all remnants which have not cooled down to temperatures comparable to that of the interstellar medium are still going to be strong x-ray sources. I would recommend avoiding them.

Now, is the expanding shock wave enough to pose a danger to a traveling spacecraft? Perhaps; unlike Earth, a spacecraft has no magnetic field to shield it from the shock. However, I suspect that shocks in the snowplow phase are usually not hot or dense enough to produce cataclysmic effects. There are certainly some supernova remnants that are young and hot and could indeed be dangerous, and from this point of view, it does make sense to map out these potential dangers. That said, keep in mind that these remnants are, on average, hundreds and hundreds of light-years apart, and it should be easy enough to avoid them.

posted over 5 years ago

HDE 226868‭

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