The Threat of Gamma Ray Bursts

Recently I stumbled into a paper estimating the number of supernovae (SN) in our galaxy (Adams et al. 2013). This reminded me of the number of news outlets that latched onto the potential of gamma ray bursts (GRBs) to create a catastrophic extinction event on Earth (here are some examples: Did Deadly Gamma-Ray Burst Cause a Mass Extinction on Earth?, Asteroids are not the only threat to life from space,  and shockingly from Nature -- 'Death Star' found pointing at Earth - that's a serious level of click-bate from such a prestigious journal).

You are welcome to read those articles and I'm not going to go into any deep detail in this post on GRB physics or planetary impacts. However, I did want to do some simple napkin math on what the probability of a direct gamma ray burst from a specific subset of core collapse SN might be on Earth. We're indebted to Dr. Enrico Cappellaro's dedicated research into SN rates within galaxies (see Cappellaro, Evans & Turatto 1999 and associated citations for newer work) for some of the broader rough estimates. There are a number of ways to determine the SN rate, but the most obvious way is to utilize observations across multiple galaxy surveys to measure the rate by look-back time. Other methods include measured pulsar birth rates (some percentage of SNs), the amount of SN remnant isotopes and future neutrino detection.

The best estimates place the current SN rate around 2-3 per century in the Milky Way (MW). And, the star formation rate (SFR) in the MW would be higher billions of years ago. Nevertheless, we'll stick with 3 as our estimate. Of course, not all SN will produce a gamma ray burst and about 10% are Type Ib/c SN that theoretically may be candidates. Plus, the difficult estimate is just how many of those are GRBs. Since GRBs are rare we'll go with an additional 10% or 2-3 per 100,000 years and round down to just 1 per 10⁵ yrs.

To be a threat the SN must have a collimated beam of gamma rays pointing directly at Earth (I'm ignoring general SN threats here). Additionally, only those close enough on our side of the galaxy would have impact. So, let's assume a radius of 4 kpc as the dangerous zone for Earth. Since the MW has a radius of about 16 kpc that sets the threat circle to 4²pi / 16²pi or 1/16. We'll very roughly assume a collimated gamma beam is about 50 square degrees of a collapsing sphere who's total is 41253 degs or 50/41253 (just how wide is a GRB collimated beam? I'm probably a bit narrow here). This gives us a rate of GRBs pointed toward Earth ~ 1 * 1/16 * 50/41253 = 7.5 x 10^-5 / 100000 yrs = 7.5 x 10^-10 yr^-1 or about one every billion years. This seems to be close to some of the papers on astrobiological extinction and the Fermi Paradox (e.g., take a look at Scalo & Wheeler 2002, Melott et al. 2004, Piran & Jimenez 2014). Clearly, the key estimate in this calculation is the GRB rate of SN in the galaxy. If anyone has some links to works on that topic I would appreciate it.

While this is a fun exercise in estimation, I did come across this very recent paper on near-Earth supernovae explosions and the need for greater research into detection of radioactive iron-60 (or ⁶⁰Fe) which is a remnant of core collapse SN (CCSNs). It's a interesting short read--worth the time (see Fields et al. 2019).

Also, if you wish to read about GRB progenitor stars, this paper (Woosley & Heger 2006) is a good overview.