…would we be in danger of Gamma radiation?
I’m not sure if the inverse-square thing works in our favor due to the distance Betelgeuse is from us, but if the star’s magnetic pole is aimed directly at us, a concentrated beam of death would be…
…a concern, yes?
My usual reference for this kind of thing, the book Death From the Skies!, says no. The surface would be largely protected from gamma rays by the atmosphere. And the intensity of gamma rays needed to significantly disrupt the ozone layer would require a supernova within 100 light-years; perhaps even 25 light-years. Betelgeuse is ~640 light-years away.
It would deposit around 10,000 tons of mass on Earth, but that’s fairly small potatoes.
That’s roughly one small potato per three square miles of Earth’s surface.
So if we get angry our skin will only turn the faintest shade of key lime green and our pants will remain intact?
Sadly, it’s more like “everyone on half the planet now has an 0.5% higher chance of getting cancer in their lifetime.” Which will make them very slightly angrier as well, but they probably won’t get 0.5% stronger.
That would take a while to get here, right? How long?
Eh… somewhere around 10-100 thousand years, give or take. It’s going a few percent of the speed of light. Which is actually kinda fast. At 5% c, it would nearly reach the total solar energy flux on Earth if it arrived in about 2 hours. Though I suppose it would probably spread out more than that.
The 10,000 tons was extrapolated from an estimate from the book that about 100 tons from the supernova that produced the Crab nebula would potentially hit us. That’s 6500 ly away, while Betelgeuse is 640, so ~10x closer means 100x the mass.
But it also says the Crab nebula debris won’t actually make it to us… intervening gas would stop it before it got here. The same is probably true of Betelgeuse, but it’s hard to be sure.
Would you get a decent amount of mass just from neutrino interactions?
If the universe gives you potatoes, make potato salad.
I mean, it depends on your definition of “decent amount”, but given that the masses of the neutrinos are so close to zero that we can’t even tell what they are, and given that the vast majority of neutrinos intersecting the Earth would just fly right on through, the answer pretty much has to be “no”.
Any mass deposited would be mostly in the form of protons and alpha particles. And if the Universe gives you protons, make salad dressing.
OK; yet Wikipedia helpfully informs me that typical supernova neutrino energies are 10 to 20 MeV. And that Kamiokande II (~3000 tons of water?) detected 12 neutrinos during SN 1987A…
Any discussion of intense neutrino flux is improved by re-reading the seminal work on the topic: Lethal Neutrinos - xkcd. 
Earth is 6e24 kg, so if we assume proportionality, that means about 2.4e19 neutrinos were absorbed by Earth. That’s much less than a mole of neutrinos, and the mass of a neutrino is much less than a hydrogen atom, so it’s way less than a gram of neutrinos.
Does the magnetosphere play into it?
My guess is: not much. Gamma rays aren’t charged, so wouldn’t be affected by the magnetosphere. The relatively slow moving gas would start ionized, but mostly recombine before it got here. There would be some fast charged particles (cosmic rays) that would be affected, but the atmosphere does a pretty good job against those anyway.
The book says though that there’s enormous uncertainty in the cosmic ray problem, due to Earth and the Sun’s magnetic field as well as other factors. To the point where estimates for the distance to a supernova where there might be a danger from cosmic rays ranges from “a few” light years up to 1000 light years. That actually encompasses Betelgeuse. I’m a little skeptical of the upper end of that range, though. The book is 17 years old so maybe there’s been some more recent research.
Would Betelgeuse exploding pose a risk to people in deep space -on a trip to Mars, for instance?
Also, Betelgeuse is pretty well-studied, and we know its axis of rotation, which is 20º off of our line of sight. A neutron star can have a magnetic field “frozen in” off of its rotational axis, but for something that’s generating its magnetic field through a dynamo, like (presumably) Betelgeuse, the magnetic axis will line up almost exactly with the rotational. In other words, the beam wouldn’t be aimed straight at us.
Intuition says that it would be fairly disastrous.
I put the question to an AI, and it actually produced some Python code to compute an answer. At first glance it looks reasonable. It gave an answer of 55-550,000 times the cosmic ray flux experienced in a 9-month journey. Since deep space trips like this are already on the dicey side, that would be a fairly disastrous increase.
I’ll look at the code in more detail later to see if the estimate holds up.
Although there would be an increase in proton flux and possibly gamma rays (although attenuation by absorption of the Local Fluff would be significant, and then the structure of a spacecraft would further absorb gammas), the big radiation threats to astronauts are still solar proton emissions and spallation of the ‘occasional’ fast moving heavy ion running into the structure and producing a spray of short-lived unstable particles.
Stranger
Yeah, the stuff won’t reach us. This is due to weak Coulomb coupling to the interstellar medium (neutral and plasma phases) leading to turbulent losses and from interstellar magnetic fields that will effectively randomize the trajectories on short distance scales (relative to the length of journey in question). Even if we forgot about those effects and the effects of the even stronger interplanetary magnetic fields, any burst of low-energy ions to the earth doesn’t add new net mass to earth since such ions would become part of the gain and loss mechanisms already present for such ions (influx from solar wind, trapping in Van Allen belts, loss to atmospheric effects, etc.), and those overwhelmingly dominant processes will continue to set the equilibrium, unfazed by transient inputs.
The neutrino question is much more subtle than it looks, because an interacting neutrino doesn’t just stop in the earth like a dust mote.
First, most of the interactions of supernova neutrinos in the earth will lead to a neutrino still leaving the earth. The simplest is neutrino-electron scattering or antineutrino-electron scattering: \nu + e\rightarrow\nu+e, or the same with \bar{\nu}. The neutrino will leave some energy behind, but it will not change the rest mass of whatever it hit.
Alternatively, the neutrino can interact with a nucleus instead of an electron. In this case, the neutrino still doesn’t have to leave its rest mass behind. In particular, “neutral current” interactions (i.e., those mediated by the Z boson) will result in the neutrino just tickling the nucleus on its way through.
In cases mediated by the W boson (“charged current” interactions), you have to go isotope by isotope and separately for neutrinos and antineutrinos and separately by “flavor” to tally it all because there are energy thresholds that restrict these reactions, and these depend on the precise nuclear transitions in the reactions. This process is energetically forbidden in most cases.
For the nucleus-disturbing interactions above that can occur (both neutral- and charged-current cases), the resulting products will typically weigh some few MeV more than what you started with, finally representing some new mass.
However, a neutrino interaction can also lead to a net loss of mass. The Super-K data mentioned upthread was mostly the reaction \bar{\nu}_e + ^1\!\rm{H}\rightarrow e^- + e^+ + n (“inverse beta decay”, wherein an antineutrino converts a hydrogen nucleus to a neutron and a positron) followed by neutron capture on another hydrogen atom to make deuterium. The positron annihilates with an atomic electron, and at the end of it all you went from twice the mass of ^1\rm{H} to the mass of just ^2\rm{H}, so things are about 1.5~\rm{MeV/c}^2 lighter in the end.
As noted above, the local proton flux should not be affected.
Oof. This thread calls back to the recent “Fate of the FQ forum in light of AI” thread. My confidence is quite low in AI’s abilities to handle the nuanced questions being posed here, and my confidence is quite high that it’s answers will look sound to a cursory inspection.