[Telgin (OP)]

For the purposes of this question, my definition of nearby is flexible, and I'm really trying to figure out at what distance a gamma-ray burst would have immediate and deadly effects on an apocalyptic scale.  So, probably a dose of 30 Grays or more at sea level.

My research has given me answers that range from a few thousand parsecs to not being deadly from direct radiation dosage even a few lightyears away because our atmosphere is so opaque to gamma-rays that the only deadly effect would come from ozone depletion over the following years from UVB exposure.

I've also been unable to determine how severe the effects of the "photochemical smog" effects would be.  With a gamma-ray burst close enough to cause death from acute radiation poisoning, would enough nitrogen compounds be formed to cause significant dimming of light?  Would the acid rain produced cause substantial climate damage?  Would the compounds be concentrated enough at sea level to be outright toxic?

The only answer I've seen remotely definitive on that stated that there would be little impact and the compounds would stay in the upper atmosphere, but that was also the source that said a GRB happening next door would have little impact and I'm not sure how much I trust it.

Bonus Question

This didn't really seem to warrant a separate thread, but would a GRB of that much intensity have any substantial impact on a planetary ring?  I suspect that the radiation pressure would have little impact over the course of a minute or two, but would it be intense enough to vaporize bits of the ring particles and thrust them out of orbit?

[Kryptid]

Just so the others know, Telgin is my brother. He's asked me this question before and I'm not sure what the answer is. I can mostly only give my intuition about it. I don't think a gamma ray burst would have any noticeable effect on a ring system around a planet because it is of such short duration.

EDIT: I think I'll try to do a calculation that I haven't done before. I'll use GRB 101225A as my example. Its isotropic energy was estimated at 7.8 x 10⁴³ joules. A sphere 1 light-year in radius has a surface area of 12.5664 square light-years. If the energy is spread out evenly over the sphere, then the energy-per-unit area received by an object 1 light-year distant from the gamma ray burst would be ~69,348,072,110 joules per square meter. Since this took place over 28 minutes (1,680 seconds), the energy flux would be ~41,278,614 watts per square meter at one light-year distance.

The surface area of a sphere goes up to the square of its radius. Doubling the radius causes the surface area to increase four-fold, and tripling it causes the surface area to increase nine-fold. At ten light-years out, the energy would be 100 times more diffuse, at 693 megajoules per square meter. The energy flux would be 413 kilowatts per square meter. At 100 light-years, these values go down to 6.9 megajoules per square meter and 4.1 kilowatts per square meter. At 1,000 light-years, it's 69 kilojoules per square meter and 41 watts per square meter. For comparison, the energy received at the Earth's surface from the Sun is 1.361 - 1.362 kilowatts per square meter.

For a spherical planetary ring particle (yes, highly idealized, I know), its cross-sectional area would be its radius squared times pi. A particle of silica 1 meter across would have a cross-sectional area of 0.79 square meters. At 1,000 light-years, it would receive 54.8 kilojoules of energy. Let's assume the ring particle would completely absorb the radiation and transform it into kinetic energy (although we know it would not, so this calculation is an overestimate). A sphere of silica 1 meter in diameter would have a volume of 520,000 cubic centimeters and a mass of 1,376.96 kilograms. This would change its velocity by 8.9216 meters per second.

That's much higher than I thought. However, much of the radiation would not be absorbed so the velocity change would no doubt be much smaller than that. Much, much smaller given that solar flux is so much higher than that yet doesn't seem to have any important effect on our orbiting spacecraft. It would be even less for larger particles, since mass increases faster than cross-sectional area does as an object grows larger. Doubling an object's diameter increases its cross-sectional area by four, but its volume by eight. So a 2-meter ring particle would only be moved half as fast as a 1-meter chunk would, a 3-meter chunk would move at a third the speed and so on.

EDIT 2: Telgin brought it to my attention that a gamma ray burst may not be spherical but instead has its energy focused into beams. Off the top of my head, I'm not sure. If that's correct, my calculations are way off and the energy received would be much, much higher than I predicted.

[evan_au]

a gamma-ray burst would have immediate and deadly effects

One impact that you may not have been considering is it's impact on our electronics.

A gamma-ray burst would produce an Electro-Magnetic Pulse (EMP) in Earth's atmosphere, and would fry all non-shielded electronics on that side of the world (ie everything that isn't military-grade).

Given that your average teenager would rather lose an arm than lose their smartphone, that is an awful lot of severed limbs!
More seriously, our transport, communications, electricity, food and water are critically dependent on electronics and computers. I think many people would die in the month or so following loss of electronics over half of the Earth.
See: https://en.wikipedia.org/wiki/Electromagnetic_pulse

impact on a planetary ring?

If the planetary ring were made of millimeter-sized grains of ice, the surface area is large and the mass is small; these could easily have the surface vaporised, imparting a considerable velocity to the small grains of ice.

This would have a bigger impact than on meter-sized rocks.

gamma-ray burst

The source of gamma-ray bursts is somewhat mysterious - and different types of GRB are probably caused by different types of energetic events. One of those candidate sources is colliding neutron stars.

There are rumours circulating in the scientific community that the LIGO/VIRGO collaboration has detected gravitational waves from a pair of colliding neutron stars, and were able to direct optical and other observatories to the right region of sky to spot the event. I guess we'll just have to wait another few months before we find out if the source of one GRB has actually been identified.
See: https://en.wikipedia.org/wiki/Gamma-ray_burst

[Telgin (OP)]

EDIT 2: Telgin brought it to my attention that a gamma ray burst may not be spherical but instead has its energy focused into beams. Off the top of my head, I'm not sure. If that's correct, my calculations are way off and the energy received would be much, much higher than I predicted.

Right.  The article linked by evan_au implies that the energy is beamed, with a jet angle ranging from 2 to 20 degrees.  That would mean that all of the energy is instead focused into two circles (one at each pole) with radius proportional to the distance.

I haven't really done rigorous math on it, but I plugged the angles into some trigonometry calculators and found that the circle radii would range from about 3.4% of the distance (for a 2 degree beam) to 36.4% of the distance (for a 20 degree beam).  So, let's assume 20 degrees for a worst case scenario.  That would mean that, at 1 light year, the energy is focused into two circles with radii of 0.364 light years.  Assuming my math is right, that gives an area of about 3.73e31 square meters per circle, or a total of 7.46e31 square meters total.

Dividing the total energy by that gives ~1,045,576,407,506 J, and over time that works out to ~622,366,909 W.  That's roughly 15 times higher.  I assume the relationship holds over longer distances since it should fall off at the square too.

Even still, I doubt that's enough to significantly disrupt a ring system.  Apparently 1m particles isn't a bad estimate, based on Saturn's rings, but the efficiency of imparting energy is surely low enough that it wouldn't matter.  Even imparting an extra 100 meters per second isn't going to deorbit much of a planetary ring, I imagine.  I am curious if it would cause visible distortions though, and how long they would last.

One impact that you may not have been considering is it's impact on our electronics.

Oh, this is absolutely true.  I didn't include all of this in my original post since it didn't feel relevant, but this is a research question for fiction taking place during a pre-industrial era.  Electronics wouldn't exist to be trashed.

That's the main reason I was looking for the parameters needed to cause wide scale rapid die off of the population.

My initial feelings after my own dodgy calculations above, were that 622 MW per square meter on the surface would utterly annihilate any life.  But, then, I realized that that rapidly falls off with distance to the point that at 1,000 light years, it's now imparting less power than the sun would.  Only 622 W or so per square meter, right?  If that's largely in gamma-rays it might still cause deadly radiation poisoning, but that doesn't factor in shielding from the atmosphere and sounds much less sure.  A research paper I found implies that the atmosphere has a shielding factor of about 1,000, so only about 0.6 W per square meter of penetrating gamma-rays.  That might be more than it sounds like, but it doesn't sound deadly, even over a few minutes.