Nov 6, 2004

The question was:

10E75 ergs are released in interplanetary space. What happens? This, of course, is speculative to the nth degree ;-) I'm writing a sci-fi novel and this admittedly unlikely event transpires. I would just like your opinion on what could happen- maybe spacetime would be warped or some other spectacular effect that would rivet your average SF reader. :-) Thanks

This is a very open-ended question. I will look at this from one particular direction only; there are many other ways to approach the problem, and I hope that you and others try some of them.

First, let me see how that total energy is diluted as it spreads outwards into the universe. If we assume it is a shell of energy expanding isotropically, then when it has a radius R, the energy passing through one square meter will be

                          total energy E
   flux of energy  f  =  ---------------
                           4 * pi * R^2

I'll convert E = 10^(75) ergs into 10^(68) Joules for convenience later. Astronomers like to measure distances in parsecs: to a rough approximation, 1 pc = 3 x 10^(16) m, and so 1 kiloparsec (kpc) is 1000 times larger, 1 Megaparsec (Mpc) is 1000 times larger than that, and so forth. 1 pc is a typical distance between neighboring stars in our part of the Milky Way, 10 kpc is the distance to the center of the Milky Way, 1 Mpc is the distance to a nearby galaxy, and 1 Gpc is would span a number of superclusters of galaxies.

Let me tabulate the flux of energy which passes through one square meter at several distances from this explosion:

                        distance from explosion
               10 pc        10 kpc       10 Mpc      10 Gpc
flux (J/m^2)  8x10^(31)    8x10^(25)   8x10^(19)    8x10^(13) 


The Earth has a cross-section area of pi times its radius, which is about 1.3 x 10^(14) square meters. We can then calculate the total energy striking the Earth:

                        distance from explosion
               10 pc        10 kpc       10 Mpc      10 Gpc
Earth (J)     1x10^(46)    1x10^(40)   1x10^(34)    1x10^(28) 


Exactly how long the explosion lasts could make a difference: is the energy released instantaneously, or over a period of one minute, or one day, or one week? I'll assume it is released all at once. I'll ignore some pretty complicated physical effects that would occur if you _did_ somehow create such a large density of energy, or watched it try to escape through itself ...

Let us suppose that all of this energy striking the Earth is absorbed by terrestrial matter. In real life, this fraction absorbed would depend on the detailed spectrum of the explosion energy -- how much in gamma rays, how much in X-rays, how much in optical light, etc. -- but I'll skip over all that detail and just assume that the explosion deposits a large amount of energy in earthly material. As a start, let's look at the effects on the atmosphere.

The total mass of the atmosphere can be very, very roughly approximated by assuming that it has a constant density of about 1 kg per cubic meter, distributed in a thin shell surrounding the surface of the Earth about 3000 m high. The volume of this shell would be V = 4*pi*Re^2*h, and the mass the volume times the density. I find a mass of about 10^(17) kg of air. The specific heat of air is very roughly 1000 Joules per kg per degree C; that means that if you add 1000 Joules to a kg of air, you raise its temperature by 1 degree C. Combining that with the total mass of the Earth's atmosphere (yes, only half would be struck by an instantaneous flash of energy, but let's ignore that for now), we find that it would take about 10^(20) Joules of energy to raise the temperature of the entire atmosphere by about 1 degree Celsius. Of course this is a gross oversimplification to reality, but it should give us an "order-of-magnitude" estimate for what might happen.

Looking at the table above, we see that even a very, very distant explosion would deposit 10^(28) Joules in and on the Earth. That would suffice to raise the temperature of the atmosphere by, well, formally by 10^8 degrees Celsius; but of course our approximations break down well before this point. It's clear that the atmosphere would be heated to the point of dissociation. Not good for life on Earth.

What about the oceans? We can use the same approximation: the oceans form a thin shell around the Earth, with an average depth of about 5000 m. We can calculate the volume of this shell, and use the density of water (1000 kg per cubic meter) to find the total mass of water. The specific heat of water is large: about 4186 Joules per kg per degree Celsius. Putting it all together, I estimate that it takes about 9x10^(24) Joules to raise the temperature of the Earth's oceans by 1 degree Celsius.

Even a very distant explosion occuring 10 Gpc from the Earth would deposit enough energy in the water to raise its temperature by about 1000 degrees Celsius; again, in real life, our approximations break down. After raising the temperature by about 70 Celsius, to the boiling point of water, the liquid oceans would boil, then continue to heat up as steam. Once again, bad news for life on Earth.

It appears that there would be plenty of energy left after the atmosphere and oceans had been destroyed (or perhaps "disrupted" might be a better way to put it). Let's look at what might happen to the crust of the Earth. Assuming that it is a thin shell of rock, about 20,000 m thick, with density 3000 kg per cubic meter and specific heat 800 Joules per kg per degree Celsius (these values are roughly those of granite), we can derive a value of about 2x10^(25) Joules needed to raise the temperature of the Earth's crust by one degree Celsius. Hmmmm. Note that this is only about twice the value needed by raise the oceans by 1 degree C, even though the Earth's crust is both thicker and denser than the oceans; the specific heat of water is much larger than that of a typical rock.

Let's continue to assume that the distant explosion deposits 10^(28) Joules, even though some of that would be used up in the heating of the atmosphere and oceans. It would appear that the crust might be heated by several hundred degrees C. That's hotter than anyone would enjoy, but perhaps not enough to melt rocks and minerals.

So, I would guess that if your enormous explosion occurred 10 Gpc from Earth, the atmosphere and oceans would be disrupted, but the Earth's crust would remain intact. Any life on Earth would very likely be destroyed. The one way you might get around this doomsday scenario is to make the explosion very brief, a matter of seconds or minutes. In that case, the energy would strike only one face of Earth, leaving the "dark side" momentarily unaffected. Lots and lots of very interesting phenomena would occur as the atmosphere and oceans reacted to half of their contents being vaporized; there would be flows of material that probably aren't really well described as "winds" or "currents". I would guess that if this event were a surprise, no humans would survive; but perhaps, just perhaps, if there were some advance warning (days? weeks? years?), those on the "dark side" of the Earth might devise some means of riding out the immediate effects. Would they be able to creep out of their shelters after a day (or week? or month? or year?) into a habitable world? Probably not. The atmosphere would probably be largely gone, and certainly whatever was left would be very different in composition (mostly water vapor?). The oceans would be greatly reduced in size.

That might make a very interesting scenario, actually.

If an explosion of the given size occurred anywhere "close" to the Earth, in the Local Supercluster of galaxies or the Local Group or the Milky Way, I think that the destruction of even the solid body of the Earth would be so extreme that you wouldn't have any survivors left for your story.