First, I should point out that Dec. 26, 2004, was a full moon. That means that the moon's and the sun's tidal forces exerted a cumulative tidal force, about three times higher than the cumulative tidal force during a half-moon. I can't quote a source now, but I'm pretty sure I've heard that earthquakes happen with greater frequency at full and new moons, and that this fact is directly attributable to the increased tidal forces. In this case, the tsunami happened at a full moon, when tidal forces were already at their highest. Throw in an extra high-speed burst, even a relatively small one, and it could have been the straw that broke the camel's back...
But on to the math. I love math. Alright, I'll admit that I haven't studied quantum gravity, and I don't know general relativity well enough to figure out the wave function of a gravitational wave, etc.
But I can at least do the "classical" math involved here. I have three hard numbers to work with:
One calculation has the giant flare on SGR 1806-20 unleashing about 10,000 trillion trillion trillion watts.
releasing more energy in a 10th of a second...
...than the Sun emits in 100,000 years
The first two numbers allow me to calculate the energy, and the third number will let me sanity check that figure.
The first number is 10**40 watts. From the second number, we get 10**39 Joules.
The third number implies that the energy output was ~100,000*30,000,000 times the energy output of the Sun in a second. The sun converts about 5 million metric tons of matter to energy per second, so that's 5x10**9kg * 9x10**16 J/kg, or about 5x10**26. So we have 3x10**12 times 5x10**26, which is 1.5x10**39. Hmm, works out.
Classical ApproachOkay, so we're looking at 10**39 J of energy, which would have a mass of about 10**22 kg (dividing through by 10**17 J/kg, since we're only worried about orders of magnitude). This is actually just within an order of magnitude of the mass of the moon. So we're talking about a moon-mass suddenly (within 1/10th of a second) disappearing. It didn't disappear, per se, but that mass is now in an expanding sphere of energy, predominately gamma rays, that we are inside of now, so that mass no longer affects us.
So we're talking about the tidal equivalent of the moon orbiting us once every 1/10th of a second at a distance of 50,000 light-years. Obviously I don't mean that literally, since that in itself would be a huge violation of the cosmic speed limit
.
Now, 50,000 light-years is about a trillion (10**12) times further from earth than the moon. Tidal forces vary inversely with the cube of the distance. So we're talking about 10**36 times smaller tidal forces, changing at a rate about 10**6 times faster than the moon's tide. Which leaves us with a "tidal jerk" of about 10**30 times smaller than the moon's.
Not-So-Classical ApproachHmm, from a strictly classical point of view, the gravitational wave was completely insignificant. I wonder how it would fare if one used the correct math. After all, the gravitational wave would have had its own energy, above and beyond the energy released in the GRB. In orbiting black holes or neutron stars, the gravitational energy released in a fraction of a second can often reach a large percentage of the total mass, perhaps exceeding a solar mass of energy released in a fraction of a second. So I wonder what the ratio of the gravitational energy to EM energy was in the blast. Let's say 1%, 10**37 J, 10**20 kg mass-equivalent. This should hopefully get us within a couple orders of magnitude, either way.
This will lead to a rather astonishing change in the numbers. For example, the moon orbits 12.4 times a year (relative to the sun), yet the gravitational energy released during its orbit is so negligible that the moon isn't falling yet. Only after the energy of earth's rotation is mostly sapped will the moon be able to start descending, ever so slowly, for tens or hundreds of billions of years, maybe longer. Let's say that it would take a billion years for the moon to lose 10,000 km of altitude, at its present orbit, if no other factors were involved (e.g., the earth's rotation rate, etc.). Using very rough figures, an orbital velocity of 1000 m/s would become roughly 985 m/s, which represents a kinetic energy difference on the order of 10**27 J, or roughly 10**10 kg. That actually works out to about a kg of mass-equivalent energy per orbit.
So the gravitational energy released by the moon's orbit is only the tiniest fraction of its mass, probably on the order of a kg per orbit, probably less, possibly far less. In that respect, this cosmic event released at least 10**20 times more energy in the form of a gravitational wave, in 1/10th of a second, than the moon can release in a full orbit. The power ratio is huge, at least 10**27. So the gravitational effect, even taking into account the 10**36 times smaller tidal forces per unit of gravitational energy, is still there, on the order of a billionth of the moon's, perhaps even a millionth. That's still very small, but not entirely insignificant.
I wish I knew the relevant math, so I could get within an order of magnitude, instead of wildly different upper and lower bounds.