Tunguska Question

[Dr. Trintignant]

Two examples. The Chicxulub dinosaur-extinction asteroid would have had essentially the same effect whether a solid rock or a swarm of infintessimal particles of the same mass, since the destruction was caused by the energy imparted to the atmosphere.

While that's certainly true, you also shouldn't underestimate how much energy the atmosphere can absorb before we notice it.

Earth receives on the order of 1.5 * 10^20 joules of solar energy in a day. It's likely that if this increased by 1% for just that day, we wouldn't notice it. So we figure that it wouldn't be such a problem to absorb 1.5 * 10^20 joules as a one-off event.

A 1 megaton nuclear weapon could easily destroy a city, and is about 4.2 * 10^15 joules. Divide our two numbers and we get about 36,000, which is way more than the total world nuclear arsenal, either in megatonnage or raw numbers. So, if we can spread out the impact enough, we can turn the equivalent of a nuclear holocaust into a slightly warm day.

The Chicxulub impact was more like 100,000,000 megatons, which would result in a fairly toasty day...

- Dr. Trintignant

 

[MG1962]

While that's certainly true, you also shouldn't underestimate how much energy the atmosphere can absorb before we notice it.

Earth receives on the order of 1.5 * 10^20 joules of solar energy in a day. It's likely that if this increased by 1% for just that day, we wouldn't notice it. So we figure that it wouldn't be such a problem to absorb 1.5 * 10^20 joules as a one-off event.

A 1 megaton nuclear weapon could easily destroy a city, and is about 4.2 * 10^15 joules. Divide our two numbers and we get about 36,000, which is way more than the total world nuclear arsenal, either in megatonnage or raw numbers. So, if we can spread out the impact enough, we can turn the equivalent of a nuclear holocaust into a slightly warm day.

The Chicxulub impact was more like 100,000,000 megatons, which would result in a fairly toasty day...

- Dr. Trintignant

I was just looking around and could not find a reference - But at one point there was a suspison that the underlay strata of the impact point contained high levels of sulphur - adding to the Dino's misery. Has this been dismissed or, is it still a valid observation?

 

[Schneibster]

I beg to differ. Let's very conservatively suppose that the threshhold between "x-ray" and "gamma ray" is 50 keV. (I'd call that a "hard x-ray", but YMMV.) To get the blackbody peak up to 50 keV, you have to heat the gas to 600,000,000 K.

Just a quick check; plus I want to see if the bugs are worked out of the laTEX implementation.

Call 50keV 25pm; Wien's law is:

[latex]\lambda_{max} = \frac{b}{T}[/latex]
where,
[latex]\lambda_{max}[/latex] is the peak,
T is temperature, and
b is the Wien constant of proportionality. For picometers, this is 2.8977685(51) × 10⁹. I'll go with 2.898 for the mantissa; no sense being ridiculously precise.

Solving for T, we get
T = b/[latex]{\lambda_{max}}[/latex]
or
T = 2.898 x 10⁹pmK/25pm
T = 115,920,000K

A slightly more moderate figure, though still of the same order of magnitude.

The laTEX implementation is still buggy; it won't correctly interpret \frac{a}{b_{c}} as a/b_c, instead putting a then nothing over b_c. It doesn't work if you leave off the braces around c either.

For comparison:

• Surface of the Sun: 5000 K
• Core of the Sun: 15,000,000 K
• Core of nuclear bomb: few x 10,000,000 K
• Highest temperature achieved on Earth: 2,000,000,000 K (Z-machine)

It's hard to create a gas that hot because, to oversimplify a bit, the hotter it gets the more efficiently it moves that heat elsewhere, both by radiation and by simply expanding under pressure.

So, when you're talking about warm things, you're talking about IR blackbody radiation. Talk about hot things and maybe you can think about the visible. If you think you're pushing the limits, it's worth thinking about UV blackbodies. Before you get to x-rays, though, you need to do a sanity check and see if the physics actually holds up. Gamma rays are almost out of the question.

Almost, but not quite. Certainly no more than a single pulse of microsecond or shorter duration. I'd sure be interested in seeing the hydrocodes for bolide impact simulations that Sandia has developed. I wonder if it even gives maximum temperature.

Let's keep in mind that we're talking about an event that takes place in an instant; this jet of hot gas emerging from the Tunguska object isn't going to last more than milliseconds, if that. And keep in mind the object is 30km up when it disintegrates to form the jet. To create a 15Mt explosion, it's going to have to have been really, really hot. Otherwise there just isn't enough energy in a 30m wide object to do that. 30m is on the close order of the size of a thermonuclear weapon, and 15Mt is thermonuclear weapon scale energy. And we're not talking about release of intrinsic energy by a chain reaction, but about purely kinetic effects. I'm guessing to get that kind of energy from that small a mass, you're going to have temperatures similar to those in the core of a nuclear weapon.

So all of a sudden it looks pretty good to me. Let's keep in mind as well that the temperature of the core of an exploding U-235 fission device is hot enough to put the peak in the X-ray; that's how most of the energy emerges from the core. The X-rays then heat the materials of the bomb and the surrounding atmosphere, and that's where the thermal pulse comes from; in addition, the shock wave comes from that, too. That sounds very much like what happened at Tunguska to me. I'd be surprised if the gas jet weren't hot enough to have a radiation peak in the X-ray, and not surprised at all to find it in the gamma.

See if you can knock a hole in my analysis.

 

[Schneibster]

Except we really haven't found all the objects yet with a potential to hit us.

10km objects? Sure we have. We haven't found a new 10km or object in years. They figure they found them all in the first pass. The only thing that's going to be that big that's not an Earth-orbit-crossing asteroid is a comet, and that we're going to see coming a long way away.

The Chixulub object is estimated at 10km; that's the prototypical dinosaur-killer, having actually killed the dinosaurs. That's a 100Gt event, something that's going to make 10m ground waves thousands of miles away, break open crustal plates, maybe disturb the magneto and cause a magnetic pole flop, and cause a nuclear winter for a while (years). We'd be lucky indeed to survive such an event at our current level of technology, and basically powerless to stop it. Forget silly Armageddon movies; we're talking about a rock six miles across, basically a few mountains mashed together. Nothing we have is going to even make a dent in that. If we figure it out with enough lead time, we might, if we're very, very lucky, have enough thermonuclear weapons in the entire Earth's arsenal to move it far enough not to hit us. Now, how you gonna deliver said thousands of nuclear weapons across tens of millions of miles of empty space? Not to mention get them all to go off at the same time so you can generate enough impulse to move said rock. Tricky, and probably requiring just about everything we have, if it's even possible. It sure as hell isn't anything that's going to be do-or-die-ten-minutes-from-impact; we'll try it, and if it doesn't work, we'll have a decade or so to contemplate our doom and maybe come up with something else to try.

Luckily, it's not a consideration; there's nothing that big coming for a long, long time, with the possible exception of a comet. Things that big only hit every hundred million years or so; we're "due," but if it doesn't happen for fifty million years, it'll still be inside the error bars.

We're up over 5,000 near Earth objects discovered with over 700 of them being large enough for planet wide devastation. 12 or so of those large ones were only discovered in 2007, so it isn't like we've yet found the bulk of the large ones and we are still finding hundreds of smaller ones every year.

0.1-1km. Those are city- to continent-sized disasters, not planetary catastrophes. You can expect one of those every hundred thousand to ten million years or so. The bigger they are, the less often they fall, is the rule for these things. Remember that volume increases as the cube of diameter.

Sure is great we're building all these cities everywhere! Wonder how long 'till one gets clobbered.

http://neo.jpl.nasa.gov/stats/

Great site; I've got it bookmarked. Haven't looked lately, so thanks for giving me an excuse.

There's only one NEO listed with a slight chance of hitting Earth and that isn't until 2048. That would be NEO 2007 VK184. It was only discovered in Nov 07. But that also means a bit more orbit calculating and we may find it really isn't coming that close.

Then there is Asteroid MN4 (apophis) and the "keyhole" hypothesis. It was only discovered in 2004. For whatever reason it doesn't rate a risky as VK184, perhaps in 2029 we'll see whether it should. In that year we are supposed to see if its orbit is perturbed and that sends it into the Earth in 2036.

Yeah, and there's a reason they named it after the villain of the Stargate series who wants to blow up Earth, too.

Keep in mind that they're rating mostly impact risk; 1s are worth watching, and each level above that is divided in three, for region, continent, and global catastrophe levels. So you've got 2-3-4, 5-6-7, and 8-9-10 for the three levels of impact risk, with the three numbers indicating how large an object we're talking about (which controls how much damage it will do). 2, 5, and 8 are megaton; 3, 6, and 9 are gigaton; and 4, 7, and 10 are dinosaur killers.

 

[Schneibster]

<snip> if we can spread out the impact enough, we can turn the equivalent of a nuclear holocaust into a slightly warm day.

Basically correct AFAIK.

The Chicxulub impact was more like 100,000,000 megatons, which would result in a fairly toasty day...

- Dr. Trintignant

100Gt is 100,000Mt. You've got three too many zeros.

The folks who play in this area are basically saying they think that the material that splashed up from the impact site re-entered the atmosphere a few minutes to an hour later and raised the temperature of the sky to a few hundred degrees pretty much everywhere on Earth. This basically broiled anything not under water or underground alive immediately, and triggered world-wide forest fires. A toasty day indeed.

 

[Cuddles]

I beg to differ. Let's very conservatively suppose that the threshhold between "x-ray" and "gamma ray" is 50 keV. (I'd call that a "hard x-ray", but YMMV.)

The usual definitions of x-ray and gamma ray are simply that gamma rays are caused by nuclear, or smaller, interactions and x-rays are everything else, it is not really anything to do with the actual wavelength. In general, gamma rays are higher energy simply because nuclear reactions give off higher energy photons, but there is a huge overlap between naturally occurring x-rays and gamma rays. High energy x-rays from synchrotrons and free electron lasers can have energies of hundreds, or even thousands, of keV. Black body radiation will never give off gamma rays because anything from black body radiation will always be x-rays by definition.

Of course, since there is no hard definition, and it is not always possible to tell where light comes from, there will always be some cases that don't quite fit. For example, at least some gamma ray bursts are probably caused by synchrotron radiation and/or bremsstrahlung and so should more properly be called x-ray bursts.

 

[Soapy Sam]

I enjoyed "Armageddon". (Sulks).

I guess we all have more probable threats to concern us, but it's certainly interesting to know the old sword of Damocles is still dangling up there.

The small ones do seem to be the real cause for concern- something 200m across could spoil our whole weekend.


What's the latest projection on Swift -Tuttle? Or does degassing make it wholly unpredictable?

 

[Dr. Trintignant]

100Gt is 100,000Mt. You've got three too many zeros.

The number I recall, and the one that Wikipedia reports, is that the Chicxulub impact was 100 teratons, not gigatons. But let's try another order-of-magnitude calculation.

The asteroid was about 10 km across, or 5x10^11 m^3 in volume.

I don't know much about the density, but being a rocky, metallic thing, it couldn't have been too far off from 10 g/cc, or 10,000 kg/m^3. Within a factor of 2, anyhow. So our mass is about 5x10^15 kg.

Asteroid velocity is around 17 km/s on average. Plug into KE=1/2*m*v^2, and we get 7.2*10^23 J. Divide again by 4.2*10^15, and we get 170,000,000 megatons, or 170 teratons.

Obviously there are several approximations in there but probably nothing that would make a factor of 1000 difference (except for plain old arithmetic errors, of course ).

- Dr. Trintignant

 

[ben m]

The usual definitions of x-ray and gamma ray are simply that gamma rays are caused by nuclear, or smaller, interactions and x-rays are everything else

That's indeed the common nuclear-physics usage---with the odd effect that, say, U235 might be said to release both a 31 keV gamma ray (from excited states of the 231Th daughter nucleus) and a 90 keV x-ray (from inner-shell excitation of the daughter atom). Ugh. 235mU has a 70 eV "gamma ray"---that's what I call FUV, but it comes from the nucleus.

But when I'm wearing my astronomer hat, almost everything comes from atomic/electronic processes, so I tend to think: if you need a semiconductor fab to build the detector, it's an x-ray. If you need a machine shop and a screwdriver, it's a gamma ray.

 

[Schneibster]

Huh, that makes about four papers I found on it wrong, Trint. Lemme check it out.

 

[Dr. Trintignant]

Huh, that makes about four papers I found on it wrong, Trint. Lemme check it out.

Sure thing; I'd be interested in seeing what the papers say. Incidentally, my density estimate was probably on the high side; densities seem to range from 7.9 g/cc for metallic asteroids down to 1.2 g/cc for "rubble pile" carbonaceous asteroids (which are more common). But that's only a factor of 8 difference, at most.

- Dr. Trintignant

 

[Schneibster]

The number I recall, and the one that Wikipedia reports, is that the Chicxulub impact was 100 teratons, not gigatons. But let's try another order-of-magnitude calculation.

The asteroid was about 10 km across, or 5x10^11 m^3 in volume.

I get 523,598,775,598 m^3, using trusty old 4/3 x pi X r^3. That's about 5 x 10^11.

I don't know much about the density, but being a rocky, metallic thing, it couldn't have been too far off from 10 g/cc, or 10,000 kg/m^3. Within a factor of 2, anyhow. So our mass is about 5x10^15 kg.

Density anywhere from 5 (stony) to 8 (nickel-iron) t/m^3. Water is 1 t/m^3. You've chosen 10, above the high end of the scale. I'll do the range from 5 to 8. That gives us 2,617,993,877,991,494kg, or 2,617,993,877,991t, at the low end, and 4,188,790,204,786,390kg or 4,188,790,204,786t at the high end. Between 2.6 x 10^15kg and 4.1 x 10^15kg.

Asteroid velocity is around 17 km/s on average.

Here we initially disagreed pretty strongly. I have 20-40km/s; however, this apparently is for comets. I found what I consider pretty reliable sources that agree with your figure, so we'll go with that.

Plug into KE=1/2*m*v^2, and we get 7.2*10^23 J. Divide again by 4.2*10^15, and we get 170,000,000 megatons, or 170 teratons.

I get 605,280,184,591,633,497,277,135J on the high end, and 378,300,115,369,770,935,798,209J on the low; that's 605 x 10^23J to 378 x 10^23J. The TNT nuclear equivalent conversion factor is 4.184GJ/t; that gives 90,415,897,554t on the low end, and 144,665,436,087t on the high end. I get 90Gt to 145Gt.

Obviously there are several approximations in there but probably nothing that would make a factor of 1000 difference (except for plain old arithmetic errors, of course ).

- Dr. Trintignant

That's what got ya; your conversion factor is for kt, not Mt. Conversion factor to kt is 4.184TJ/kt; to Mt is 4.184PJ/Mt, and peta is 10^18, not 10^15, which is tera. Off by three orders of magnitude, which is what I originally thought.

ETA: GAH! I screwed up and used 10^12 for giga, not 10^9; 10^12 is tera. My bad. You're correct, it's 90-144Tt. That makes 10^15 peta, not 10^18.

Now for those sources.

 

[davefoc]

Schneibster,
I was with you, I thought, when you said that the impact might have generated gamma rays. I wasn't sure that there would be a significant amount but I thought your point was that the radiation created would follow a black body curve and there would be some gamma radiation in the tail.

Now it seems that you were saying that radiation might have peaked in the gamma range? That seems doubtful as your calculation of 115,000,000 degrees suggested to me, but maybe I am completely confused either by what you meant or the actual physics.

 

[Dr. Trintignant]

I get 605,280,184,591,633,497,277,135J on the high end, and 378,300,115,369,770,935,798,209J on the low; that's 605 x 10^23J to 378 x 10^23J. The TNT nuclear equivalent conversion factor is 4.184GJ/t; that gives 90,415,897,554t on the low end, and 144,665,436,087t on the high end. I get 90Gt to 145Gt.

That's what got ya; your conversion factor is for kt, not Mt. Conversion factor to kt is 4.184TJ/kt; to Mt is 4.184PJ/Mt, and peta is 10^18, not 10^15, which is tera. Off by three orders of magnitude, which is what I originally thought.

I think your numbers are still wrong here; 378,300,115,369,770,935,798,209 J divided by 4,184,000,000 J/t is 90,415,897,554,916 t, or 90 Tt.

- Dr. Trintignant

 

[Madalch]

I have always loved this cartoon:
http://angryflower.com/helpin.html

 

[Dr. Trintignant]

ETA: GAH! I screwed up and used 10^12 for giga, not 10^9; 10^12 is tera. My bad. You're correct, it's 90-144Tt. That makes 10^15 peta, not 10^18.

Ahh, looks like you caught it on your own. And I caught my density error . Maybe the papers said "billion tons" and they were using the old British meaning of "billion"?

- Dr. Trintignant

 

[Schneibster]

Went looking and the sources didn't say what I thought they did. It was late; I must have confused my gigas and teras, as I did just above.

 

[Soapy Sam]

What's the odd gazillion, between friends?

 

[Schneibster]

Schneibster,
I was with you, I thought, when you said that the impact might have generated gamma rays. I wasn't sure that there would be a significant amount but I thought your point was that the radiation created would follow a black body curve and there would be some gamma radiation in the tail.

Now it seems that you were saying that radiation might have peaked in the gamma range? That seems doubtful as your calculation of 115,000,000 degrees suggested to me, but maybe I am completely confused either by what you meant or the actual physics.

I didn't complete the thought.

Let's follow the logic from the other end. To create a nuclear explosion in the tens of megatons, the initial temperature of the exploding core has to be on the close order of hundreds of millions of degrees in a device on the close order of tens of meters in size. This is of the same or one lesser order of magnitude than the thirty meter object estimated for Tunguska. To create a 15Mt explosion, then, the temperature has to have briefly been on the close order of tens to hundreds of millions of degrees; any less and there will not be sufficient energy to create an explosion so large from an object so small.

I have never touched the physics of how such a high temperature could come to be; I'm pretty certain that to get a result that's within even multiple orders of magnitude of the correct one, you're going to need numerical simulations, which ain't happenin' on this here cute little laptop anytime this year. To give you an idea of what's involved, first we need to remember that at the speeds such an object is moving, the compression wave in front of it is basically going to consist of trapped air, incapable of escaping due to the speed of the oncoming object; so you can model the bolide as cylindrical column of compression. The pressure increases extremely quickly, driving the temperature very high. As temperature rises, the bolide vaporizes from the front, adding to the material available, but absorbing heat as latent heat of liquifaction and vaporization.

Basically, the Tunguska object encountered the top of the troposphere as a solid barrier which caused it to vaporize at impact; the vaporized bolide, along with a comparatively small amount of superheated, ionized air then formed a gas jet that struck the surface of the Earth at hypersonic velocity. The heat pulse from the impact with the troposphere would have briefly been in the hundreds of millions of degrees, generating a blackbody radiation peak in the gamma; the bulk of this pulse would have been absorbed by the atmosphere and bolide body, and turned to lower frequencies and re-emitted.

Some of the gamma, however, would escape the region where the bolide was being vaporized, and even a small percentage would yield a fairly powerful gamma pulse. Obviously, however, the bulk of the gamma rays were absorbed by material in the immediate vicinity, because otherwise not enough energy would remain to create the gas jet.

It's likely that anyone looking directly at the explosion at any distance from which it would be visible on the surface would be at minimum temporarily flash blinded (which is what happens when you look at a light so bright it consumes all the photosensitive dye in your retina; the dye is regenerated, but it takes a while). If they were close, retinal burns and permanent blindness would result, but it's possible being blinded would be the least of their problems since third-degree flash burns would also be a likely result of being that close. In 1908, third-degree flash burns over any significant portion of the body would likely be a death sentence. Being actually inside or even in direct line-of-sight of the fireball's impact with the surface would result in instant personal vaporization. Effects in between would range in severity.

I suspect that anyone who could get enough gamma radiation to cause radiation sickness would have far worse problems than that; whether other physical effects of the radiation would linger would depend on the material affected. Gamma doesn't make things radioactive the way neutrons do, so it would just be the one pulse. Without any other source of radiation, I'm not sure wood, water, or stone could retain anything measurable a hundred years later, but it's not impossible.

To conclude, basically, from a distance, your "tail" of gamma is about what you'd see; most of the gamma and X-ray radiation created at tropospheric impact would be absorbed in the immediate vicinity of the impact, and contribute to the temperature of the fireball, which would then shoot down to the surface. But inside the fireball, at the moment of its creation, you'd get very high gamma or X-ray flux, just as you do at the detonation of a nuclear weapon. Everything else that happened would just be the aftereffects of that pulse, again, just as it is in a nuclear explosion.

Is that clearer?

And again, I still invite criticism and the detection of any holes in the reasoning. There are folks here other than me who can contribute to our understanding of what happened if they choose.

 

[Soapy Sam]

Let me just check.
You're saying anyone close enough to be irradiated would be flash boiled as well, so the putative gamma ray peak becomes sorta...marginal?