Wednesday, October 8, 2014
Modeling An Asteroid Strike Using A Nuclear Explosion Code
The above (2D) computational simulation for the Chelyabinsk asteroid's atmospheric wake, after being adapted from Sandia's code for modeling nuclear explosions. Each panel is a cross-sectional slice at the same time location along the asteroid's path for different times after the energy was deposited. (From Physics Today, Sept.)
The Feb. 15, 2013 asteroid airburst over Chelyabinsk, Russia has now gone down in infamy after the 20 m diameter object, entering the Earth's atmosphere at 19 km/s , blew up and shattered windows miles away - shaking the residents from their day to day routines. Of course, getting an actual reliable estimate of the magnitude of the blast - which was compared to an airburst nuclear explosion - has proven difficult.
But, as reported in Physics Today (September, p. 32) this has now been accomplished thanks to a 3-dimensional simulation using a shock code developed at Sandia National Laboratories, originally intended to model nuclear explosions. The code, input into Sandia's 'Red Sky' supercomputer, showed that the Chelyabinsk blast was of at least a half megaton, or comparable to the yield of many U.S. warheads on ICBMs, like the 'Minuteman'.
Some of the information and insights that the Sandia team has assembled with other data:
- The entry at 19 km/s meant that it originated from the asteroid belt between Mars and Jupiter - not from a ballistically launched missile whose velocity would only be about 11.2 km/s or a short period comet with a mean speed of 35 km/s.
- The altitude of the blast indicated the object was small and weak. The diameter of 20 m (66 feet) was estimated base on the observed velocity factored together with the assumed density of the material.
- The asteroid first felt the presence of Earth's atmosphere while it was thousands of miles above the Pacific Ocean and for a dozen minutes the 10,000 ton rock fell swiftly and unobserved passing at shallow angle through the atmosphere where the molecular mean free path was much greater than the 20 m diameter.
- When it crossed over the border into Russia at 3:20:20 UT and was 100 km in altitude 99.99997 % of the atmosphere still lay beneath it.
- For the better part of 10 seconds the asteroid hurtled through the air as a rigid body moving at a shallow angle, 17 degrees relative to the horizon and descending 1 km for every 3 km of flight.
- At about 45 km altitude the entry dynamics began to change. The dynamic pressure then built up from 0.7 Mpa (millions of Pascals, where 1 Pa = 1 atm equivalent), Within a couple more seconds, below 40 km, pressure on the now fracturing asteroid increased past 1 MPa, breaking it into a number of smaller fragments.
- As the pressure then grew exponentially the process cascaded and formed ever smaller fragments that rapidly increased the surface to volume ratio. As the fragments ablated the hot gas between them built up finally resulting in a chain reaction and a massive explosion converting the asteroid's kinetic energy into heat and pressure (yielding the shock wave that shattered windows).
- Only one significant piece-fragment remained post-explosion. This continued to fall like a ballistic missile in 'dark flight' at terminal velocity until it punched through the ice of frozen Lake Chebarkul. This 1.5 m diameter boulder thereby became the largest Chelyabinsk object found.
While all these facts provoke interest, the authors are quick to point out that the asteroid airburst should not be simply compared to or called "an explosion". They note that technically an explosion represents a "point source" with radial symmetry, i.e. energy is radiated in all directions from the source and the peak pressure on the ground below decays radially.
But the asteroid airburst does not act the same way and instead its profile - including shock waves changes. For example, at the beginning of its flight it behaves more like a supersonic jet but at the end more like a textbook explosion. As noted by the authors (p. 35):
"In Chelyabinsk, the energy deposition that led to the explosion took place in stages and was spread out over a long distance because of the shallow entry angle. Energy was deposited at linear densities greater than 1 kiloton per kiliometer and rose to a peak of 80 kt/km; most of the energy deposition occurred at altitudes from about 38 km down to 23 km. It took four seconds for this to happen during which the asteroid left a 50 km wake of hot expanding gas and ablation products."
The preceding gives a good synopsis of the asteroid's behavior. Sadly, as the authors also warn, it can't be generalized to extrapolate to all asteroids - even if they are roughly the same size. The problem is the angle of entry which can vary markedly (obviously) and also the fact you're not going to get staged fragmentation over long distances. For example, nearly 24 years ago in Barbados I observed a large object blow up over Mt. Tenantry, Barbados that appeared to enter from a much steeper angle. Alas, when we went out to the site, nothing could be found, no residue or even a crater.
The authors themselves (ibid.) make reference to the Tunguska event in Siberia, in 1908 and note it was "a much more abrupt explosion".
Finally, in terms of energy released, we learn (p. 36):
"The Chelyabinsk airburst was roughly two orders of magnitude more energetic than the approximately 10 kiloton Sikhote-Alin asteroid event of 1947 and roughly an order of magnitude less energetic than the 3 - 15 megaton Tunguska blast of 1908."
This puts it at the half megaton release mark. The authors admit there remains "incredible uncertainty in the energy estimates for smaller impact events making it difficult to quantify future hazards." For that reason, it is "incredibly important" that "high precision" values have been forthcoming from analysis of the Chelyabinsk event.
Let us hope the Sandia nuclear shock code can be developed or refined for other objects and ultimately enable us to forecast in advance the devastation from future asteroids. That is, assuming we can find them before they strike! There is also the potential - given we can find these objects - to maybe eliminate the threats entirely. See e.g.