Using nuclear devices to terraform Mars: Elon Musk's nuclear proposal? Elon Musk has recently suggested Using nuclear devices to terraform Mars. In the past, comet related ideas were mooted, but Musk seems, to me anyway, to be a  man in a hurry and perhaps his idea has some merit, as waiting around for suitable comets may take a while and involve large energy expenditure. 

The businessman has often stated that he thinks humans should colonize Mars, and now it seems he’ll stop at nothing to get his way.
  “It is a fixer-upper of a planet,” Musk told Colbert. “But eventually you could transform Mars into an Earth-like planet.”
  There’s a fast way and a slow way to do that. The slow way involves setting up lots of pumps and generators to warm up the red planet so that its frozen carbon dioxide melts and wraps the planet in a thicker atmosphere. The thicker blanket of CO2 helps the planet warm up further, thus melting more carbon dioxide, and the positive feedback loop continues. (This is essentially what we’re doing on Earth, and it’s called global warming.)
  There's a simpler and cheaper way to warm up Mars. “The fast way is, drop thermonuclear weapons over the poles,” said Musk.

I can't immediately find an estimate of the volume of the carbon dioxide on (or under) the Martian surface but this source Water on Mars gives an estimate of water ice volume:

Water on Mars exists today almost exclusively as ice, with a small amount present in the atmosphere as vapor. The only place where water ice is visible at the surface is at the north polar ice cap. Abundant water ice is also present beneath the permanent carbon dioxide ice cap at the Martian south pole and in the shallow subsurface at more temperate latitudes. More than five million cubic kilometers of ice have been identified at or near the surface of modern Mars, enough to cover the whole planet to a depth of 35 meters. Even more ice is likely to be locked away in the deep subsurface.

Physically, and I do want to stick to the physics, particularly the atmospheric physics, rather than engineering,  is this idea feasible? 
Has Musk done his homework as regards:


*

*The amount of nuclear material needed? (And the undoubted outcry over its transport from Earth using potentially highly explosive rockets in the first place)?

*Is the gravity of Mars strong enough to retain the water vapour involved?  I am guessing it is.

*Will  atmospheric pressure help retain the water vapour produced or is his idea enough to produce a relatively dense atmosphere?

*Finally, Musk is a businessman selling a possible project, and that implies, understandably I suppose, that  dramatic publicity is involved. Would a set of mirrors in orbit do the job just as efficiently, although over a longer timescale?
 A: 
Has Musk done his homework?

With regard to the basic idea of using nuclear weapons to release CO2 and thereby warm Mars, no, he hasn't. I suspect this was either Bored Elon Musk speaking, or perhaps the Elon Musk who didn't quite deny being a super villain ( 1-900-MHA-HAHA Elon Musk?) in that interview with Colbert.
CO2's enthalpy of sublimation is about 26 kJ/mol, or 590 kJ/kg. The Tsar Bomba released 210 petajoules of energy. Suppose Musk manages to explode a Tsar Bomba equivalent over one of Mars' poles, with all of the energy going into sublimating CO2, and all of that newly created gaseous CO2 remaining resident in the atmosphere for a while. That's an extra 355 megatons of CO2 added to Mars' atmosphere.
That sounds like a lot. It's not. It's a tiny, tiny amount compared to the 25 teratons of CO2 in Mars' atmosphere. We've just blown up the biggest device invented by humankind and have only increased Mars' atmospheric CO2 content by an immeasurably small amount.
Most of Mar's CO2 is in its atmosphere, not its icecaps. If we used 20,000 or so Tsar Bomba equivalents we could theoretically increase Mars' CO2 content by 25 to 33%. That's not going to do much. (By way of comparison, it's the consequences of a doubling of the Earth's atmospheric CO2 content that have people concerned.)
Even though Mars has considerably more CO2 in its atmosphere than does the Earth, the greenhouse effect on Mars is considerably smaller than it is on Earth. There are a number of reasons for this:


*

*Adding ever more CO2 to an atmosphere has a logarithmic effect. Adding more CO2 to Mars' already saturated atmosphere won't have much of an effect.

*Mars low gravitational acceleration means the dry adiabatic lapse rate on Mars is less than half that on Earth. Greenhouse gases move an atmosphere away from an isothermal atmosphere toward an adiabatic atmosphere. Mars thin atmosphere and low lapse rate alone explain most of why the greenhouse effect on Mars is significantly less than that on Earth.

*There are two bands in the thermal infrared where CO2 is a very good absorber/emitter of radiation. One peaks at Earth equatorial temperatures (Mars doesn't get anywhere near that hot), the other peaks at Earth polar temperatures (that's Mars). That lower peak means that, except for polar regions, Earth's middle troposphere to upper stratosphere are extremely opaque to infrared radiation. Mars atmosphere on the other hand gets increasingly more transparent in the infrared with increased altitude.


Nukes could help warm Mars. Mars' energy budget varies considerably with Mars' weather. Mars occasionally suffers planet-wide dust storms. While those dust storms increase Mars' albedo, they change the energy flux to and from the surface by more than enough to compensate for this lost incoming energy. If the goal is to heat Mars up, it would make a lot more sense to nuke Mars' equatorial regions instead of its poles. We'd have to do this on a regular basis to have any effect. Whether or not this is a good idea is a different question.
