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?