I also thought that most folk who live in areas where there are polar bears tote sidearms. The obvious defensive weapon I should think would be a large calibre revolver. Easy and quick to use and not much to go wrong. You could use it just the same as a rifle to make big bangs to scare them away if things haven't got too up close and personal. [Pedro]
That's the case in the US, many deerhunters carrying a large calibre revolver loaded with full-house soft-points, likewise some wilderness walkers and campers. However, one of the US gun mags, Wolfe Publishing's 'Rifle' if memory serves did a study of this, and looked at historic / recorded encounters. Their findings weren't very encouraging for the 44 Mag handgun toting brigade. The most dangerous situation is surprising a brown bear in heavy cover, especially a female with cubs. When you see the bear / it sees you, you're invariably close - a few yards, 50 at most. Deerhunters / walkers etc normally carry their revolver in a traditional belt-holster. On such an encounter, the bear will either decide to quit and leg it, or attack immediately, no delay with much quicker reaction times than those of the average human. if the latter, the magazine writers and consultant gave the human one to three seconds depending on the intial distance between parties to unholster revolver, raise it and fire. Large bears on the attack apparently run VERY fast. I think 15-20 mph was quoted. In tests using magzine staffers, the conclusion was that it was highly unlikelly you'd get a shot off before the bear hit you.
Looking at recorded instances (of those few who survived), any who actually used a handgun did so AFTER the bear had already grabbed them in the classic 'bearhug' and was mauling the victim. It was luck whether his physical position vis a vis the bear was such that the human could get the gun out and its muzzle up against the attacker. A typical case involving a famous tracker and outdoorsman had him clutched front to front against the bear's torso and he worked the revolver up between their bodies while the bear was raking his back with its claws, and managed to fire upwards shooting the bear through its chin and up through the head. All of these survivors had serious, potentially life threatening injuries despite shooting their bears and had to get themselves to civilisation while in a bad way after tending wounds as best they could and staunching blood loss.
In Alaska and northern Canada, many professional guides and savvy locals carry large (.45 and .50) calibre, short-barrel lever-action carbines with a round in the chamber, the .50 Alaskan and .450 Marlin chamberings typical. They're already in the hand if a bear is suddenly encountered, can be swung really fast, and fire some serious weight of lead, plus four or five shots can be got off in as many seconds. Rifles are usually modified Marlin 336s. Cut-down Ruger 77s in 375 H&H, or the more modern Ruger Magnum version are popular in heavy Alaskan grizzly country. The wet climate and salt-air in coastal regions kills rifles really quickly and Marlin magnums are reliable and cheap to replace every couple of years in this harsh environment.