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The governor of Svalbard requires firearms of adequate power to protect against polar bears. Here are the requirements:

2.Types of firearms
2.1. Rifles

The acquisition, use, trade and import of rifles for use as protection against polar bears is permitted in Svalbard, pursuant to the Firearms Act and Firearms Regulations.
2.1 Rifles used for protection against polar bears shall have a minimum calibre of .308W or 30-06 (7.62 mm). Rifle bullets shall be expanding, with a minimum bullet weight of 11.5 g. The required impact energy shall be 2,700 J, measured at a distance of 100 m.
For reasons of precision, range, functionality in cold conditions and stopping power, the Governor of Svalbard recommends the use of rifles as the primary means of protection against polar bears, rather than other types of firearms.
Hiring out rifles is permitted. For more detailed conditions regarding this, please refer to Section 4.2.2. Shotguns
The acquisition, use, trade and import of shotguns for use as protection against polar bears is permitted in Svalbard, pursuant to the Firearms Act and Firearms Regulations.
2.2 Shotguns used for protection against polar bears shall have a minimum calibre of 12, and should have a magazine permitting a minimum of four shots (automatic or pump-action shotgun). The use of slugs (shotgun ammunition comprised of one projectile) is recommended for protection against polar bears.
However, the Governor of Svalbard warns that most magazine-fed shotguns tend to have problems with icing and condensation, and require more preventive maintenance work if they are to function in difficult conditions. Because of this, combined with the fact that shotguns have less precise sights and a limited range, the Governor of Svalbard recommends the use of rifles as the primary means of protection against polar bears.
The Governor of Svalbard advises against the use of double-barrelled shotguns for protection against polar bears, because of the number of available shots.
It is prohibited to hire out shotguns for protection against polar bears.
2.3. Handguns/revolversHandguns for competition and practice can legally be used in the field for protection against polar bears, provided that the Governor of Svalbard has granted a special permit for this.
This combination of usage purposes shall be stated explicitly on the firearm permit and may only be granted upon application to the Governor of Svalbard. This permit may only be granted if the applicant meets the requirements for documented activity in an approved shooting association.
Handguns for which an applicant is seeking a permit for use as protection against polar bears shall have a minimum calibre of 44. Ammunition to be used for protection against polar bears shall have a minimum weight of 15.5 g and a minimum muzzle energy of 1,200 J.

In English measurement, that is 885 ft-lbs, with a minimum bullet weight of 239 grains. Full power .44 magnum loads, .480 Ruger, .454 Casull, .500 Smith & Wesson and .460 Smith & Wesson would qualify. Some .41 magnum loads would qualify.

Those who would carry a pistol for protection in Svalbard need to show they have participated in organized pistol training four times in the last year, before they can be approved.