grand veneur
AH elite
a good deal of inuits/eskimos only have .243s or .22 centerfires, lol and these guys are your backup. (they go through a fair amount of ammo AND TP.)
It depends on how you hunt the polar bear. Traditionally, polar bear hunting is primarily a wintertime hunting and with dog-sleds.
I have never hunted polar bears, but I have hunted a few times Muskox with dogsleds in Greenland in the wintertime. When the Muskox herd is spotted, you release a few dogs, they keep the game on the place and you can go and shot one at a very short distance. A comparable technique was used by the native for polar bear hunting. With the help of the dogs, the hunter can go very near to the bear and shoot it to death with a rifle of different caliber, certainly not always elegant, but also possible with rifles of smaller caliber. In Greenland I only met native polar bear hunters who were armed with rifles mainly caliber 30-06 Springfield, some even with rifles caliber 375 H&H Magnum.