Brown dwarf? Some sputtering early attempts at fusion, but not enough to become self-sustaining.

13 Mj is on the low side of the definition. It's not a definitive number and goes as high as 80 Mj, depending who you ask.

13 Mj is the current mass at which people think deuterium fusion can start. Above 80 Mj, hydrogen fusion will start.

These numbers depend on a lot of details of stellar atmospheres.

I took a graduate-level Stellar Atmospheres class from S. Kumar, who first theorized about this class of not-quite-star.