From the in-game description:
"White Dwarf stars are stellar remnants. Nuclear fusion has now ceased, and in the absence of radiation pressure the core has collapsed to a tiny fraction of the diameter of the original star, heating it up greatly before it begins its slow cooling down phase. Surface temperatures are usually between 8,000 K and 40,000 K so these stellar remnants are blue-white."
Be careful around them, their tiny size can deceive inexperienced pilots. Give them a wide berth when trying to get past them. However, if you're feeling adventurous, super-cruising within the jet stream has some interesting effects, most notably a temporary boost to your jump range.