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J005311 is two white dwarf stars that have merged in such a way, that, well they merged instead of exploding. (Only 7 or so such mergers have been found.) Its stellar wind is blowing at 16,000 km per second and has reached a surface temperature of 200,000 C. The weird thing is it emits no light, and only shines in infrared..

When it runs out of material to burn, in a few thousand years it will likely collapse under its own gravity, the electrons and protons fusing into neutrons, turning the Frankenstar into a low-mass neutron star.

Scientists have believe it is currently large enough to kick start nuclear fusion again. My question, is what is it burning? Shouldn't the core be iron? Which takes more energy to fuse than it releases? Is it burning carbon and oxygen in outer belts above the iron core?

Finally why is it not emitting light?

The paper being referenced is Gvaramadze et al. 2019; they note that the observations agree with models of super-Chandrasekhar mass remnants of carbon-oxygen white dwarf collisions, carried out by Schwab et al. 2016. Schwab et al.'s models predict that post-collision, slightly off-center carbon fusion will occur in the remnant. This fusion leads to a so-called "carbon flame", a deflagration (note: not a detonation) wave that travels towards the remnant's center, over the course of about $2times10^4$ years.

Once the flame reaches the center, it lifts the preexisting degeneracy, allowing for Kelvin-Helmholtz contraction; if the remnant exceeds $1.35-1.37M_odot$ (as J005311 is believed to), off-center neon fusion will be triggered, leading to a neon-oxygen analog of the carbon flame, also propagating towards the center. Schwab et al. also find that this flame will not fully lift the central degeneracy. Assuming there is no off-center silicon burning, the remnant will at this point become a silicon-dominated white dwarf; if silicon burning occurs (as it did in some models), it is likely that the resulting iron core would collapse into a neutron star.

The process is expected to take $sim20,000$ years, and given the size of the nebula, it appears that the central star is $sim16,000$ years old. Given the expected timescales of carbon and neon (extremely short, compared to carbon) burning, it seems likely that the star is currently undergoing carbon fusion, rather than neon or silicon burning.

Strictly speaking, it is not the star itself that is emitting no optical light; that is true of the nebula surrounding it (the nebula is the source of the mid-infrared emission, as detected by WISE, not the central star). Gvaramadze et al. looked for an optical counterpart in the INT Photometric H$alpha$ Survey of the Northern Galactic Plane (IPHAS) and found no optical emission. They attribute this to the paucity of hydrogen and helium; along with the high temperature of the star, which triply ionizes oxygen, the composition means that there are really no strong sources of optical lines, which is why it didn't show up on IPHAS.