No more burning

There is no fuel to burn. These are giant cinders radiating their left-over heat into the vacuum of space. Bottom line is that all their properties are determined by their mass (through gravitation.) The mass of a neutron star is constrained on the high end by gravity and on the low end by the minimum it takes to allow a star to go supernova.

Based on the understanding of all the forces in play, if you can estimate the mass, you can calculate its size. So when you find one that is significantly smaller/larger than expected, either the mass estimate is wrong, your measurements are wrong, or the thing isn't made up of neutrons.

I suspect a similar line of reasoning for the colder object based on specific rates of heat radiation for neutron matter.

Keep in mind that this is just a guess.

They determined the temperature by comparing with the well-known [link|http://www.phys.virginia.edu/CLASSES/252/black_body_radiation.html|black body spectrum] to find the temperature. Once they find a temperature, assuming that they have an estimate of the distance (probably done by estimating the distance to the nebula associated with the supernova), they can then look at how bright it is and figure out how big it's cross-sectional area is.

Which leads me to wonder how they ruled out any number of options. For instance with the dim one, what if there is just a dust cloud between us and it? (Say, there happened to be a bulge in the nebula between us and it. For a sideways picture of what that might look like go [link|http://www.cosmiverse.com/reflib/Image_Gallery/messier/messier7.html|here].) As for the cold one, suppose that neutron stars can go through a phase transition of some sort (much like freezing in regular materials), then it could have cooled off rather suddenly from currently unknown internal dynamics.

Rather more prosaic than claiming a new form of matter, but both seem like plausible options to me. (Note that a lot of astronomy rests on very long chains of assumptions. What they are trying to find out is very hard to verify.)

Cheers,
Ben

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