Brightness of neutron stars

[factotum]

I did find one place that calculates the luminosity of a neutron star at 1 million K and a diameter of 20 km (more or less average for neutron stars) to be 18% that of the sun. Red dwarves peak at only 10% the luminosity of the sun. That's a lot of energy from such a little ball.

1 million K is a lot of temperature! Even the largest blue-white stars only have a surface temperature of 40,000 K. Since you can approximate the energy output of stars as black body radiation (it's a lot more complicated, of course, but it's a good first approximation) this explains why most of their output is in the X-ray spectrum, too.