What is the Cooling Time of a Neutron Star?

[Thecla]

TL;DR

Length of time it takes a neutron star to cool to room temperature

Neutron stars have surface temperatures of 1,000,000 degrees K. Yet they are not creating energy like a normal star. They are just cooling off. How long does it take for such a star to cool to room temperature, 300 degrees K.?

 

[berkeman]

What reading have you been doing about this question so far? Also, is this a schoolwork question?

 

[Thecla]

No it is not a school question. I assume these stars have been around millions of year. I don't know. I can't see how something radiates all this energy at T^4 and still stays hot for so long.

 

[snorkack]

I wonder about it, too.
I can see some links:
https://arxiv.org/pdf/astro-ph/0409751.pdf
https://cds.cern.ch/record/620491/files/0306143.pdf
http://www.ioffe.ru/astro/Stars/Paper/ofengeim_yak17mn.pdf
As you see, they systematically cut off at mere 10 Myr.
How cold exactly do neutron stars get at 12...13 Gyr?
Milky Way should be full of neutron stars that are 12...13 Gyr old, which formed in young Milky Way and have since been orbiting on high inclination orbits in Milky Way corona along with (but outside) globular clusters.
While their brightness drops with T⁴, what is their heat capacity doing?