High School What is the Cooling Time of a Neutron Star?

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Neutron stars, with surface temperatures around 1,000,000 K, are in a cooling phase rather than generating energy like typical stars. The discussion revolves around the time it takes for these stars to cool to room temperature (300 K), with estimates suggesting they could remain hot for millions of years. Research indicates that neutron stars may cool significantly over 10 billion years, raising questions about their thermal properties and heat capacity as they age. The Milky Way is believed to contain many neutron stars that are 12 to 13 billion years old, formed during its early stages. The cooling process and energy radiation of neutron stars continue to intrigue astrophysicists.
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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.?
 
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What reading have you been doing about this question so far? Also, is this a schoolwork question?
 
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.
 
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?
 

Thread 'Luminous Fast Blue Optical Transients (LFBOTs)'

UC Berkely, December 16, 2025 https://news.berkeley.edu/2025/12/16/whats-powering-these-mysterious-bright-blue-cosmic-flashes-astronomers-find-a-clue/ AT 2024wpp, a luminous fast blue optical transient, or LFBOT, is the bright blue spot at the upper right edge of its host galaxy, which is 1.1 billion light-years from Earth in (or near) a galaxy far, far away. Such objects are very bright (obiously) and very energetic. The article indicates that AT 2024wpp had a peak luminosity of 2-4 x...
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