What is the Cooling Time of a Neutron Star?

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SUMMARY

Neutron stars, with surface temperatures reaching 1,000,000 degrees K, primarily cool over time rather than generating energy like typical stars. The cooling process can take millions of years, with estimates suggesting that neutron stars may cool to room temperature (300 degrees K) over a period of approximately 10 billion years (10 Gyr). The discussion highlights the need for further understanding of the heat capacity of neutron stars as their brightness diminishes according to the Stefan-Boltzmann law (T^4). Relevant research papers provide insights into the cooling mechanisms and historical context of neutron stars within the Milky Way.

PREREQUISITES
  • Understanding of neutron star physics
  • Familiarity with the Stefan-Boltzmann law
  • Knowledge of stellar evolution and lifecycle
  • Basic concepts of heat capacity in astrophysical contexts
NEXT STEPS
  • Research the cooling rates of neutron stars using the Stefan-Boltzmann law
  • Explore the implications of neutron star heat capacity on their thermal evolution
  • Study the formation and distribution of neutron stars in the Milky Way
  • Examine the provided research papers for detailed astrophysical models
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Astronomers, astrophysicists, and students interested in stellar evolution, particularly those focusing on neutron star characteristics and their cooling processes.

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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.?
 
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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?
 

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