What is the Cooling Time of a Neutron Star?

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Discussion Overview

The discussion centers on the cooling time of neutron stars, specifically how long it takes for them to cool from their initial surface temperatures of approximately 1,000,000 degrees K to room temperature (300 degrees K). The scope includes theoretical considerations and implications of neutron star thermodynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that neutron stars are not generating energy like normal stars but are instead cooling off.
  • Another participant questions the duration it takes for neutron stars to cool, expressing uncertainty about their longevity and energy radiation.
  • A different participant references literature that suggests neutron stars may cool significantly over 10 million years, raising questions about their temperatures after 12 to 13 billion years.
  • Concerns are raised about the relationship between brightness, which decreases with temperature to the fourth power (T^4), and the heat capacity of neutron stars as they age.

Areas of Agreement / Disagreement

Participants express curiosity and uncertainty regarding the cooling process of neutron stars, with no consensus on the exact cooling time or the implications of their thermal properties over billions of years.

Contextual Notes

Participants mention the lack of clarity regarding the heat capacity of neutron stars and how it may change as they cool, indicating potential limitations in understanding the cooling process.

Thecla
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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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