Is a Core Temperature of 3.14*(10^7) K Feasible for a 50 Solar Mass Star?

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SUMMARY

A core temperature of 3.14*(10^7) K for a 50 solar mass star is feasible and falls within the expected range for Main Sequence stars, which typically have core temperatures between 4 million and 40 million K. This temperature is only slightly higher than the Sun's core temperature of 1.5*(10^7) K. The CNO cycle's reaction rate increases significantly with temperature, approximately proportional to T^17, indicating that even minor temperature increases can dramatically affect a star's energy output.

PREREQUISITES
  • Understanding of stellar evolution and Main Sequence stars
  • Knowledge of core nuclear fusion processes, particularly the CNO cycle
  • Familiarity with temperature scales in astrophysics
  • Basic concepts of stellar mass and its impact on core temperature
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  • Research the CNO cycle and its temperature dependence in stellar environments
  • Study the relationship between stellar mass and core temperature in Main Sequence stars
  • Explore the implications of core temperature variations on stellar luminosity and lifespan
  • Examine case studies of massive stars and their evolutionary paths
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Astronomers, astrophysicists, and students studying stellar dynamics and nuclear fusion processes in massive stars.

maggiemicmuc
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I'm wondering how realistic it is for a 50 solar mass star to have a core temperature of 3.14*(10^7) K. This isn't much greater than the core temperature of the sun, which is 1.5*(10^7) K. Have I made some huge miscalculation, or does this seem feasible?

Thanks.
 
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maggiemicmuc said:
I'm wondering how realistic it is for a 50 solar mass star to have a core temperature of 3.14*(10^7) K. This isn't much greater than the core temperature of the sun, which is 1.5*(10^7) K. Have I made some huge miscalculation, or does this seem feasible?

Thanks.

Core temperature only varies by an order of magnitude in Main Sequence stars - roughly 4 million to 40 million K, from the smallest M to the biggest O star. Remember the reaction rate of the CNO cycle goes up ~(T)17 so only a small rise has a huge effect on a star's output.
 

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