How much does the gravitational redshift change a neutron star

quorums15lep 2022-05-13 Answered
How much does the gravitational redshift change a neutron star emission spectra disturbing so the measurement of its surface temperature?
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Answers (1)

stafninumfu1tf
Answered 2022-05-14 Author has 19 answers
The standard gravitational redshift formula applies to neutron stars.
This means that if a distant observer observes a spectral feature that was emitted at a rest wavelength of λ 0 from the NS surface, then it will be observed at a wavelength
λ = λ 0 ( 1 2 G M R c 2 ) 1 / 2   ,
where M and R are the neutron star mass and radius (actually the Schwarzschild r coordinate of its surface).
Since establishing a temperature from a blackbody spectrum involves finding the peak wavelength, then the observed temperature is reduced by
T = T 0 ( 1 2 G M R c 2 ) 1 / 2   .
The ratio M / R probably does vary a little bit (up to a factor of 2) between the most and least massive neutron stars. Roughly, M / R M, since the equilibrium radii of neutron stars are insensitive to their mass (in most models).
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