# How much does the gravitational redshift change a neutron star

How much does the gravitational redshift change a neutron star emission spectra disturbing so the measurement of its surface temperature?
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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 ${\lambda }_{0}$ from the NS surface, then it will be observed at a wavelength

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

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, $M/R\propto M$, since the equilibrium radii of neutron stars are insensitive to their mass (in most models).