# By how much does the gravitational redshift change a neutron star emission spectrum, thus disturbing the measurement of its surface temperature?

How much does the gravitational redshift change a neutron star emission spectra disturbing so the measurement of its surface temperature? I remember some tv-shows talking about Italian pasta when talking about neutron stars....does this imply neutron stars are not all of same density so gravitational redshift differs depending on differences in densities between 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 $$\lambda = \lambda_0\left(1 -\frac{2GM}{Rc^2}\right)^{-1/2}\ ,$$ 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 $$T = T_0\left(1-\frac{2GM}{Rc^2}\right)^{1/2}\ .$$
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, $$M/R \propto M$$, since the equilibrium radii of neutron stars are insensitive to their mass (in most models).