Thermal Radiation from Compact Objects in Curved Space-Time

TL;DR

This paper demonstrates that the observed thermal luminosity of compact objects in curved space-time is significantly higher than in flat space, due to gravitational redshift effects, impacting interpretations of X-ray emissions from neutron stars and ultra-compact objects.

Contribution

The paper derives a simple factor increase in observed luminosity due to gravitational redshift, emphasizing its importance for understanding thermal radiation from ultra-compact objects.

Findings

Observed luminosity is increased by a factor of (1+z_b)^2 due to gravitational redshift.

For neutron stars, the luminosity could be underestimated by about 20% if relativistic effects are ignored.

Ultra-compact objects could have even higher surface redshifts, significantly affecting their thermal emission observations.

Abstract

We highlight here the fact that the distantly observed luminosity of a spherically symmetric compact star radiating thermal radiation isotropically is higher by a factor of $(1+z_{\rm b})^2$ compared to the corresponding flat space-time case, where $z_{\rm b}$ is the surface gravitational redshift of the compact star. In particular, we emphasize that if the thermal radiation is indeed emitted isotropically along the respective normal directions at each point, this factor of increment $(1+z_{\rm b})^2$ remains unchanged even if the compact object would lie within its {\em photon sphere}. Since a canonical neutron star has $z_{\rm b} \approx 0.1$, the actual X-ray luminosity from the neutron star surface could be $\sim 20 \%$ higher than what would be interpreted by ignoring the general relativistic effects described here. For a static compact object, supported by only isotropic pressure, compactness is limited by the Buchdahl limit $z_{\rm b} < 2.0$. However, for compact objects supported by anisotropic pressure, $z_{\rm b}$ could be even higher ($z_{\rm b} < 5.211$). In addition, in principle, there could be ultra-compact objects having $z_{\rm b} \gg 1$. Accordingly, the general relativistic effects described here might be quite important for studies of thermal radiation from some ultra-compact objects.