  Far away observers can in principle bound from below the dimensionless
maximum-density parameter $\Lambda\equiv4\pi R^2\rho_{\text{max}}$ of a compact
star by measuring the gravitational redshift factor
$z\equiv\nu_{\text{e}}/\nu_{\infty}-1$ of photons that were emitted from the
{\it surface} of the star: $\Lambda\geq{3\over2}[1-(1+z)^{-2}]$ [here $R$ is
the radius of the star and $\{\nu_{\text{e}},\nu_{\infty}\}$ are respectively
the frequency of the emitted light as measured at the location of the emission
and by asymptotic observers]. However, if photons that were created somewhere
{\it inside} the star can make their way out and reach the asymptotic
observers, then the measured redshift parameter $z$ may not determine uniquely
the surface properties of the star, thus making the above bound unreliable. In
the present compact paper we prove that in these cases, in which the creation
depth of a detected photon is not known to the far away observers, the
empirically measured redshift parameter can still be used to set a (weaker)
lower bound on the dimensionless density parameter of the observed star:
$\Lambda\geq{3\over2}[1-(1+z)^{-2/3}]$.
