Radio galaxy. In 1962 an intense extraterrestrial source of radio radiation was optically identified as a starlike object with an angular radius of approximately $\frac{1^{\prime \prime}}{2}$ of are, It was at first thought to be a star in our galaxy giving off radio waves, but subsequently its spectrum was obtained and its spectral lines were found to be very considerably red-shifted. For instance, an atomic oxygen line with wavelength $\lambda$ normally $3.727 \times 10^{-5} \mathrm{~cm}$ was identified at $\lambda=5.097 \times 10^{-5} \mathrm{~cm} .$ One
explanation took it to be an exceedingly massive star with a spectrum gravitationally red-shifted. If this hypothetical radio star is in our galaxy, its distance must be less than $10^{22} \mathrm{~cm}$ from the earth. ${ }^{1}$
(a) Calculate from the angular diameter and the red shift, the mass and mean density of the star under this hypothesis, assuming the distance to be $10^{22} \mathrm{~cm}$. Is this a reasonable explanation of this object? Ans. Mass is $1.0 \times 10^{44} \mathrm{~g}$, mean density is $1.7 \times$ $10^{-6} \mathrm{~g} / \mathrm{cm}^{3} .$ This does not seem reasonable, as the mass is about $0.1$ of the total mass of our galaxy (use the result of Prob. 2).
(b) An alternative suggestion was that it might be a peculiar "radio galaxy," with its red shift following the usual recessional red-shift relation given in Chap. 10. Calculate its distance on this second hypothesis. Ans. $6 \times 10^{9}$ light yr $\left(5.6 \times 10^{27} \mathrm{~cm}\right)$
(c) Does the radio-galaxy hypothesis conform with this expectation? Ans. Yes; it has a radius of about $10^{22} \mathrm{~cm}$. This is in the usual range of galactic radii.