Gravitational Red Shift of Hydrogen 21-cm. Radiation as a Method to measure Galactic Gravitational Potential

Abstract

THE 21-cm. hyperfine emission from the neutral hydrogen atom has an exceedingly narrow natural width, corresponding to a transition probability of 2.84 × 10⁻¹⁵ sec.⁻¹. Consequently, in principle, small variations in its frequency resulting from gravitational effects offer a method to measure gravitational potential in our Galaxy, provided that they are not too small compared with the temperature broadening. The galactic disk is well known to emit 21-cm. radiation, and from its observed Doppler shifts the radial dependence of its rotational velocity has been deduced. Because the true Doppler shifts of galactic rotational motion are large, it may be difficult to detect the expected gravitational shift, which also looks like a Doppler shift. But, in principle, the two effects may be separated because the true Doppler shifts have opposite signs at the same radius on opposite sides of the galactic centre, whereas the gravitational frequency shift has the same sign.