The Speed of Light is a constant in a vacuum.
Close objects like stars can be measured with basic geometry using the PARALLAX method. Observing the star’s apparent shift in position from different parts of the Earth’s orbit.
Galaxies are much farther away and require using the Red Shift of it’s light to measure the distance. The farther away it is the more Red Shifted its light will be. Certain elements produce dark lines in the spectrum of light, so looking at the spectrum of the light and noting how much a certain element is shifted tells you how far away it is............
Ah. Now it makes sense. Thanks. I’d forgotten all about the PARALLAX method.
In a large HII region, all ionizating radiation eventually becomes Lyman-alpha. These Lyman-alpha photons “bounce” around the atoms, causing excitation from the ground state to the first Lyman level. The atom may then un-excite itself releasing another Lyman-alpha photon and return to its ground state.
But at this ground state, the electron may have its spin aligned or opposed to its “orbit.” The difference between these two states yields the so-called spin temperature.
I don’t know the odds of the two states resulting from the re-combination. They would depend on the motion of the atoms, the kinetic temperature of the hydrogen atoms.
A quasar is certainly a large source of ionizing radiation, so the quasar’s radiation would affect the spin temperature and thus the strength of the 21-cm radiation.
Of course, the 21-cm radiation would be affected by the red-shift value of the galaxy itself.