The spectrum of far away galaxies is from the combined motions of all of the material in them. Some stars in a far away galaxy are moving toward us, so their absorption lines will be blueshifted. Other stars will have redshifted lines because they are moving away from us. The resulting spectral lines from the entire galaxy blend together to form a FAT line. The more random motion there is in an elliptical galaxy, the greater the spread in the distribution of velocities and the fatter the resulting galaxy spectral lines will be.
More massive galaxies have more gravity so their stars are accelerated to faster orbital speeds.
More massive galaxies should have broader lines and if the luminosity correlates with the mass, the more massive galaxies should have greater luminosity. This is known as the Faber-Jackson relation . An elliptical galaxy's luminosity can be found from the velocity dispersion of the stars in the central few kiloparsecs of the galaxy. In 1977 Brent Tully and Richard Fisher discovered a similar relation between the rotational velocity of the disk and the luminosity of a spiral galaxy. The rotational velocity is found from the 21-cm emission of the neutral atomic hydrogen gas in the outer parts of the disk.