Question

Explain why the broadening of a spectral line from a distant spiral galaxy is related to the distance to the galaxy and how the Tulley-Fisher relationship determines this distance from the spectral lines broadening.

Answer 1

Spiral galaxies have flattened disk central bulges and spiral arms. they are divided on the basis of the bulge, tightness of the spiral structure. Tully-Fisher relation is a meauring tools, an empirical correlaion between rotational velocity anf luminosity in spiral galaxies.(In other words, It relates rotational speeds of galaxies as measured by the broadness of their emission lines to their luminosities.)

The Tully-Fisher relation uses the close correlation between the rotational speed of a spiral galaxy and its luminosity as a distance indicator because the greater the mass of galaxy, the faster it spin, and the more mass there is to give off light.

Blue shifted and Red shifted lines from individual stars in the galaxy blend together to form broadened absorption lines in the galaxy spectrum. If the spread in velocities is greater the blended absorption lines are fatter. This happens for more massive and luminous galaxies. some stars are far away galaxy are moving toward us so their lines will be blueshifted other stars are redshifted lines. If an object has a larger redshift that means moving away from us at larger velocity. If an object has a smaller redshift it means its closer. The spectral lines from the entire galaxy blend together to form a FAT line.

The rotation of a galaxy result in spectral line broadening by the shifted lines from the two moving sides if the galaxy combines with the unshifted line from thee center, resulting in a broader frequency distribution and by light from opposite sides of galaxy is shifted in different directions causing the spectral lines to move to higher to lower frequencies relative to unshifted line.

To determine the distance to a galaxy, need to measure its apparent size and use the small angle equation a=s/d. where a=measured angular size, s= galaxy true size and d = distance of the galaxy.