Question

why this is really interesting in astronomers....?

the local pattern speed=(orbital frequency) - (epicyclic frequency)/2 is really close to constant with radius.

why is this interesting for astronomers trying to explain spiral arms?

Answer 1

        Spiral arms are regions of stars that extend from the center of spiral and barred spiral galaxies.Thin regions resembles a spiral and thus give spiral galaxies their name .Naturally different classification of spiral galaxies have distinct arm stuctures .Sc and SBc galaxies ,for instance, have very loose arms,whereas Sa and SBa galaxies have tightly wrapped arms .either way spiral arms contain many young ,blue stars due to high mass density and high rate of star formation ,which makes arms so bright .