# Are larger stars rounder?

The Earth is a very smooth sphere, and the Sun even more so, with only minor fluctuations. I am wondering: are larger stars even rounder? Intuitively, that seems self evident, but I am not so sure. For instance, the hydrostatic equilibrium causes larger stars to be much less dense than red dwarfs. So what is the most important factor for how round a star is, a higher mass, or less activity? The most prominent cause of irregularities is of course the rotation rate of the star, which is pretty much independent of size. Ignoring that, do larger stars have smaller a deviations from the ellipsoid relative to their size?

Edit

As it seems like the "other than rotation rate" criterion is not really meaningfull, I now terminate it.

• What do you mean by rounder? – Rob Jeffries Apr 29 '16 at 19:04
• Indeed, more round is smaller irregularities relative to size. – Hohmannfan Apr 29 '16 at 19:10
• I have tried to edit the question now, to make it more clear I am asking about irregularities, not oblateness. – Hohmannfan Apr 29 '16 at 19:21
• I thought larger stars tended to have higher angular velocity than smaller stars? – called2voyage Apr 29 '16 at 19:25
• I have no idea how you would define an irregularity for a gaseous spheroid. In any case, we have no images or measurements of this for stars other than the Sun. – Rob Jeffries Apr 29 '16 at 21:24

The distribution is not smooth and uniform (McNally noticed a strange discontinuity in angular momentum per unit mass right for A0 and A5 stars; see his Figure 2); Barnes (2003) observed two distinct populations in open clusters, consisting of slower rotators (the I sequence) and faster rotators (the C sequence). Stars may migrate from one sequence to another as they evolve. Interestingly enough, stars on the I sequence lose angular momentum $J$ faster than stars on the C sequence: $$\frac{\mathrm{d}J}{\mathrm{d}t}\propto-\omega^n,\quad\text{where}\begin{cases} n=3\text{ on the I sequence}\\ n=1\text{ on the C sequence}\\ \end{cases}$$ Here, of course, $\omega$ is angular velocity. These results obey Skumanich's law.
Oblateness can be determined from mass, radius, and angular velocity as $$f=\frac{5\omega^2R^3}{4GM}$$ Using this and McNally's data, some quick calculations get me the following table: $$\begin{array}{|c|c|} \hline \text{Spectral type} & f/f(\text{O}5) \\ \hline \text{O}5 & 1\\ \hline \text{B}0 & 1.28\\ \hline \text{B}5 & 1.84\\ \hline \text{A}0 & 1.67\\ \hline \text{A}5 & 1.35\\ \hline \text{F}0 & 0.482\\ \hline \text{F}5 & 0.0387\\ \hline \text{G}0 & 0.000314\\ \hline \end{array}$$