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This question about why is the Sun so spherical and it's corresponding answer made me wonder:

If some younger stars that are rotating faster than the sun are more oblate, then how oblate are they?

And is there a theoretical maximum to this shape before the star rips itself apart because its spinning too fast? Or (in theory at least) could a star spin so fast that it appears disk-shaped?

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Altair, Vega, and Regulus A are perhaps the most famous examples of stars that have been "flattened" by rapid rotation. Some studies (mentioned in Yoon et al. (2010) suggest that Vega is rotating at 70-90% percent of the speed at which it would break up (its rotational velocity is about 20 km/s). Regulus is even closer to this breakup speed: If its rotational velocity increased by 15%, it would break up (see McAlister et al. (2005)).

The critical (tangential) velocity - the point at which material will start to form a disk - for a star of mass $M$ and equatorial radius $R_e$ is given (see Townsend et al. (2004)) by $$v_c=\sqrt{\frac{GM}{R_e}}$$ This should look familiar - in fact, it is $\frac{1}{\sqrt{2}}$ times the escape velocity. Van Belle et al. (2001) came up with a slightly different expression by accounting for the relationship between angular velocity and radius. Other models to exist, generally in different proportions.

Here's an artist's rendering of Vega compared to the Sun:


Courtesy of Wikipedia user RJHall under the Creative Commons Attribution-Share Alike 3.0 Unported license.

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    $\begingroup$ Now I'm extremely curious what a star looks like when it tears apart (assuming that it's possible) $\endgroup$ – Wayne Werner Sep 23 '15 at 18:46
  • $\begingroup$ @WayneWerner How would a mass of gas with such a high angular momentum form a star in the first place? $\endgroup$ – Random832 Sep 23 '15 at 20:35
  • $\begingroup$ @Random832 I'm assuming "magic"... maybe it accelerated due to some outside gravitational influence ¯_(ツ)_/¯ - though apparently Regulus is very nearly there? $\endgroup$ – Wayne Werner Sep 23 '15 at 20:39
  • $\begingroup$ @Random832 Angular momentum transfer can happen in a bunch of ways, so it's totally plausible that a star formed spinning at a lower speed and then "spun up". $\endgroup$ – HDE 226868 Sep 23 '15 at 20:45

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