# Stars at near break-up rotation rates

Accretion discs are ubiquitous in astrophisics. As a direct corollary, they are important for the following question.

Consider the following model, representing one of the most simple models for accretion discs. A central object is a star (pre-MS, WD or NS, but not a BH) of mass $M$, surrounded by a thin flat disc of material, which continuosly feeds the star at a rate $\dot{M}$, such that $M/\dot{M}$ is much larger than thermal and dynamical timescale of the star (i.e. accretion rate is slow).

Everywhere in the accretion disc its local motion is nearly circular and nearly Keplerian. Therefore, at the interface of the star and the disc the disc will always tend to make the star rotate at nearly-Keplerian velocities. From the other hand, if the stellar outer parts were to rotate at nearly-Keplerian velocities, these parts would become gravitationaly detached from the star, which would have significant consequences for the stellar shape and structure. Surely, though, the process is going to be slow and the acquired angular momentum will be redistributed within the star.

Now the question: What will be happening to the star if it approaches nearly break-up velocities due to such a spin-up? This involves a few subquestions: How close the rotation rate can actually get to the critical one? If it can get close enough, how would the whole process look like? That is, what would happen in the short term to the star when the effects of rotation will start to affect its structure? What would happen to the star in the long term?

I would like to keep this problem as a purely hydrodynamical one. That is, assume, that the only laws involved are hydrodynamical and gravitational ones, with some constant accretion rate supported. In reality magnetic fields would also play an important role for some stars, and stellar winds could also possibly be important.

Examples of the decribed systems are numerous. It might concern cataclysmic variables, millisecond pulsars, pre-main sequence star in a protoplanetary disc, and many more.

• Not exactly what you're asking, but probably still of interest: the CHARA array has actually been used to image some stellar objects rotating at large percentages of breakup speed, and the deformations in shape and odd distribution of surface flux is clearly visible in the reconstructed images. (Don't have citations handy but I can probably dig them up...) Dec 12 '13 at 7:35
• @Shinrai, very nice! Thank you very much, I'll try to find them. Dec 12 '13 at 14:02

I have not the qualification to answer the question in its whole but the question is interesting (I worked on Be Stars which are episodically surrounded by an decretion disk and which rotates at nearly critical velocities. The phenomenon in Be stars is different from accreting stars. The only consequences of subcritical velocity is a flattened envelope and modification of its inner structure and of the oscillations modes found in these stars (if you have time and curiosity, a good example of flattened star with Keplerian rotating decretion disk is Achernar, a Be star observed using interferometry --> Have a look at Meilland et al. 2007: www.aanda.org/articles/aa/pdf/2007/10/aa4848-06.pdf)

Anyway...