Rotational broadening and conservation of angular momentum in post-extreme horizontal branch stars

We show that the recent realization that isolated post-extreme horizontal branch (post-EHB) stars are generally characterized by rotational broadening with values of $V_{\rm rot} \sin i$ between 25 and 30 km~s$^{-1}$ can be explained as a natural consequence of the conservation of angular momentum from the previous He-core burning phase on the EHB. The progenitors of these evolved objects, the EHB stars, are known to be slow rotators with an average value of $V_{\rm rot} \sin i$ of $\sim$7.7 km~s$^{-1}$. This implies significant spin-up between the EHB and post-EHB phases. Using representative evolutionary models of hot subdwarf stars, we demonstrate that angular momentum conservation in uniformly rotating strutures (rigid-body rotation) boosts that value of the projected equatorial rotation speed by a factor $\sim$3.6 by the time the model has reached the region of the surface gravity-effective temperature plane where the newly-studied post-EHB objects are found. This is exactly what is needed to account for their observed atmospheric broadening. We note that the decrease of the moment of inertia causing the spin-up is mostly due to the redistribution of matter that produces more centrally-condensed structures in the post-EHB phase of evolution, not to the decrease of the radius per se.