The nature of the Schoenberg-Chandrasekhar limit

We present a comprehensive description of the Sch\"onberg--Chandrasekhar (S--C) transition, which is an acceleration of the stellar evolution from the nuclear to the thermal time scales occurring when the fractional mass of the helium core reaches a critical value, about 0.1. It occurs in the 1.4 to 7 M$_\odot$ mass range due to impossibility of maintaining the thermal equilibrium after the nuclear energy sources in the core disappear. We present the distributions of the hydrogen abundance, the energy generation rate and the temperature for stars crossing that limit. We confirm that a sharp S--C limit is present for strictly isothermal cores, but it is much smoother for real stars. The way the boundary of the core is defined is important for the picture of this transition. With a strict definition of the core as the region where the helium abundance is close to null, it occurs in an extended range of the fractional core mass of roughly 0.03 to 0.11. The cause of that is a gradual core contraction causing a correspondingly gradual loss of the core isothermality with the increasing core mass. On the other hand, when using definitions allowing for some H abundance in the core, the S--C transition is found to be sharper, at the fractional core mass of between about 0.07 and 0.11. Still, it is more a smooth transition than a sharp limit. We have also searched for specific signatures of that transition, and found that it is associated with the stellar radius first decreasing and then increasing again. We have considered whether the S--C limit can be used as a diagnostic constraining the evolutionary status of accreting X-ray binaries, but found such uses unfounded.