# Why does the convective core in an intermediate to high mass star shrink?

The image below shows the evolution of the hydrogen mass fraction profile for a 5 solar mass star in the main sequence. I would expect that the size of the convective core stays roughly constant as the hydrogen is been fused, leading to a final step-like profile when the core hydrogen is exhausted. However, all the literature and simulations show a clear slope in the final step-like profile which results from the shrinking of the convective core.

Does anyone have any insight about the reason behind the shrinking?

(source of the image: http://astro.if.ufrgs.br/evol/evolve/hansen/StellarEvolnDemo/m5z02evoln.html)

Edit 1:

Below is the evolution of the temperature profile for the same star. Feel free to comment on it.

Personally, I am surprised how little the temperatures change. Since the main nuclear reaction is the CNO cycle which scale as $$~T^{16}$$, I was expecting a much more violent change. However, the central temperature only increases in about 30% during the whole main sequence. Interesting.

Edit 2:

I thought a nice explanation could be in the Ledoux criterion for convection. This criterion states that chemical gradients have a stabilizing effect against convection (i.e., it impedes convection) which would lead to the conclusion that, at the interface between the radiative and convective zone, the radiative transport would take over. However, I simulate the evolution with and without the Ledoux criterion and in both cases the convective core shrinks.

• It’s more than 20 years ago, since I worked in that area. I vaguely remember that this effect results from the models as a matter of fact. The physical parameters that regulate the onset of convection, the adiabatic and the actual temperature gradient, both depend in a similar way on the changes of properties of stellar matter with radius, and I had no satisfying explanation to why the point of onset moves inwards with time. I’m looking forward to a proper answer! – Hartmut Braun Nov 23 '19 at 10:18
• I don't suppose you can plot the central temperature too? – Rob Jeffries Nov 23 '19 at 10:50
• @RobJeffries - I added the temperature profile evolution. Please, feel free to comment on it. – Stefano Nov 23 '19 at 15:37
• Makes me wonder if anyone's ever gotten numbers on the heat capacities of the various totally ionized nuclei. Differences could easily change convection properties. – Wayfaring Stranger Nov 23 '19 at 20:04
• The Ledoux Criterion is only relevant if the core is about to increase in size (instead of shrinking). In that case the lighter layers above heavier material have a stabilizing effect (as the Ledoux criterion predicts) and the core cannot immediately grow. In the convection zone there is no chemical gradient because of convective mixing and the Schwarzschild criterion applies. – Hartmut Braun Nov 25 '19 at 20:47

The interior radiative temperature gradient is proportional to the opacity and the outward energy flux, and inversely proportional to $$T^4$$. As the star evolves on the main sequence, the central temperature goes up and the opacity (e.g. Kramer's opacity goes as $$T^{-7/2}$$ goes down. You are also removing free electrons (combining them with protons to form He) which reduces the Thomson/Compton scattering opacity. This means the radiative temperature gradient goes down and can fall below the adiabatic gradient, meaning that energy transport reverts to being radiative.