In the solar temperature graph, why does the temperature drop suddenly in the convective zone? Is it because some energy is needed for ionisation?
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The temperature gradient in the convection zone is basically the adiabatic temperature gradient - that is what defines the convection zone. The adiabatic temperature gradient can be written $$\frac{dT}{dr} = -\left(1 - \gamma^{-1}\right)\frac{\mu}{k_B} \frac{GM(r)}{r^2}\ , $$ where $\gamma$ is the usual ratio of specific heats, $\mu$ is the mean particle mass and $M(r)$ is the mass within radius $r$.
In the convection zone $M(r) \simeq M_{\odot}$ and is roughly constant, but $r$ is of course increasing. $\mu$ is also roughly constant. The gas becomes less ionised so $\gamma$ gets a little smaller below the surface, but there are no major changes until you get to quite low temperatures ($10^5 > T > 10^4$ K - Baturin et al. 2021). Overall $dT/dr$ is almost constant, with the increasing $r$ meaning it becomes a little smaller in magnitude with increasing radius.
So what is going on? Well, the main effect is that you are just looking at a plot with a logarithmic scale on the y-axis. If you look instead at a solar model on a linear scale you can see that indeed $|dT/dr|$ slightly decreases with radius in the convection zone.
i.e. if $dT/dr$ is roughly constant, then $d \log T/dr = T^{-1}dT/dr$ and increases with decreasing $T$.
