We perform a calibration of the mixing length of convection in stellar structure models against realistic 3D radiation-coupled hydrodynamics ( RHD ) simulations of convection in stellar surface layers , determining the adiabat deep in convective stellar envelopes .

The mixing-length parameter \alpha is calibrated by matching averages of the 3D simulations to 1D stellar envelope models , ensuring identical atomic physics in the two cases .
This is done for a previously published grid of solar-metallicity convection simulations , covering from 4 200 K to 6 900 K on the main sequence , and 4 300–5 000 K for giants with \log g = 2.2 .

Our calibration results in an \alpha varying from 1.6 for the warmest dwarf , which is just cool enough to admit a convective envelope , and up to 2.05 for the coolest dwarfs in our grid .
In between these is a triangular plateau of \alpha \sim 1.76 .
The Sun is located on this plateau and has seen little change during its evolution so far .
When stars ascend the giant branch , they largely do so along tracks of constant \alpha , with \alpha decreasing with increasing mass .