The Mixing Length in Convective Stellar Envelopes is Proportional to Distance from the Convective Boundary

Abstract

A calibration of two different stellar convection theories is made by theoretically reproducing with stellar models the effective temperatures of very luminous red supergiants. This calibration is then compared with previous calibrations using less luminous objects. The corresponding range of stellar masses is 1--20 Msolar. For consistency with previous work, the calibrating parameter is taken to be the convective mixing length l. If l is assumed to be proportional to the local pressure scale height Hp, the constant of proportionality alpha P must vary significantly with stellar mass. If, however, l is assumed to be proportional to the distance z below the outer boundary of the convection zone, the constant of proportionality alpha z emerges as a universal constant, within the uncertainties due to possible errors of the observed effective temperatures and of the theoretically calculated low-temperature opacities. In particular, standard mixing-length theory yields a constant alpha z = 2, whereas the new full-spectrum-of-turbulence theory of Canuto & Mazzitelli yields a constant alpha z = 1. Physical constraints, laboratory experiments, and observations of turbulent convection in the Earth's atmosphere indicate alpha z