Effects of changes in convective efficiency on the solar radius and luminosity

A sequence of solar models has been constructed in order to investigate the sensitivity of the solar radius and luminosity to small changes in the ratio alpha of the mixing length lambda to the pressure-scale height Hp throughout the solar convective envelope. The basic procedure for determining this sensitivity was to impose a perturbation in alpha within the convective envelope and then to follow the resulting changes in the solar radius delta R and luminosity delta L for the next 10 to the 6th power yrs. These calculations gave the following results. (1) A perturbation in alpha produces immediate changes in the solar radius and luminosity. Initially delta L and delta alpha are related by delta L/L = 0.30 delta alpha/alpha. (2) The value of the ratio w = delta log R/delta log L is strongly time dependent. Its value just after the perturbation in alpha is 6.5 x 10 to the minus 4th power. (3) The ratio H = (delta log L) d delta log R/dt is much less time dependent and is a more suitable means for relating the changes in the solar radius and luminosity. (4) Both of these ratios imply that for any reasonable change in the solar luminosity the corresponding change in the solar radius is negligible.