Irradiance or luminosity changes?
  Whereas a variation of the solar luminosity, L, will inevitably cause a similar change of the total solar irradiance, S, the opposite is not true. In fact, the bulk of the days to months variations of S can be explained entirely in terms of the passage of active regions across the solar disk. In this case, L remains essentially unchanged.   For the total irradiance variation observed over the solar cycle, the issue is more uncertain. One view explains this modulation primarily as a combined action of active regions and magnetic network. These components would be superposed to an otherwise unchanging photosphere. the other view suggests that the activity cycle modulation of S is primarily produced by a variation of L (both in terms of R and T_{eff}) caused by structural reajustments of the interior of the Sun induced by a changing magnetic field. We will present evidence in support of this second interpretation, and a model for it. We will also present the S variations over the last 5 centuries implied by our model. 
Sabatino Sofia (Yale) and Linghuai H. Li (Yale)