The relationship between bipolar magnetic regions and their sunspots

Context. The relationship between bipolar magnetic regions (BMRs) and their sunspots is an important property of the solar magnetic field, but it is not well constrained. One consequence is that it is a challenge for surface flux transport models (SFTMs) based on sunspot observations to determine the details of BMR emergence, which they require as input, from such data. Aims. We aimed to establish the relationship between the amount of magnetic flux in newly emerged BMRs and the area of the enclosed sunspots, and examine the results of its application to an established SFTM. Methods. Earlier attempts to constrain BMR magnetic flux were hindered by the fact that there is no extensive and reliable record of the magnetic and physical properties of newly emerged BMRs currently available. We made use of the empirical model of the relationship between the disc-integrated facular and network magnetic flux and the total surface coverage by sunspots reported in a recent study. The structure of the model is such that it enabled us to establish, from these disc-integrated quantities, an empirical relationship between the magnetic flux and sunspot area of individual newly emerged BMRs, circumventing the lack of any proper BMR database. Results. Applying the constraint on BMR magnetic flux derived here to an established SFTM retained its key features, in particular its ability to replicate various independent datasets and the correlation between the model output polar field at the end of each cycle and the observed strength of the following cycle. The SFTM output indicates that facular and network magnetic flux rises with increasing sunspot magnetic flux at a slowing rate such that it appears to gradually saturate. This is analogous to what earlier studies comparing disc-integrated quantities sensitive to the amount of faculae and network present to sunspot indices had reported. The activity dependence of the ratio of facular and network flux to sunspot flux is consistent with the findings of recent studies: although the Sun is faculae-dominated (such that its brightness is mostly positively correlated with activity), it is only marginally so as facular and network brightening and sunspot darkening appear to be closely balanced