How faculae and network relate to sunspots, and the implications for solar and stellar brightness variations

Abstract

Context. How global faculae and network coverage relates to that of sunspots is relevant to the brightness variations of the Sun and Sun-like stars. Aims. We aim to extend and improve on earlier studies that established that the facular-to-sunspot-area ratio diminishes with total sunspot coverage. Methods. Chromospheric indices and the total magnetic flux enclosed in network and faculae, referred to here as “facular indices”, are modulated by the amount of facular and network present. We probed the relationship between various facular and sunspot indices through an empirical model, taking into account how active regions evolve and the possible non-linear relationship between plage emission, facular magnetic flux, and sunspot area. This model was incorporated into a model of total solar irradiance (TSI) to elucidate the implications for solar and stellar brightness variations. Results. The reconstruction of the facular indices from the sunspot indices with the model presented here replicates most of the observed variability, and is better at doing so than earlier models. Contrary to recent studies, we found the relationship between the facular and sunspot indices to be stable over the past four decades. The model indicates that, like the facular-to-sunspot-area ratio, the ratio of the variation in chromospheric emission and total network and facular magnetic flux to sunspot area decreases with the latter. The TSI model indicates the ratio of the TSI excess from faculae and network to the deficit from sunspots also declines with sunspot area, with the consequence being that TSI rises with sunspot area more slowly than if the two quantities were linearly proportional to one another. This explains why even though solar cycle 23 is significantly weaker than cycle 22, TSI rose to comparable levels over both cycles. The extrapolation of the TSI model to higher activity levels indicates that in the activity range where Sun-like stars are observed to switch from growing brighter with increasing activity to becoming dimmer instead, the activity-dependence of TSI exhibits a similar transition. This happens as sunspot darkening starts to rise more rapidly with activity than facular and network brightening. This bolsters the interpretation of this behaviour of Sun-like stars as the transition from a faculae-dominated to a spot-dominated regime.

The relationship between bipolar magnetic regions and their sunspots

“…Various studies found the facular area to increase with increasing sunspot area at a diminishing rate such that it appears to gradually saturate (Foukal 1993(Foukal , 1996(Foukal , 1998Chapman et al 1997;Shapiro et al 2014). Solanki & Fligge (1998) and Yeo et al (2020) (hereafter YSK), compared various disc-integrated quantities that are sensitive to the amount of faculae and network present to sunspot area and/or sunspot number and returned analogous results. As first pointed out by Foukal (1993), these results suggest that the balance between the competing effects of bright faculae and network and of dark sunspots on solar irradiance might shift towards the latter as we go from low to high activity levels.…”

“…In this section we derive an empirical relationship between the amount of magnetic flux in each newly emerged bipolar magnetic region or BMR, Φ BMR , and the area of the enclosed sunspots, A BMR,S . For this purpose we employ the empirical model of the relationship between the disc-integrated facular and network magnetic flux, ΣΦ FN , and the total surface coverage by sunspots, ΣA S , recently reported by YSK (Yeo et al 2020). The YSK model is given by…”

“…In this study we aim to establish the relationship between the amount of magnetic flux in each newly emerged BMR, Φ BMR , and the area of the enclosed sunspots, A BMR,S . We make use of the empirical model relating the disc-integrated facular and network magnetic flux, ΣΦ FN , to the total surface coverage by sunspots, ΣA S presented by YSK (Yeo et al 2020), which builds A28, page 2 of 12 on the earlier work by Preminger & Walton (2005, 2006a,b, 2007, abbreviated here as PW. As we demonstrate, the set-up of the YSK model allows us to establish from it an empirical relationship between Φ BMR and A BMR,S while circumventing the lack of a proper database of newly emerged BMRs.…”

How faculae and network relate to sunspots, and the implications for solar and stellar brightness variations(Corrigendum)

“…Similar toTable 1inYeo et al (2020), except with the correct values of h 1 . CaIIK S A 5.030 × 10 −6 0.5854 57.41 8.228 × 10 −2 F Lα S A 7.198 × 10 −7 0.6642 72.34 5.852 × 10 −3 F MgII S A 3.256 × 10 −6 0.7129 54.10 0.1497 F φ S A 1.992 × 10 −4 0.8429 33.46 0.1824 F 10.7 S N1 7.334 × 10 −2 1.073 13.41 65.10 F CaIIK S N1 1.357 × 10 −5 0.7913 34.84 8.243 × 10 −2 F Lα S N1 3.230 × 10 −6 0.7960 49.25 5.861 × 10 −3 F MgII S N1 1.614 × 10 CaIIK S G2 7.421 × 10 −5 0.9240 36.82 8.218 × 10 −2 F Lα S G2 1.564 × 10 −5 1.002 48.40 5.850 × 10 −3 F MgII S G2 8.279 × 10 −5 1.105 34.04 0.1499 F…”

“…This is a corrigendum to Yeo et al (2020). We had listed the wrong values for the parameter h 1 in Table 1.…”