with a $\Delta$T of 1500K, given a single filling factor $f$.

For the smaller spot (Fig. \[fig:stellar\_surface\], right panel, red error bars) we infer a higher filling factor (approximately 0.85), and for the larger spot (Fig. \[fig:stellar\_surface\], right panel, blue error bars) a lower filling factor (approximately 0.4). The larger spot can be understood as a large active region on the stellar surface with a relatively low density of smaller dark spots. The smaller spot however has a high density of smaller dark spots leading to the greater contrast.

### Facula properties {#sec:facula_properties}

As discussed in section \[sec:spots\_vs\_faculae\] the occultation of a bright region, analogous to a Solar facula, is our favoured interpretation for these data. Unlike spots, the flux contrasts of faculae increase at the stellar limb as they display limb brightening behaviour (e.g. @Unruh1999) and so the assumption that the modelled spots follow the same limb darkening as the star does not hold in this case. Therefore Eqn. \[eq:filling\_factor\] cannot be used to calculate the temperature of the facula so we report only the flux contrasts of the facula in Table \[tab:fit\_results\] which indicate the hot spot is $\sim 10\%$ brighter in all three bands. Solar faculae are 