A New Reconstruction of the Sun’s Magnetic Field and Total Irradiance since 1700

<jats:title>Abstract</jats:title> <jats:p>We model the Sun’s large-scale magnetic field and total solar irradiance (TSI) since 1700 by combining flux transport simulations with empirical relationships between facular brightening, sunspot darkening, and the total photospheric flux. The photospheric field is evolved subject to the constraints that (1) the flux emergence rate scales as the yearly sunspot numbers, and (2) the polar field strength at solar minimum is proportional to the amplitude of the following cycle. Simulations are performed using both the recently revised sunspot numbers and an average of these numbers and the Hoyt–Schatten group numbers. A decrease (increase) in the polar field strength from one cycle to the next is simulated either by increasing (decreasing) the poleward flow speed, or by decreasing (increasing) the average axial tilts of active regions; the resulting photospheric field evolution is very similar whichever parameter is varied. Comparisons between irradiance data and both the simulated and observed photospheric field suggest that TSI and facular brightness increase less steeply with the field strength at solar minimum than at other phases of the cycle, presumably because of the dominance of small-scale ephemeral regions when activity is very low. This relative insensitivity of the irradiance to changes in the large-scale field during cycle minima results in a minimum-to-minimum increase of annual TSI from 1700 to 1964 (2008) of 0.2 (0.06) W m<jats:sup>−2</jats:sup>, a factor of 2–3 smaller than predicted in earlier reconstructions where the relation between facular brightness and field strength was assumed to be independent of cycle phase.</jats:p>