How much do underestimated field strengths from Zeeman-Doppler imaging affect spin-down torque estimates?

Abstract

Numerous attempts to estimate the rate at which low-mass stars lose angular momentum over their lifetimes exist in the literature. One approach is to use magnetic maps derived from Zeeman-Doppler imaging (ZDI) in conjunction with so-called "braking laws". The use of ZDI maps has advantages over other methods because it allows information about the magnetic field geometry to be incorporated into the estimate. However, ZDI is known to underestimate photospheric field strengths due to flux cancellation effects. Recently, Lehmann et al. (2018) conducted synthetic ZDI reconstructions on a set of flux transport simulations to help quantify the amount by which ZDI underestimates the field strengths of relatively slowly rotating and weak activity solar-like stars. In this paper, we evaluate how underestimated angular momentum-loss rate estimates based on ZDI maps may be. We find that they are relatively accurate for stars with strong magnetic fields but may be underestimated by a factor of up to $\sim$10 for stars with weak magnetic fields. Additionally, we re-evaluate our previous work that used ZDI maps to study the relative contributions of different magnetic field modes to angular momentum-loss. We previously found that the dipole component dominates spin-down for most low-mass stars. This conclusion still holds true even in light of the work of Lehmann et al. (2018).