1. Q: How is flux removed from the photosphere? Each 11-year cycle, c. 3000 active regions, each with c. 10 22 Mx, emerge. What processes remove all this flux? The short answer is CANCELLATION --- the “mutual apparent loss of flux in closely spaced magnetogram features of opposite polarity” (Livi et al. 1985)

2. Changes in LOS flux are quantitatively related to PIL Doppler shifts multiplied by transverse field strengths. From Faraday’s law, Since flux can only emerge or submerge at a PIL, From LOS m’gram: Summed Dopplergram and transverse field along PIL pixels. (Eqn. 2) In the absence of errors, ΔΦ LOS /Δt =ΔΦ PIL /Δt. (Eqn. 1)

3. Let’s test the method with HMI data! An automated method (Welsch & Li 2008) identified PILs in a subregion of AR 11117. Note predominance of redshifts.

4. Problem: We must remove the convective blueshift! HMI’s Doppler shifts are not absolutely calibrated! (Helioseismology uses time differences in Doppler shifts.) There’s a well-known intensity-blueshift correlation, because rising plasma (which is hotter) is brighter (see, e.g., Gray 2009; Hamilton and Lester 1999; or talk to P. Scherrer). Because magnetic fields suppress convection, lines are redshifted in magnetized regions. From Gray (2009): Bisectors for 5 spectral lines on the Sun are shown on an absolute velocity scale. The dots indicate the lowest point on the bisectors. (The dashed bisector is for λ6256.) Lines formed deeper in the atmosphere, where convective upflows are present, are blue-shifted.

5. So we must calibrate the bias in the zero-velocity v 0 in estimated Doppler shifts before we can study cancellation. From Eqn. 2, a bias velocity v 0 implies := “magnetic length” of PIL But ΔΦ LOS should match ΔΦ PIL, so we can solve for v 0 : (Eqn. 3) NB: v 0 should be the SAME for ALL PILs ==> solve statistically!

6. The inferred offset velocity v 0 can be used to correct Doppler shifts along PILs.