Magnetic Flux Emergence and Decay Rates for Preceder and Follower Sunspots Observed with HMI

We quantify the emergence and decay rates of preceder (p) and follower (f) sunspots within 10 active regions from 2010 to 2014 using Space-weather Helioseismic Magnetic Imager Active Region Patch data. The sunspots are small to mid-sized regions and contain a signed flux within a single polarity sunspot of (1.1-6.5) x 10(21) Mx. The net unsigned flux within the regions, including plage, ranges from (5.1-20) x 10(21) Mx. Rates are calculated with and without intensity contours to differentiate between sunspot formation and flux emergence. Signed flux emergence rates, calculated with intensity contours, for the p (f) spots average 6.8(4.9) x 10(19) Mx hr(-1), while decay rates are -1.9(-3.4) x 10(19) Mx hr(-1). The mean, signed flux emergence rate of the regions, including plage, is 7.1 x 10(19) Mx hr(-1), for a mean peak flux of 5.9 x 10(21) Mx. Using a synthesis of these results and others reported previously, there is a clear trend for larger flux regions to emerge faster than smaller ones. Observed emergence rates (d phi/dt, Mx hr(-1)) scale with total signed peak flux,(phi) over tilde (max), as a power law with an exponent of 0.36, i.e., d phi/dt = Alpha(phi) over tilde (0.36)(max). The observed rates may assist in constraining the boundary and initial conditions in simulations which already demonstrate increased rates for flux tubes with higher buoyancy and twist, or in the presence of a strong upflow. Overall, the observed emergence rates are smaller than those in simulations, which may indicate a slower rise of the flux in the interior than what is captured in simulations.