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

## TL;DR

This study quantifies the emergence and decay rates of sunspots using HMI data, revealing that larger flux regions emerge faster and that observed rates are generally lower than simulation predictions.

## Contribution

It provides the first detailed measurements of flux emergence and decay rates for preder and follower sunspots, establishing a power-law relationship with peak flux.

## Key findings

- Larger flux regions emerge faster than smaller ones.
- Emergence rates scale with peak flux as a power law with exponent 0.36.
- Observed emergence rates are smaller than those predicted by simulations.

## Abstract

We quantify the emergence and decay rates of preceder (p) and follower (f) sunspots within ten active regions from 2010-2014 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 $(1.1-6.5)\times 10^{21}$ Mx. The net unsigned flux within the regions, including plage, ranges from $(5.1-20)\times 10^{21}$ 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) $\times 10^{19}$ Mx h$^{-1}$, while decay rates are $-1.9 (-3.4)\times 10^{19}$ Mx h$^{-1}$. The mean, signed flux emergence rate of the regions, including plage, is $7.1 \times 10^{19}$ Mx h$^{-1}$ for a mean peak flux of $5.9 \times 10^{21}$ 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 h$^{-1}$) scale with total signed peak flux, $\tilde{\phi}_{max}$, as a power law with an exponent of 0.36, i.e., $d{\phi}/dt = A \tilde{\phi}_{max}^{0.36}$. 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 captured in simulations.