Investigation of White-light Emission in Compact Flares

White-light flares (WLFs) are usually tend to be those very large flares. Nevertheless, several small and compact WLFs have been reported and thought to be produced by low-height magnetic reconnection. However, whether low-height magnetic reconnection can efficiently produce WLFs remains unclear. For the first time, we conduct a statistical study of the WL emission in compact flares to address this question. Using over a decade observations from the \textit{Solar Dynamics Observatory} (SDO), we identify 28 compact flares, including 19 C-class and 9 B-class flares. We find these compact flares can be classified into three types based on the magnetic configuration of the flare, corresponding to the U-shape loop (type I), the flux emergence near sunspot (type II), and the fan-spine like structure (type III). For each type, the flares numbers are 9 (7 C-calss and 2 B-class), 9 (3 C-calss and 6 B-calss) and 10 (9 C-calss and 1 B-calss), respectively. We find the occurrence rate of WLFs in compact flares is $\sim60.7\%$ (17/28), and for the C-class the rate can be up to $\sim89.5\%$ (17/19). No WLF was found in B-class compact flares. The occurrence rates for three types are $\sim77.8\%$ (7/9), $\sim11.1\%$ (1/9) and 90\% (9/10), respectively. And for the C-class flares, the occurrence rates for three types are 100\% (7/7), $\sim33.3\%$ (1/3) and 100\% (9/9), respectively. Our results suggest type-I and type-III compact flares are more likely to produce WL emissions.