Secular Light Curves of main-belt comets 133P/Elst-Pizarro, 176P/LINEAR, 288P/(300163) and 433P/(248370)

Among the main-belt comets (MBCs) that have been discovered, 133P/Elst-Pizarro, 176P/LINEAR, 288P/(300163) and 433P/(248370) do not have obvious coma, and the amplitudes of their Secular Light Curves (SLCs) are less than 3 mag. Through the SLCs, we can better understand the activity status and decay process of these four low-level active MBCs, and then understand the activity evolution of the MBCs. To get the SLCs of these four MBCs, we collected 2,962 observations (span 5-6 apparitions) and used improved methods (subtract the opposition and aspect angle effects). According to the SLCs and related parameters, we get the following conclusions: (1) 133P/Elst-Pizarro and 176P/LINEAR had activity decay characteristics. For 133P/Elst-Pizarro, the amplitude of SLC was 2.4 mag in 1996+2001 perihelion passages, but changed to 1.2 mag in 2007+2013 perihelion passages. The time T-OFF and distance R-OFF at the turn off point of activity changed significantly, from T-OFF = 388 +/- 20 d and R-OFF = 3.04 +/- 0.02 au (1996+2001) to T-OFF = 230 +/- 13 d and R-OFF = 2.81 +/- 0.02 au (2007+2013). For 176P/LINEAR, the amplitude of SLC during 2005 perihelion passage was 0.37 mag, while during 2011, 2017 and 2022 perihelion passages, it did not show activity. (2) 133P/Elst-Pizarro and 176P/LINEAR had the aspect angle effect. That could mean the nuclei of 133P/Elst-Pizarro and 176P/LINEAR have large obliquity and axis ratio. (3) The equinox of 133P/Elst-Pizarro was close to perihelion (Delta t = 45d, anomaly = 12 degrees) and 176P reaches the solstice near perihelion (Delta t = 69d, anomaly = 18 degrees). (4) 288P/(300163) had a large asymmetry parameter R-OFF/R-ON, which means that the sublimation takes place in depth, not just in the surface. (5) It can also be seen from SLC that 433P/(248370) had been active since 2010 perihelion passage, which was earlier than previously reported in 2016. But, SLC of 433P did not show activity near the perihelion in 2005. 433P had photometric anomaly (similar to 0.5 mag), from Delta t = 94 to 138 d or R = 2.425 to 2.481 au in 2021 perihelion passage. (6) The PAGE and TAGE of four comets were determined.