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Type Ia supernovae (SNe Ia) originate from thermonuclear explosions of carbon-oxygen white dwarfs at masses approaching the Chandrasekhar limit, and are widely used as standard candles for cosmological distances. However, the progenitor system and explosion mechanism of SNe Ia are still unclear. The circumstellar environment of SNe Ia has received increasing attention in recent decades. The distance and other geometric properties of the circumstellar material provide essential clues for exploring the physical origin of SNe Ia. At the same time, the scattering of circumstellar dust can produce observable effects on the light curve, spectrum, and polarization during the late phase of SNe Ia. The spectroscopically normal SNe Ia can be classified into two categories: normal-velocity and high-velocity ones. The high-velocity SNe Ia have an apparent blue excess within a few months after the maximum brightness. This blue excess can be fitted by circumstellar dust scattering. Meanwhile, fitting the late-phase spectrum or imaging polarization of SNe Ia can constrain the grain size or the geometric distribution of circumstellar dust, respectively. The result indicates that multi-epoch image polarimetry during the late phase of SNe Ia is a crucial probe to reveal the characteristics of circumstellar dust. [ABSTRACT FROM AUTHOR]

Fast Radio Bursts (FRBs) are extra-galactic origin milli-second duration bright radio bursts. Theoretically, FRBs may produce optical counterparts with durations from milliseconds to hours. The FRB optical counterparts may be detectable in future large field telescopes, including the China Space Station Telescope (CSST), the 2.5-meter Wide Field Survey Telescope (WFST) lead by the University of Science and Technology of China (USTC) and the Purple Mountain Observatory (PMO), and the Earth 2.0 (ET). The fast radio burst optical counterparts are grouped into millisecond time-scale optical counterparts, hourly time-scale optical counterparts, and optical afterglow for our study. The first two can be generated by the high-energy extension of the radio radiation of fast radio bursts and the inverse Compton scattering of high-energy electrons. The event rates highly depend on the optical-to-radio flux ratio η ν. For millisecond duration optical counterparts, the detection rate of WFST, CSST, and ET can reach hundreds per year in an ideal case. If η ν ∼ 10 − 3 , the corresponding annual detection rates of WFST and CSST are in the order of 1, and the annual detection rate of ET is 19.5. For the hourly timescale optical counterparts, ideally, the age of the supernova remnant is 5 years, η ν is about 10 − 6 , and the annual detection rates are above 100. The X-ray counterpart of FRB 200428 indicates that FRBs may produce relativistic outflow, which will interact with the interstellar medium to produce optical afterglows. Combined with the standard afterglow model, the detectability of optical afterglow is explored with a simulation of fast radio bursts following the redshift and energy distribution from the literature. With a total energy-radio energy ratio similar to FRB 200428, (ζ = 10 5), the estimated annual detection rates of CSST, WFST, and ET are 1.3, 1.0, and 67, respectively. [ABSTRACT FROM AUTHOR]