Abstract　 　　  

    Planetary nebulae (PNe), descendents of the low- and intermediate-mass stars, are widespread in the universe and are excellent tracers of kinematics, chemistry, and stellar populations of host galaxies. Spectroscopic observations of PNe provide not only accurate velocities, precision abundance measurements of elements, and constraints of physical conditions (temperature and density), but also helps to assess the reliability of atomic data. 

  In the seemingly well established field of nebular astrophysics, there has been a long-standing dichotomy in plasma diagnostics and heavy elemental abundances determined using the traditional method based on collisionally excited lines (CELs) on the one hand, and optical recombination lines (ORLs)/continua on the other. In the past two decades, deep spectroscopic observations and surveys of PNe have been carried out to investigate this so-called ORL versus CEL "abundance and temperature discrepancy", but no consensus has reached as to its astrophysical origin. In this talk, I will present very deep spectroscopy of PNe, and introduce the calculations of new effective recombination coefficients for heavy element ORLs, and review recent progress in nebular astrophysics since the availability of new and high-quality atomic data.

  In order to investigate the formation history and peer into the origin of substructures of the Andromeda galaxy (M31) using PNe as a proxy, we carried out deep spectroscopy of PNe associated with the most prominent substructures such as the Northern Spur and the Southern Giant Stellar Stream (i.e., the Giant Stream), using the 10.4m Gran Telescopio Canarias (GTC, La Palma, Spain). In this talk, I will also present the most intriguing results of these observations.