Lawrence Berkeley National Laboratory

High-ionization iron coronal lines (CLs) are a rare phenomenon observed in galaxy and quasi-stellar object spectra that are thought to be created by high-energy emission from active galactic nuclei and certain types of transients. In cases known as extreme coronal line emitting galaxies (ECLEs), these CLs are strong and fade away on a time-scale of years. The most likely progenitors of these variable CLs are tidal disruption events (TDEs), which produce sufficient high-energy emission to create and sustain the CLs over these time-scales. To test the possible connection between ECLEs and TDEs, we present the most complete variable ECLE rate calculation to date and compare the results to TDE rates from the literature. To achieve this, we search for ECLEs in the Sloan Digital Sky Survey (SDSS). We detect sufficiently strong CLs in 16 galaxies, more than doubling the number previously found in SDSS. Using follow-up spectra from the Dark Energy Spectroscopic Instrument and Gemini Multi-Object Spectrograph, Wide-field Infrared Survey Explorer mid-infrared observations, and Liverpool Telescope optical photometry, we find that none of the nine new ECLEs evolve in a manner consistent with that of the five previously discovered variable ECLEs. Using this sample of five variable ECLEs, we calculate the galaxy-normalized rate of variable ECLEs in SDSS to be (equeation presented). Our rates are one to two orders of magnitude lower than TDE rates from the literature, which suggests that only 10-40 per cent of all TDEs produce variable ECLEs. Additional uncertainties in the rates arising from the structure of the interstellar medium have yet to be included.