The rate of extreme coronal line emitters in the Baryon Oscillation Spectroscopic Survey LOWZ sample

Extreme coronal line emitters (ECLEs) are a rare class of galaxy that exhibit strong, high-ionization iron coronal emission lines in their spectra. In some cases, these lines are transient and may be the result of tidal disruption event (TDEs). To test this connection, we calculate the rate of variable ECLEs (vECLEs) at redshift $\sim0.3$. We search for ECLEs in the Baryon Oscillation Spectroscopic Survey (BOSS) LOWZ sample and discover two candidate ECLEs. Using follow-up spectra from the Dark Energy Spectroscopic Instrument and Gemini Multi-Object Spectrograph, and mid-infrared observations from the Wide-field Infrared Survey Explorer, we determine that one of these galaxies is a vECLE. Using this galaxy, we calculate the galaxy-normalized vECLE rate at redshift $\sim0.3$ to be $R_\mathrm{G}=1.6~^{+3.8}_{-1.4}\times10^{-6}~\mathrm{galaxy}^{-1}~\mathrm{yr}^{-1}$ and the mass-normalized rate to be $R_\mathrm{M}=7~^{+16}_{-6}\times10^{-18}~\mathrm{M_\odot^{-1}}~\mathrm{yr}^{-1}$. This is then converted to a volumetric rate of $R_\mathrm{V}=1.8~^{+4.5}_{-1.5}\times10^{-9}~\mathrm{Mpc}^{-3}~\mathrm{yr}^{-1}$. Formally, the LOWZ vECLE rates are $2-4$ times lower than the rates calculated from the Sloan Digital Sky Survey Legacy sample at redshift $\sim0.1$. However, given the large uncertainties on both measurements, they are consistent with each other at $1\sigma$. Both the galaxy-normalized and volumetric rates are one to two orders of magnitude lower than TDE rates from the literature, consistent with vECLEs being caused by $5-20$ per cent of all TDEs.