Quasi-Stellar Objects acting as potential Strong Gravitational Lenses in the SDSS-III BOSS survey

We present a sample of 12 Quasi-Stellar Objects (QSOs) potentially acting as strong gravitational lenses on background Emission Line Galaxies (ELG) or Lyman-$\alpha$ Emitters (LAEs) selected selected through a systematic search of the 297301 QSOs in the Sloan Digital Sky Survey (SDSS)-III Data Release 12. Candidates are identified by looking for compound spectra, where emission lines at a redshift larger than that of the quasar can be identified in the residuals after a QSO spectral template is subtracted from the observed spectra. The narrow diameter of BOSS fibers (2") then ensures that the object responsible for the additional emission lines must lie close to the line of sight of the QSO and hence provides a high probability of lensing. Among the 12 candidates identified, 9 have definite evidence for the presence of a background ELG identified by at least 4 higher-redshift nebular emission lines. The remaining $3$ probable candidates present a strong asymmetrical emission line attributed to a background Lyman-$\alpha$ emitter (LAE). The QSO-ELG (QSO-LAE) lens candidates have QSO lens redshifts in the range $0.24\lesssim z_{QSO} \lesssim 0.66$ ($0.75 \lesssim z_{QSO} \lesssim 1.23$ ) and background galaxy redshifts in the range $0.48 \lesssim z_{S,ELG} \lesssim 0.94$ ($2.17 \lesssim z_{S,LAE} \lesssim 4.48$). We show that the algorithmic search is complete at >90% for QSO-ELG systems, whereas it falls at 40-60% for QSO-LAE, depending on the redshift of the source. Upon confirmation of the lensing nature of the systems, this sample may quadruple the number of known QSOs acting as strong lenses. We have determined the completeness of our search, which allows future studies to compute lensing probabilities of galaxies by QSOs and differentiate between different QSO models. (Abridged)