We validated our results against different selection effects due to redshift, luminosity, incompleteness of the FIRST survey, and incomplete radio counter-part identifications. However, we have not explicitly checked for any bias due to incomplete target selection in the DR16Q catalogue. As quasars are chosen for spectroscopic observations in SDSS primarily based on their photometric properties, our analysis can be biased due to the differential target selection completeness for BALQSOs and non-BALQSOs. As BALQSOs are significantly dust-reddened compared to non-BALQSOs, the completeness of BALQSOs is expected to be less. Allen et al. (2011) computed this difference in the selection probabilities using simulated BAL and non-BALQSO magnitudes and found that the completeness is very high for both BALQSOs and non-BALQSOs with z  2.1 and i  19.1, drops sharply for a narrow region close to z ∼ 2.6 and rises again for higher redshifts. This completeness difference can introduce some bias for analysis involving optically selected samples. To our rescue, eBOSS also targets all SDSS point sources that are within 1 arcsec of a radio detection in the FIRST point source catalogue (Myers et al. 2015). As our final sample is radio-selected BAL quasars and non-BAL quasars, we do not expect the behaviour of the BAL fraction to be severely influenced by any incompleteness effects. As with the case of dust-reddening, strong absorption troughs can make the broadband magnitude appear fainter for a BALQSO than an equivalent non-BALQSO. C iv BAL troughs fall in the SDSS i band for the redshift range 3.5  z  4.4. Our BAL quasar sample contains 82 quasars (4 per cent) in the redshift range where the i band luminosities are underestimated due to the presence of C iv BAL absorption. Additionally, a small fraction of quasars (1 per cent) should be LoBALs and FeLoBALs where the i-band luminosities are affected by Mg ii, Al iii, and Fe ii broad absorption. The orientation indicator, radio-to-optical core luminosity has the i-band optical luminosity in the denominator. Although the fraction of BALQSOs containing strong BAL features within the i-band wavelengths is less, any correction of the optical luminosities will further push these sources to lower log(RI) bins, thereby increasing the BAL fraction at higher orientation angles. Likewise, Hewett & Foltz (2003) suggest that optically bright BAL quasars are half as likely as non-BAL quasars to be detectable as S$_{1.4 \,\mathrm{ GHz}}\, \ge$ 1 mJy sources. To probe this, we divided the sample into three optical luminosity bins, (i) Log(Li band) ≤ 24 W/Hz, (ii) 24 W/Hz  Log(Li band) ≤ 25 W/Hz, and (iii) Log(Liband) > 25 W/Hz, and studied the distribution of radio luminosity of BAL and non-BAL quasars. We do not see any difference in the distribution of radio luminosity between BAL and non-BAL quasars for the lower optical luminosity bins. But, for the highest luminosity bin, we see that the BAL quasars have statistically lower radio luminosities as compared to the non-BAL quasars (p-value of KS test  0.05). Thus, a flux-limited survey like FIRST would have missed a fraction of optically bright BAL quasars that have radio fluxes below the FIRST sensitivity. As these missed BAL quasars have low radio luminosities and high optical luminosities, a correction for the missed quasars would only populate the lower log(RI) bins. This again will amplify the already seen trend of BAL fraction increase at high orientation angles. To ensure that the optically bright sources are not biasing the BAL fraction trend, we excluded the optically bright sources from our sample and then studied the variation of BAL fraction as a function of orientation. The pruned sample also follows the trend of high BAL fraction for high orientation angles.
Citation: Myers et al. 2015
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