Is There a Quad Problem among Optical Gravitational Lenses?

TL;DR

This paper investigates the low occurrence of four-image gravitational lenses in optical surveys compared to radio surveys, suggesting implications for the quasar luminosity function.

Contribution

It revisits the quad lens fraction in optical surveys by incorporating selection effects, reconciling observations with theoretical models.

Findings

Observed optical quad fraction is lower but consistent with predictions.

Radio lenses have a higher quad fraction than optical lenses.

Results imply a shallow faint end slope of the quasar luminosity function.

Abstract

Most of optical gravitational lenses recently discovered in the Sloan Digital Sky Survey Quasar Lens Search (SQLS) have two-images rather than four-images, in marked contrast to radio lenses for which the fraction of four-image lenses (quad fraction) is quite high. We revisit the quad fraction among optical lenses by taking the selection function of the SQLS into account. We find that the current observed quad fraction in the SQLS is indeed lower than, but consistent with, the prediction of our theoretical model. The low quad fraction among optical lenses, together with the high quad fraction among radio lenses, implies that the quasar optical luminosity function has a relatively shallow faint end slope.