CONSTRAINING THE LIFETIME AND OPENING ANGLE OF QUASARS USING FLUORESCENT Lyα EMISSION: THE CASE OF Q0420–388

A toy model is developed to understand how the spatial distribution of fluorescent emitters in the vicinity of bright quasars could be affected by the geometry of the quasar bi-conical radiation field and by its lifetime. The model is then applied to the distribution of high-equivalent-width Lyα emitters (with rest-frame equivalent widths above 100 Å, threshold used in, e.g., Trainor & Steidel) identified in a deep narrow-band 36 × 36 arcmin2 image centered on the luminous quasar Q0420–388. These emitters are found near the edge of the field and show some evidence of an azimuthal asymmetry on the sky of the type expected if the quasar is radiating in a bipolar cone. If these sources are being fluorescently illuminated by the quasar, the two most distant objects require a lifetime of at least 15 Myr for an opening angle of 60° or more, increasing to more than 40 Myr if the opening angle is reduced to a minimum of 30°. However, some other expected signatures of boosted fluorescence are not seen at the current survey limits, e.g., a fall off in Lyα brightness, or equivalent width, with distance. Furthermore, to have most of the Lyα emission of the two distant sources to be fluorescently boosted would require the quasar to have been significantly brighter in the past. This suggests that these particular sources may not be fluorescent, invalidating the above lifetime constraints. This would cast doubt on the use of this relatively low equivalent width threshold and thus also on the lifetime analysis in Trainor and Steidel.