Preprint typeset using LATEX style emulateapj v. 5/2/11 ARECIBO PULSAR SURVEY USING ALFA. III. PRECURSOR SURVEY AND POPULATION SYNTHESIS

The Pulsar Arecibo L-band Feed Array (PALFA) Survey uses the ALFA 7-beam receiver to search both inner and outer Galactic sectors visible from Arecibo (32◦. `. 77 ◦ and 168◦. `. 214◦) close to the Galactic plane (|b|. 5◦) for pulsars. The PALFA survey is sensitive to sources fainter and more distant than have previously been seen because of Arecibo’s unrivaled sensitivity. In this paper we detail a precursor survey of this region with PALFA, which observed a subset of the full region (slightly more restrictive in ` and |b |. 1◦) and de-tected 45 pulsars. Detections included one known millisecond pulsar and 11 previously unknown, long-period pulsars. In the surveyed part of the sky that overlaps with the Parkes Multibeam Pulsar Survey (36 ◦. `. 50◦), PALFA is probing deeper than the Parkes survey, with four discoveries in this region. For both Galactic mil-lisecond and normal pulsar populations, we compare the survey’s detections with simulations to model these populations and, in particular, to estimate the number of observable pulsars in the Galaxy. We place 95 % con-fidence intervals of 82,000 to 143,000 on the number of detectable normal pulsars and 9,000 to 100,000 on the number of detectable millisecond pulsars in the Galactic disk. These are consistent with previous estimates. Given the most likely population size in each case (107,000 and 15,000 for normal and millisecond pulsars, respectively) we extend survey detection simulations to predict that, when complete, the full PALFA surve