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 ($32^{\circ}\lesssim \ell \lesssim 77^{\circ}$ and $168^{\circ}\lesssim \ell \lesssim 214^{\circ}$) close to the Galactic plane ($|b|\lesssim5^{\circ}$) for pulsars. 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 $\ell$ and $|b|\lesssim1^{\circ}$) and detected 45 pulsars. For both Galactic millisecond 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\% confidence 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 survey should have detected $1,000\substack{+330 \\ -230}$ normal pulsars and $30\substack{+200 \\ -20}$ millisecond pulsars. Identical estimation techniques predict that $490\substack{+160 \\ -115}$ normal pulsars and $12\substack{+70 \\ -5}$ millisecond pulsars would be detected by the beginning of 2014; at the time, the PALFA survey had detected 283 normal pulsars and 31 millisecond pulsars, respectively.