New distant companions to known nearby stars.: II.: Faint companions of Hipparcos stars and the frequency of wide binary systems

We perform a search for faint, common proper motion companions of Hipparcos stars using the recently published Lepine-Shara Proper Motion-North catalog of stars with proper motion mu > 0.15 yr(-1). Our survey uncovers a total of 521 systems with angular separations 3 < Delta theta < 1500, with 15 triples and 1 quadruple. Our new list of wide systems with Hipparcos primaries includes 130 systems identified here for the first time, including 44 in which the secondary star has V > 15.0. Our census is statistically complete for secondaries with angular separations 20 < Delta theta < 300 and apparent magnitudes V < 19.0. Overall, we find that at least 9.5% of nearby (d < 100 pc) Hipparcos stars have distant stellar companions with projected orbital separations s > 1000 AU. We observe that the distribution in orbital separations is consistent with Opik's law, f (s) ds similar to s(-1) ds, only up to a separation s approximate to 4000 AU, beyond which it follows a more steeply decreasing power law f (s) ds similar to s(-1) ds with l = 1.6 +/- 0.1. We also find that the luminosity function of the secondaries is significantly different from that of the single stars' field population, showing a relative deficiency in low-luminosity (8 < M-V < 14) objects. The observed trends suggest either a formation mechanism biased against low-mass companions, or a disruption over time of systems with low gravitational binding energy.