  Stars with hot Jupiters have obliquities ranging from 0-180 degrees, but
relatively little is known about the obliquities of stars with smaller planets.
Using data from the California-Kepler Survey, we investigate the obliquities of
stars with planets spanning a wide range of sizes, most of which are smaller
than Neptune. First, we identify 156 planet hosts for which measurements of the
projected rotation velocity (vsini) and rotation period are both available. By
combining estimates of v and vsini, we find nearly all the stars to be
compatible with high inclination, and hence, low obliquity (less than about 20
degrees). Second, we focus on a sample of 159 hot stars (> 6000K) for which
vsini is available but not necessarily the rotation period. We find 6 stars for
which vsini is anomalously low, an indicator of high obliquity. Half of these
have hot Jupiters, even though only 3% of the stars that were searched have hot
Jupiters. We also compare the vsini distribution of the hot stars with planets
to that of 83 control stars selected without prior knowledge of planets. The
mean vsini of the control stars is lower than that of the planet hosts by a
factor of approximately pi/4, as one would expect if the planet hosts have low
obliquities. All these findings suggest that the Kepler planet-hosting stars
generally have low obliquities, with the exception of hot stars with hot
Jupiters.
