  KA1858+4850 is a narrow-line Seyfert 1 galaxy at redshift 0.078 and is among
the brightest active galaxies monitored by the Kepler mission. We have carried
out a reverberation mapping campaign designed to measure the broad-line region
size and estimate the mass of the black hole in this galaxy. We obtained 74
epochs of spectroscopic data using the Kast Spectrograph at the Lick 3-m
telescope from February to November of 2012, and obtained complementary V-band
images from five other ground-based telescopes. We measured the H-beta light
curve lag with respect to the V-band continuum light curve using both
cross-correlation techniques (CCF) and continuum light curve variability
modeling with the JAVELIN method, and found rest-frame lags of lag_CCF = 13.53
(+2.03, -2.32) days and lag_JAVELIN = 13.15 (+1.08, -1.00) days. The H-beta
root-mean-square line profile has a width of sigma_line = 770 +/- 49 km/s.
Combining these two results and assuming a virial scale factor of f = 5.13, we
obtained a virial estimate of M_BH = 8.06 (+1.59, -1.72) x 10^6 M_sun for the
mass of the central black hole and an Eddington ratio of L/L_Edd ~ 0.2. We also
obtained consistent but slightly shorter emission-line lags with respect to the
Kepler light curve. Thanks to the Kepler mission, the light curve of
KA1858+4850 has among the highest cadences and signal-to-noise ratios ever
measured for an active galactic nucleus; thus, our black hole mass measurement
will serve as a reference point for relations between black hole mass and
continuum variability characteristics in active galactic nuclei.
