  We first reported evidence for differential rotation of Kappa1 Ceti in Paper
I. In this paper we demonstrate that the differential rotation pattern closely
matches that for the Sun. This result is based on additional MOST
(Microvariability & Oscillations of STars) observations in 2004 and 2005, to
complement the 2003 observations discussed in Paper I. Using StarSpotz, a
program developed specifically to analyze MOST photometry, we have solved for
k, the differential rotation coefficient, and P_{EQ}, the equatorial rotation
period using the light curves from all three years. The spots range in latitude
from 10 to 75 degrees and k = 0.090^{+0.006}_{-0.005} -- less than the solar
value but consistent with the younger age of the star. k is also well
constrained by the independent spectroscopic estimate of vsini. We demonstrate
independently that the pattern of differential rotation with latitude in fact
conforms to solar.
  Details are given of the parallel tempering formalism used in finding the
most robust solution which gives P_{EQ} = 8.77^{+0.03}_{-0.04} days -- smaller
than that usually adopted, implying an age < 750 My. Our values of P_{EQ} and k
can explain the range of rotation periods determined by others by spots or
activity at a variety of latitudes. Historically, Ca II activity seems to occur
consistently between latitudes 50 and 60 degrees which might indicate a
permanent magnetic feature. Knowledge of k and P_{EQ} are key to understanding
the dynamo mechanism and rotation structure in the convective zone as well
assessing age for solar-type stars. We recently published values of k and
P_{EQ} for epsilon Eri based on MOST photometry and expect to analyze MOST
light curves for several more spotted, solar-type stars.
