An Improved Distance to NGC 4258 and its Implications for the Hubble
  Constant
  NGC 4258 is a critical galaxy for establishing the extragalactic distance
scale and estimating the Hubble constant (Ho). Water masers in the nucleus of
the galaxy orbit about its supermassive black hole, and very long baseline
interferometric observations of their positions, velocities, and accelerations
can be modeled to give a geometric estimate of the angular-diameter distance to
the galaxy. We have improved the technique to obtain model parameter values,
reducing both statistical and systematic uncertainties compared to previous
analyses. We find the distance to NGC 4258 to be 7.576 +/- 0.082 (stat.) +/-
0.076 (sys.) Mpc. Using this as the sole source of calibration of the
Cepheid-SN Ia distance ladder results in Ho = 72.0 +/- 1.9 km/s/Mpc, and in
concert with geometric distances from Milky Way parallaxes and detached
eclipsing binaries in the LMC we find Ho = 73.5 +/- 1.4 km/s/Mpc. The improved
distance to NGC 4258 also provides a new calibration of the tip of the red
giant branch of M_{F814W} = -4.01 +/- 0.04$ mag, with reduced systematic errors
for the determination of Ho compared to the LMC-based calibration, because it
is measured on the same Hubble Space Telescope photometric system and through
similarly low extinction as SN Ia host halos. The result is Ho = 71.1 +/- 1.9
km/s/Mpc, in good agreement with the result from the Cepheid route, and there
is no difference in Ho when using the same calibration from NGC 4258 and the
same SN Ia Hubble diagram intercept to start and end both distance ladders.
