The UV Continuum of z > 1 Star-forming Galaxies in the Hubble
  Ultraviolet UltraDeep Field
  We estimate the UV continuum slope, beta, for 923 galaxies in the range 1 < z
< 8 in the Hubble Ultradeep Field (HUDF). These data include 460 galaxies at 1
< z < 2 down to an absolute magnitude M_{UV} = -14 (~0.006 L*_{z=1}; 0.02
L*_{z=0}), comparable to dwarf galaxies in the local universe. We combine deep
HST/UVIS photometry in F225W, F275W, F336W wavebands (UVUDF) with recent data
from HST/WFC3/IR (HUDF12). Galaxies in the range 1 < z < 2 are significantly
bluer than local dwarf galaxies. We find their mean (median) values <beta> =
-1.382 (-1.830) +/- 0.002 (random) +/- 0.1 (systematic). We find comparable
scatter in beta (standard deviation = 0.43) to local dwarf galaxies and 30%
larger scatter than z > 2 galaxies. We study the trends of beta with redshift
and absolute magnitude for binned sub-samples and find a modest color-magnitude
relation, dbeta/dM = -0.11 +/- 0.01 and no evolution in dbeta/dM with redshift.
A modest increase in dust reddening with redshift and luminosity, Delta E(B-V)
~ 0.1, and a comparable increase in the dispersion of dust reddening at z < 2,
appears likely to explain the observed trends. At z > 2, we find trends that
are consistent with previous works; combining our data with the literature in
the range 1 < z < 8, we find a color evolution with redshift, dbeta/dz = -0.09
+/-0.01 for low luminosity (0.05 L*_{z=3}), and dbeta/dz = -0.06 +/-0.01 for
medium luminosity (0.25 L*_{z=3}) galaxies.
