The K giant stars from the LAMOST survey data II: the Hercules stream in
  radial migration
  We estimate the age for the individual stars located at the lower part of the
red giant branch from the LAMOST DR2 K giant sample. Taking into account the
selection effects and the volume completeness, the age--metallicity map for the
stars located between 0.3 and 1.5 kpc from the Sun is obtained. A significant
substructure (denoted as the \it{narrow stripe}) located from (age,
[Fe/H])$\sim$(5, 0.4) to (10 Gyr, -0.4 dex) in the age--metallicity map is
clearly identified. Moreover, the \it{narrow stripe} stars are found the
dominate contributors to several velocity substructures, including the
well-known Hercules stream. The substantially large difference between the
observed guiding-center radii and the birth radii inferred from the
age--metallicity relation is evident that the \it{narrow stripe} stars have
been radially migrated from about R$\sim4$ kpc to the solar neighborhood. This
implies that the Hercules stream may not be owe to the resonance associated
with the bar, but may be the kinematic imprint of the inner disk and later
moved out due to radial migration. We estimate that the traveling speed of the
radial migration are roughly 1.1$\pm0.1$ kpc Gyr$^{-1}$, equivalent with about
$1.1\pm0.1$ km s$^{-1}$. This is in agreement with the median $v_R$ of
$2.6^{+1.8}_{-1.9}$ km s$^{-1}$ of the \it{narrow stripe}. We also obtain that
about one third stars in the solar neighborhood are radially migrated from
around 4 kpc. Finally, we find that the radial migration does not lead to
additional disk thickening according to the distribution of $z_{max}$.
