Spatial distribution of star formation related to ionized regions
  throughout the inner Galactic plane
  We present a comprehensive statistical analysis of star-forming objects
located in the vicinities of 1 360 bubble structures throughout the Galactic
Plane and their local environments. The compilation of ~70 000 star-forming
sources, found in the proximity of the ionized (Hii) regions and detected in
both Hi-GAL and GLIMPSE surveys, provided a broad overview of the different
evolutionary stages of star-formation in bubbles, from prestellar objects to
more evolved young stellar objects (YSOs). Surface density maps of star-forming
objects clearly reveal an evolutionary trend where more evolved star-forming
objects are found spatially located near the center, while younger star-forming
objects are found at the edge of the bubbles. We derived dynamic ages for a
subsample of 182 Hii regions for which kinematic distances and radio continuum
flux measurements were available. We detect ~80% more star-forming sources per
unit area in the direction of bubbles than in the surrounding fields. We
estimate ~10% clump formation efficiency (CFE) of Hi-GAL clumps in bubbles,
twice the CFE in fields not affected by feedback. We find higher CFE of
protostellar clumps in younger bubbles, whose density of the bubble shells is
higher. We argue that the formation rate from prestellar to protostellar phase
is probably higher during the early stages of the bubble expansion. Evaluation
of the fragmentation time inside the shell of bubbles advocates the
preexistence of clumps in the medium before the bubble, as supported by
numerical simulations. Approximately 23% of the Hi-GAL clumps are found located
in the direction of a bubble, with 15% for prestellar clumps and 41% for
protostellar clumps. We argue that the high fraction of protostellar clumps may
be due to the acceleration of the star-formation process cause by the feedback
of the (Hii) bubbles.
