Numerical Simulation and Completeness Survey of Bubbles in the Taurus
  and Perseus Molecular Clouds
  Previous studies have analyzed the energy injection into the interstellar
matter due to molecular bubbles. They found that the total kinetic energies of
bubbles are comparable to, or even larger than, those of outflows but still
less than the gravitational potential and turbulence energies of the hosting
clouds. We examined the possibility that previous studies underestimated the
energy injection due to being unable to detect dim or incomplete bubbles. We
simulated typical molecular bubbles and inserted them into the $^{13}$CO Five
College Radio Astronomical Observatory maps of the Taurus and Perseus Molecular
Clouds. We determined bubble identification completeness by applying the same
procedures to both simulated and real data sets. We proposed a detectability
function for both the Taurus and Perseus molecular clouds based on a
multivariate approach. In Taurus, bubbles with kinetic energy less than ~$1
\times 10^{44}$ erg are likely to be missed. We found that the total missing
kinetic energy in Taurus is less than a couple of $10^{44}$ erg, which only
accounts for around 0.2% of the total kinetic energy of identified bubbles. In
Perseus, bubbles with kinetic energy less than ~$2 \times 10^{44}$ erg are
likely to be missed. We found that the total missing kinetic energy in Perseus
is less than $10^{45}$ erg, which only accounts for around 1% of the total
kinetic energy of identified bubbles. We thus conclude that previous manual
bubble identification routines used in Taurus and Perseus can be considered to
be energetically complete. Therefore, we confirm that energy injection from
dynamic structures, namely outflows and bubbles, produced by star formation
feedback are sufficient to sustain turbulence at a spatial scale from ~0.1 to
~2.8 pc.
