Gas infalling motions in the envelopes of Very Low Luminosity Objects
  We present the results of a single dish survey toward 95 VeLLOs in optically
thick (HCN 1-0) and thin ($\rm N_2H^+$ 1-0) lines performed for the purpose of
understanding the physical processes of inward motions in the envelopes of the
VeLLOs and characterizing their true nature. The normalized velocity
differences ($\delta V_{HCN}$) between the peak velocities of the two lines
were derived for 41 VeLLOs detected in both lines. The $\delta V$ distribution
of these VeLLOs is found to be significantly skewed to the blue, indicating the
dominance of infalling motions in their envelopes. The infall speeds were
derived for 15 infall candidates by using the HILL5 radiative transfer model.
The speeds were in the range of 0.03 $\rm km~s^{-1}$ to 0.3 $\rm km~s^{-1}$,
with a median value of 0.16 $\rm km~s^{-1}$, being consistent with the
gravitational free-fall speeds from pressure-free envelopes. The mass infall
rates calculated from the infall speeds are mostly of the order of $10^{-6}
M_{\odot}~yr^{-1}$ with a median value of $\rm 3.4 \pm 1.5 \times 10^{-6}
M_{\odot}~yr^{-1}$. These are found to be also consistent with the values
predicted with the inside-out collapse model and show a fairly good correlation
with the internal luminosities of the VeLLOs. This again indicates that the
infall motions observed toward the VeLLOs are likely to be due to the
gravitational infall motions in their envelopes. Our study suggests that most
of the VeLLOs are potentially faint protostars while two of the VeLLOs could
possibly be proto-brown dwarf candidates.
