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We present the results of a single dish survey toward 95 VeLLOs in opticallythick (HCN 1-0) and thin ($\rm N_2H^+$ 1-0) lines performed for the purpose ofunderstanding the physical processes of inward motions in the envelopes of theVeLLOs and characterizing their true nature. The normalized velocitydifferences ($\delta V_{HCN}$) between the peak velocities of the two lineswere derived for 41 VeLLOs detected in both lines. The $\delta V$ distributionof these VeLLOs is found to be significantly skewed to the blue, indicating thedominance of infalling motions in their envelopes. The infall speeds werederived 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 thegravitational free-fall speeds from pressure-free envelopes. The mass infallrates 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 valuespredicted with the inside-out collapse model and show a fairly good correlationwith the internal luminosities of the VeLLOs. This again indicates that theinfall motions observed toward the VeLLOs are likely to be due to thegravitational infall motions in their envelopes. Our study suggests that mostof the VeLLOs are potentially faint protostars while two of the VeLLOs couldpossibly be proto-brown dwarf candidates.

Gas infalling motions in the envelopes of Very Low Luminosity Objects