Probing Velocity Structures of Protostellar Envelopes: Infalling and Rotating Envelopes within Turbulent Dense Cores

We have observed the three low-mass protostars, IRAS 15398-3359, L1527 IRS, and TMC-1A, with the ALMA 12 m array, the ACA 7 m array, and the IRAM-30 m and APEX telescopes in the C¹⁸O J = 2-1 emission. Overall, the C¹⁸O emission shows clear velocity gradients at radii of ~100-1000 au, which likely originate from the rotation of envelopes, while velocity gradients are less clear and velocity structures are more perturbed on scales of ~1000-10,000 au. IRAS 15398-3359 and L1527 IRS show a break at radii of ~1200 and ~1700 au in the radial profile of the peak velocity, respectively. The peak velocity is proportional to r ^-1.38 or r ^-1.7 within the break radius, which can be interpreted as indicating the rotational motion of the envelope with a degree of contamination by gas motions on larger spatial scales. The peak velocity follows v _peak ∝ r ^0.68 or v _peak ∝ r ^0.46 outside the break radius, which is similar to the J/M-R relation of dense cores. TMC-1A exhibits a radial profile of the peak velocity that is not consistent with the rotational motion of the envelope nor the J/M-R relation. The origin of the relation of v _peak ∝ r ^0.46-r ^0.68 is investigated by examining correlations of the velocity deviation (δ v) and the spatial scale (τ) in the two sources. The obtained spatial correlations, δ v ∝ τ ^~0.6, are consistent with the scaling law predicted by turbulence models, which may suggest that large-scale velocity structures originate from turbulence.