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

Abstract

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.