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tokens: can be constrained to be From this equation, we can satisfy the observed mass scale () using reasonable θ and ε values. Although the individual parameters are still uncertain, the calculation shows that the gravitational contraction could release sufficient kinetic energy to account for the observed gas motion. Figure 4. A zoom-in of the PV plot along the three filaments. (a) The systemic velocity map showing the PV cuts. (b)–(d) The PV plot along the three directions. For each filament, the offset is measured from the MMS-7 centre. The solid line represents the v ( r ) function that closely goes through the spine of the PV emission region. The v ( r ) function is calculated from equation ( 5 ). The two dashed lines represent the v ( r ) curves with c 0 varying by a factor of 0.5 and 2, respectively. In (b) and (d), the red solid line denotes the central velocity variations along the PV sampling direction. 4.3 Velocity variations Despite the agreement in energy budget, the velocity distribution still has two features deviating from the modelled v ( r ) curves that should be further examined. First, the theoretical v ( r ) function will approach infinity towards the centre, while the observed velocity profiles are terminated at final velocities around the centre. For the NW filament (Fig. 4b ), the velocity profile reaches the maximum value in the area of r 4 arcsec around the centre. This area is comparable to the size of MMS-7 core ( r = 3.7 arcsec). As a reasonable explanation, this energy release of could be largely transferred to MMS-7, accelerating this core as an entire body to the final velocity. Second, although the three filaments have a similar velocity increase towards the centre, their final velocities are different. This could be attributed to IRAC-2405 and 2407. As shown in Fig. 4(d) , the north filament becomes weaker at IRAC-2407, but still connected to MMS-7, and the gas structure follows the v ( r ) curve well. This suggests that the gas motion is still towards the centre and would reach the same velocity with MMS-7. The south filament, according to its velocity gradient, could have a similar connection to MMS-7 except for a more significant interruption by IRAC-2406 (Core-2). The two YSOs could have dissipated the surrounding N 2 H + component but not significantly affected the global inward motion towards MMS-7. For the NW filament, its outer part ( r > 20 arcsec) could also be affected by the local dense cores. As seen in Fig. 4(b) , the emission region largely deviates from the v ( r ) curve in the spatial range between Core-3 and Core-4 with a value of Δ v ≃ 1.0 km s −1 , suggesting that the gas motion could be affected by these two cores. Although the filaments exhibit these systematic velocity variations, the N 2 H + (1 0 −0 1 ) line profile is usually single-peaked and has a relatively small linewidth of Δ v 0.65 km s −1 over the whole region. This suggests that the filaments should have no further internal