Abstract Theoretically, stars formed from the collapse of cores in molecular clouds. Historically, the core had been assumed to be a singular isothermal sphere (SIS), and the collapse had been investigated in a self-similar manner. When the rotation and magnetic fields lead to non-symmetric collapse, a spheroidal shape may occur. Here, the result of the centrifugal force and magnetic field gradient is assumed to be in the normal direction to the rotational axis, and its components are supposed to be a fraction β of the local gravitational force. In this research, a collapsing SIS core is considered to find the importance that the parameter β plays in the oblateness of the mass shells, which are the crests of the expansion waves. We apply the Adomian decomposition method to solve the system of nonlinear partial differential equations because the collapse does not occur in a spherically symmetric and self-similar manner. In this way, we obtain a semi-analytical relation for the mass infall rate of the shells in the envelope. Near the rotational axis, decreases with the increase of the non-dimensional radius ξ, while a direct relation is observed between and ξ ̇ in the polar regions are greater than their the equatorial regions. Also, the values of equatorial values, and this difference occurs more often at smaller values of ξ. Overall, the results show that before reaching the crest of the expansion wave, the visible shape of the molecular cloud cores can evolve into oblate spheroids. The ratio of major to minor axes of oblate cores increases when increasing the parameter β, and its value can approach the observed elongated shapes of cores in the maps of molecular clouds, such as those in Taurus and Perseus.

Keywords ISM: clouds — ISM: evolution — stars: formation – methods: analytical

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