Astrophys Space Sci (2021) 366:23 https://doi.org/10.1007/s10509-021-03929-3 ORIGINAL ARTICLE A study on the formation of field, binary or multiple stars: a 2D approach through dynamical system Ashok Mondal 1 · Tanuka Chattopadhyay 1 · Anisha Sen 1 Received: 26 November 2020 / Accepted: 13 February 2021 / Published online: 24 February 2021 © The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature 2021 Abstract A dynamical model has been developed to en- visage the star formation scenario in filamentary molecular clouds. In the present work a double well potential has been considered to find the number of stable stationary points as the origin of field star, binary stars or stellar associations. It is found that low density structure can lead to the for- mation of field stars while an intermediate density structure is favourable for formation of binary stars. Stellar associa- tions are generally prevalent in dense filamentary molecular clouds. Keywords ISM: clouds · Stars: formation 1 Introduction Astronomers have observed that most of the stars in the Uni- verse are formed in binaries or multiple systems. The ques- tion remains how do binary or multiple stars system form along with field stars? It’s a big unsolved problem yet. Many scientists have tried to develop a complete theory to under- stand the origin of these binaries as a gravitationally bound system, but none of them have become able to explain prop- erly the reason behind it. In 1883, Lord Kelvin proposed the rotational fission theory. According to this theory, a star would spin faster and faster during contraction until it broke up into a binary star. But in 1986, Durisen et al. (1986) showed the invalidity of the fission theories. They showed that the ejected matter would end up astrailing spiral arms of gas rather than as a different conjunctive star. In 1991, Boss B A. Mondal ammath_rs@caluniv.ac.in 1 Department of Applied Mathematics, University of Calcutta, 92 A.P.C Road, Kolkata 700009, India (1991) proposed the ‘fragmentation theory’ which is now considered as the most successful theory of the formation of binary stars as a whole although a more holistic approach is in demand for their formation and evolution process. Many astronomers have found that the structure of the in- terstellar medium (ISM) is highly filamentary on all scales and star formation is hermetically related to self-gravitating filaments (Schneider and Elmegreen 1979; Hartmann 2002; Myers 2009; Flagey et al. 2009). Also, the Large scale Her- schel and Plank observations of Sub-millimeter dust emis- sion revealed a universal web-like filamentary structure in the ISM (Pilbratt et al. 2010; Contreras et al. 2013 André et al. 2016; Bresnahan et al. 2018). First, these filamentary webs of cold ISM are formed from the interplay between interstellar shock waves, gravity, and magnetic fields. Then gravity takes over playing a key role in creating the core and protostars form from this cloud through fragmentation. In the present work, we have analyzed the evolution of a set of nonlinear dynamical equations to understand the ori- gin of the binary and multiple stars system. We have consid- ered different types of double-well potentials which give rise to almost similar type of density structure as observed in fil- amentary molecular clouds (here after MC) and performed the stability analysis of these molecular clouds under the in- fluence of these potentials. The concept of double-well po- tentials is widely used in the field of quantum mechanics which deals with microscopic scales. In the present work for the first time, we have extended this concept for macro- scopic scales e.g. MC so as to understand the origin of the formation mechanism of binary and multiple star systems using linear stability analysis method. We have analyzed one generalized version of double-well potential under various physical conditions. We have shown the effect of the pres- ence of rotation in the process of star formation.