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The study of prestellar cores is critical as they set the initial conditionsin star formation and determine the final mass of the stellar object. To date,several hypotheses are describing their gravitational collapse. We performdetailed line analysis and modelling of H$_{2}$D$^{+}$ 110 -111 andN$_{2}$H$^{+}$ 4-3 emission at 372 GHz, using 2'x2' maps (JCMT). Our goal is totest the most prominent dynamical models by comparing the modelled gaskinematics and spatial distribution (H$_{2}$D$^{+}$ and N$_{2}$H$^{+}$) withobservations towards four prestellar (L1544, L183, L694-2, L1517B) and oneprotostellar core (L1521f). We perform a detailed non-LTE radiative transfermodelling using RATRAN, where we compare the predicted spatial distribution andline profiles of H$_{2}$D$^{+}$ and N$_{2}$H$^{+}$ with observations towardsall cores. To do so, we adopt the physical structure for each core predicted bythree different dynamical models taken from literature: Quasi-EquilibriumBonnor-Ebert Sphere (QE-BES), Singular Isothermal Sphere (SIS), andLarson-Penston (LP) flow. Our analysis provides an updated picture of thephysical structure of prestellar cores. We find that the SIS model can beclearly excluded in explaining the gas emission towards the cores, but a largersample is required to differentiate clearly between the LP flow, the QE-BES andthe static models. All models of collapse underestimate the intensity of thegas emission by up to several factors towards the only protostellar core in oursample, indicating that different dynamics take place in different evolutionarycore stages. If the LP model is confirmed towards a larger sample of prestellarcores, it would indicate that they may form by compression or accretion of gasfrom larger scales. If the QE-BES model is confirmed, it means that quasihydrostatic cores can exist within turbulent ISM.

Mapping the H$_{2}$D$^{+}$ and N$_{2}$H$^{+}$ emission towards prestellar cores. Testing dynamical models of the collapse using gas tracers