Chemical analysis of prestellar cores in Ophiuchus yields short timescales and rapid collapse

Sun-like stars form from the contraction of cold and dense interstellar clouds. How the collapse proceeds and the main physical processes driving it, however, are still under debate and a final consensus on the timescale of the process has not been reached. Does this contraction proceed slowly, sustained by strong magnetic fields and ambipolar diffusion, or is it driven by fast collapse with gravity dominating the entire process? One way to answer this question is to measure the age of prestellar cores through statistical methods based on observations or via reliable chemical chronometers, which should better reflect the physical conditions of the cores. Here we report APEX observations of ortho-H$_2$D$^+$ and para-D$_2$H$^+$ for six cores in the Ophiuchus complex and combine them with detailed three-dimensional magneto-hydrodynamical simulations including chemistry, providing a range of ages for the observed cores of 100-200 kyr. The outcome of our simulations and subsequent analysis provides a good matching with the observational results in terms of physical (core masses and volume densities) and dynamical parameters such as the Mach number and the virial parameter. We show that models of fast collapse successfully reproduce the observed range of chemical abundance ratios as the timescales to reach the observed stages is shorter than the free-fall time of the cores and much shorter than the ambipolar diffusion time, measured from the electron fraction in the simulations. Our work establishes the ortho-H$_2$D$^+$/para-D$_2$H$^+$ ratio as a reliable chemical clock and opens up to the possibility of exploring the star formation process in a statistically relevant sample through observations of these tracers.