Abstract
Context. In order to understand the formation of the first stars, which set the transition between the Dark Ages and Cosmic Dawn epochs, it is necessary to provide a detailed description of the physics at work within the first clouds of gas which, during their gravitational collapse, will set the conditions for stars to be form through the mechanism of thermal instability. Aims. Our objective is to study in detail the molecular cooling of gas in the halos preceding the formation of the first stars. We are furthermore assessing the sensitivity of the 21cm hydrogen line to this cooling channel. Results. We present the CHEMFAST code, that we developed to compute the cosmological 21cm neutral hydrogen line inside collapsing matter overdensity. We precisely track evolution in the abundances of ions, atoms and molecules through a network of chemical reactions. Computing the molecular thermal function due to the excitation of the rotational levels of the H2 molecule, we find it strongly affects the gas temperature inside collapsing clouds of $10^8$ M$_\odot$. The gas temperature falls at the end of the collapse, when the molecular cooling takes over the heating due to gravitation. Conclusions. We find that the 21cm brightness temperature inside the collapsing cloud presents an emission feature, different from the one predicted in expansion scenario. It moreover follows the same behavior as the gas temperature, as it is also strongly affected by the molecular cooling. This makes it a promising probe in order to map the collapsing halos and thermal processes at work inside them.