Sub-parsec resolution cosmological simulations of star-forming clumps at high redshift with feedback of individual stars

We introduce a new set of zoom-in cosmological simulations with sub-pc resolution, intended to model extremely faint, highly magnified star-forming stellar clumps, detected at z = 6.14 thanks to gravitational lensing. The simulations include feedback from individual massive stars (in both the pre-supernova and supernova phases), generated via stochastic, direct sampling of the stellar initial mass function. We adopt a modified 'delayed cooling' feedback scheme, specifically created to prevent artificial radiative loss of the energy injected by individual stars in very dense gas (n similar to 10(3)-10(5) cm(-3)). The sites where star formation ignites are characterized by maximum densities of the order of 10(5) cm(-3) and gravitational pressures P-grav/k >10(7) K cm(-3), corresponding to the values of the local, turbulent regions where the densest stellar aggregates form. The total stellar mass at z = 6.14 is 3.4x 10<^>7 M-circle dot, in satisfactory agreement with the observed stellar mass of the observed systems. The most massive clumps have masses of similar to 10(6)M(circle dot) and half-mass sizes of similar to 100 pc. These sizes are larger than the observed ones, including also other samples of lensed high-redshift clumps, and imply an average density one orders of magnitude lower than the observed one. In the size-mass plane, our clumps populate a sequence that is intermediate between the ones of observed high-redshift clumps and local dSph galaxies.