Shaping a high-mass star-forming cluster through stellar feedback. The case of the NGC 7538 IRS 1-3 complex

Context: NGC 7538 IRS 1-3 is a high-mass star-forming cluster with several detected dust cores, infrared sources, (ultra)compact H$_{\rm II}$ regions, molecular outflows, and masers. In such a complex environment, important interactions and feedback among the embedded objects are expected to play a major role in the evolution of the region. Aims: We study the dust, kinematic, and polarimetric properties of the NGC 7538 IRS 1-3 region to investigate the role of the different forces interplaying in the formation and evolution of high-mass star-forming clusters. Methods: We perform SMA high angular resolution observations at 880 $\mu$m with the compact configuration. We develop the RATPACKS code to generate synthetic velocity cubes from models of choice to be compared to the observational data. We develop the "mass balance" analysis to quantify the stability against gravitational collapse accounting for all the energetics at core scales. Results: We detect 14 dust cores from 3.5 $M_{\odot}$ to 37 $M_{\odot}$ arranged in two larger scale structures: a central bar and a filamentary spiral arm. The spiral arm presents large scale velocity gradients in H$^{13}$CO$^+$ 4-3 and C$^{17}$O 3-2, and magnetic field segments well aligned to the dust main axis. The velocity gradient is well reproduced by a spiral arm expanding at 9 km s$^{-1}$ with respect to the central core MM1, which is known to power a large precessing outflow. The energy of the outflow is comparable with the spiral arm kinetic energy, which is dominant over gravitational and magnetic energies. In addition, the dynamical ages of the outflow and spiral arm are comparable. ... (Full abstract in the pdf version)