The evolution of the internal structure of massive star forming regions in the Milky Way as revealed by ALMA

We analyze the structure of 15 protocluster forming regions in the Milky Way using their $1.3$ mm continuum emission maps from the ALMA-IMF large program. The analysis of the clouds structure is performed using the delta-variance spectrum technique. The calculated spectra display a self-similar regime on small scales as well as the presence of a prominent bump on larger scales and whose physical size, $L_{\mathrm{h}\mathrm{u}\mathrm{b}}$, falls in the range of $\approx 7000$ au to $60000$ au. These scales correspond to the sizes of the most compact clumps within the protocluster forming clouds. A significant correlation is found between $L_{\mathrm{h}\mathrm{u}\mathrm{b}}$ and the surface density of the free-free emission estimated from the integrated flux of the H41$\alpha$ recombination line $\left({\mathrm{\Sigma }}_{\mathrm{H}41\alpha }^{\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{e}-\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{e}}\right)$ as well as a significant anti-correlation between $L_{\mathrm{h}\mathrm{u}\mathrm{b}}$ and the ratio of the 1.3 mm to 3 mm continuum emission fluxes $\left(S_{1.3\mathrm{m}\mathrm{m}}^{\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{u}\mathrm{d}}\mathrm{/}{S}_{3\mathrm{m}\mathrm{m}}^{\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{u}\mathrm{d}}\right)$. Smaller values of $\left(S_{1.3\mathrm{m}\mathrm{m}}^{\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{u}\mathrm{d}}\mathrm{/}{S}_{3\mathrm{m}\mathrm{m}}^{\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{u}\mathrm{d}}\right)$ and larger values of ${\mathrm{\Sigma }}_{\mathrm{H}41\alpha }^{\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{e}-\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{e}}$ correspond to more advanced evolutionary stages of the protocluster forming clumps. Hence, our results suggest that the sizes of the densest regions in the clouds are directly linked to their evolutionary stage and to their star formation activity with more evolved clouds having larger protocluster forming clumps. This is an indication that gravity plays a vital role in regulating the size and mass growth and star formation activity of these clumps with ongoing gas accretion