Nageen Pervaiz, Guo-Yin Zhang, Alexander Men'shchikov, Jin-Zeng Li

We present a comprehensive analysis of dense cores and filamentary structures in the M16 Eagle Nebula using high-resolution ($11.7^{\prime\prime}$) surface density and temperature maps derived from \textit{Herschel} observations. Using the \textit{hires} algorithm for map construction and the \textit{getsf} method for source and filament extraction, we identified 233 cores and 111 filaments in this massive star-forming region. The filaments exhibit a median width of 0.4\,pc -- and a median linear density of 61\,$M_\odot$\,pc$^{-1}$, with 76\% being supercritical for gravitational fragmentation. Our radial analysis of the $\sim$60\,pc diameter shell driven by the central NGC 6611 cluster reveals strong enhancements in structure formation: filament formation efficiency (FFE) is 2.3 times higher within the shell (peaking at 22\%), while core density shows a concurrent 1.5-fold enhancement. The moderate correlation between core density and FFE ($r=0.67$) indicates coupled formation processes. Theoretical analysis demonstrates that observed surface densities exceed the critical threshold for fragmentation by a factor of $\sim$8, with a fragmentation timescale ($\sim$1.5--2.0\,Myr) comparable to the shell's dynamical age ($\sim$1.0--1.3\,Myr), indicating we are observing fragmentation in progress. These results reveal a hierarchical fragmentation sequence -- shell compression $\rightarrow$ filament formation $\rightarrow$ core formation -- providing clear observational evidence for positive feedback where massive star formation triggers secondary structure formation in the surrounding molecular cloud.