Observations of AGN-driven feedback: dynamics and ionization of the filaments in M87

We present a comprehensive kinematic and ionization analysis of the warm ionized filaments(similar to 104 K) in M87, the central galaxy of the Virgo cluster, using new integral field spectroscopy from MEGARA (Multi-Espectrografo en GTC de Alta Resolucion para Astronom & imath;a, GTC) and SITELLE (Spectrometre ` Imageur a` Transformee de Fourier pour l Etude en Long et en Large de raies d Emission, CFHT). MEGARA targets the southeastern (SE) filaments (similar to 3 kpc from the nucleus) coincident with the only known molecular gas clump, and the far eastern (FE) filament (similar to 15 kpc), spatially isolated within an old radio lobe. SITELLE fully maps the filaments, offering the first complete views of their kinematics and excitation. Combined with archival ALMA (Atacama Large Millimeter Array), MUSE (Multi-Unit Spectroscopic Explorer), and Chandra data, these observations offer a multiphase view of gas dynamics. The filaments display complex motions inconsistent with simple rotation. Velocity structure functions (VSFs) of the warm and cold gas in the central and SE filaments show consistent steep slopes (> 2/3) and flattening on small scales of a few hundred parsecs, possibly suggesting energy injection from Type Ia supernovae, though interpretation is method-limited. The FE filament shows lower VSF amplitude, suggesting less active driving. ALMA CO emission is cospatial and kinematically aligned with the ionized gas, the latter showing broader velocity dispersions. Ionization diagnostics indicate AGN (active galactic nucleus)-related processes (e.g. shocks) dominate, with higher energy excitation near the radio lobes and (lower energy) fossil feedback signatures in the FE filament. Finally, the filaments follow the same strong H alpha-X-ray surface brightness correlation seen in other clusters, supporting local thermal coupling between phases. However, the FE filament deviates from this trend, possibly due to uplift from past AGN outbursts or limitations in the analysis method.