HST view of NGC 5044: Constraints on Filament Widths, Magnetic Support, Multiphase Structure, and Comparison with Cluster Environments

We present new Hubble Space Telescope (HST) imaging of ionised filaments in the brightest group galaxy NGC 5044. These filaments extend several kiloparsecs and have widths of $\sim$50--120 pc, with some as narrow as those in cluster cores and others broader, reflecting the lower confining pressure in groups. Filament width ($W$) scales with ambient pressure ($P$) as $W \propto P^{-0.4}$. Combining HST, ALMA, and MUSE data, we measure column densities and magnetic field strengths. Equipartition fields decline from $\sim$40 $\mu$G at the centre to $\sim$20 $\mu$G at 5 kpc, about 2--3 times weaker than in clusters. Dynamical stability requires stronger radial fields ($\sim$10$^2$ $\mu$G), consistent with simulations and magnetic draping, though such high values exceed Faraday Rotation Measure limits. Turbulence and cosmic rays also contribute support. Group and cluster filaments are stable against gravitational collapse, and ultraviolet imaging reveals no star formation in NGC 5044 ($<$10$^{-3}$ M$_\odot$ yr$^{-1}$). NGC 5044 hosts an ionised gas core within its Bondi radius with $n_e \propto r^{-1}$ and filling factor $f \gtrsim 3 \times 10^{-3}$, that is connected to the extended filaments, suggesting a channel for gas inflow toward the black hole. Group and cluster filaments likely share a common origin, with magnetic fields and AGN feedback preserving their structure. Ambient pressure and dust survival regulate molecular gas formation. Lower-pressure groups favour broader, more diffuse filaments with sporadic molecular clumps and weaker dust shielding, whereas higher-pressure clusters host narrower strands with stronger molecular-ionised gas alignment. We predict that (i) filament width scales with ambient pressure, (ii) filament-coincident Faraday rotation structures emerge at $\leq 0.1$ kpc resolution, and (iii) molecular/ionised gas co-spatiality is weaker in groups than in clusters.