A multi-wavelength approach to active galactic nuceli feedback in low ionisation nuclear emission-line regions: The case of NGC 4438

The outflows generated by active galactic nuclei (AGNs) may play a crucial role in galaxy evolution. In order to better understand how the feedback from AGNs works, multi-wavelength studies, including of low-luminosity AGNs (LLAGNs), are required. In particular, the presence of multi-phase outflows in low ionisation nuclear emission-line regions (LINERs) has been confirmed to be frequent but the mechanisms that launch them are still being studied. We aim to explore the connections between the ionised gas outflow, radio continuum structures, and X-ray emission detected in the LINER NGC, 4438. We sought morphological and energetic evidence of jet-mode feedback to reveal how a jet may modify the ionised gas structure and determine whether the ionised gas outflow can be driven by the jet. We analysed L-, C-, and X-band images (from 1. 4 to 12 GHz) of the LINER NGC, 4438, and combined high-resolution data from the enhanced Multi Element Radio Linked Interferometer Network (e-MERLIN) and Karl G Jansky Very Large Array (VLA). We produced radio flux and spectral index maps from which we characterised the source. In particular, we created an energetic model that allows us to estimate the power, age, magnetic field, and the velocity of the particles of the jet. We incorporated optical integral field spectroscopy (IFS) data (GTC/MEGARA) and Chandra X-ray data, with comparable resolution, to better trace the outflow, the AGN, and their potential connection. We present new L-, C-, and X-band high-resolution, high-sensitivity radio images and spectral-index maps that probe ∼25 pc scales in NGC 4438. These data reveal a close morphological correspondence between the radio structures and the ionised gas bubble. Using a spatially resolved energetic model based on radio flux and spectral index, we disentangle the compact AGN emission from the extended bubble for the first time, establishing distinct physical origins for each structure. We measure a kinetic power of ∼ 5, erg, s for the radio bubble, which exceeds the power of the ionised outflow by more than three orders of magnitude. 10^ 44 -1 Our multi-wavelength analysis indicates that NGC 4438 is undergoing jet-mode feedback, where a low-luminosity, weakly collimated jet impacts the dense northern interstellar medium. This interaction drives shock-ionised gas, produces a moderate-velocity outflow that removes material from the region, and generates thermal X-ray emission coincident with the radio and Hα cavity.