JADES and BlackTHUNDER: rest-frame Balmer-line absorption and the local environment in a Little Red Dot at z = 5

We present a broad-line AGN at z=5.077, observed with both NIRSpec/MSA and NIRSpec/IFU by the JADES and BlackTHUNDER surveys. The target exhibits all the hallmark features of a 'Little Red Dot' (LRD) AGN. The combination of spatially resolved and high-resolution spectroscopy offers deeper insight into its nature. The H$α$ line has multiple components, including two broad Gaussians, yielding a black-hole mass of $\log(M_{\rm BH}/M_\odot)=7.65$, while the narrow [O III]$λ$5007 gives a galaxy dynamical mass of $\log(M_{\rm dyn}/M_\odot)=9.1$ suggesting a dynamically overmassive black hole relative to the host galaxy. The target is immersed in a 7-kpc wide pool of ionized gas and has three neighbours: a satellite galaxy, a possible satellite/gas cloud and a tentatively detected spatially detached outflow. H$α$ shows strong absorption, deeper than the continuum, thus ruling out a stellar origin, and with velocity and velocity dispersion of v=-13 km s$^{-1}$ and $σ$=120 km s$^{-1}$. There is tentative evidence (2.6 $σ$) of temporal variability in the EW of the H$α$ absorber over two rest-frame months. If confirmed, this would suggest a highly dynamic environment. Notably, while the H$α$ absorber is clearly visible and even dominant in the high-resolution G395H observations, it is not detected in the medium-resolution G395M data of the same epoch. This implies that the current incidence rate of absorbers in LRDs - and especially of rest-frame absorbers - may be severely underestimated, because most LRDs rely on lower-resolution spectroscopy. In this context, the high incidence rate of rest-frame absorbers in LRDs may indicate a configuration that is either intrinsically stationary, such as a rotating disc, or that exhibits time-averaged stability, such as an oscillatory 'breathing mode' accretion of cyclic expansion and contraction of the gas around the SMBH.