Next-generation Exo-REM atmospheric models: application to VHS 1256 b to emulate patchy clouds

Condensate clouds are a defining feature of brown dwarf and exoplanet atmospheres, producing a broad range of colours on the CMD and giving rise to spectral features such as the distinct $\sim 10 \mu$m spectral imprint. Cloud cover is likely to be heterogeneous in many objects, with observed rotational variability providing evidence for the presence of thick and thin cloud regions rotating in and out of view. Yet current 1D atmosphere models often fail to reproduce the spectra of highly cloudy substellar objects, especially those with complex cloud structures. We address these limitations by upgrading the Exo-REM atmosphere model, and by devising a more nuanced approach to describe heterogeneous cloud cover with pre-computed 1D grids. We present new Exo-REM grids, hereafter Exo-REM k26, featuring critical updates: (1) the incorporation of a cloud sedimentation parameter, $f_{sed}$, to govern cloud opacity, thereby enabling even the reddest of objects to be accessed on a CMD, revealing a trend of decreasing $f_{sed}$ along the L--T transition (2) the substantial update of molecular opacities and abundances used, including new experimentally validated alkali line lists, and (3) the implementation of strict convergence criteria that entirely avoid unstable model solutions. Correcting an erroneous $\text{CH}_3\text{D}$ abundance leads to spectral changes for low-$T_{eff}$ objects. Applying Exo-REM k26 to the cool GJ 504 b thus leads to a revision of its parameters ($T_{eff} = 473^{+14}_{-12}$ K, $\log g = 4.0 \pm 0.1$ dex). For the variable VHS 1256 b, a two-column framework that emulates cloud heterogeneities achieves an improved global fit over a single 1D model. A ~60-40% split of thick and thin clouds best describes its atmosphere, further confirming the presence of patchy clouds. This reproduces the strong $10 \mu$m silicate absorption in the JWST data of VHS 1256 b.