  Extremely large telescopes (ELTs) provide an opportunity to observe surface
inhomogeneities for ultracool objects including M dwarfs, brown dwarfs (BDs),
and gas giant planets via Doppler imaging and spectro-photometry techniques.
These inhomogeneities can be caused by star spots, clouds, and vortices. Star
spots and associated stellar flares play a significant role in habitability,
either stifling life or catalyzing abiogenesis depending on the emission
frequency, magnitude, and orientation. Clouds and vortices may be the source of
spectral and photometric variability observed at the L/T transition of BDs and
are expected in gas giant exoplanets. We develop a versatile analytical
framework to model and infer surface inhomogeneities which can be applied to
both spectroscopic and photometric data. This model is validated against a slew
of numerical simulations. Using archival spectroscopic and photometric data, we
infer star spot parameters (location, size, and contrast) and generate global
surface maps for Luhman 16B (an early T dwarf and one of our solar system's
nearest neighbors at a distance of approximately 2 pc). We confirm previous
findings that Luhman 16B's atmosphere is inhomogeneous with time-varying
features. In addition, we provide tentative evidence of longer timescale
atmospheric structures such as dark equatorial and bright mid-latitude to polar
spots. These findings are discussed in the context of atmospheric circulation
and dynamics for ultracool dwarfs. Our analytical model will be valuable in
assessing the feasibility of using ELTs to study surface inhomogeneities of gas
giant exoplanets and other ultracool objects.
