We study the red-optical photometry of the ultra-hot Jupiter WASP-121 b as observed by the Transiting Exoplanet Survey Satellite (TESS) and model its atmosphere through a radiative transfer simulation. Given its short orbital period of $sim1.275$ days, inflated state and bright host star, WASP-121 b is exceptionally favorable for detailed atmospheric characterization. Towards this purpose, we use texttt{allesfitter} to characterize its full red-optical phase curve, including the planetary phase modulation and the secondary eclipse. We measure the day and nightside brightness temperatures in the TESS passband as $3012substack{+40 -42}$ K and $2022substack{+254 -602}$ K, respectively, and do not find a statistically significant phase shift between the brightest and substellar points. This is consistent with an inefficient heat recirculation on the planet. We then perform an atmospheric retrieval analysis to infer the dayside atmospheric properties of WASP-121 b such as its bulk composition, albedo and heat recirculation. We confirm the temperature inversion in the atmosphere and suggest H$^-$, TiO and VO as potential causes of the inversion, absorbing heat at optical wavelengths at low pressures. Future HST and JWST observations of WASP-121 b will benefit from its first full phase curve measured by TESS.
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