Reflection upper estimates for 51 Peg b change with TESS trend fits in sectors 56 and 83 for a circular orbit at 49.8°

We test how instrumental trend fits affect reflected-light estimates for the known planet 51 Peg b. We use public TESS 120-second data from sectors 56 and 83. We assume a circular 4.2307966-day orbit, a fixed orbital clock, a Lambert phase function, and a 49.8-degree inclination. We fit one common planet contrast and separate trends in each visit. We also allow a separate sine at 4.55 days in each visit, as motivated by Gaidos et al. (2025). With a linear time trend and 2, 4, 6, or 8 instrumental vectors, approximate one-sided 95% upper estimates of the full-phase contrast are 257, 190, 135, and 104 parts per million (ppm). The same fits without the nearby sine give 163, 108, 87, and 76 ppm. Each estimate is conditional on its correction model. An exact linear response calculation shows that an omitted 4.55-day sine with 25 ppm semi-amplitude in each visit can bias the planet contrast by 46 to 49 ppm over free phases. A large-radius, high-albedo example gives 150.1 ppm, so its exclusion does not hold across the tested corrections. All 16 artificial signal tests recover the added amplitude to within 0.009%. The error rule covers the true amplitude in 98.9% to 100% of 2,000 Gaussian noise draws per setting across 14 settings. These tests do not cover unknown errors in the instrumental correction or signal shape. The fits do not establish a reflected-light detection. We publish the frozen inputs, provenance, full model grid, response calculation, validation results, figures, and code for offline reproduction.

51 Peg b · TESS · reflected light · phase curves · instrumental trends · model sensitivity · open data