Free orbital periods do not remove the HD 191939 timing mass discrepancy in a coplanar six-planet model

We refit 102 published transit times of HD 191939 with free orbital periods and phases in a coplanar six-planet model. The best tested fit gives masses of 2.01 and 1.97 Earth masses for c and d, with chi-square 134.23. Fixing c at its RV central mass of 8 Earth masses gives d a mass of 6.14 and chi-square 180.74. Fixing both RV central masses gives chi-square 255.51. Thus fixed periods are not a sufficient cause of the earlier low timing mass. Season deletion moves the fitted mass of c from 2.01 to 0.10, 0.125 or 2.73 Earth masses, and point predictions of deleted times can fail badly. These predictions omit parameter uncertainty. We give a conditional model test, not a revised mass. Limits include reused timing measurements, fixed outer orbits, a local search, fixed noise errors and no RV or stability fit. Code, selected measurements, fit parameters and numerical checks are included.

HD 191939 · transit timing variations · mass eccentricity degeneracy · orbital periods · season deletion