Eta Carinae's historical light curve: evidence for cyclic Roche lobe overflow from the primary star
The large amount of ground-based photometric measurements of $\eta$ Carinae obtained since 1940 have remained problematic for quantitative modeling due to the blending of flux from the stellar core and the surrounding circumstellar nebula. In the era of the Hubble Space Telescope, spatially resolved imaging & spectrophotometry have enabled disentanglement of these components, allowing recovery of the stellar core $V$-band brightness from ground-based observations. We isolate the $V$-band fluxes of the stellar core and nebula using 1999--2020 HST (ACS and STIS) observations, and use these to calibrate coeval ground-based photometry. The main finding is an orbital light curve with an amplitude $\Delta m \approx \pm 0.2\,$mag, many times higher than that modeled by ellipsoidal deformation of the primary. The observations suggest that Roche lobe overflow starts at $- 75$ days before periastron in coincidence with the start of rising in the orbital light curve, and remains for 150 days. An expanding (and afterwards dissipating) gas cloud reflecting the light from the primary would explain the observed large amplitude of the orbital light curve. A sharp periodic photometric peak occurs at $\sim -18$ days from the periastron. It is followed by a broad minimum around the superior conjunction of the secondary (T$_0+5.2$ days), which we interpret as a partial eclipse of the ejected material, in coincidence with the \emph{shallow minimum} in X-rays, which also has been attributed to an eclipse.