BINARY CENTRAL STARS OF PLANETARY NEBULAE DISCOVERED THROUGH PHOTOMETRIC VARIABILITY. IV. THE CENTRAL STARS OF HaTr 4 AND Hf 2-2

We explore the photometrically variable central stars of the planetary nebulae HaTr 4 and Hf 2-2. Both have been classified as close binary star systems previously based on their light curves alone. Here, we present additional arguments and data confirming the identification of both as close binaries with an irradiated cool companion to the hot central star. We include updated light curves, orbital periods, and preliminary binary modeling for both systems. We also identify for the first time the central star of HaTr 4 as an eclipsing binary. Neither system has been well studied in the past, but we utilize the small amount of existing data to limit possible binary parameters, including system inclination. These parameters are then compared to nebular parameters to further our knowledge of the relationship between binary central stars of planetary nebulae and nebular shaping and ejection.