Chromospherically active stars. XXIV. The giant, single-lined binaries HD 37824, HD 181809, and HD 217188

We have obtained spectroscopy and photometry of three chromospherically active, single-lined spectroscopic binaries, HD 37824 (V1149 Ori), HD 181809 (V4138 Sgr), and HD 217188 (AZ Psc). HD 37824 has a circular orbit with a period of 53.57 days. Its primary is a K0 III star, while the secondary is likely a G or K dwarf. HD 181809 has an orbit with a period of 13.04667 days and a low eccentricity of 0.040. The primary has a spectral type of K0 III-IV, and its secondary is probably an M dwarf. The orbit of HD 217188 has a period of 47.1209 days and a moderately high eccentricity of 0.470. The spectral type of the primary is K0 III, while the secondary is likely an M dwarf. All three systems are estimated to have near solar iron abundances. Photometric observations spanning 15-16 years for all three stars yield mean photometric periods of 53.12, 59.85, and 90.89 days for HD 37824, HD 181809, and HD 217188, respectively. Thus, HD 37824 is rotating synchronously with the orbital period, while HD 181809 and HD 217188 are both rotating considerably slower than synchronously. All three stars show long-term variations in mean brightness and photometric amplitude, but no correlations are observed between the seasonal mean brightness, photometric amplitude, and seasonal photometric period in any of the stars. No clear evidence for long-term periodic variations in any of these parameters is present. The circular orbit of HD 37824 and the synchronous rotation of its K giant argue that the star is in the core helium-burning phase of its evolution. The giant components of HD 181809 and HD 217188 are asynchronous rotators, and both systems have eccentric orbits. Thus, those two stars are likely first-ascent giants.