HL Dra: an active Algol-like binary system with a pulsating component star and a cool third body

HL Draconis (HL Dra) is an oscillating eclipsing binary with an orbital period of 0.944276 d. By analysing the light curves observed with the Transiting Exoplanet Survey Satellite (TESS), it has been detected that HL Dra is an Algol-like binary system with a mass ratio of 0.361, where the radius filling factor (=r/RL) of the primary and secondary component is $87\, {{\ \rm per\ cent}}$ and $98\, {{\ \rm per\ cent}}$, respectively. The secondary component is almost filling its critical Roche lobe, but not entirely. The absolute parameters of the component are estimated in this paper. Both the variable O’Connell effect and the existence of superflares indicate that the secondary should have strong magnetic activities. It is discovered that the O − C curve shows a sinusoidal variation with a period of 129.88 yr. This cyclic change might be caused by the effects of the light travel time as a result of the presence of a cool red dwarf third body. The correlations between the changes of the O − C diagrams and the variable O’Connell effect during TESS observations might be caused by the magnetic activity of the secondary (i.e. the Applegate mechanism). After removal of the binary model, a total of 252 pulsation frequencies are detected from the high-precision photometric data of TESS, including 28 multiplets of tidally split frequencies. We identify two radial modes, 21 non-radial p-modes and three non-radial f-modes from the possible independent frequencies. All of these features reveal that HL Dra is a very interesting system for further investigations of binary formation and evolution, and for tidal interactions on stellar pulsations and on magnetic activities.