Modulation of the Blazhko Cycle in LS Her

We present analysis of the RR Lyrae star, LS Her and confirm the previously reported modulation to its Blazhko cycles. We performed Fourier analysis on two sectors (Sector 24 & 25) of data from the Transiting Exoplanet Survey Satellite (TESS) spanning 53 days. We find LS Her to have a primary pulsation period of 0.2308 d and a Blazhko period of 12.7 d in keeping with previously reported results. We also identified side-band frequencies around the Blazhko multiplets suggesting the Blazhko cycle is modulated on a time scale of 112 days. Analysis of the Blazhko effect using the TESS data clearly shows a changing amplitude and phase throughout the four Blazhko cycles. We compared our modeled results, which were based on our TESS frequency analysis, to TESS data (Sector 51) taken ~700 days later and found our modulation model was not a good representation of the data. We then coupled our TESS analysis with the modulation frequency results from Wils et al. (MNRAS 387 (2008) 783-787) and found excellent agreement with the Sector 51 data. To further test this result we obtained ground-based, V-magnitude observations of LS Her in the summer of 2022. This data also showed excellent agreement with our coupled modulation model. We have verified that LS Her is a Blazhko star with a modulated Blazhko period of 109 days, stability over the 862 days of observations, and possible stability lasting over 15 years. We discuss the ramifications of the modulation for other Blazhko stars that show Blazhko effect changes over time.