Potential Tertiary Effects on the LISA Verification Binary HM Cancri

Two groups recently analyzed the long-term orbital evolution of HM Cancri, which is one of the most important verification binaries for the space gravitational wave detector LISA. By using the reported first and second derivatives of its orbital frequency $f$, we discuss potential tertiary effects on this binary. We found that, in contrast to the first derivative $\dot{f}$, the second derivative $\ddot{f}$ might be strongly affected by a dark tertiary component such as an old white dwarf with an outer orbital period of $\sim$250 years.