Potential Tertiary Effects on the LISA Verification Binary HM Cancri

TL;DR

This paper investigates how a dark tertiary companion, like an old white dwarf, could influence the long-term orbital evolution of the HM Cancri binary, a key LISA verification source, especially affecting its second derivative of orbital frequency.

Contribution

It introduces the possibility that a dark tertiary object significantly impacts the orbital frequency derivatives of HM Cancri, highlighting a new factor in gravitational wave source modeling.

Findings

The second derivative of the orbital frequency may be strongly affected by a tertiary companion.

A dark tertiary object with a ~250-year orbit could influence the binary's orbital evolution.

The first derivative of the orbital frequency is less affected by tertiary effects.

Abstract

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.