No period change in two long-period AM CVn binaries

Ultracompact binary systems, consisting of two compact objects in an orbit $\lesssim 0.5 {\rm R}_\odot$, should exhibit measurable rates of orbital period change ($\dot{P} \ne 0$) due to the emission of gravitational waves (GWs). Measurements of $\dot{P}$ have so far been limited to the shortest-period ultracompact binaries ($\lesssim 20$  min). Among the AM CVn-type subclass, several works have proposed the presence of extra angular momentum loss beyond GW emission, with magnetic braking being a widely discussed mechanism. If present, this magnetic braking would dominate the angular momentum loss of AM CVn-type binaries with orbital periods $\gtrsim 30$ min. In this work, we present a long-term eclipse timing study of two AM CVn-type binaries, YZ LMi and Gaia14aae, with respective orbital periods of 28.3 min and 49.7 min and continuous observations since 2006 and 2015. Both systems show $\dot{P}$ consistent with zero within $2\sigma$. Their $3\sigma$ upper limits are $1.1 \times 10^{-13}\, {\rm s \, s}^{-1}$ and $9.7 \times 10^{-14}\, {\rm s \, s}^{-1}$, respectively. These non-detections are most simply explained by a scenario in which secular angular momentum loss is not substantially stronger than GW emission at all orbital periods, but is combined with deviations from the secular $\dot{P}$ whose time-scales span decades but whose amplitude is $\lesssim 10^{-13}\, {\rm s \, s}^{-1}$. Our non-detections of $\dot{P}$ represent a limit on the strength of any enhanced angular momentum loss beyond pure GW emission.