No period change in two long-period AM CVn binaries

Ultracompact binary systems, consisting of two compact objects in an orbit ≲ 0.5R_⊙⁠, should exhibit measurable rates of orbital period change (⁠P ≠ O⁠) due to the emission of gravitational waves (GWs). Measurements of
have so far been limited to the shortest-period ultracompact binaries (⁠≲ 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 ≲ 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
consistent with zero within 2σ⁠. Their 3σ upper limits are 1.1 x 10¹³ s s^-1 and 9.7 x 10¹⁴s 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 P whose time-scales span decades but whose amplitude is ≲ 10¹³s s^-1⁠. Our non-detections of P represent a limit on the strength of any enhanced angular momentum loss beyond pure GW emission.