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Using the Bayesian Analysis of Stellar Evolution-9 code and Gaia DR3, Pan-STARRS, and 2MASS data, we identify photometric binaries in 35 open clusters (OCs) and constrain their masses. We find a strong correlation between the binary fraction and cluster dynamical age and an even stronger correlation between core binary fraction and cluster dynamical age. We find that the binary mass-ratio (q) distribution of dynamically young OCs is statistically distinct from that of the old OCs. On average, dynamically young OCs display multimodalqdistributions rising toward unity and toward our detection limit ofq= 0.5 while more dynamically evolved clusters display more uniformqdistributions, often with a peak nearq= 1. Interestingly, the uniformqdistribution with a peak nearq= 1 is consistent with binaries in the field. We also observe a similar transition from multimodal to unimodalqdistributions when comparing low-mass to high-mass OCs in our sample. Finally, we find a correlation between the medianqof the binary population in a cluster and the cluster dynamical age. We interpret these results as an indication that dynamical encounters tend to increase the fraction of high-mass-ratio binaries within a given cluster—in particular within the cluster’s core, where stellar dynamics are likely more important. This may be the result of stellar exchanges that tend to produce binaries with largerqand/or the preferential disruption or evaporation of lower-qbinaries. 

We identify observational signatures suggesting a history of dynamical instability in 26 out of 34 M-dwarf multi-planet systems containing no large planets. These systems may have primarily formed in a gas-rich environment, potentially hosted more planets, and were more compact. We extend previous simulations of the formation of the TRAPPIST-1 system to 100 Myr to test the stability of these systems without gas. We find that the absence of a strong mean motion resonance in the innermost planet pair and the absence of three-body resonances throughout the system are likely to result in the merging and ejection of planets after the gas disk disperses. The runs that experience such an instability tend to produce final systems with lower multiplicities, period ratios larger than two, increased orbital spacings, higher planetary angular momentum deficits, and slightly smaller mass ratios between adjacent planets. Remarkably, we find these same trends in the observations of M-dwarf multi-planet systems containing no large planets. Our work allows us to identify specific systems that may have experienced an instability, and it suggests that only  ∼25% of these systems formed in their current observed state, while most systems were likely more compact and multiplicitous earlier in time. Previous research indicates that planets that have experienced a late-stage giant impact may potentially be more habitable than those that did not. With this in mind, we suggest systems around M-dwarfs that contain period ratios larger than two be given priority in the search for habitable worlds. 

Abstract We study the effects of general relativity (GR) on the evolution and alignment of circumbinary disks around binaries on all scales. We implement relativistic apsidal precession of the binary into the hydrodynamics codephantom. We find that the effects of GR can suppress the stable polar alignment of a circumbinary disk, depending on how the relativistic binary apsidal precession timescale compares to the disk nodal precession timescale. Studies of circumbinary disk evolution typically ignore the effects of GR, which is an appropriate simplification for low-mass or widely separated binary systems. In this case, polar alignment occurs, provided that the disks initial misalignment is sufficiently large. However, systems with a very short relativistic precession timescale cannot polar align and instead move toward coplanar alignment. In the intermediate regime where the timescales are similar, the outcome depends upon the properties of the disk. Polar alignment is more likely in the wavelike disk regime (where the disk viscosity parameter is less than the aspect ratio,α<H/r), since the disk is in good radial communication. In the viscous disk regime, disk breaking is more likely. Multiple rings can destructively interact with one another, resulting in short disk lifetimes and the disk moving toward coplanar alignment. Around main-sequence star or stellar mass black hole binaries, polar alignment may be suppressed far from the binary, but in general, the inner parts of the disk can align to polar. Polar alignment may be completely suppressed for disks around supermassive black holes for close binary separations. 

Abstract Mutually misaligned circumbinary planets may form in a warped or broken gas disk or from later planet–planet interactions. With numerical simulations and analytic estimates we explore the dynamics of two circumbinary planets with a large mutual inclination. A coplanar inner planet causes prograde apsidal precession of the binary and the stationary inclination for the outer planet is higher for larger outer planet orbital radius. In this case a coplanar outer planet always remains coplanar. On the other hand, a polar inner planet causes retrograde apsidal precession of the binary orbit and the stationary inclination is smaller for larger outer planet orbital radius. For a range of outer planet semimajor axes, an initially coplanar orbit is librating meaning that the outer planet undergoes large tilt oscillations. Circumbinary planets that are highly inclined to the binary are difficult to detect—it is unlikely for a planet to have an inclination below the transit detection limit in the presence of a polar inner planet. These results suggest that there could be a population of circumbinary planets that are undergoing large tilt oscillations.