Resonant planetary systems contain at least one planet pair with orbital periods librating at a near-integer ratio (2/1, 3/2, 4/3, etc.) and are a natural outcome of standard planetary formation theories. Systems with multiple adjacent resonant pairs are known as resonant chains and can exhibit three-body resonances—characterized by a critical three-body angle. Here we study three-body angles as a diagnostic of resonant chains through tidally damped N-body integrations. For each combination of the 2:1, 3:2, 4:3, and 5:4 mean motion resonances (the most common resonances in the known resonant chains), we characterize the three-body angle equilibria for several mass schemes, migration timescales, and initial separations. We find that under our formulation of the three-body angle, which does not reduce coefficients, 180° is the preferred libration center, and libration centers shifted away from 180° are associated with nonadjacent resonances. We then relate these angles to observables, by applying our general results to two transiting systems: Kepler-60 and Kepler-223. For these systems, we compare N-body models of the three-body angle to the zeroth order in e approximation accessible via transit phases, used in previous publications. In both cases, we find the three-body angle during the Kepler observing window is not necessarily indicative of the long-term oscillations and stress the role of dynamical models in investigating three-body angles. We anticipate our results will provide a useful diagnostic in the analysis of resonant chains.

W49B is a supernova remnant (SNR) discovered over 60 yr ago in early radio surveys. It has since been observed over the entire wavelength range, with the X-ray morphology resembling a centrally filled SNR. The nature of its progenitor star is still debated. Applying Smoothed Particle Inference techniques to analyze the X-Ray emission from W49B, we characterize the morphology and abundance distribution over the entire remnant. We also infer the density structure and derive the mass of individual elements present in the plasma. The morphology is consistent with an interaction between the remnant and a dense medium along the eastern edge, and some obstruction toward the west. We find a total mass of 130 M and an estimated ejecta mass of 1.2 M . Comparison of the inferred abundance values and individual element masses with a wide selection of SN models suggests that deflagration-to-detonation (DDT) Type Ia models are the most compatible, with Fe abundance being the major discriminating factor. The general agreement between our abundance measurements and those from previous studies suggests that disagreement between various authors is more likely due to the choice of models used for comparison, rather than the abundance values themselves. While our abundance results lean toward a Type Ia origin, ambiguities in the interpretation of various morphological and spectral characteristics of W49B do not allow us to provide a definitive classification.

The discovery and characterization of extrasolar planets using radial velocity (RV) measurements is limited by noise sources from the surfaces of host stars. Current techniques to suppress stellar magnetic activity rely on decorrelation using an activity indicator (e.g., strength of the Ca ii lines, width of the cross-correlation function, broadband photometry) or measurement of the RVs using only a subset of spectral lines that have been shown to be insensitive to activity. Here, we combine the above techniques by constructing a high-signal-to-noise activity indicator, the depth metric  ( t ) , from the most activity-sensitive spectral lines using the “line-by-line” method of Dumusque (2018). Analogous to photometric decorrelation of RVs or Gaussian progress regression modeling of activity indices, time series modeling of  ( t ) reduces the amplitude of magnetic activity in RV measurements; in an αCenB RV time series from HARPS, the RV rms was reduced from 2.67 to 1.02 m s−1.  ( t ) modeling enabled us to characterize injected planetary signals as small as 1 m s−1. In terms of noise reduction and injected signal recovery,  ( t ) modeling outperforms activity mitigation via the selection of activity-insensitive spectral lines. For Sun-like stars with activity signals on the m s−1 level, the depth metric independently tracks rotationally modulated and multiyear stellar activity with a level of quality similar to that of the FWHM of the CCF and log R HK ′ . The depth metric and its elaborations will be a powerful tool in the mitigation of stellar magnetic activity, particularly as a means of connecting stellar activity to physical processes within host stars.

Misalignments between planetary orbits and the equatorial planes of their host stars are clues about the formation and evolution of planetary systems. Earlier work found evidence for a peak near 90° in the distribution of stellar obliquities, based on frequentist tests. We performed hierarchical Bayesian inference on a sample of 174 planets for which either the full three-dimensional stellar obliquity has been measured (72 planets) or for which only the sky-projected stellar obliquity has been measured (102 planets). We investigated whether the obliquities are best described by a Rayleigh distribution or by a mixture of a Rayleigh distribution representing well-aligned systems and a different distribution representing misaligned systems. The mixture models are strongly favored over the single-component distribution. For the misaligned component, we tried an isotropic distribution and a distribution peaked at 90° and found the evidence to be essentially the same for both models. Thus, our Bayesian inference engine did not find strong evidence favoring a “perpendicular peak,” unlike the frequentist tests. We also investigated selection biases that affect the inferred obliquity distribution, such as the bias of the gravity-darkening method against obliquities near 0° or 180°. Further progress in characterizing the obliquity distribution will probably require the construction of a more homogeneous and complete sample of measurements.

No abstract