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1. Modeling the Free Inclinations of the Classical Kuiper Belt with the von Mises–Fisher Distribution

   https://doi.org/10.3847/2515-5172/ace4c3  

   Malhotra, Renu ; Roy, Supriya ( July 2023 , Research Notes of the AAS)

   The orientations of orbital planes of minor planets are directional random variables. Their free inclination is the deviation of the orbit plane from the plane forced by the major planets. We construct a model of the distribution of free inclinations of classical Kuiper Belt objects (CKBOs) based on the von Mises–Fisher (vMF) distribution function, the analog of the normal distribution for directional statistics. The CKBOs are known to have a “cold” component of orbit planes concentrated near the forced plane and a more widely dispersed “hot” component. Adopting a model with a linear combination of two vMF functions, we find that the cold and hot components account for 57% and 43%, characterized by widths of 1.°7 and 12.°9, respectively. This model improves upon previous models based on smaller observational samples and empirical choices of functional forms for inclination distributions.

    

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2. Refining the Stellar Parameters of τ Ceti: a Pole-on Solar Analog

   https://doi.org/10.3847/1538-3881/ace906  

   Korolik, Maria ; Roettenbacher, Rachael M. ; Fischer, Debra A. ; Kane, Stephen R. ; Perkins, Jean M. ; Monnier, John D. ; Davies, Claire L. ; Kraus, Stefan ; Le Bouquin, Jean-Baptiste ; Anugu, Narsireddy ; et al ( August 2023 , The Astronomical Journal)

   To accurately characterize the planets a star may be hosting, stellar parameters must first be well determined.τCeti is a nearby solar analog and often a target for exoplanet searches. Uncertainties in the observed rotational velocities have made constrainingτCeti’s inclination difficult. For planet candidates from radial velocity (RV) observations, this leads to substantial uncertainties in the planetary masses, as only the minimum mass ($m\sin i$) can be constrained with RV. In this paper, we used new long-baseline optical interferometric data from the CHARA Array with the MIRC-X beam combiner and extreme precision spectroscopic data from the Lowell Discovery Telescope with EXPRES to improve constraints on the stellar parameters ofτCeti. Additional archival data were obtained from a Tennessee State University Automatic Photometric Telescope and the Mount Wilson Observatory HK project. These new and archival data sets led to improved stellar parameter determinations, including a limb-darkened angular diameter of 2.019 ± 0.012 mas and rotation period of 46 ± 4 days. By combining parameters from our data sets, we obtained an estimate for the stellar inclination of 7° ± 7°. This nearly pole-on orientation has implications for the previously reported exoplanets. An analysis of the system dynamics suggests that the planetary architecture described by Feng et al. may not retain long-term stability for low orbital inclinations. Additionally, the inclination ofτCeti reveals a misalignment between the inclinations of the stellar rotation axis and the previously measured debris disk rotation axis (i_disk= 35° ± 10°).

    

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3. Free Inclinations for Trans-Neptunian Objects in the Main Kuiper Belt

   https://doi.org/10.3847/1538-4365/ac559a  

   Huang, Yukun ; Gladman, Brett ; Volk, Kathryn ( April 2022 , The Astrophysical Journal Supplement Series)

   There is a complex inclination structure present in the trans-Neptunian object (TNO) orbital distribution in the main classical-belt region (between orbital semimajor axes of 39 and 48 au). The long-term gravitational effects of the giant planets make TNO orbits precess, but nonresonant objects maintain a nearly constant “free” inclination (I_free) with respect to a local forced precession pole. Because of the likely cosmogonic importance of the distribution of this quantity, we tabulate free inclinations for all main-belt TNOs, each individually computed using barycentric orbital elements with respect to each object’s local forcing pole. We show that the simplest method, based on the Laplace–Lagrange secular theory, is unable to give correct forcing poles for objects near theν₁₈secular resonance, resulting in poorly conservedI_freevalues in much of the main belt. We thus instead implemented an averaged Hamiltonian to obtain the expected nodal precession for each TNO, yielding significantly more accurate free inclinations for nonresonant objects. For the vast majority (96%) of classical-belt TNOs, theseI_freevalues are conserved to < 1° over 4 Gyr numerical simulations, demonstrating the advantage of using this well-conserved quantity in studies of the TNO population and its primordial inclination profile; our computed distributions only reinforce the idea of a very coplanar surviving “cold” primordial population, overlain by a largeI-width implanted “hot” population.

    

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4. Rotation Periods, Inclinations, and Obliquities of Cool Stars Hosting Directly Imaged Substellar Companions: Spin–Orbit Misalignments Are Common

   https://doi.org/10.3847/1538-3881/acbd34  

   Bowler, Brendan P. ; Tran, Quang H. ; Zhang, Zhoujian ; Morgan, Marvin ; Ashok, Katelyn B. ; Blunt, Sarah ; Bryan, Marta L. ; Evans, Analis E. ; Franson, Kyle ; Huber, Daniel ; et al ( March 2023 , The Astronomical Journal)

   The orientation between a star’s spin axis and a planet’s orbital plane provides valuable information about the system’s formation and dynamical history. For non-transiting planets at wide separations, true stellar obliquities are challenging to measure, but lower limits on spin–orbit orientations can be determined from the difference between the inclination of the star’s rotational axis and the companion’s orbital plane (Δi). We present results of a uniform analysis of rotation periods, stellar inclinations, and obliquities of cool stars (SpT ≳ F5) hosting directly imaged planets and brown dwarf companions. As part of this effort, we have acquired new$v\sin i_{*}$values for 22 host stars with the high-resolution Tull spectrograph at the Harlan J. Smith telescope. Altogether our sample contains 62 host stars with rotation periods, most of which are newly measured using light curves from the Transiting Exoplanet Survey Satellite. Among these, 53 stars have inclinations determined from projected rotational and equatorial velocities, and 21 stars predominantly hosting brown dwarfs have constraints on Δi. Eleven of these (52${}_{-11}^{+10}$% of the sample) are likely misaligned, while the remaining 10 host stars are consistent with spin–orbit alignment. As an ensemble, the minimum obliquity distribution between 10 and 250 au is more consistent with a mixture of isotropic and aligned systems than either extreme scenario alone—pointing to direct cloud collapse, formation within disks bearing primordial alignments and misalignments, or architectures processed by dynamical evolution. This contrasts with stars hosting directly imaged planets, which show a preference for low obliquities. These results reinforce an emerging distinction between the orbits of long-period brown dwarfs and giant planets in terms of their stellar obliquities and orbital eccentricities.

    

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5. Von Zeipel – Lidov – Kozai cycles in action: Kepler triples with eclipse depth variations: KICs 6964043, 5653126, 5731312, and 8023317

   https://doi.org/10.1093/mnras/stac1983  

   Borkovits, T. ; Rappaport, S. A. ; Toonen, S. ; Moe, M. ; Mitnyan, T. ; Csányi, I. ( July 2022 , Monthly Notices of the Royal Astronomical Society)

   We report the results of the photodynamical analyses of four compact, tight triple stellar systems, KICs 6964043, 5653126, 5731312, and 8023317, based largely on Kepler and TESS data. All systems display remarkable eclipse timing and eclipse depth variations, the latter implying a non-aligned outer orbit. Moreover, KIC 6964043 is also a triply eclipsing system. We combined photometry, ETV curves, and archival spectral energy distribution data to obtain the astrophysical parameters of the constituent stars and the orbital elements with substantial precision. KICs 6964043 and 5653126 were found to be nearly flat with mutual inclinations imut = 4${_{.}^{\circ}}$1 and 12${_{.}^{\circ}}$3, respectively, while KICs 5731312 and 8023317 (imut = 39${_{.}^{\circ}}$4 and 55${_{.}^{\circ}}$7, respectively) are found to lie in the high imut regime of the von Zeipel-Kozai-Lidov (ZKL) theorem. We show that, currently, both high inclination triples exhibit observable unusual retrograde apsidal motion. Moreover, the eclipses will disappear in all but one of the four systems within a few decades. Short-term numerical integrations of the dynamical evolution reveal that both high inclination triples are currently subject to ongoing, large amplitude (Δe ∼ 0.3) inner eccentricity variations on centuries-long time-scales, in accord with the ZKL theorem. Longer-term integrations predict that two of the four systems may become dynamically unstable on ∼ Gyr time-scales, while in the other two triples common envelope phases and stellar mergers may occur. Finally, we investigate the dynamical properties of a sample of 71 KIC/TIC triples statistically, and find that the mutual inclinations and outer mass ratios are anticorrelated at the 4σ level. We discuss the implications for the formation mechanisms of compact triples.

    

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