Correction: Iriarte et al. A Unimodal/Bimodal Skew/Symmetric Distribution Generated from Lambert’s Transformation. Symmetry 2021, 13, 269

Iriarte, Yuri A.; Castro, Mário de; Gómez, Héctor W.

doi:10.3390/sym13122304

Cited by 1 publication

(2 citation statements)

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“…Here we adopt a flexible model introduced by Iriarte et al (2021) called the Lambert generalized bimodal (LGB) distribution, which was developed to introduce skewness to the generalized bimodal distribution. The LGB distribution has four parameters: the location parameter µ (defined for all real numbers), the scale parameter σ (defined for positive numbers), and the shape parameters γ (defined over [0, 2)) and α (defined over (0, e), where e is Euler's constant).…”

Section: The Underlying Distribution Of ∆I With Hierarchical Bayesian...mentioning

confidence: 99%

“…The LGB distribution has four parameters: the location parameter µ (defined for all real numbers), the scale parameter σ (defined for positive numbers), and the shape parameters γ (defined over [0, 2)) and α (defined over (0, e), where e is Euler's constant). Depending on these parameters, the LGB distribution can be unimodal, bimodal, symmetric, or asymmetric; examples of the diversity of shapes can be seen in Figure 1 of Iriarte et al (2021). γ controls the bimodality of the distribution, and α determines the relative heights of the bimodal peaks or unimodal asymmetry.…”

Section: The Underlying Distribution Of ∆I With Hierarchical Bayesian...mentioning

confidence: 99%

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Rotation Periods, Inclinations, and Obliquities of Cool Stars Hosting Directly Imaged Substellar Companions: Spin-Orbit Misalignments are Common

Bowler¹,

Tran²,

Zhang³

et al. 2023

Preprint

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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 (∆i). 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 ∆i. Eleven of these (52 +10 −11 % of the sample) are likely misaligned, while the remaining ten host stars are consistent with spin-orbit alignment. As an ensemble, the minimum obliquity distribution between 10-250 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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Section: The Underlying Distribution Of ∆I With Hierarchical Bayesian...mentioning

confidence: 99%

Section: The Underlying Distribution Of ∆I With Hierarchical Bayesian...mentioning

confidence: 99%

Rotation Periods, Inclinations, and Obliquities of Cool Stars Hosting Directly Imaged Substellar Companions: Spin-Orbit Misalignments are Common

Bowler¹,

Tran²,

Zhang³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Correction: Iriarte et al. A Unimodal/Bimodal Skew/Symmetric Distribution Generated from Lambert’s Transformation. Symmetry 2021, 13, 269

Abstract: In the original article [...]

Cited by 1 publication

References 2 publications

Rotation Periods, Inclinations, and Obliquities of Cool Stars Hosting Directly Imaged Substellar Companions: Spin-Orbit Misalignments are Common

Rotation Periods, Inclinations, and Obliquities of Cool Stars Hosting Directly Imaged Substellar Companions: Spin-Orbit Misalignments are Common

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