{"title":"C","authors":"P. O. Brasil, D. Nesvorný, R. Gomes","doi":"10.1017/9781139018159.004","DOIUrl":"https://doi.org/10.1017/9781139018159.004","url":null,"abstract":"Doppler and transit observations of exoplanets show a pile-up of Jupiter-size planets in orbits with a 3 day period. A fraction of these hot Jupiters have retrograde orbits with respect to the parent star’s rotation, as evidenced by the measurements of the Rossiter–McLaughlin effect. To explain these observations we performed a series of numerical integrations of planet scattering followed by the tidal circularization and migration of planets that evolved into highly eccentric orbits. We considered planetary systems having three and four planets initially placed in successive mean-motion resonances, although the angles were taken randomly to ensure orbital instability in short timescales. The simulations included the tidal and relativistic effects, and precession due to stellar oblateness. Our results show the formation of two distinct populations of hot Jupiters. The inner population (Population I) is characterized by semimajor axis a < 0.03 AU and mainly formed in the systems where no planetary ejections occurred. Our follow-up integrations showed that this population was transient, with most planets falling inside the Roche radius of the star in <1 Gyr. The outer population of hot Jupiters (Population II) formed in systems where at least one planet was ejected into interstellar space. This population survives the effects of tides over >1 Gyr and fits nicely the observed 3 day pile-up. A comparison between our three-planet and four-planet runs shows that the formation of hot Jupiters is more likely in systems with more initial planets. Due to the large-scale chaoticity that dominates the evolution, high eccentricities and/or high inclinations are generated mainly by close encounters between the planets and not by secular perturbations (Kozai or otherwise). The relative proportion of retrograde planets seems of be dependent on the stellar age. Both the distribution of almost aligned systems and the simulated 3 day pile-up also fit observations better in our four-planet simulations. This may suggest that the planetary systems with observed hot Jupiters were originally rich in the number of planets, some of which were ejected. In a broad perspective, our work therefore hints on an unexpected link between the hot Jupiters and recently discovered free floating planets.","PeriodicalId":312352,"journal":{"name":"The Cambridge Kant Lexicon","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132935079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"I","authors":"I. Verwendungsrichtlinien","doi":"10.1017/9781139018159.010","DOIUrl":"https://doi.org/10.1017/9781139018159.010","url":null,"abstract":"Diese Richtlinien sind Bestandteil der Bewilligung. Sie gelten für die drei Förderlinien \"Exzellenzcluster\", \"Graduiertenschulen\" und \"Zukunftskonzepte\" (im Folgenden: \"Exzellenzeinrichtungen\") gleichermaßen. Sie sind verbindlich, soweit in den Bewilligungsschreiben nicht ausdrücklich etwas anderes festgelegt ist. Sie sind von der Hochschule und dem Sprecher der Exzellenzeinrichtung bei der ersten Mittelanforderung anzuerkennen.","PeriodicalId":312352,"journal":{"name":"The Cambridge Kant Lexicon","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122095335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A","authors":"Solusi, Gambar","doi":"10.1017/9781139018159.002","DOIUrl":"https://doi.org/10.1017/9781139018159.002","url":null,"abstract":"Parametric Linear Programming is a development model of sensitivity analysis in which the inputs coefficient changes simultaneously. This model develops problem-solving in which the input coefficients are not definitely known, but it can be estimated within a certain interval according to the expected level of confidence. This paper outlines the benefits of Parametric Linear Programming to analyze the fluctuations impact of the objective function coefficients and constants of the optimal solution. It was proven that the input coefficient change at certain intervals did not alter the optimal solution that has been obtained previously.","PeriodicalId":312352,"journal":{"name":"The Cambridge Kant Lexicon","volume":"37 26","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120865517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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