Rosette modes of oscillations of rotating stars caused by close degeneracies. III. JWKB analysis

Takata Masao

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Rosette modes of oscillations of rotating stars caused by close degeneracies. III. JWKB analysis

机译：由近乎简并性引起的旋转星振荡的玫瑰花模式。三， JWKB分析

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Anasymptoticanalysisisdevelopedtodescriberosettemodesofoscillationsinrotatingstars,whichhavebeenrecentlydiscoveredinnumericalcomputations.Thenameofthemodescomesfromcharacteristicrosettepatternsofthedistributionsofthekinetic-energydensityonthemeridionalplane.Ashavebeenshowninthepreviouspapersinthisseries,thephysicalreasonfortheformationofthesemodesistherotation-inducedinteractionamongseveralgravitymodeswithalmostthesamefrequenciesandsuccessivesphericaldegreesofthesameparity.Thisformationprocessisdescribedintheframeworkofthequasi-degenerateperturbationtheory.Inthispaper,thematrixeigenvalueproblem,whichappearsintheperturbationanalysis,issolvedanalytically,usingasymptoticexpressionsofeigenfunctions,whichareobtainedbyassumingthatthewavelengthofoscillationsinthehorizontaldirectionissufficientlysmall.Byfurtherassumingthatthenumberofinteractingmodesislarge,simpleexpressionsoftheeigenfunctionsandeigenfrequenciesofrosettemodesareobtained.Becausetheseexpressionscandescribetheessentialpartofcharacteristicsofrosettemodes,theyareusefulinunderstandinggeneralpropertiesofrosettemodesthatarecommontoanyequilibriumstructure.

机译：Anasymptoticanalysisisdevelopedtodescriberosettemodesofoscillationsinrotatingstars，whichhavebeenrecentlydiscoveredinnumericalcomputations.Thenameofthemodescomesfromcharacteristicrosettepatternsofthedistributionsofthekinetic-energydensityonthemeridionalplane.Ashavebeenshowninthepreviouspapersinthisseries，thephysicalreasonfortheformationofthesemodesistherotation-inducedinteractionamongseveralgravitymodeswithalmostthesamefrequenciesandsuccessivesphericaldegreesofthesameparity.Thisformationprocessisdescribedintheframeworkofthequasi-degenerateperturbationtheory.Inthispaper，thematrixeigenvalueproblem，whichappearsintheperturbationanalysis，issolvedanalytically，usingasymptoticexpressionsofeigenfunctions，whichareobtainedbyassumingthatthewavelengthofoscillationsinthehorizontaldirectionissufficientlysmall.Byfurtherassumingthatthenumberofinteractingmodesislarge，simpleexpressionsoftheeigenfunctionsandeigenfrequenciesofrosettemodesareobtained.Becausetheseexpressionscandescribetheessentialpartofcharac立体模式，在理解平衡结构常见的线性模式的一般特性时很有用。

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《PASJ: Publications of the Astronomical Society of Japan》 |2014年第4期|共页
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Takata Masao;
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Rosette modes of oscillations of rotating stars caused by close degeneracies. III. JWKB analysis

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