Mode Mixing and Rotational Splittings. II. Reconciling Different Approaches to Mode Coupling
In the mixed-mode asteroseismology of subgiants and red giants, the coupling between the p- and g- mode cavities must be understood well in order to derive localized estimates of interior rotation from measurements of mode multiplet rotational splittings. There exist now two different descriptions o...
| Hlavní autoři: | , |
|---|---|
| Médium: | Článek |
| Jazyk: | English |
| Vydáno: |
IOP Publishing
2023-01-01
|
| Edice: | The Astrophysical Journal |
| Témata: | |
| On-line přístup: | https://doi.org/10.3847/1538-4357/acbf2f |
| _version_ | 1827830855451541504 |
|---|---|
| author | J. M. Joel Ong Charlotte Gehan |
| author_facet | J. M. Joel Ong Charlotte Gehan |
| author_sort | J. M. Joel Ong |
| collection | DOAJ |
| description | In the mixed-mode asteroseismology of subgiants and red giants, the coupling between the p- and g- mode cavities must be understood well in order to derive localized estimates of interior rotation from measurements of mode multiplet rotational splittings. There exist now two different descriptions of this coupling: one based on an asymptotic quantization condition, and the other arising from the coupling matrices associated with “acoustic molecular orbitals.” We examine the analytic properties of both, and derive closed-form expressions for various quantities—such as the period-stretching function τ —which previously had to be solved for numerically. Using these, we reconcile both formulations for the first time, deriving relations by which quantities in each formulation may be translated to and interpreted within the other. This yields an information criterion for whether a given configuration of mixed modes may meaningfully constrain the parameters of the asymptotic construction, which is likely not satisfied by the majority of first-ascent red giant stars in our observational sample. Since this construction has been already used to make rotational measurements of such red giants, we examine—through a hare-and-hounds exercise—whether, and how, such limitations affect these existing measurements. While averaged estimates of core rotation seem fairly robust, template-matching using the asymptotic construction has difficulty reliably assigning rotational splittings to individual multiplets, or estimating the mixing fractions ζ of the most p -dominated mixed modes, where such estimates are most needed. We finally discuss implications for extending the two-zone model of radial differential rotation, e.g., via rotational inversions, with these methods. |
| first_indexed | 2024-03-12T04:34:34Z |
| format | Article |
| id | doaj.art-24f242d869b543e387b1d35f945b1689 |
| institution | Directory Open Access Journal |
| issn | 1538-4357 |
| language | English |
| last_indexed | 2024-03-12T04:34:34Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | The Astrophysical Journal |
| spelling | doaj.art-24f242d869b543e387b1d35f945b16892023-09-03T09:56:32ZengIOP PublishingThe Astrophysical Journal1538-43572023-01-0194629210.3847/1538-4357/acbf2fMode Mixing and Rotational Splittings. II. Reconciling Different Approaches to Mode CouplingJ. M. Joel Ong0https://orcid.org/0000-0001-7664-648XCharlotte Gehan1https://orcid.org/0000-0002-0833-7084Institute for Astronomy, University of Hawai’i , 2680 Woodlawn Drive, Honolulu, HI 96822, USA ; joelong@hawaii.edu; Department of Astronomy, Yale University , 52 Hillhouse Avenue, New Haven, CT 06511, USAMax-Planck-Institut für Sonnensystemforschung , Justus-von-Liebig-Weg 3, D-37077 Göttingen, Germany; Instituto de Astrofíca e Ciências do Espaço Universidade do Porto , CAUP, Rua das Estrelas, PT4150-762 Porto, PortugalIn the mixed-mode asteroseismology of subgiants and red giants, the coupling between the p- and g- mode cavities must be understood well in order to derive localized estimates of interior rotation from measurements of mode multiplet rotational splittings. There exist now two different descriptions of this coupling: one based on an asymptotic quantization condition, and the other arising from the coupling matrices associated with “acoustic molecular orbitals.” We examine the analytic properties of both, and derive closed-form expressions for various quantities—such as the period-stretching function τ —which previously had to be solved for numerically. Using these, we reconcile both formulations for the first time, deriving relations by which quantities in each formulation may be translated to and interpreted within the other. This yields an information criterion for whether a given configuration of mixed modes may meaningfully constrain the parameters of the asymptotic construction, which is likely not satisfied by the majority of first-ascent red giant stars in our observational sample. Since this construction has been already used to make rotational measurements of such red giants, we examine—through a hare-and-hounds exercise—whether, and how, such limitations affect these existing measurements. While averaged estimates of core rotation seem fairly robust, template-matching using the asymptotic construction has difficulty reliably assigning rotational splittings to individual multiplets, or estimating the mixing fractions ζ of the most p -dominated mixed modes, where such estimates are most needed. We finally discuss implications for extending the two-zone model of radial differential rotation, e.g., via rotational inversions, with these methods.https://doi.org/10.3847/1538-4357/acbf2fAsteroseismologyStellar oscillationsRed giant starsTheoretical techniquesComputational methods |
| spellingShingle | J. M. Joel Ong Charlotte Gehan Mode Mixing and Rotational Splittings. II. Reconciling Different Approaches to Mode Coupling The Astrophysical Journal Asteroseismology Stellar oscillations Red giant stars Theoretical techniques Computational methods |
| title | Mode Mixing and Rotational Splittings. II. Reconciling Different Approaches to Mode Coupling |
| title_full | Mode Mixing and Rotational Splittings. II. Reconciling Different Approaches to Mode Coupling |
| title_fullStr | Mode Mixing and Rotational Splittings. II. Reconciling Different Approaches to Mode Coupling |
| title_full_unstemmed | Mode Mixing and Rotational Splittings. II. Reconciling Different Approaches to Mode Coupling |
| title_short | Mode Mixing and Rotational Splittings. II. Reconciling Different Approaches to Mode Coupling |
| title_sort | mode mixing and rotational splittings ii reconciling different approaches to mode coupling |
| topic | Asteroseismology Stellar oscillations Red giant stars Theoretical techniques Computational methods |
| url | https://doi.org/10.3847/1538-4357/acbf2f |
| work_keys_str_mv | AT jmjoelong modemixingandrotationalsplittingsiireconcilingdifferentapproachestomodecoupling AT charlottegehan modemixingandrotationalsplittingsiireconcilingdifferentapproachestomodecoupling |