New Techniques for Rotational Measurements from Mixed-Mode Asteroseismology
AAS 241
12 January 2023
Why Rotation?
- Gyrochronology: rotation gives ages (e.g. Skumanich 1972).
- Rotation tells us about stellar activity (e.g. Noyes+ 1984)
- Rotation needed to fully explain stellar evolution (e.g. Pinsonneault+ 1992)
Almost all rotational measurements are at the stellar
surface.
Interior rotation is much more poorly constrained.
(sun-like star)
Spectroscopic \(v \sin i\):
\(\sim \text{PHz}\) regime \(\to\)
Photometric \(P_\text{rot}\):
\(\ll 1\ \mu\text{Hz}\)
\(\downarrow\)
Mode mixing yields avoided crossings
between multiplet components of identical \(m\)
(cf. Mosser+ 2012, Ouazzani+ 2013, Deheuvels+ 2017)
\[\small\psi_\text{mol} = {\color{blue}\sum_i c_{1,i} \psi_{1,i}} + {\color{orange}\sum_j c_{2,j} \psi_{2,j}}\]
\[\iff\]
\[\small\vec{\xi}_\text{mixed} \sim {\color{grey}
\sum_i c_{\pi, i} \vec{\xi}_{\pi,i}} + {\color{red} \sum_j c_{\gamma, j}
\vec{\xi}_{\gamma,j}}\]
(Ong & Basu 2020)
Ong, Bugnet & Basu (2022):
generalisation to include rotational effects
Reggae
Stretched Echelle Power Diagrams
Cross-Correlation Functions
\[ CCF(C_\text{mag}, \delta\nu_\text{rot}) = \int \mathrm{PS}(\nu) \cdot \sum_j \delta(\nu - \tau^{-1}(\nu_j - m \delta\nu_\text{rot})) \mathrm d \nu \]
