TAPIR Seminar
Joel Ong
Hubble Fellow, Univ. of Hawaiʻi at Mānoa
September 13, 2024
(RHD simulations courtesy of Joel D. Tanner)
Convection excites
pressure waves (p-modes).
Power spectra of MDI dopplergrams
(roughly 5-minute oscillations)
p-mode frequencies satisfy
Stochastic,
broad-band
excitation
Evolved stars dominate our asteroseismic sample.
(e.g. only
Pressure waves (p-modes)
propagate isotropically.
Buoyancy waves (g-modes)
propagate anisotropically.
(proxy for age
Mixed modes exhibit
avoided crossings
between underlying p- and g-modes.
Pure p-modes:
Pure g-modes:
Mixed modes probe radial differential rotation
in two zones (core vs. envelope).
Cumulative sensitivity
pure g-mode pure p-mode
Mode mixing yields avoided crossings
between multiplet components of identical
(cf. Mosser+ 2012, Ouazzani+ 2013, Deheuvels+ 2017)
Brute-force numerical solution (quantitative)
vs
JWKB approximation (qualitative)
Energy eigenvalues and mixing coefficients are solutions to the
Generalised Hermitian Eigenvalue Problem
Mixed mode
frequencies and mixing coefficients can likewise be found by solving
the
Generalised Hermitian Eigenvalue Problem:
(Ong & Basu 2020)
(Ong & Basu 2020)
Rotation gives a Quadratic Hermitian Eigenvalue
Problem
(Ong et al. 2022):
Very high
but otherwise innocuous
But Kepler says
(and theory says so too…)
Rotational splittings from seismology:
Gaia RV scatter rules out
large RV semiamplitudes…
up to 99-day rotational period…
Remaining permissible orbits are
unstable to tidal dissipation!
From Huber et al. 2013
Mixed modes probe radial differential rotation
in two zones (core vs. envelope).
Cumulative sensitivity
Even the most p-dominated mixed modes
are sensitive to core rotation!
Cumulative sensitivity
From Huber et al. 2013
Caveats:
Model-dependence? Short Cadence?
Amplitudes? Linewidths?
Mixed modes may be described as
“acoustic molecular orbitals”:
Ong
& Basu 2020, ApJ, 898, 127
We find rapid rotation in Zvrk with seismology
(confirmed independently with TESS, ASAS-SN,
Chemical and dynamical constraints
strongly suggest an engulfment scenario.
Constraints on engulfment age (
Ong
et al. 2024, ApJ, 966, 42
We extend this formalism to the tensor product
of the radial and horizontal problem.
Application to Kepler-56 suggests internal
misalignment.
Follow-up Rossiter-McLaughlin RV measurements
may further constrain geometry.
A better understanding of gravitoacoustic
mixed modes, and how they respond to
rotation,
has permitted us to diagnose signatures of
planetary engulfment and core-envelope
misalignment.
For fixed
For fixed
Let’s associate with each mass shell at
(as is customary), and also an axis
specified by usual vector addition.
We only assume that the pure p- and g-mode
solutions
are separately amenable to separation of
variables;
the mixed-mode eigenfunctions need not be.
Rotational signal probably got
detrended away
by systematic corrections…
Very suggestive…
but is this real?
Probably yes!
Asteroseismology:
Photometry:
Spectroscopy:
Gaia DR3: