Research
Theoretical Asteroseismology
Stars are made of fluids, and (small) perturbations to this fluid may propagate as sound waves. Waves of certain shapes may constructively interfere with themselves when they resonate at certain characteristic frequencies associated with the structure of the star, yielding a normal mode of oscillation at each frequency where this is possible. Since stars are (mostly) spherically symmetric, the shapes of these normal modes can be described by spherical harmonics, indexed by quantum numbers \(l\) and \(m\), in addition to their radial order \(n\). We measure these normal-mode frequencies using time-series observations of stellar surfaces.
Observationally, some stars (like the Sun) show normal-mode frequencies which approximately satisfy a “comb” parameterisation: \[\nu_{n\ell m} = \Delta\nu\left(n + {\ell \over 2} + \epsilon_{\ell m}(\nu)\right),\] where \(\Delta\nu\) is called the “large frequency separation”. This is what we would expect for sound waves (“p-modes”, because pressure provides the restoring force) in a spherically-shaped resonant mode cavity, where a more or less constant overtone spacing emerges, given by the sound-crossing time. \(\epsilon_{\ell m}(\nu)\) is a function of frequency that specifies the eigenvalues for a given pair of \(\ell, m\), and containes information about how the star’s internal structure differs from being a truly homogenous “spherical mode cavity”.
On the other hand, some other normal-mode frequencies satisfy a converse eigenvalue relation, \[{1 \over \nu_{n\ell m}} = \Delta\Pi_\ell\left(n + {\ell \over 2} + \epsilon_{\ell m}(\nu)\right),\] where it is the mode periods, rather than frequencies, which have a characteristic “undertone” period spacing relative to the fundamental mode. Waves of this kind are buoyancy waves (“g-modes”, because gravity provides the restoring force), not unlike those which you might see on the surface of a body of water, or reflected in the undulatory motions of clouds in the atmosphere.
Accurate measurement of these eigenvalues requires quite long observational campaigns. Often, the only quantities that are directly accessible are average values of \(\Delta\nu\) and \(\epsilon\), as well as a characteristic excitation frequency called \(\nu_\text{max}\). Moreover, many unconstrained aspects of stellar surface astrophysics (e.g. global magnetic activity, radiative turbulence) enter into the boundary problem via the choice of surface boundary conditions. These perturb theoretical results relative to the frequencies observed in real stars.
Much of my research pertains to understanding, analytically, how these two kinds of normal modes relate to the internal structures of stars, react to each other, and respond to perturbations not captured in our computational modelling. Recent highlights include:
- Constructing integral estimators of various seismic diagnostics for stellar structure and evolution;
- Deriving a weak-interaction limit (and corresponding scattering-matrix elements) to describe the coupling of different mode cavities in evolved stars, via analogies with few-body quantum mechanics.
- Understanding how multicavity oscillations might be used to probe various aspects of stellar rotation and internal structure.
Selected Publications:
- Ong, J. M. J., & Basu, S. 2020, ApJ, 898, 127 — Hybridisation of standing waves
- Ong, J. M. J., et al. 2021, ApJ, 920, 8 — Avoided crossings and perturbation theory
- Ong, J. M. J., et al. 2022, ApJ, 940, 18 — Avoided crossings in rotating stars
- Ong, J. M. J., & Gehan, C. 2023, ApJ, 946, 92 — Translating between coupling matrices and JWKB analysis
Asteroseismology as a Tool
Astronomers are often more interested in the inverse problem: that is, in inferring properties of a star given a set of observed oscillation frequencies. For example, we might infer masses, radii, and ages by comparing these mode frequencies against computational models of stellar structure. Alternatively, we might infer rotation rates and magnetic field strengths, if we are able to examine how modes of different \(m\) pulsate at different frequencies.
Some of my recent work involves using these diagnostics of internal rotation to make interesting inferences about interactions between stars and their interactions with companions (e.g. planets). Highlights of this include a chemically anomalous, rapidly-rotating, planet-engulfment candidate, as well as a red giant whose core and envelope rotate separately around axes pointing in different directions.
For the past few years, I’ve also been working on results from the NASA Transiting Exoplanet Survey Satellite (TESS) mission through the TESS Asteroseismic Science Consortium (TASC) (in working groups 1 and 2), helping to constrain the global properties and interior structures of these stars in this manner. For this purpose, I am both a methodologist and a practitioner: I develop and investigate methods used in deriving these constraints, as well as actually perform the calculations for actual stars. I’m glad to be able to make contributions to such a large collaboration. Interesting stars I’ve studied on include:
- TOI-197, which formed the basis of the first TESS asteroseismology paper since other people found a “hot Saturn” exoplanet around it
- ν Indi, a metal-poor but otherwise chemically enriched star with unusual kinematic properties, which was observed with TESS
- KIC 8144907, perhaps the most metal-poor star whose age we have pinned down using asteroseismology
Selected Publications:
- Ong, J. M. J., et al. 2024, ApJ, 966, 42 — A rapidly-rotating planet-engulfment candidate
- Ong, J. M. J., submitted to ApJ — Kepler-56, whose core and envelope rotate around different axes
Extreme Precision Radial Velocity (EPRV) Instrumentation
The tale of exoplanet detection and discovery is long and storied, but the oldest and still most reliable way of detecting planets, and measuring their masses, is through the radial velocity method, which requires spectroscopic characterisation. As planets orbit their stars, they exert an opposite gravitational pull on the star that causes it to also orbit (much more slowly) their common centre of mass, moving towards and then away from us over time. From Earth, we are able to measure this time-varying reflex velocity by the Doppler shift it induces on stellar spectra.
These measurements are made on high-resolution spectrographs. One of them, the EXtreme PREcision Spectrograph, was built at Yale. I wrote parts of its calibration and analysis software, including its template cross-correlation-function (CCF) radial velocity code, and various infrastructural components of its automated optimal-extraction data reduction pipeline.
While the ultimate goal of EXPRES is, of course, to discover long-period, low-mass planets with the radial-velocity method that would otherwise not be accessible to short-baseline space photometry, the high-resolution spectra returned from this process are very useful for other purposes. One example of this is Doppler imaging of active stellar surface, which can be further refined by way of joint constraints with contemporaneous photometry.
More recently, I’ve become a regular observer on the Keck Planet Finder instrument on Maunakea, Hawaiʻi, and have conducted some of the earliest science using it.
Selected Publications:
- Blackman, Ong, et al. 2019 — wavelength-dependent barycentric corrections
- Petersburg, Ong, et al. 2020 — The EXPRES data reduction pipeline
Publications
Major Contributions
-
Hatt, E. J., Ong, J. M. J., Nielsen, M. B., et al., MNRAS, 534,
1060
“Asteroseismic Signatures of Core Magnetism and Rotation in Hundreds of Low-Luminosity Red Giants” -
Hon, M. T. Y., Li, Y., & Ong, J. M. J. 2024, ApJ, 973,
154
“Flow-Based Generative Emulation of Grids of Stellar Evolutionary Models” -
Lindsay, C. J., Ong, J. M. J., & Basu, S. 2024, ApJ, 965,
171
“Fossil Signatures of Main-sequence Convective Core Overshoot Estimated through Asteroseismic Analyses” -
Rui, N. Z., Ong, J. M. J., Mathis, S. 2024, MNRAS, 527,
6346,
“Asteroseismic g-mode period spacings in strongly magnetic rotating stars” -
Lindsay , C. J., Ong, J. M. J., & Basu, S. 2023, ApJ, 950,
19,
“Near-Core Acoustic Glitches are Not Oscillatory: Consequences for Asteroseismic Probes of Convective Boundary Mixing” -
Campante, T., Li, T., Ong, J. M. J., et al. 2023, AJ, 165,
214,
“Revisiting the Red-giant Branch Hosts KOI-3886 and ι Draconis: Detailed Asteroseismic Modeling and Consolidated Stellar Parameters” -
Saunders , D., Ong, J. M. J., & Basu, S. 2023, ApJ, 947,
22,
“Evolutionary and Observational Properties of Red Giant Acoustic Glitch Signatures” -
Lindsay, C. J., Ong, J. M. J., Basu, S. 2022, ApJ, 931,
116,
“Mixed-Mode Asteroseismology of Red Giant Stars Through the Luminosity Bump” -
Petersburg, R. R., Ong, J. M. J., Zhao, L. L., et al. 2020, AJ,
159, 187,
“An Extreme-precision Radial-velocity Pipeline: First Radial Velocities from EXPRES” -
Blackman, R., Ong, J. M. J., & Fischer, D. 2019, AJ, 158,
40,
“The Measured Impact of Chromatic Atmospheric Effects on Barycentric Corrections: Results from the EXtreme PREcision Spectrograph” -
Viani, L. S., Basu, S., Ong, J. M. J., Bonaca, A., & Chaplin,
W. J. 2018, ApJ, 858, 28
“Investigating the Metallicity-Mixing-length Relation”
Presentations
Here is an archive of science presentations I’ve given recently.
Talks
- Understanding Mixed Modes (for Fun and for Profit): KU Leuven, November 2024
- Asteroseismic Diagnistics of Engulfment and Misalignment: TAPIR Seminar, Caltech, September 2024
- Asteroseismic Diagnistics of Core-Envelope Rotational Misalignment: TASC VIII/KASC XV, Porto, July 2024
- Solar-Like Oscillations: Life After Kepler (invited review; recording): TASC VII/KASC XIV, Honolulu, July 2023
- TESS Observes a Rapidly-Rotating Engulfment Candidate (invited): TESS Mission Update, MIT (virtual), July 2023
- Solar-Like Oscillations: Past, Present, & Future: Tsinghua University (virtual), February 2023
- Recent Advances in Gravitoacoustic Mixed-Mode Asteroseismology: Indiana University Bloomington (virtual), January 2023
- New Techniques for Asteroseismic Rotational Measurements: AAS 241 (Seattle), January 2023
- New Methods for Seismic Analysis with Gravitoacoustic Mixed Modes: IfA Colloquium, October 2022
- Prospects for Seismic Probes of Radial Differential Rotation: NHFP Symposium, STScI, September 2022
- An Integral Estimator for \(\nu_\mathrm{max}\): Birmingham Sun, Stars and Exoplanets Seminar (chalk talk), July 2022
- Mixed Modes in Theory and Practice: The Good Vibrations Seminar (virtual), December 2021
- Helium Abundances from Subgiant Ensemble Asteroseismology: TESS Science Conference II, MIT (virtual), August 2021
- Rethinking the Surface Term: iSIMBA Seminar, Aarhus (virtual), February 2021
- Structural and Evolutionary Diagnostics from Phase Functions: TASC5/KASC13, Boston, July 2019
- Deviations from the Scaling Relation of the Large Frequency Separation: TASC4/KASC12, Aarhus, July 2018
Posters
- Resolving an Asteroseismic Catastrophe: What do Red Giant Small Separations Signify?: TASC8/KASC15, Porto, July 2024
- Asteroseismic Diagnostics of Core-Envelope Misalignment: TASC7/KASC14, Honolulu, July 2023
- Interactions between differential rotation and mixed-mode coupling in evolved stars: TASC6/KASC13, Leuven, July 2022
- Seismic Constraints on Helium Abundances from the TESS Southern CVZ: Cool Stars XXI, Toulouse, July 2022
- Mixed Modes and the Asteroseismic Surface Term: PLATO Conference (virtual), October 2021
Teaching
I enjoy making interactive visualisations of asteroseismic phenomena for pedagogical purposes — I have found them very helpful in allowing my students to build physical and mathematical intuition by playing around with the parameters of these toys at their own time and pace. If you should choose to use them in your own teaching or presentations, I would very much appreciate attribution.
Over the years, I’ve accumulated enough of these toys that even displaying a subset of them is no longer easy to do on a single page. I’ve now started to group them thematically. Please select a series of toys to view:
Gravitoacoustic Mixed Modes
As stars evolve across the Hertzsprung gap and up the red giant branch, the frequencies of their p-modes decrease over time, and those of their g-modes increase over time. I show below how the power spectrum of such a star might change if we were able to follow it over evolutionary timescales. During the time interval shown, we have one g-mode (at low frequency at first, whose location is shown with the orange dashed line) coming into resonance, and then off resonance, with a p-mode (shown with the blue dashed line.)
Naively, one would expect that this means at some point one would obtain a pair of p- and g-modes with identical frequencies. However, what happens instead is that the p- and g-mode cavities couple to each other (described with the \(\alpha\) parameter in the figure). As a result of this coupling, the actual normal modes that exist in these evolved stars are neither pure p-modes nor pure g-modes — they exhibit mixed character. They behave like p-modes in the envelope, and like g-modes in the core. When the two mode cavities are coupled in this fashion, the two modes smoothly interchange character — the g-mode becomes a p-mode, and vice versa.
This kind of phenomenon is called an avoided crossing. We describe how modes progress through avoided crossings with “mixing fractions” \(\zeta\) assigned to each mode. Conventionally, pure p-modes have \(\zeta = 0\), pure g-modes \(\zeta = 1\), and modes of mixed character take intermediate values.
A good physical analogy for how these modes behave can be found by thinking about how atomic orbitals hybridise to form molecular orbitals in chemistry.
It turns out that this construction also exhibits avoided crossings! Rather than two hydrogen atoms, let’s permit the nuclear charges \(Z_1\) and \(Z_2\) of the two atoms to vary. An avoided crossing emerges as the ground states of the two atoms enter and leave resonance with each other.
The situation in asteroseismology is entirely analogous! We may decompose a mixed mode that shows both p- and g-like character into a linear combination of notional pure p- and pure g-mode eigenfunctions.
Rotation
The horizontal components of mode eigenfunctions are, in slowly rotating stars, described by the spherical harmonics. Modes which propagate in the prograde direction will appear, to a stationary nonrotating observer, to oscillate more rapidly than modes which propagate in the retrograde direction. The inclination of the stellar rotational axis relative to the observer will determine which modes appear to cancel out when integrated over the visible disc, and which modes appear to oscillate the most.
The observational effect of the above dynamics is to turn each peak in the observed power spectrum into a multiplet of modes. The degree \(\ell\) of the multiplet determines the number of components, \(2\ell + 1\), while the inclination of the rotational axis determines the distribution of observed power between multiplet components.
In evolved stars, we observe modes of mixed p- and g-like character. These are the result of two mode cavities coupling to produce avoided crossings. The interaction between this mode coupling and the rotational splittings yields quite complicated observational morphology for the rotational multiplets (here shown only for \(\ell = 1\)).
Core-Envelope Misalignment
We ordinarily think of stars as rotating around only a single axis. However, there do exist stars where this isn’t true — e.g. in stars whose cores and envelopes are effectively decoupled, these different parts of them may rotate around different axes. In principle, we describe the coordinate transformation between the core’s corotating frame to the envelope’s corotating frame using three Euler angles, \(\alpha, \beta, \gamma\). However, the Euler angles \(\alpha\) and \(\gamma\) don’t really matter observationally: they describe rotations of the overall orientation of the star, or around the propagation axis of the waves, that leave the mode frequencies invariant.
There are two ways of parameterising the overall geometry of such a misaligned system. On one hand, we may use inclination angles \(i_\text{core}\) and \(i_\text{env}\) for the projected inclinations of the core and envelope angular momentum vectors against the line of sight, as well as a further obliquity angle \(\lambda\) to fully specify a spherical triangle, as shown below. On the other hand, we might specify e.g. \(i_\text{env}\) only implicitly, and instead explicitly parameterise the same spherical triangle using the misalignment Euler angle \(\beta\) and a further interior angle \(\varphi\) for one corner of the spherical triangle.
In the presence of this misalignment, the phenomenology of how different multiplet components depend on viewing angle is also modified. The distribution of power between the components of a multiplet now also depends on the mixing fractions \(\zeta\) of different multiplet components — and those are themselves also modified by misalignment, since the shapes of the avoided crossings change too!
Cover image: EXPRES echellogram of 55 Cancri in April 2019. Image credit: Lily Zhao.
Footer: Legendre polynomials; original work.