Reggae: Dipole Modes from PBJam¶
Contents:
Reggae is a diagnostic tool for generating optimal parameters describing dipole mixed modes under the nonasymptotic matrix-coupling scheme of Ong & Basu (2020) used in the second release of PBjam (see Nielsen et al. 2021).
Since the primary samples of the PLATO mission consist mainly of main-sequence and subgiant stars, PBjam implements a parameterisation of dipole modes suitable to these stars, outside the red-giant “asymptotic” regime. Reggae assists in the task of manually fine-tuning the dipole-mode model, and checking the quality of both our initial guesses and fitted solutions. An important part of this tuning is visual assessment of how well the data matches posterior samples for these parameters. Such asteroseismic visualisations often use the échelle power diagram near \(\nu_{\mathrm{max}}\) as a diagnostic tool, with clearly-defined ridges emerging on this diagram for p-modes, such as in main-sequence stars.
We found Reggae very helpful both for these tuning and visualisation tasks, and also as a didactic aid to understanding the dipole mixed-mode parameters. As such, we release it publicly in advance of the second PBjam version, as we believe the community will benefit from access to such a visualisation tool. This will also assist future users of PBjam in devising ad-hoc prior constraints on the mixed-mode parameters, should they wish not to rely on the prior included with it.
Mode Identification¶
The key task that Reggae is intended to perform is mode identification: specifically, assigning mixing fractions and radial orders to dipole mixed gravitoacoustic modes.
We implement a generative model for dipole gravitoacoustic mixed modes using the parameterisation of Ong & Basu (2020). At present, the frequency-dependent coupling strength is described with two parameters (one for each of the two matrices entering into the parameterisation), with a conversion to the asymptotic \(q\) provided by an expression in Ong & Gehan (2023). This expression is in turn used to generate stretched echelle power plots for diagnostic purposes.
In full, the generative model accepts the following parameters:
\(\Delta\Pi_0\), the notional period spacing of the g-mode cavity; this is related to the period spacing of any given \(\ell\) as \(\Delta\Pi_\ell = \Delta\Pi_0 / \sqrt{\ell(\ell + 1)}\).
\(p_L\) and \(p_D\), the two coupling parameters described above.
\(\epsilon_g\), a g-mode phase offset.
\(\log \left(\delta\omega_\mathrm{rot, g} / \mathrm{\mu Hz}\right)\) and \(\log \left(\delta\omega_\mathrm{rot, p} / \mathrm{\mu Hz}\right)\) — the implementation of the PSD model (below) accepts separate values of the core (g-mode) and envelope (p-mode) rotational splittings. The pure p- and g-modes are split into multiplets separately before mode-coupling calculations are performed, thereby fully accounting for near-degeneracy asymmetric rotational splittings.
\(\delta_{01}\), an additional phase offset for the dipole p-modes relative to the asymptotic solution found by pbjam.
\(\alpha_g\), a curvature parameter for the g-modes (mirroring that of the p-modes in pbjam’s asymptotic parameterisation).
\(i\), the inclination of the rotational axis.
This description of the mixed mode frequencies is used to construct models of the power spectral density, from which constraints on its parameters may be derived. For the purpose of assisting in this task, we moreover implement a GUI console.
Contributing¶
Reggae is currently developed by the following team:
Joel Ong (Mode frequency generative model + GUI)
Martin B. Nielsen (PSD model)
Guy R. Davies
Emily Hatt
We welcome contributions from the community. Easy ways to get started include:
Finding bugs in our code — please open GitHub issues for these.
Implementing feature suggestions — we welcome pull requests!