Inferring solar differential rotation and viscosity via passive imaging with inertial waves

TL;DR

The paper addresses inferring solar interior properties, specifically viscosity $\gamma$ and differential rotation $\Omega$, from surface inertial waves using a passive imaging framework. It derives a forward model yielding a scalar equation for each $(\omega,m)$, $-\gamma \Delta_m^2\Psi - i\omega \Delta_m\Psi + i m \beta_\Omega \Delta_m\Psi - i m \alpha_\Omega \Psi = f$, and formulates an inverse problem to recover $\gamma$ and $\Omega$ from cross-covariance data, leveraging a known source strength $\Pi_f$. An accelerated Nesterov Landweber algorithm is used to simultaneously recover $\gamma$ and $\beta=\Omega$ from a single frequency-longitude mode, achieving accurate reconstructions rapidly (≈200 iterations in ≈2 s on CPU) and demonstrated with synthetic tests. The work establishes the feasibility of passive-imaging-based solar interior inference and charts a path toward applying the method to solar-like parameters and real data from SDO/HMI, potentially enabling deep interior constraints from long-lived inertial waves. The approach promises new avenues for probing the Sun’s interior dynamics by exploiting cross-covariance informed inversions of inertial-wave data.

Abstract

The recent discovery of inertial waves on the surface of the Sun offers new possibilities to learn about the solar interior. These waves are long-lived with a period on the order of the Sun rotation period ($\sim$27 days) and are sensitive to parameters deep inside the Sun. They are excited by turbulent convection, leading to a passive imaging problem. In this work, we present the forward and inverse problem of reconstructing viscosity and differential rotation on the Sun from cross-covariance observations of these inertial waves.

Figures (1)

• Figure 1: Simultaneous reconstruction of viscosity/rotation (top) and resulting covariance images (bottom). $\text{Error}_x=\|x_\text{reco}-x_\text{true}\|/\|x_\text{true}\|$.