Estimation of gravitational wave from solar emerging magnetic flux tube

TL;DR

This paper assesses gravitational waves produced by the buoyant emergence of magnetic flux tubes in the solar convection zone. It develops a quasi-static, catenary-based flux-tube model and a quadrupole radiation framework to estimate the GW amplitude and dominant frequency, highlighting the transient, non-stationary nature of the signal. The main finding is that a single flux-tube emergence near 1 AU would generate extremely small strains (roughly $h \sim 10^{-42}$ at $f \sim 10^{-5}$ Hz), while collective effects and proximity (e.g., $r\sim 0.04$ AU) could enhance the signal to around $h \sim 10^{-28}$, still far below current PTA sensitivities. The study concludes that detection with present or near-future detectors remains challenging, but the distinctive time-domain signature motivates high-cadence observations and future, more detailed modeling (including 3D simulations) to explore solar contributions to the low-frequency gravitational-wave foreground.

Abstract

This study investigates the gravitational waves (GWs) generated by the emergence of magnetic flux tubes in the solar convection zone. We focus on the upward buoyancy of magnetic flux tubes, which leads to significant magnetic activity and the formation of active region sunspots. This study adopts parameters representative of a moderate-sized solar active region to estimate the GWs generated by the emergence of magnetic flux tubes. Our results indicate that the GW strain amplitude, achievable through signal superposition and detection at close proximity (e.g., approximately one solar radius from the solar surface), may reach $\sim$10$^{-29}$. The characteristic GW frequency is estimated at $\sim$10$^{-5}$ Hz, placing it at the high-frequency end of the sensitivity band of Pulsar Timing Array (PTA) methods. However, the estimated strain amplitudes remain orders of magnitude below the sensitivity thresholds of current and foreseeable gravitational wave detectors. Notably, reducing the cadence $Δt$ of Pulsar Timing Array (PTA) observations to approximately 2 hours ($Δt = 2\text{hours}$) would raise the maximum detectable frequency to about $5.8 \times 10^{-5} \text{Hz}$, thereby encompassing the dominant spectral component of solar activity-related GWs predicted in this study, offering a potential pathway for future detection. Successful detection in the future may help to predict the super solar active region emergence in space weather forecasting.

Figures (7)

• Figure 1: GW Model for Single-Source: The source oscillating along the $y$ axis (double arrow), and the transverse stretching - compressing mode of the GW in the direction of $\theta=\frac{\pi}{2}$(schematic of field lines), a represents the amplitude. Source: Maggiore08.
• Figure 2: Flowchart of the gravitational wave estimation framework.
• Figure 3: Catenary model, red line represents bottom of convection zone, green line represents the most marginal catenary, blue line represents the solar surface.
• Figure 4: The figure illustrates a cluster of downward-opening catenary curves, sharing coincident x-axis intersections, as an approximation to the two-dimensional magnetic flux tube model.
• Figure 5: Temporal evolution of the equivalent density $\rho$ during flux tube ascent. The orange curve is the cubic interpolation fitting curve based on the original data, and the 2591 black dots represent raw data points.