Simulation of Solar Surface Flux Transport Constrained by Magnetic Power Spectra. I. Flux Transport Parameter

Abstract: The multi-scale structure of the solar surface magnetic field is essential for understanding both the Sun's internal dynamo processes and its external magnetic activity. The surface flux transport (SFT) model has been successful in describing the large-scale evolution of the surface field, but its ability to capture observed multi-scale features, quantified by magnetic power spectra, remains uncertain. Here, we evaluate the SFT model by comparing observed and simulated power spectra across a broad range of spatial scales and by analyzing the effects of key transport parameters. We find that the simulations reproduce the observed spectra well at spherical harmonic degrees $l\lesssim60$, but diverge progressively at smaller spatial scales $l\gtrsim60$. This divergence likely arises from the diffusion approximation used to model the random walk of supergranulation. Power at $20 \lesssim l \lesssim 60$ is primarily determined by the magnetic flux sources, while at $l \lesssim 20$, the spectra are more sensitive to transport parameters. The meridional flow profile, including its equatorial gradient, peak latitude, and polar distribution, along with turbulent diffusivity, has distinct impacts on the low-degree modes ($l \leq 5$). In particular, a comparison of the $l$=3 and $l$=5 multipoles strengths suggests that the poleward flow above $\sim\pm60^\circ$ latitudes is very weak. This study presents the first quantitative validation of SFT models using magnetic power spectra and provides new constraints on surface flux transport physics.