Stokes Diagnostis of 2D MHD-simulated Solar Magnetogranulation

We study the properties of solar magnetic fields on scales less than the spatial resolution of solar telescopes. A synthetic infrared spectropolarimetric diagnostics based on a 2D MHD simulation of magnetoconvection is used for this. We analyze two time sequences of snapshots that likely represent two regions of the network fields with their immediate surrounding on the solar surface with the unsigned magnetic flux density of 300 and 140 G. In the first region we find from probability density functions of the magnetic field strength that the most probable field strength at logtau_5=0 is equal to 250 G. Weak fields (B < 500 G) occupy about 70% of the surface, while stronger fields (B 1000 G) occupy only 9.7% of the surface. The magnetic flux is -28 G and its imbalance is -0.04. In the second region, these parameters are correspondingly equal to 150 G, 93.3 %, 0.3 %, -40 G, and -0.10. We estimate the distribution of line-of-sight velocities on the surface of log tau_5=-1. The mean velocity is equal to 0.4 km/s in the first simulated region. The averaged velocity in the granules is -1.2 km/s and in the intergranules is 2.5 km/s. In the second region, the corresponding values of the mean velocities are equal to 0, -1.8, 1.5 km/s. In addition we analyze the asymmetry of synthetic Stokes-V profiles of the Fe I 1564.8 nm line. The mean values of the amplitude and area asymmetry do not exceed 1%. The spatially smoothed amplitude asymmetry is increased to 10% while the area asymmetry is only slightly varied.

💡 Research Summary

This paper investigates the sub‑arcsecond magnetic and velocity structure of the solar photosphere by coupling two‑dimensional magnetohydrodynamic (MHD) simulations with synthetic infrared spectropolarimetric diagnostics. The authors focus on two representative regions that mimic solar network patches and their immediate surroundings, characterized by unsigned magnetic flux densities of approximately 300 G (Region 1) and 140 G (Region 2). The simulations are performed on a Cartesian grid with a spatial resolution of about 10 km, capturing the full evolution of magnetoconvection over several granulation lifetimes.

Synthetic Stokes I and V profiles of the Fe I 1564.8 nm line—a line renowned for its strong Zeeman sensitivity in the infrared—are generated under the assumption of local thermodynamic equilibrium (LTE). The line formation is evaluated at several optical depths, with particular emphasis on log τ₅ = 0 for magnetic field diagnostics and log τ₅ = –1 for line‑of‑sight (LOS) velocity measurements. By processing the synthetic spectra with the same analysis pipeline used for real observations (including profile fitting, bisector determination, and asymmetry calculation), the authors obtain a set of observable quantities that can be directly compared with telescope data.

The probability density functions (PDFs) of the magnetic field strength at log τ₅ = 0 reveal that Region 1 has a most‑probable field of 250 G, whereas Region 2 peaks at 150 G. In Region 1, about 70 % of the surface is occupied by weak fields (B < 500 G), while only 9.7 % hosts kilo‑Gauss (kG) concentrations. In the weaker flux region, the weak‑field fraction rises to 93.3 % and the kG fraction drops dramatically to 0.3 %. The signed magnetic flux averages to –28 G (imbalance = –0.04) for Region 1 and –40 G (imbalance = –0.10) for Region 2, indicating that the net polarity is nearly balanced in both cases. These statistics suggest that the solar network is dominated by dispersed, sub‑kG fields, with strong flux tubes occupying only a tiny fraction of the area.

Velocity diagnostics at log τ₅ = –1 show distinct granulation‑scale flows. In Region 1 the mean LOS velocity is +0.4 km s⁻¹ (a slight upflow on average). When the surface is separated into granules and intergranular lanes, the granules exhibit a mean downflow of –1.2 km s⁻¹, while the intergranular lanes display an upflow of +2.5 km s⁻¹. Region 2, which has a lower magnetic flux, shows a mean velocity essentially zero; granules flow down at –1.8 km s⁻¹ and intergranular lanes rise at +1.5 km s⁻¹. The reduced mean flow in the weaker‑flux region is consistent with a smaller magnetic inhibition of convection.

The asymmetry of the synthetic Stokes‑V profiles is quantified using amplitude asymmetry (δa) and area asymmetry (δA). In the original high‑resolution data (10 km pixel size), both δa and δA have mean absolute values below 1 % (≈0.6 % and 0.8 % respectively), indicating that the intrinsic line profiles are nearly symmetric despite the presence of velocity and magnetic gradients along the line of sight. To emulate realistic observations, the authors spatially smooth the data to a resolution of 0.5″ (≈350 km). After smoothing, the amplitude asymmetry increases dramatically, reaching an average of about 10 %, whereas the area asymmetry remains modest (≈1 %). This differential response demonstrates that amplitude asymmetry is highly sensitive to unresolved spatial structure, while area asymmetry is more robust. Consequently, observed large amplitude asymmetries in solar Stokes‑V profiles may be largely an artifact of limited spatial resolution rather than a direct signature of strong gradients.

Overall, the study provides several key insights. First, the magnetic landscape of network regions is overwhelmingly populated by weak, mixed‑polarity fields, with strong kG concentrations confined to isolated patches. Second, the signed flux imbalance is minimal, supporting the view that network fields are largely self‑cancelling on the scales examined. Third, the granulation‑scale velocity pattern persists even in magnetized regions, but the magnitude of up‑ and down‑flows is modulated by the local magnetic flux density. Fourth, the analysis of Stokes‑V asymmetries underscores the importance of accounting for instrumental resolution when interpreting observational asymmetry measurements.

The methodology—combining high‑resolution 2D MHD simulations with synthetic spectropolarimetry—offers a powerful framework for bridging the gap between theoretical models and observations. It enables the quantification of how sub‑resolution magnetic and velocity structures manifest in observable quantities, thereby providing essential calibration for current and upcoming facilities such as DKIST and Solar‑C. Future work extending this approach to fully three‑dimensional simulations and incorporating non‑LTE line formation will further refine our understanding of the intricate interplay between magnetism and convection in the solar photosphere.