tokens: detected magnetic patches with red and blue lines (panel c). The intensity is normalized with the average intensity. The white and black magnetic fields indicate the positive and negative magnetic fields, respectively. The magnetic field is distributed in a network with a scale of several 10 Mm, and the structure of supergranulation can be seen. We note that although the maximum value of the colour bar for the magnetic field is 300 G, the maximum magnetic field strength exceeds 1000 G. The red and blue contours in panel (c) indicate positive and negative magnetic patches, respectively. Figure 3. The radiative intensity (panel a), the vertical magnetic field strength (panel b), and the detection of magnetic patches (panel c). The intensity is normalized by the average intensity I ⊙ . Panels (b) and (c) show the vertical magnetic field at τ = 0.01 surface. The red and blue lines indicate positive and negative magnetic patches, respectively. Fig. 4 shows the vertical magnetic field convolved with PSF and the detected features. The figure shows the raw simulated magnetic field (panel a), the magnetic field with the PSF of the Hinode /SOT (panel b), and the magnetic field with the PSF of SDO /HMI (panel c). SDO /HMI (panel c) shows the most diffused patches, and the field strength is weak on average. Figure 4. Magnetic field strength convolved with different kinds of PSF. The simulated raw magnetic field data (panel a), data convolved with the PSF of Hinode /SOT PSF (panel b), and data convolved with the PSF of SDO /HMI (panel c). Fig. 5 shows the probability density function (PDF) of the magnetic flux at the photosphere. Orange, green, and blue lines indicate the magnetic flux in the original raw data, the data with the PSF of Hinode /SOT, and the data with the PSF of SDO /HMI, respectively. The black line indicates the fitting result for a range that clearly shows the power-law distribution. The slope increases with increasing resolution, i.e. the raw simulation data show a steeper slope than the data with Hinode and SDO PSF. The power-law index of the PDF with Hinode ’s PSF (green line) is –1.848, consistent with Parnell et al. ( 2009 ), which showed –1.85 for the power-law index with the Hinode observation. This suggests that the simulated magnetic field data reproduce the real Sun nicely and support the appropriateness of the model in this study. Figure 5. The probability density function (PDF) at the photosphere. Orange, green, and blue lines indicate the PDF of the raw simulation data, the data with Hinode /SOT’s PSF, and the data with SDO /HMI’s PSF, respectively. The black lines are the fitted lines for their power-law distribution. Fig. 6 shows the results of our analysis for the detected magnetic field depths. |〈 B z 〉| means the absolute value of the vertical magnetic field averaged over each magnetic patches. We divide the horizontal axis into 100 bins. Each bin has the same size in logarithmic and linear scales for magnetic flux
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