Spatial power spectrum of the photospheric magnetic field during solar minimum

Abstract

Context. During solar minima the spatial power spectrum of the photospheric magnetic field is dominated by the low-degree zonal (axisymmetric; m = 0) harmonic components, reflecting the large polar coronal holes of unipolar magnetic field. However, measuring polar fields is difficult because of the unequal visibility of the two poles during most of the year and the small line-of-sight component of the roughly radial field at high solar latitudes. Aims. In this paper we derive the spatial power spectrum of the photospheric magnetic field in terms of the harmonic coefficients of the radial component (Br) as well as in terms of the harmonic coefficients of the internal potential (known as Gauss coefficients). We calculate the zonal spatial power spectrum using Mount Wilson Observatory synoptic maps from 1995–1996, during the solar minimum between solar cycles 22 and 23, and investigate how filling or not filling the polar data gaps affects the zonal harmonic coefficients. Methods. We eliminated the vantage point effect by removing the highest 5° of the measured magnetic field and calculating the latitudinal profile of the zonal median field over the two years, which ensured equal latitudinal data coverage of both solar hemispheres. We then derived the zonal harmonic coefficients using this latitudinal profile of Br. Results. We find that when the polar data gaps are left unfilled, a strong artificial power above l = 8 is produced. Only the first five zonal harmonic coefficients can be considered reliable in this case. Therefore polar filling is essential to obtain a realistic spatial power spectrum. Filling the polar gap with a constant (non-zero) value yields zonal harmonics that are reliable up to l = 9. We find that the zonal octupole component contributes most to the total spatial power, more than the zonal dipole, even during the solar minimum conditions. This difference is seen more clearly in the case of polar filling. We also prove that the asymmetry of the polar fields during this solar minimum is statistically significant. Conclusions. Our results emphasize the importance of filling the polar data gaps in order to obtain a correct estimate of the spatial power spectrum of the photospheric field. This helps in estimating the reliability of polar fields and the large-scale structure in synoptic maps of different origin. Our results also verify the asymmetric nature of the polar fields, which is important for the heliospheric magnetic field and for solar dynamo modeling.