Chunlan Jin & Jingxiu Wang
Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences
The 11 year solar cycle was discovered in 1843 by observing the sunspot numbers. The basic mechanism of the solar cycle may be explained by a mean-field magnetohydrodynamic dynamo. Observationally, the inter-network (IN) magnetic field provides new constraints and challenges to our understanding of the solar cycle. Although being the weakest component of solar magnetism, solar IN magnetic field contributes ~1026 Mx of magnetic flux to the solar surface each day , over 4 orders of magnitude higher than that from the active regions.
Figure 1 | The cyclic variation of the inter-network (IN) magnetic field: (a) the area occupied by the IN region relative to the solar disk; (b) the IN magnetic flux density; (c) the monthly sunspot number.
By combining the observations from several space missions (SDO/HMI, SOHO/MDI, and Hinode), the cyclic variation of solar IN field has been quantified by Jin & Wang [2,3]. Taking advantage of the high spatial resolution and consistent polarization sensitivity of Hinode SOT/SP, we identify IN elements in more than 1000 SOT/SP magnetograms from January 2007 to August 2014. We find that from the minimum to the maximum phase of Cycle 24, the flux density of IN region is invariant at 10±1 G (Figure 1b). We determine the area occupied by the IN elements using HMI and MDI full-disk magnetograms (Figure 1a). The ratio of the IN area to the solar disk decreases from solar minimum to maximum but always exceeds 60%. We further find that the imbalance of the IN horizontal and vertical components is constant at 8.7 . Our findings support the idea that the IN field is generated by small-scale, local dynamo, independent of its global counterpart.
Figure 2 | The Spearman’s rank correlation coefficients between the sunspot number and the cyclic variation of flux density of magnetic structures with different fluxes. The color bar represents the correlation confidence level. The vertical dotted line distinguishes the magnetic structures observed by MDI from Hinode/SP.
Combining these studies with our previous work , we derive the cyclic variation of solar magnetic flux spectrum. Using a reliable feature identification algorithm, we are able to show the solar cycle variation of quiet Sun magnetic elements, ranging from 1016 Mx (the detection limit of HMI and SOT/SP) through 1018 Mx (the detective limit of MDI) to 1020 Mx in flux. The flux density of individual structures exhibit very different correlations with the sunspot number across the flux spectrum (Figure 2). The non-correlated component, at the small end, is the IN field as described above. The positively correlated component is likely to be the debris of decayed sunspots. The more interesting component lies in the range from several 1018 Mx to 3×1019 Mx, which shows anti-correlation with the sunspot number.
The identity of the anti-correlated component in solar magnetism may resolve the long-standing mystery of coronal X-ray bright points, which are anti-phased with solar cycle. Several possibilities are proposed by Jin et al. , including the interaction between local and global dynamos. A more recent simulation by Karak & Brandenburg  clearly reproduces the anti-correlation between the variation of the small-scale field and sunspot cycle, and interprets the anti-correlation as a consequence of the local, small-scale dynamo suppressed by the global dynamo.
 Zhou, G. P., Wang, J. X. & Jin, C. L., 2013, SoPh, 283, 73
 Jin, C. L. & Wang, J. X., 2015a, ApJ, 806, 174
 Jin, C. L. & Wang, J. X., 2015b, ApJ, in press, arXiv: 1505.06519
 Jin, C. L., Wang, J. X., Song, Q. & Zhao, H., 2011, ApJ, 731, 37
 Karak, B. B. & Brandenburg, A., 2015, arXiv: 1505.06632