Here we use the PFSS model and photospheric data from Wilcox Solar Observatory, SOHO/MDI, SDO/HMI, and SOLIS to compare the coronal field with heliospheric magnetic field measured at 1 au, compiled in the NASA/ NSSDC OMNI 2 data set. We calculate their mutual polarity match and the power of the radial decay, p, of the radial field using different source surface distances and different number of harmonic multipoles. We find the average polarity match of 82% for the declining phase, 78%-79% for maxima, 76%-78% for the ascending phase, and 74%-76% for minima. On an average, the source surface of 3.25 R S gives the best polarity match. We also find strong evidence for solar cycle variation of the optimal source surface distance, with highest values (3.3 R S ) during solar minima and lowest values (2.6 R S -2.7 R S ) during the other three solar cycle phases. Raising the number of harmonic terms beyond 2 rarely improves the polarity match, showing that the structure of the HMF at 1 au is most of the time rather simple. All four data sets yield fairly similar polarity matches. Thus, polarity comparison is not affected by photospheric field scaling, unlike comparisons of the field intensity.

We derive the longest uniform record of rotational intensities solar coronal magnetic field since 1968 and compare it with the heliospheric magnetic field (HMF) observed at the Earth. We scale the Mount Wilson Observatory and Wilcox Solar Observatory observations of the photospheric magnetic field to the level of the Synoptic Optical Long-term Investigations of the Sun/Vector Spectro Magnetograph and apply the potential field source surface model to calculate the coronal magnetic field. We find that the evolution of the coronal magnetic field during the last 50 yr agrees with the HMF observed at the Earth only if the effective coronal size, the distance of the coronal source surface of the HMF, is allowed to change in time. We calculate the optimum source surface distance for each rotation and find that it experienced an abrupt decrease in the late 1990s. The effective volume of the solar corona shrunk to less than one half during a short period of only a few years. We note that this abrupt shrinking coincides with other changes in solar magnetic fields that are likely related to the decrease of the overall solar activity, i.e., the demise of the Grand Modern Maximum.

Aims. The heliospheric current sheet (HCS) has been observed to be southward shifted in the late declining to minimum phase of the solar cycle. Here we study the existence of a simultaneous shift in the heliosphere and in the corona using a robust new method. Methods. We use the synoptic maps of the photospheric field of the Wilcox Solar Observatory (WSO) and the Mount Wilson Observatory (MWO) together with the potential field source surface (PFSS) model to calculate the coronal magnetic field and compare it with the simultaneous heliospheric magnetic field of the NASA/NSSDC OMNI 2 dataset. We divide the magnetic field into the two sectors, towards (T) and away (A) from the Sun, and calculate how often the sector polarities at 1 AU and in the corona match each other. We divide the sectors both at 1 AU and in the corona. We also calculate the annual (T − A)/(T + A) ratios of sector occurrence both at 1 AU and in the corona. Results. We verify that the HCS/neutral line is southward shifted both in the corona and heliosphere. We find that the coronal shift is systematically larger than the simultaneous heliospheric shift. Conclusions. The fact that the southward shift of the coronal neutral line is larger than the simultaneous shift of the heliospheric current sheet at 1 AU implies that the radial evolution of the magnetic field between the two sites is different between the northern and southern hemispheres.

Aims. We study the properties of the coronal magnetic field according to the current sheet source surface (CSSS) model in 1976–2017 for all physically reasonable values of the three model parameters (cusp surface radius Rcs, source surface radius Rss, and current parameter a), and compare the CSSS field with the potential field source surface (PFSS) model field. Methods. We used the synoptic maps of the photospheric magnetic field from the Wilcox Solar Observatory (WSO), National Solar Observatory/Kitt Peak (NSO/KP), and the NSO Synoptic Optical Long-term Investigations of the Sun Vector Spectromagnetograph (SOLIS/VSM) in order to calculate the coronal magnetic field according to the CSSS and PFSS models. We calculated the coronal field strength, its latitudinal variation and neutral line location, as well as its polarity match with the heliospheric magnetic field. Results. The CSSS model can correct the erroneous latitudinal variation of the PFSS model if the source surface is sufficiently far out with respect to the cusp surface (Rss ≥ 3 ⋅ Rcs). The topology of the neutral line only slightly depends on source surface radius or current parameter, but excludes very low values of the cusp surface (Rcs ≤ 1.5). A comparison of the polarities gives an optimum cusp surface radius that varies in time between 2 and 5; a stronger current yields a larger optimum Rcs. Interestingly, the optimum polarity match percentages and optimum radii vary very similarly in the two models over the four solar cycles we studied. Conclusions. The CSSS model can produce a stronger total coronal flux than the PFSS model and correct its latitudinal variation. However, the topology of the CSSS model is rather independent of horizontal currents and remains very similar to that of the PFSS model. Therefore, the CSSS model cannot improve the match of field polarities between corona and heliosphere.

<p>Several studies have noted on changes in the properties of sunspots, and in the mutual relations between various global parameters of solar magnetic activity (e.g. UV/EUV irradiance, radio and IR emissions, TSI/SSI), as well as between solar and ionospheric parameters since the onset of solar cycle 23. These changes have been suggested to be related to the overall reduction of solar activity at the aftermath of the decline of the Grand modern maximum of solar activity that prevailed during most of the 20th century. We have recently derived the longest record of coronal magnetic field intensities since 1968 using Mount Wilson Observatory and Wilcox Solar Observatory observations of the photospheric magnetic field and the PFSS model, and compared it with the heliospheric magnetic field observed at the Earth. We found that the time evolution of the coronal magnetic field during the last 50 years agrees with the heliospheric magnetic field only if the effective coronal size, the distance of the coronal source surface of the heliospheric magnetic field, is allowed to change in time. We calculated the optimum distance for each solar rotation and found that it experienced an abrupt decrease in the late 1990s. The effective volume of the solar corona shrunk to less than one half of its previous value during a short period of only a few years. This shrinking was related with a systematic change in the structure of the coronal magnetic field during the same time interval. We review these dramatic changes in the solar corona and discuss their possible connection to the changes in the different solar activity parameters and the reduction of the overall solar activity.</p>