All Figures

$\begin{figure} \par\includegraphics[width=12cm,clip]{5871fig1.eps}\end{figure}$ Figure 1: Latitude dependence of the longitudinally averaged source surface field, $\vert B_{\rm r}(R_{\rm ss},\lambda)\vert$ , during times of three solar activity minima (Carrington rotations 1643, 1781, 1909; left panels) and three maxima (Carrington rotations 1688, 1819, 1961; right panels), respectively, obtained on the basis of the WSO photospheric field maps. Cases considered are the PFSS model with $R_{{\rm ss}}=2.5~R_{\odot}$ ( a), b)), the CSSS model with $R_{\rm cusp} = 1.7~R_{\odot}$ and $R_{{\rm ss}}=2.5~R_{\odot}$ ( c), d)), as well as the CSSS model with $R_{\rm cusp} = 1.7~R_{\odot}$ and $R_{\rm ss}=10~R_{\odot}$ ( e), f)). The Ulysses result of a latitude-independent field is only reproduced by a CSSS model with a source surface located in the region of the Alfvénic point, $r \geq 10~R_{\odot}$ .
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{5871fig2.eps}\end{figure}$ Figure 2: Mean radial flux density at 1 AU ( $\langle B_{\rm E}\rangle$ , see Eq. (5), left panels) and radial field near Earth ( $B_{\rm {E}}$ , see Eq. (6), right panels) for the same extrapolations as in Fig. 1 (solid lines) in comparison with the measured radial IMF component (OMNI data, dotted lines). The extrapolations are based on the WSO synoptic maps of the photospheric magnetic field. All data are 3-month averages. The results for $\langle B_{\rm E}\rangle$ (proportional to the total open flux) fit the data reasonably well for PFSS as well as CSSS extrapolations. However, only in the case of CSSS with $R_{\rm ss}=10~R_{\odot}$ (panel f)) is the extrapolated near-ecliptic field consistent with the actual data.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=270,width=7.65cm,clip]{5871fig3.eps}\end{figure}$ Figure 3: Latitude profiles of the meridional flow velocity. The profile used for the simulations presented here (solid line) has been roughly adapted to helioseismological measurements (dashed lines with year labels, cf. Gizon & Duvall 2004). Also shown are the profiles adopted in other studies with flux transport models. flow WS: Wang & Sheeley (2003a) and Wang et al. (2005); flow vB: van Ballegooijen et al. (1998) and Baumann et al. (2004).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=270,width=7.5cm,clip]{5871fig4.eps}\end{figure}$ Figure 4: Longitude-averaged photospheric magnetic field, unsigned and integrated over latitude, as a function of time (three-months averages). Shown are the result from our flux transport simulations (FTM, full line) with sources taken from the SOON sunspot area database together with the observed data (dotted line) based upon the NSO/Kitt peak synoptic magnetograms (courtesy of D. Hathaway, NASA/MSFC). The conversion factor between bipolar magnetic region area and input magnetic flux for the flux transport simulations has been chosen such that the two curves show a reasonable agreement. The calibrated curves for different values of the proportionality factor, f, in the latitudinal tilt angle profile, $\gamma =f\lambda$ , are nearly identical for $f\leq 0.5$ . Shown here is the curve for f=0.15.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7.75cm,clip]{5871fig5.eps}\end{figure}$ Figure 5: Averaged unsigned photospheric field as a function of time. The symbols represent data from Mt. Wilson Observatory and Wilcox Solar Observatory, respectively (cf. Arge et al. 2002). The curves give three-months averaged results from flux transport simulations for two values of the proportionality factor, f, in the latitudinal tilt angle profile, calibrated by requiring consistency with the longitudinally averaged flux density (see Fig. 4). While the curve for f=0.5 (dashed line) shows a much too small average surface field, the result for f=0.15 (solid line) is consistent with the data.
Open with DEXTER

In the text

$\begin{figure} \par\hspace*{1.2cm}\includegraphics[width=15.25cm,clip]{5871fig6a... ...\vspace*{3mm} \par\includegraphics[width=16.2cm,clip]{5871fig6c.eps}\end{figure}$ Figure 6: Simulated and observed time-latitude plots (butterfly diagrams) of the longitudinally averaged radial magnetic field at the solar surface. Upper panel: result of the flux transport simulation (running time averages of over 27 days) based upon SOON sunspot data with a value of f=0.15 for the tilt angle slope. Lower panel: evolution of the observed field from NSO Kitt Peak synoptic maps (courtesy D. Hathaway). Simulation and observation are in qualitative agreement, particularly concerning the poleward surges of following-polarity magnetic flux leading to the reversals of the polar fields.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=270,width=7.5cm,clip]{5871fig7.eps}\end{figure}$ Figure 7: Evolution of polar fields (average field strength poleward of $\pm$ $70\deg$ latitude) in the flux transport simulation. South (North) polar fields are indicated by the thick (thin) line. The field amplitudes and reversal times are consistent with the observational results presented by Dikpati et al. (2004, cf. their Fig. 3#. Owing to the calibration of the flux transport model (see Fig. 4), the curves for different values of the proportionality factor, f, in the latitudinal tilt angle profile, $\gamma =f\lambda$ , are nearly identical as long as $f\leq 0.5$ . Shown here is the case f=0.15.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=270,width=7.4cm,clip]{5871fig8a.eps}\vspace*{3mm} \includegraphics[angle=270,width=7.4cm,clip]{5871fig8b.eps}\end{figure}$ Figure 8: Temporal evolution of the mean unsigned radial field at 1 AU: comparison between measurements (dashed lines, OMNI data) and CSSS extrapolations (solid lines, $R_{\rm cusp} = 1.7~R_{\odot}$ , $R_{\rm ss}=10~R_{\odot}$ ) based on flux transport simulations with input from the SOON sunspot group areas. The upper panel shows the case f=0.15 (tilt angle profile as consistently determined by comparison with observed surface fluxes, see Figs. 4 and 5). The lower panel shows the case f=0.5. In this case, the overall amplitude of the open flux is too low. In addition, there is a phase shift between the curves, although they are not in antiphase (see, e.g., Mackay et al. 2002b) owing to the effect of the decay term in the flux transport equation (Baumann et al. 2006). Clearly, the simulation with f=0.15 yields a reasonable representation of the measurements.
Open with DEXTER

In the text