1. SPD – June 2006 Solar Polar Flux – 1996-2006 - MDI The Sun’s Polar Magnetic Flux 1996-2006 Observed with SOHO/MDI J. Todd Hoeksema E.E. Benevolenskaya, Y. Liu P.H. Scherrer & X.P. Zhao Stanford University

2. SPD – June 2006 Solar Polar Flux – 1996-2006 - MDI Figure 1 a)Apparent values of the magnetic flux of the radial field component in the latitude zones from 78 o to 88 o in Northern (blue line) and Southern (red line) hemispheres b)The fraction of positive polarity magnetic flux in Northern (blue line) and Southern (red line) hemispheres c) Total signed magnetic flux. The polar magnetic field reversal was in CR1975± 2 (April 2001) in the North and in CR1981± 2 (September 2001) in South. Figure 1

3. SPD – June 2006 Solar Polar Flux – 1996-2006 - MDI The apparent values of the total unsigned magnetic flux Fr = |F+| + |F-| for the polar caps 78 o – 88 o are presented in Figure 1a for reduced- resolution synoptic maps (1 o in both latitude and longitude). There is a N-S asymmetry in the distributions of the total polar magnetic flux for low-resolution maps: F r = 1.5-1.8 x 10 22 Mx and F r = 2.0-2.5 x 10 22 Mx for the North and South polar caps before CR2007 (September 2003). After that, the total magnetic flux increases slightly in North and decreases in the South. The positive |F+| /Fr fraction of the magnetic flux is plotted in Figure 1b. Total signed flux is present in Figure 1c. The time of reversals can be easily determined at |F+| /Fr = 0.5. This was in CR1974 (March 2001) in the North and in CR1980 (August 2001) in South. This is close to the periods obtained by Durrant and Wilson ( Solar Physics, 2003): CR1975 in North and CR1981 in South using the Kitt Peak synoptic maps. Figure 1

4. SPD – June 2006 Solar Polar Flux – 1996-2006 - MDI Figure 2 a) b) c) d) Magnetic Field Observational Variation SOHO Rotated SOHO Nominal

5. SPD – June 2006 Solar Polar Flux – 1996-2006 - MDI Figure 2 - MDI Spatial Noise Pattern Left column: Magnetic maps averaged over 60 min periods a) Upper: B when SOHO/MDI was rotated, P_angle = 180.0 o. b) Lower: B when SOHO/MDI was not rotated, P_angle = 0.0 o. Right Column: The Noise level as σ - distribution of 1 min images in 60 min series: c) Upper: σ-distribution when SOHO/MDI was rotated, P_angle = 180.0 o d) Lower: σ-distribution when SOHO/MDI was not rotated, P_angle = 0.0 o Figure 3 – MDI Noise for 5-min and 1-min Magnetograms One-hour noise level along the central meridian as σ-distribution for the two kinds of MDI magnetograms Left: images averaged over 5 minutes on-board (a, c) and Right: 1 min magnetograms (b, d) for two time sets in 1 hour series. Upper: SOHO/MDI was rotated. Lower: SOHO/MDI was not rotated. Figure 2, 3

6. SPD – June 2006 Solar Polar Flux – 1996-2006 - MDI N-S sigma distributions along CM Figure 3 MDI Rotated MDI Nominal 5min Mags1min Mags

7. SPD – June 2006 Solar Polar Flux – 1996-2006 - MDI Figure 4. Variations of the value of apparent total unsigned flux as function of the number of images averaged for the polar caps: a) for North and b) for South Figure 5. Synoptic magnetic maps of CR2027 (25 February – 25 March, 2005) a) is constructed from a single image at each point, i.e. without any averaging. b) is constructed by averaging 60 images at each point. Latitude in sin (latitude). Resolution is 1 o in both latitude and longitude. Figure 6. Noise level (σ – distribution) versus latitude for CR 1993 and CR 2020 for 5 min and 1 hour averaged magnetograms. a) σ=9.3G for 87 o N-88 o N and σ=10.7G for 80 o S-81 o S; (P_angle = 0.0 o ) b) σ=2.7G for 87 o N-88 o N and σ=4.8G for 80 o S-81 o S; (P_angle = 0.0 o ) c) σ=9.7G for 87 o N-88 o N and σ=12.3G for 80 o S-81 o S; (P_angle = -180.0 o ) d) σ=3.9G for 87 o N-88 o N and σ=4.8G for 80 o S-81 o S; (P_angle = -180.0 o )

8. SPD – June 2006 Solar Polar Flux – 1996-2006 - MDI Figure 4 The apparent total unsigned magnetic flux of polar caps, 78-88 o computed using various numbers of averaged images during favorable polar viewing conditions. NORTH: CR1993-Aug 2002; CR2020-Aug 2004; CR2033-Aug 2005 SOUTH: CR1960-Mar 2000; CR2013-Feb 2004; CR 2027-Mar 2005 P-angle = 180 for CR 2013, CR2020, CR2027 & CR 2033 P-angle = 0 for CR 1960 and CR 1993

9. SPD – June 2006 Solar Polar Flux – 1996-2006 - MDI Figure 5 Single Mag 60 Mags Sine

10. SPD – June 2006 Solar Polar Flux – 1996-2006 - MDI Figure 6 SOHO Rotated SOHO Nominal

11. SPD – June 2006 Solar Polar Flux – 1996-2006 - MDI The value of the apparent total polar magnetic flux depends on the number of averaged images (Figures 4, 5). The pixel noise level of the MDI magnetograms was estimated by Ortiz et.al (2002). The 1-σ noise level for 1-min longitudinal magnetograms is 20 G. The magnetic noise level for 5-min magnetograms is about 9G. The random noise level decreases as 1/√N, where N is number of observations. The noise level is 2.8G for 50 min and 2.6 G for 60 min. They concluded that 20-min averages have a reasonably low noise level. They also noted the increase of the noise in the bottom right of the image, which we can see in Figure 2 (c,d). This is caused by systematic errors in the tuning of MDI. There is some discrepancy in the apparent values of the total magnetic flux estimated from synoptic maps obtained from 15 averaged images per day and the consecutive 1 min images averaged for 60 min (see Figures 1a and 4a ). For example, for CR 2033 (8 Aug – 4 Sep 2005) the total magnetic flux was 2.25610 22 Mx for 15 images taken during day but it is higher for any number of averaged images up to N=60. We expect this is connected with the reduction of the supergranulation noise, which is more completely suppressed in the first case.

12. SPD – June 2006 Solar Polar Flux – 1996-2006 - MDI The effect of MDI shutter noise on the apparent polar magnetic flux. The shutter noise of the SOHO/MDI instrument induces a small random offset into the magnetic measurements that is uniform over the disk. (Liu, Zhao & Hoeksema, 2004). The offset is removed from each magnetogram. We have estimated the magnetic flux of north polar cap (78 o N-88 o N) during the CR2033 with offset correction and without offset correction. There is a small difference in the relative positive magnetic flux and magnetic strength. With correction we obtain (|F + |/ F r )= 0.3616 and the averaged radial component of the magnetic field is B r =- 8.13G. Without the correction (|F + |/ F r )= 0.3676 and the averaged radial component of the magnetic field is B r = -7.62G. There is only a small difference in the apparent total magnetic flux. For example, the total unsigned magnetic flux in CR2021 is 1.7524 x 10 22 Mx without correction and it is 1.7912 x 10 22 Mx with correction.

13. SPD – June 2006 Solar Polar Flux – 1996-2006 - MDI Summary The value of the apparent total magnetic flux depends on the number of averaged magnetograms in the synoptic map. The apparent values decreases with the number of the averaged magnetograms due to random noise reduction. Shutter noise contributes a small portion to the estimation of the total unsigned magnetic flux of polar caps. Systematic errors are not reduced. Individual magnetograms reveal the non-uniform σ-distribution over solar disk. The noise increases to the SW on normal magnetograms, and in the NE when SOHO/MDI is rotated by 180 o. Other effects make it difficult to estimate the “true” polar flux. References Benevolenskaya, E.E., 2004, A&A, 428, L5. Durrant, C.J., & P.R. Wilson, 2003, Solar Phys., 214, 23. Liu, Y., X.P. Zhao, & J.T. Hoeksema, 2004, Solar Phys., 219, 39. Ortiz, S.K. Solanki, V. Domingo, M. Fligge, & B. Sanahuja, 2002, A&A, 388, 1036.