Accurate Polar and small scale observations during the solar cycle Elena E. Benevolenskaya Yang Liu J. Todd Hoeksema Stanford University HMI/AIA meeting, Monterey, February, 2006

Figure 1. a) Estimated 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 Hemispheres (red line); b) The relative positive polarity parts of magnetic flux in Northern (blue line) and Southern hemispheres (red line). 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.

The estimated values of the total unsigned magnetic flux Fr = |F+| + |F-| for polar caps 78 o – 88 o are presented in Figure 1 (a) for low-resolution synoptic maps (with step 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 = x 1022 Mx and Fr = x 1022 Mx for the North and South polar caps, correspondingly, before CR2007 (September 2003). After that, the total magnetic flux displays a small increasing in North and decreasing in South. The positive |F+| /Fr part of the magnetic flux is plotted in Figures 4 (b). 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 (2003): CR1975 in North and CR1981 in South using the Kitt Peak synoptic maps.

Figure 2 a) b) c) d)

Figure 2. Magnetic maps averaged over 60 min for periods: a) When SOHO/MDI was rotated, P_angle = o. b) When SOHO/MDI was not rotated, P_angle = 0.0 o. Noise level as σ - distribution for 1 min images in 60 min series: c) for P_angle = o and d) for P_angle = 0.0 o. Figure 3. Noise level as σ - distribution for images averaged over 5 min (a, c) and 1 min image (b, d) for two time sets in 1 hour series. Top panels: SOHO/MDI was rotated. Bottom panels: SOHO/MDI was not rotated. Figure 4. Variations of the values of total unsigned flux as function of number averaged images for polar caps: a) for North and b) for South Figure 5. Synoptic magnetic maps for CR2027 (25February – 25 March, 2005) obtained without and with averaged: a) one image, b) 60 images. Latitude in sin (latitude). Resolution is 1o 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 = 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 = o )

N-S sigma distributions Figure 3

Figure 4

The values of the total polar magnetic flux are depended on the number of averaged images (Figure1). The noise level of the MDI magnetograms was estimated by Ortiz et.al (2002). They obtained that the 20 min averaged MDI magnetograms have a reasonably low noise level. The averaged magnetic noise level for 5 min integrated magnetograms is about 9G. But 1-σ noise level for 1 min longitudinal magnetograms is 20 G. They, also found the increase of the noise in the direction SW limb, which we can see in Figure 2 (c,d). The predicted noise level decreases as 1/√N, where N is number of consequent images. If the noise level for 1 min image is about 20G, it is 9G for 5 min, 2.8G for 50 min and 2.6 G for 60 min averaged images. There is some discrepancy in the values of the total magnetic flux which estimated from synoptic maps obtained from 15 averaged images per day and the consecutive 1 min images averaged over 60 min (see Figures 1 (a) and 4 (a) ). For example, for CR 2033 (8 August – 4 September, 2005) the total magnetic flux was e+022 Mx for 15 images taken during day and it is higher for any consequent averaged images up to the N=60. It is connected with the reduction of the supergranulation noise which more hopefully suppressed in the first case.

Figure 5

Figure 6

Influence of the Shutter noise on the estimation of the polar magnetic flux. The shutter noise of the SOHO/MDI instrument induces a small random ‘offset’ into the magnetic measurements. It was determined by Yang Liu, Xuepu Zhao and J.Todd Hoeksema (2004). The correction is applied to each magnetogram and this ‘offset’ is subtracted. We have estimated the magnetic flux of north polar cap (78oN-88oN) during the CR2033 with ‘offset’ correction and no ‘offset’ correction. There is a small difference in the relative positive magnetic flux and magnetic strength. With correction we obtain (|F+|/ Fr)= , and the averaged radial component of the magnetic field is B r =- 8.13G. No correction (|F+|/ Fr)= and averaged radial component of the magnetic field is B r = -7.62G. There is a small differences for total magnetic flux. For example, the total unsigned magnetic flux in CR2021 is x 1022 Mx without correction and it is x 1022 Mx with correction.

Conclutions The estimated values of the total magnetic flux depends on the number of averaged magnetograms in the synoptic map, it is decreased with the number of the averaged magnetograms due to noise reduction. Shutter noise contributes a small portion in the estimation of the total unsigned magnetic flux of polar caps for the individual synoptic map. The individual magnetograms reveal the non- uniform σ-distribution over solar disk. The noise increases in the SW direction on normal magnetograms, and in the NE direction, when SOHO/MDI is rotated by 180 o. References E. E. Benevolenskaya, 2004, A&A, 428, L5 C. J. Durrant, and P. R. Wilson, 2003, Solar Phys., 214, 23 Y. Liu, Xuepu Zhao, and J. T. Hoeksema, 2004, Solar Phys., 219, 39 Ortiz, S. K. Solanki, V. Domingo, M. Fligge, and B. Sanahuja, 2002, A&A, 388, 1036