B. Lekshmi1, Dibyendu Nandy1,2, H. M. Antia3
1. Center of Excellence in Space Sciences India, Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, West Bengal
2. Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, West Bengal,India
3. Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
Meridional flow, the large scale axisymmetric flow of plasma from the equator to the poles on the solar surface plays an important role in driving the solar dynamo. Velocity at different latitudes and depths vary with the solar cycle and are not symmetric across the equator. We analyze the temporal variation in the hemispherical asymmetry of the meridional flow at the near-surface layers of the Sun and find that it is related to the asymmetry in the sunspot cycle and surprisingly, precedes the solar cycle[1].
Meridional flow measurements from Helioseismic and Magnetic Imager (HMI) and Global Oscillation Network Group (GONG) ring-diagram pipelines starting from 2010 April and 2001 July, respectively, till 2018 December are used for our analysis. Velocity averaged over 11 and 8 years, respectively, for GONG and HMI measurements are removed from the observed velocities to obtain the temporal variation in the meridional flow. Magnetic flux calculated from Michelson Doppler Imager (MDI) and HMI synoptic magnetograms and the sunspot number data (SSN) obtained from SILSO World Data Center are used to explore the relationship between flow asymmetries and the sunspot cycle. It can be observed from Figure 1 that the residual velocities are not symmetric across the equator and the sunspot distribution follows the residual velocity band.
Figure 1| Contour plots of residual meridional flow velocities calculated from GONG (top panel) and HMI (bottom panel) measurements at 0.997R. Black dots represent the sunspot distribution for the same period.
For further analysis, the residual velocity obtained from both GONG and HMI and the magnetic flux is averaged over active latitude. We calculate the hemispherical asymmetry in the residual meridional flow (δVN － δVS) and magnetic flux ( FN － FS) over the active latitudes using this averaged velocity and flux. The detailed procedure can be found in reference[1].
The top panel of Figure 2 shows that the asymmetry in velocity is related to the sunspot cycle asymmetry. We generate 1000 random sets of asymmetries in velocity, flux and SSN by adding random errors (within the standard error of each quantity) to the mean observed value at different depths. A time-delayed correlation analysis is performed between the velocity and magnetic flux sets over a range of time delays (0 – 5 yr) with the asymmetry in velocity preceding the flux asymmetry. A similar analysis is performed between the asymmetries in velocity and SSN. The mean correlation coefficients (r) with 99.9% confidence and the corresponding time delays along with standard deviation obtained by correlating the 1000 pairs at different depths are given in the table below.
Figure 2| (Top) Temporal variation of the asymmetry in residual meridional flow over active latitude obtained from GONG (solid magenta lines) and HMI (dashed magenta lines) measurements. Green and blue curves represent the asymmetries in average magnetic flux and sunspot number. Error bars on the top right corner represent the mean standard error in the asymmetries. (Middle) Liner fit to the asymmetry in average residual meridional flow from GONG (HMI) represented by filled (open) circles as a function of asymmetry in magnetic flux where the velocity precedes by 3.5 (3.4) yr. (Bottom) Liner fit to the asymmetry in velocities from GONG (HMI) as a function of SSN with the velocity asymmetry preceding by 3.5 (3.4) yr. Black dotted lines represent the 95% confidence bounds.
We observe that the asymmetry in meridional flow precedes the asymmetry in the sunspot cycle by 3.1 – 3.6 yr and that they are anti-correlated. The correlation and time-delays are similar for both GONG and HMI measurements. The observed anti-correlation corresponds to the inflow of plasma to the regions of strong magnetic flux which in-turn decreases the net meridional flow[2,3]. Independent study shows that the time-varying meridional flow appears at mid-latitudes about three years before the appearance of cycle 24 magnetic activity in synoptic maps[4] which is similar to the time-delay we observe. We propose that the asymmetry in the meridional flow can be a precursor of the sunspot cycle asymmetry, and maybe related to early signature of the build-up of solar cycle magnetic fields, perhaps through non-local processes[5]. Further theoretical studies are necessary to firmly establish the origin of this time-dependent correlation between residual flow amplitude and sunspot cycle asymmetries.
Table 1| Table showing the correlation coefficients (r) and time delays between the asymmetries of velocity with magnetic flux and SSN, respectively as a function of depth.
References
[1] Lekshmi B., Nandy D., Antia H. M., 2019, MNRAS, 489, 714
[2] Hathaway D. H., Rightmire L., 2011, ApJ, 729, 80
[3] Zhao J., Kosovichev A. G., Bogart R. S., 2014, ApJ, 789, L7
[4] Komm R., González Hernández I., Howe R., Hill F., 2015b, Solar Phys., 290, 3113
[5] Spruit, H. C. 2003, Solar Phys., 213, 1