Shuhong Yang1,2,7, Jie Jiang3, Zifan Wang1,2,7, Yijun Hou1,2,7, Chunlan Jin1,2,7, Qiao Song4,6, Yukun Luo3, Ting Li1,2,7, Jun Zhang5, Yuzong Zhang1,2,7, Guiping Zhou1,2,7, Yuanyong Deng1,2,7, Jingxiu Wang1,2,7
1. National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China
2. School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China
3. School of Space and Environment, Beihang University, Beijing 102206, China
4. Key Laboratory of Space Weather, National Satellite Meteorological Center (National Center for Space Weather), China Meteorological Administration, Beijing 100081, China
5. School of Physics and Materials Science, Anhui University, Hefei 230601, China
6. Innovation Center for FengYun Meteorological Satellite (FYSIC), Beijing 100081, China
7. State Key Laboratory of Solar Activity and Space Weather, Beijing 100190, China
Meridional flow in the Sun is thought to play an important role in determining the magnetic structure and strength in the polar regions[1]. There are some methods to determine the meridional flow, e.g., direct Doppler-shift measurement, tracer tracking, and helioseismology analysis. However, meridional flow near the solar poles is still unclear.
The Hinode Spectro-polarimeter (SP) provides high spatial-resolution and polarimetric precision measurement of the photospheric vector magnetic field. The SP polar observations obtained from 2012 to 2021 and released at ISEE, Nagoya University, are used to study magnetic fields in the polar caps. Every year for each pole, a batch of about 10 magnetograms with an interval of about 3 days is adopted (see Table 1 in Ref. [2]).
The 10-yr SP observations show that in each polar cap, during most of the time of the solar cycle except for the period around the polarity reversal, the higher the latitude, the weaker the radial magnetic flux density in general[3] (as shown in Fig. 1). Then, one question is raised: which kind of meridional flow could result in the polar magnetic distribution pattern as observed by Hinode?
Surface flux transport (SFT) models have been remarkably successful in reproducing the magnetic field patterns at the solar surface. In these models, meridional flow, differential rotation, and supergranular diffusion are included. To explore the meridional flow, an SFT model[4] is used to simulate the global radial magnetic field. For the first time, the SP high-resolution observations of the vector magnetic fields in polar caps are used to directly constrain the SFT simulation[3].
Figure 1| Magnetic supersynoptic map created from Hinode/SP radial magnetograms.
In the simulation, the initial condition of the magnetic field is the radial magnetic field synoptic map of Carrington Rotation (CR) 2097 observed by the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO). The magnetic source term consists of active regions identified and extracted from HMI synoptic maps during CRs 2097-2236. For the meridional flow in the SFT model, a double-cell profile with a counter-cell in the polar cap is adopted.
Figure 2| Radial flux density as a function of latitude in 2017 and 2020, respectively. The color and black symbols represent the observations from Hinode/SP and SDO/HMI, respectively. The solid curves are the simulated results, and the dotted curve is the corresponding fitted result.
The simulation results of different counter-cell flow value cases are compared to the polar field observations of Hinode. The results reveal that when assuming a counter-cell meridional flow from the pole to 70° latitude with the maximum amplitude of 3 m/s, the simulation fits the observation well (Fig. 2).
Based on the observation and simulation, the meridional flow pattern of the Sun can be deduced (see Fig. 3). Figure 3a shows the meridional flow at the solar surface. The poleward meridional flow is located within 0-70° latitude with the maximum amplitude of 11 m/s at 35° latitude and the equatorward meridional flow is located within 70-90° latitude with the maximum amplitude of 3 m/s at 80° latitude.
Figure 3| Schematic cartoon showing the meridional flow pattern of the Sun. (a) Velocity distribution of the meridional flow at the solar surface. The blue and red arrows represent the poleward meridional flow and the equatorward meridional flow, respectively. (b) Meridional flow as a function of latitude and depth assuming a single cell in radius. The blue and red closed loops represent the main-cell and the counter-cell, respectively.
For the meridional flow in the solar convection zone, previous studies have given different conclusions, i.e., either one cell or two cells in the radial direction. Assuming that there is a single cell in the radial direction[5], then the flow pattern is deduced to consist correspondingly of two meridional circulation cells in each hemisphere, forming a double-cell flow pattern in the solar convection zone, as shown in Fig. 3b. The main-cell and counter-cell meridional flows meet at the solar surface with the latitude of 70° and return in the subsurface via equatorward and poleward flows, respectively.
For more details, please refer to the recent publications [2,3].
References
[1] Hathaway, D., & Rightmire, L. 2010, Science, 327, 1350
[2] Yang, S., Jiang, J., Wang, Z., et al. 2024, RAA, 24, 075015
[3] Yang, S., Jiang, J., Wang, Z., et al. 2024, ApJ, 970, 183
[4] Jiang, J., Cameron, R. H., & Schüssler, M. 2014, ApJ, 791, 5
[5] Gizon, L., Cameron, R., Pourabdian, M., et al. 2020, Science, 368, 1469