Fadil Inceoglu1,2,3, Rachel Howe4,5, Paul T. M. Loto’aniu1,2
1. Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, Boulder, CO, USA
2. National Centers for Environmental Information, National Oceanographic and Atmospheric Administration, Boulder, CO, USA
3. GFZ German Research Centre for Geosciences, Wissenschaftpark “Albert Einstein”, Telegrafenberg, 14473 Potsdam, Germany
4. School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
5. Stellar Astrophysics Centre (SAC), Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
The Sun shows magnetic activity cycles with timescales extending from months to centuries. The most known of these is the Schwabe cycles (SC). The Sun also exhibits quasi-biennial oscillations (QBOs), which are superimposed on the SC. The period of the QBOs ranges between 0.6 and 4 years with a clear separation at 1.5 year, and the QBOs are in-phase with the SC. The QBOs have been observed from the subsurface magnetic fields to the neutron counting rates on Earth1. Among the underlying physical mechanisms, we can count a secondary dynamo and tachocline nonlinear oscillations (TNOs) (see Ref  for further references).
To investigate whether the QBOs are also present in the differential rotation at the target depths of 0.90R⊙, 0.95R⊙, and 0.99R⊙, we used data from SOHO/MDI and SDO/HMI for solar cycles 23 and 24, respectively.
We calculated the differential rotation rates based on regularized least squares (RLS) code using frequencies derived from MDI and HMI data for solar cycles 23 and 24, respectively. The rotation rate residuals, which we used in our further analyses, were calculated by removing the temporal mean from the MDI data for solar cycle 23, and the HMI data for solar cycle 24. Furthermore, as it is known that the QBO signals are generally suppressed by the SC, we used empirical mode decomposition (EMD) to remove these effects and investigated the existence and spatiotemporal behaviors of the QBOs (Figure 1).
Following the EMD analyses, we found that the internal mode functions of the rotation rate residuals (hereby IMFs) show faster-than-average and slower-than-average flow bands at each target depth and their amplitudes increase with increasing depth. The IMFs also show different patterns as we go deeper in the solar convection zone, as well as in each solar cycle (Figure 1).
Figure 1| Left and right panels show the IMFs at target depths of 0.90R⊙, 0.95R⊙, and 0.99R⊙ for solar cycle 23 (MDI/SOHO) and 24 (HMI/SDO). The vertical solid lines show solar cycle maxima, while the vertical dashed lines show the starts and ends of the solar cycles. Note that the values are flipped around the equator.
To further investigate the spatiotemporal behavior of the QBO-like signals in the IMFs, we performed continuous wavelet transformation (CWT). To calculate the CWTs, we first averaged the IMFs into low (0o – 30o), mid (30o – 50o) and high (50o – 70o) latitudinal bands.
The CWTs show the existence of the QBO-like signals (p<0.01), generally in each depth and latitudinal band during solar cycles 23 and 24 (Figure 2 for solar cycle 24). These signals show different characteristics at each depth and latitudinal band.
Figure 2| CWTs of the IMFs target depths and latitude bands as indicated on the figures. The red contours represent the significance level of 0.01, while the hatched area marks the cone of influence, where the CWTs might be influenced by the edge effects.
Our results are in line with those from the surface magnetic fields, which showed that the QBO-like signals are distributed over all latitudes and the period is concentrated around 1.5 – 4 years. The spatiotemporal behaviors also show patterns similar to those from the radial and meridional components of the surface magnetic fields. Additionally, we also detected QBO-like signals in the high latitudinal band, which is also in line with those from the high-latitude solar faculae.
Figure 3| Left panel shows the IMFs at target depths and latitudinal bands as indicated on subpanels. The right panel shows the standard deviation in each IMF as a function of depth. Color-shaded areas show the 1σ standard deviation interval calculated for the IMFs. The vertical solid lines show the solar cycle maxima, while the dashed lines show the cycle minima. The vertical gray-shaded areas show the overlapping time period between two data sets.
We also further investigated the amplitude-depth relationship of the IMFs at each latitudinal band and target depth. Interestingly, we observed that the amplitudes of the QBO-like signals clearly increase with increasing depth (Figure 3). This feature might point to a deeper source region for the QBO-signals. Dikpati et al. suggested that the QBO-type signals can be generated via TNOs, which is defined as the periodic energy exchange between the differential rotation and the magnetic Rossby waves at the tachocline. During the phase when the magnetic Rossby waves steal kinetic energy from the differential rotation and grow, the upper boundary of the tachocline becomes maximally deformed, creating bulges and depressions. This process might eventually give rise to the buoyant rise of the toroidal magnetic field lines residing there through the convection zone
As a follow-up study, we plan to include the magnetic field strengths together with flow fields to study the causal interactions between them in the Schwabe and the QBO timescales.
 Inceoglu, F., Simoniello, R., Arlt, R., & Rempel, M. 2019, A&A, 625, A117
 Howe, R., Hill, F., Komm, R., et al. 2018, ApJL, 862, L5
 Vecchio, A., Laurenza, M., Meduri, D., Carbone, V., & Storini, M. 2012, ApJ, 749, 27
 Deng, L. H., Fei, Y., Deng, H., Mei, Y., & Wang, F. 2020, MNRAS, 494, 4930
 Dikpati, M., Cally, P. S., McIntosh, S. W., & Heifetz, E. 2017, NatSR, 7, 14750