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Causal Interaction between the subsurface rotation rate residuals and radial magnetic field in different timescales

We studied the presence and spatiotemporal characteristics and evolution of the variations in the differential rotation rates and radial magnetic fields in the Schwabe and Quasi-biennial-oscillation (QBO) timescales. To achieve these objectives, we used rotation rate residuals and radial magnetic field data from the Michelson Doppler Imager on the Solar and Heliospheric Observatory and the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory, extending from May 1996 to August 2020, covering solar cycles 23 and 24, respectively. Under the assumption that the radial surface magnetic field is non-local and the differential rotation is symmetric around the equator, our results suggest that the source region of the Schwabe cycle is confined between $\sim$30$^{\circ}$ N and S throughout the convection zone. As for the source region of the QBO, our results suggest that it is below 0.78R$_{\odot}$.