Temporal Variation of Angular Momentum in the Solar Convection Zone

We derive the angular momentum as a function of radius and time with the help of the rotation rates resulting from inversions of helioseismic data obtained from the Global Oscillation Network Group (GONG) and the Michelson Doppler Imager (MDI) and the density distribution from a model of the Sun. The base of the convection zone can be identified as a local maximum in the relative angular momentum after subtracting the contribution of the solid-body rotation. The angular momentum as a function of radius shows the strongest temporal variation near the tachocline. This variation extends into the lower convection zone and into the radiative interior and is related to the 1.3 yr periodicity found in the equatorial rotation rate of the tachocline. In the upper convection zone, we find a small systematic variation of the angular momentum that is related to torsional oscillations. The angular momentum integrated from the surface to a lower limit in the upper convection zone provides a hint that the torsional oscillation pattern extends deep into the convection zone. This is supported by other quantities such as the coefficients of a fit of Legendre polynomials to the rotation rates as a function of latitude. The temporal variation of the coefficient of P₄, indicative of torsional oscillations, suggests that the signature of these flows in the inversion results extend to about r ≈ 0.83 R_☉. With the lower limit of integration placed in the middle or lower convection zone, the angular momentum fluctuates about the mean without apparent trend, i.e., the angular momentum is conserved within the measurement errors. However, when integrated over the layers slightly below the convection zone (0.60-0.71 R_☉), the angular momentum shows the 1.3 yr period and hints at a long-term trend that might be related to the solar activity cycle.