Modeling Solar Oscillation Power Spectra. III. Spatiotemporal Spectra of Solar Granulation Velocity Field as Seen in HMI Velocity Measurements

We suggest a physically motivated model of the uncorrelated background, which can be used to improve the accuracy of helioseismic frequency measurements when the background contributes significantly to the formation of spectral lines of acoustic resonances. The basic assumption of our model is that the correlation length of the convective motions is small compared with the horizontal wavelength R _⊙/ℓ of the observations, where ℓ is the degree of the spherical harmonic Y _{ℓ m} (θ, φ). When applied to solar power spectra at frequencies below acoustic resonances, the model reveals a distinct sensitivity to solar rotation: advection of the convective velocity pattern brings spatial correlations in the apparent stochastic velocity field (temporal correlations in the corotating frame induce spatial correlations in the inertial frame). The induced spatiotemporal correlations manifest themselves as an antisymmetric component in the dependence of the convective noise power on azimuthal order m, which allows us to address the solar differential rotation. With 360 days of data obtained by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, we measure three components of the rotation rate as a function of latitude using only ℓ = 300. This result indicates that the model suggests a new way of measuring solar subsurface rotation. This approach can complement traditional measurements based on correlation tracking.