The radial gradient of the near-surface shear layer of the Sun

Context. Helioseismology has provided unprecedented information about the internal rotation of the Sun. One of the important achievements was the discovery of two radial shear layers: one near the bottom of the convection zone (the tachocline) and one near the surface. These shear layers may be important ingredients for explaining the magnetic cycle of the Sun. Aims. We measure the logarithmic radial gradient of the rotation rate (dln Omega/dln r) near the surface of the Sun using 15 years of f mode rotational frequency splittings from the Michelson Doppler Imager (MDI) and four years of data from the Helioseismic and Magnetic Imager (HMI). Methods. We model the angular velocity of the Sun in the upper similar to 10 Mm as changing linearly with depth and use a multiplicative optimally localized averaging inversion to infer the gradient of the rotation rate as a function of latitude. Results. Both the MDI and HMI data show that dln Omega/dln r is close to -1 from the equator to 60 degrees latitude and stays negative up to 75 degrees latitude. However, the value of the gradient is different for MDI and HMI for latitudes above 60 degrees. Additionally, there is a significant difference between the value of dln Omega/dln r using an older and recently reprocessed MDI data for latitudes above 30 degrees. Conclusions. We could reliably infer the value of dln Omega/dln r up to 60 degrees, but not above this latitude, which will hopefully constrain theories of the near-surface shear layer and dynamo. Furthermore, the recently reprocessed MDI splitting data are more reliable than the older versions which contained clear systematic errors in the high degree f modes.