We have developed a comprehensive catalog of the variable differential rotation measured near the solar photosphere. This catalog includes measurements of these flows obtained using several techniques: direct Doppler, granule tracking, magnetic pattern tracking, global helioseismology, as well as both time-distance and ring-diagram methods of local helioseismology. We highlight historical differential rotation measurements to provide context, and thereafter provide a detailed comparison of the MDI-HMI-GONG-Mt. Wilson overlap period (April 2010 – Jan 2011) and investigate the differences between velocities obtained from different techniques and attempt to explain discrepancies. A comparison of the rotation rate obtained by magnetic pattern tracking with the rotation rates obtained using local and global helioseismic techniques shows that magnetic pattern tracking measurements correspond to helioseismic flows located at a depth of 25 to 28 Mm. In addition, we show the torsional oscillation from Sunspot Cycles 23 and 24 and discuss properties that are consistent across measurement techniques. We find that acceleration derived from torsional oscillation is a better indicator of long-term trends in torsional oscillation compared to the residual velocity magnitude. Finally, this analysis will pave the way toward understanding systematic effects associated with various flow measurement techniques and enable more accurate determination of the global patterns of flows and their regular and irregular variations.

A new fitting methodology is presented that is equally well suited for the estimation of low-, medium-, and high-degree mode parameters from m-averaged solar oscillation power spectra of widely differing spectral resolution. This method, which we call the "Windowed, MuLTiple-Peak, averaged-spectrum" or WMLTP Method, constructs a theoretical profile by convolving the weighted sum of the profiles of the modes appearing in the fitting box with the power spectrum of the window function of the observing run, using weights from a leakage matrix that takes into account observational and physical effects, such as the distortion of modes by solar latitudinal differential rotation. We demonstrate that the WMLTP Method makes substantial improvements in the inferences of the properties of the solar oscillations in comparison with a previous method, which employed a single profile to represent each spectral peak. We also present an inversion for the internal solar structure, which is based upon 6366 modes that we computed using the WMLTP method on the 66 day 2010 Solar and Heliospheric Observatory/MDI Dynamics Run. To improve both the numerical stability and reliability of the inversion, we developed a new procedure for the identification and correction of outliers in a frequency dataset. We present evidence for a pronounced departure of the sound speed in the outer half of the solar convection zone and in the subsurface shear layer from the radial sound speed profile contained in Model S of Christensen-Dalsgaard and his collaborators that existed in the rising phase of Solar Cycle 24 during mid-2010.

We use global heliseismic data from the Global Oscillation Network Group, the Michelson Doppler Imager on board the Solar and Heliospheric Observatory, and the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, to examine the behavior, during the rising phase of Solar Cycle 24, of the migrating zonal flow pattern known as the torsional oscillation. Although the high-latitude part of the pattern appears to be absent in the new cycle when the flows are derived by subtracting a mean across a full solar cycle, it can be seen if we subtract the mean over a shorter period in the rising phase of each cycle, and these two mean rotation profiles differ significantly at high latitudes. This indicates that the underlying high-latitude rotation has changed; we speculate that this is in response to weaker polar fields, as suggested by a recent model.

We present the first characterization of high-degree modes (i.e., up to 900 or 1000), using three instruments and three epochs corresponding to the 2001, 2002 and 2010 MDI Dynamics runs. For 2001, we analyzed MDI full-disk Dopplergrams, while for 2002, we analyzed MDI and GONG full-disk Dopplergrams, and for 2010 we analyzed MDI, GONG and HMI full-disk Dopplergrams. These Dopplergrams were spatially decomposed up to l = 900 or 1000, and power spectra for all degrees and all azimuthal orders were computed using a high-order multi-taper, power spectrum estimator. These spectra were then fitted for all degrees and all azimuthal orders, above = 100, and for all orders with substantial amplitude. Fitting at high degrees generates ridge characteristics, characteristics that do not correspond to the underlying mode characteristics. We used a sophisticated forward modeling to recover the best possible estimate of the underlying mode characteristics (mode frequencies, as well as linewidths, amplitudes and asymmetries). We present the first attempt to apply this method to three instruments and three epochs. The derived sets of corrected mode characteristics (frequencies, line widths, asymmetries and amplitudes) are presented and compared.

Solar oscillation frequencies are known to follow the trend of solar cycle and show a strong correlation with various activity indices. However, the extended minimum between cycles 23 and 24 has raised several questions on the correlation between frequencies and solar activity where frequencies with different mode sets sensed different minima. In this paper, we analyze intermediate-degree mode frequencies as the Sun emerges from the unusually long period of minimal magnetic activity to study their behaviour with activity indices and compare results with the corresponding phase of cycle 23. We show that a model based on the rising phase of cycle 23 is a good predictor for behaviour in the rising phase of cycle 24.

We present the first accurate characterization of high-degree modes, derived using the best Michelson Doppler Imager (MDI) full-disk full-resolution data set available. A 90 day long time series of full-disk 2 arcsec pixel−1 resolution Dopplergrams was acquired in 2001, thanks to the high rate telemetry provided by the Deep Space Network. These Dopplergrams were spatially decomposed using our best estimate of the image scale and the known components of MDI's image distortion. A multi-taper power spectrum estimator was used to generate power spectra for all degrees and all azimuthal orders, up to ℓ = 1000. We used a large number of tapers to reduce the realization noise, since at high degrees the individual modes blend into ridges and thus there is no reason to preserve a high spectral resolution. These power spectra were fitted for all degrees and all azimuthal orders, between ℓ = 100 and ℓ = 1000, and for all the orders with substantial amplitude. This fitting generated in excess of 5.2 × 106 individual estimates of ridge frequencies, line widths, amplitudes, and asymmetries (singlets), corresponding to some 5700 multiplets (ℓ, n). Fitting at high degrees generates ridge characteristics, characteristics that do not correspond to the underlying mode characteristics. We used a sophisticated forward modeling to recover the best possible estimate of the underlying mode characteristics (mode frequencies, as well as line widths, amplitudes, and asymmetries). We describe in detail this modeling and its validation. The modeling has been extensively reviewed and refined, by including an iterative process to improve its input parameters to better match the observations. Also, the contribution of the leakage matrix on the accuracy of the procedure has been carefully assessed. We present the derived set of corrected mode characteristics, which includes not only frequencies, but line widths, asymmetries, and amplitudes. We present and discuss their uncertainties and the precision of the ridge-to-mode correction schemes, through a detailed assessment of the sensitivity of the model to its input set. The precision of the ridge-to-mode correction is indicative of any possible residual systematic biases in the inferred mode characteristics. In our conclusions, we address how to further improve these estimates, and the implications for other data sets, like GONG+ and HMI.

The Birmingham Solar-Oscillations Network (BiSON) has been collecting helioseismic data for the last three solar cycles. We use these data to determine whether the internal properties of the Sun during the minimum preceding cycle 24 was different compared to that preceding cycle 23.

After the late start to Cycle 24 there are some indications that activity may have peaked as early as late 2011 and that the polar-field reversal has already occurred in the North. We use helioseismic measurements of the migrating zonal flow pattern known as the torsional oscillation to estimate the length of the solar cycle, and find that it has held steady at about 12.3 years since late 2009, which would point to solar maximum in 2013 as expected.

We describe and apply a new helioseismic method for measuring solar subsurface axisymmetric meridional and zonal flow. The method is based on a theoretical model of the response of global-oscillation eigenfunctions to the flow velocity and uses cross spectra of the time-varying coefficients in the spherical-harmonic expansion of the photospheric Doppler-velocity field. Eigenfunction changes modify the leakage matrix, which describes the sensitivity of the spherical-harmonic coefficients to the global-oscillation modes. The form of the leakage matrix in turn affects the theoretically expected spherical-harmonic cross spectra. Estimates of internal meridional and zonal flow were obtained by fitting the theoretical flow-dependent cross spectra to spherical-harmonic cross spectra computed from approximately 500 days of full-disk Dopplergrams from the Helioseismic and Magnetic Imager (HMI) on the SDO spacecraft. The zonal-flow measurements, parameterized in the form of “a” coefficients, substantially agree with measurements obtained from conventional global-mode-frequency analysis. The meridional-flow estimates, in the form of depth-weighted averages of the flow velocity, are similar to estimates obtained from earlier analyses, for oscillation modes that penetrate the outermost one-third of the convection zone. For more deeply penetrating modes, the inferred flow velocity increases significantly with penetration depth, indicating the need for either a modification of the simple conveyor-belt picture of meridional flow or improvement in the cross-spectral model.

We present the hest to date determination of high-degree mode parameters obtained from a ninety day long time series of full-disk full-resolution Michelson Doppler Imager (MDI) Dopplergrams. These Dopplergrams were decomposed using our best estimate of the image scale and the known components of MDI's image distortion. The spherical harmonic decomposition was carried out up to = 1000, and a high-order sine multi-taper power spectrum estimator was used to generate power spectra. These power spectra were fitted for all degrees and all azimuthal orders, for 100 <= C <= 1000, and for all radial orders with substantial amplitude, generating some 6 x 10(6) estimates of ridge frequencies, line-widths, amplitudes and asymmetries. We used a sophisticated forward modeling of the mode to ridge blending, to recover the best possible estimate of the underlying mode characteristics.

The Helioseismic and Magnetic Imager (HMI; Scherrer & Schou 2011) is one of the three instruments aboard the Solar Dynamics Observatory (SDO) that was launched on February 11, 2010 from Cape Canaveral, Florida. The instrument began to acquire science data on March 24. The regular operations started on May 1. HMI measures the Doppler velocity and line-of-sight magnetic field in the photosphere at a cadence of 45 seconds, and the vector magnetic field at a 135-second cadence, with a 4096 x 4096 pixels full disk coverage. The vector magnetic field data is usually averaged over 720 seconds to suppress the p-modes and increase the signal-to-noise ratio. The spatial sampling is about 0 ''.5 per pixel. HMT observes the Fe I 6173 angstrom absorption line, which has a Lande factor of 2.5. These data are further used to produce higher level data products through the pipeline at the HMI-ALA Joint Science Operations Center (JSOC) - Science Data Processing (Scherrer et al. 2011) at Stanford University. In this paper, we briefly describe the data products, and demonstrate the performance of the HMI instrument. We conclude that the HMI is working extremely well.

The zonal flows known as the torsional oscillation have by now been observed for more than 15 years using observations from the Michelson Doppler Imager (MDI) and Global Oscillation Network Group (GONG). Even with this limited set of data it is clear that there are significant differences between the cycles, as also evidenced by the prolonged recent solar minimum.Here we discuss some of these differences and their significance. In particular we discuss the slower development of the current solar cycle and the lack of a polar branch in the torsional oscillation. We will also compare results from MDI and the Helioseismic Magnetic Imager (HMI) and discuss the prospects for generating longer consistent sets of observations.