We present and discuss results from time-distance helioseismic measurements of meridional circulation (MC) in the solar convection zone using 4 yrof Doppler velocity observations by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. Using abuilt-inmass conservation constraint in terms of the stream function,we invert helioseismic travel times to infer the MC in the solar convection zone. We find that the return flow that closes the MC is possibly beneath the depth of 0.77 R e . We discuss the significance of this result in relation to other helioseismic inferences published recently and possible reasons for the differences in the results. Our results show clearly the pitfalls involved in the measurements of material flows in the deep solar interior given the current limits on the signal-to-noise ratio and our limited understanding of systematics in the data. We also discuss the implications of our results for the dynamics of solar interior and popular solar dynamo models.

While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this article, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out a helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by Gizon et al. (2009aGizon et al. ( , 2009b. We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat.

We study properties of waves of frequencies above the photospheric acoustic cut-off of ≈ 5.3 mHz, around four active regions, through spatial maps of their power estimated using data from the Helioseismic and Magnetic Imager (HMI) and Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). The wavelength channels 1600Å and 1700Å from AIA are now known to capture clear oscillation signals due to helioseismic p-modes as well as waves propagating up through to the chromosphere. Here we study in detail, in comparison with HMI Doppler data, properties of the power maps, especially the so called "acoustic halos" seen around active regions, as a function of wave frequencies, inclination, and strength of magnetic field (derived from the vector-field observations by HMI) and observation height. We infer possible signatures of (magneto)acoustic wave refraction from the observation-height dependent changes, and hence due to changing magnetic strength and geometry, in the dependences of power maps on the photospheric magnetic quantities. We discuss the implications for theories of p-mode absorption and mode conversions by the magnetic field.

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Context. The solar meridional flow is an essential ingredient in flux-transport dynamo models. However, no consensus on its subsurface structure has been reached. Aims. We merge the data sets from SOHO/MDI and SDO/HMI with the aim of achieving a greater precision on helioseismic measurements of the subsurface meridional flow. Methods. The south-north travel-time differences are measured by applying time-distance helioseismology to the MDI and HMI medium-degree Dopplergrams covering May 1996-April 2017. Our data analysis corrects for several sources of systematic effects: P-angle error, surface magnetic field effects, and center-to-limb variations. For HMI data, we used the P-angle correction provided by the HMI team based on the Venus and Mercury transits. For MDI data, we used a P-angle correction estimated from the correlation of MDI and HMI data during the period of overlap. The center-to-limb effect is estimated from the east-west travel-time differences and is different for MDI and HMI observations. An interpretation of the travel-time measurements is obtained using a forward-modeling approach in the ray approximation. Results. In the latitude range 20 • -35 • , the travel-time differences are similar in the southern hemisphere for cycles 23 and 24. However, they differ in the northern hemisphere between cycles 23 and 24. Except for cycle 24's northern hemisphere, the measurements favor a single-cell meridional circulation model where the poleward flows persist down to ∼0.8 R , accompanied by local inflows toward the activity belts in the near-surface layers. Cycle 24's northern hemisphere is anomalous: travel-time differences are significantly smaller when travel distances are greater than 20 • . This asymmetry between northern and southern hemispheres during cycle 24 was not present in previous measurements, which assumed a different P-angle error correction where south-north travel-time differences are shifted to zero at the equator for all travel distances. In our measurements, the travel-time differences at the equator are zero for travel distances less than ∼30 • , but they do not vanish for larger travel distances. This equatorial offset for large travel distances need not be interpreted as a deep cross-equator flow; it could be due to the presence of asymmetrical local flows at the surface near the end points of the acoustic ray paths. Conclusions. The combined MDI and HMI helioseismic measurements presented here contain a wealth of information about the subsurface structure and the temporal evolution of the meridional circulation over 21 years. To infer the deep meridional flow, it will be necessary to model the contribution from the complex time-varying flows in the near-surface layers.