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Register a new userSolar meridional circulation from twenty-one years of SOHO/MDI and SDO/HMI observations: Helioseismic travel times and forward modeling in the ray approximation
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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. An interpretation of the travel-time measurements is obtained using a forward-modeling approach in the ray approximation. 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 24s northern hemisphere, the measurements favor a single-cell meridional circulation model where the poleward flows persist down to $sim$0.8 $R_odot$, accompanied by local inflows toward the activity belts in the near-surface layers. Cycle 24s northern hemisphere is anomalous: travel-time differences are significantly smaller when travel distances are greater than 20$^circ$. This asymmetry between northern and southern hemispheres during cycle 24 was not present in previous measurements (e.g., Rajaguru & Antia 2015), 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 $sim$30$^circ$, 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.
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We present and discuss results from time-distance helioseismic measurements of meridional circulation in the solar convection zone using 4 years of Doppler velocity observations by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). Using an in-built mass conservation constraint in terms of the stream function we invert helioseismic travel times to infer meridional circulation in the solar convection zone. We find that the return flow that closes the meridional circulation is possibly beneath the depth of $0.77 R_{odot}$. 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 signal-to-noise 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.
Using a 3D global solver of the linearized Euler equations, we model acoustic oscillations over background velocity flow fields of single-cell meridional circulation with deep and shallow return flows as well as a double-cell meridional circulation profile. The velocities are generated using a mean-field hydrodynamic and dynamo model -- moving through the regimes with minimal parameter changes; counter-rotation near the base of the tachocline is induced by sign inversion of the non-diffusive action of turbulent Reynolds stresses ($Lambda$-effect) due to the radial inhomogeneity of the Coriolis number. By mimicking the stochastic excitation of resonant modes in the convective interior, we simulate realization noise present in solar observations. Using deep-focusing to analyze differences in travel-time signatures between the three regimes, as well as comparing to solar observations, we show that current helioseismology techniques may offer important insights about the location of the return flow, however, that it may not be possible to definitively distinguish between profiles of single-cell or double-cell meridional circulation.
In the quiet solar photosphere, the mixed polarity fields form a magnetic carpet, which continuously evolves due to dynamical interaction between the convective motions and magnetic field. This interplay is a viable source to heat the solar atmosphere. In this work, we used the line-of-sight (LOS) magnetograms obtained from the Helioseismic and Magnetic Imager (HMI) on the textit{Solar Dynamics Observatory} (textit{SDO}), and the Imaging Magnetograph eXperiment (IMaX) instrument on the textit{Sunrise} balloon-borne observatory, as time dependent lower boundary conditions, to study the evolution of the coronal magnetic field. We use a magneto-frictional relaxation method, including hyperdiffusion, to produce time series of three-dimensional (3D) nonlinear force-free fields from a sequence of photospheric LOS magnetograms. Vertical flows are added up to a height of 0.7 Mm in the modeling to simulate the non-force-freeness at the photosphere-chromosphere layers. Among the derived quantities, we study the spatial and temporal variations of the energy dissipation rate, and energy flux. Our results show that the energy deposited in the solar atmosphere is concentrated within 2 Mm of the photosphere and there is not sufficient energy flux at the base of the corona to cover radiative and conductive losses. Possible reasons and implications are discussed. Better observational constraints of the magnetic field in the chromosphere are crucial to understand the role of the magnetic carpet in coronal heating.
Time-distance helioseismology is a technique for measuring the time for waves to travel from one point on the solar surface to another. These wave travel times are affected by advection by subsurface flows. Inferences of plasma flows based on observed travel times depend critically on the ability to accurately model the effects of subsurface flows on time-distance measurements. We present a Born approximation based computation of the sensitivity of time distance travel times to weak, steady, inhomogeneous subsurface flows. Three sensitivity functions are obtained, one for each component of the 3D vector flow. We show that the depth sensitivity of travel times to horizontally uniform flows is given approximately by the kinetic energy density of the oscillation modes which contribute to the travel times. For flows with strong depth dependence, the Born approximation can give substantially different results than the ray approximation.
Accurate determination of the rotation rate in the radiative zone of the sun from helioseismic observations requires rotational frequency splittings of exceptional quality as well as reliable inversion techniques. We present here inferences based on mode parameters calculated from 2088-days long MDI, GONG and GOLF time series that were fitted to estimate very low frequency rotational splittings (nu < 1.7 mHz). These low frequency modes provide data of exceptional quality, since the width of the mode peaks is much smaller than the rotational splitting and hence it is much easier to separate the rotational splittings from the effects caused by the finite lifetime and the stochastic excitation of the modes. We also have implemented a new inversion methodology that allows us to infer the rotation rate of the radiative interior from mode sets that span l=1 to 25. Our results are compatible with the sun rotating like a rigid solid in most of the radiative zone and slowing down in the core (R_sun < 0.2). A resolution analysis of the inversion was carried out for the solar rotation inverse problem. This analysis effectively establishes a direct relationship between the mode set included in the inversion and the sensitivity and information content of the resulting inferences. We show that such an approach allows us to determine the effect of adding low frequency and low degree p-modes, high frequency and low degree p-modes, as well as some g-modes on the derived rotation rate in the solar radiative zone, and in particular the solar core. We conclude that the level of uncertainties that is needed to infer the dynamical conditions in the core when only p-modes are included is unlikely to be reached in the near future, and hence sustained efforts are needed towards the detection and characterization of g-modes.
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