Solar Interior

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T L Duvall - One of the best experts on this subject based on the ideXlab platform.

  • detection of equatorward meridional flow and evidence of double cell meridional circulation inside the sun
    The Astrophysical Journal, 2013
    Co-Authors: Junwei Zhao, Alexander G. Kosovichev, R.s. Bogart, T L Duvall, Thomas Hartlep
    Abstract:

    Meridional flow in the Solar Interior plays an important role in redistributing angular momentum and transporting magnetic flux inside the Sun. Although it has long been recognized that the meridional flow is predominantly poleward at the Sun's surface and in its shallow Interior, the location of the equatorward return flow and the meridional flow profile in the deeper Interior remain unclear. Using the first 2 yr of continuous helioseismology observations from the Solar Dynamics Observatory/Helioseismic Magnetic Imager, we analyze travel times of acoustic waves that propagate through different depths of the Solar Interior carrying information about the Solar Interior dynamics. After removing a systematic center-to-limb effect in the helioseismic measurements and performing inversions for flow speed, we find that the poleward meridional flow of a speed of 15 m s–1 extends in depth from the photosphere to about 0.91 R ☉. An equatorward flow of a speed of 10 m s–1 is found between 0.82 and 0.91 R ☉ in the middle of the convection zone. Our analysis also shows evidence of that the meridional flow turns poleward again below 0.82 R ☉, indicating an existence of a second meridional circulation cell below the shallower one. This double-cell meridional circulation profile with an equatorward flow shallower than previously thought suggests a rethinking of how magnetic field is generated and redistributed inside the Sun.

  • detection of equatorward meridional flow and evidence of double cell meridional circulation inside the sun
    arXiv: Solar and Stellar Astrophysics, 2013
    Co-Authors: Junwei Zhao, Alexander G. Kosovichev, R.s. Bogart, T L Duvall, Thomas Hartlep
    Abstract:

    Meridional flow in the Solar Interior plays an important role in redistributing angular momentum and transporting magnetic flux inside the Sun. Although it has long been recognized that the meridional flow is predominantly poleward at the Sun's surface and in its shallow Interior, the location of the equatorward return flow and the meridional flow profile in the deeper Interior remain unclear. Using the first two years of continuous helioseismology observations from the Solar Dynamics Observatory / Helioseismic Magnetic Imager, we analyze travel times of acoustic waves that propagate through different depths of the Solar Interior carrying information about the Solar Interior dynamics. After removing a systematic center-to-limb effect in the helioseismic measurements and performing inversions for flow speed, we find that the poleward meridional flow of a speed of 15 m/s extends in depth from the photosphere to about 0.91 R_sun. An equatorward flow of a speed of 10 m/s is found between 0.82 to 0.91 R_sun in the middle of the convection zone. Our analysis also shows evidence of that the meridional flow turns poleward again below 0.82 R_sun, indicating an existence of a second meridional circulation cell below the shallower one. This double-cell meridional circulation profile with an equatorward flow shallower than previously thought suggests a rethinking of how magnetic field is generated and redistributed inside the Sun.

  • systematic center to limb variation in measured helioseismic travel times and its effect on inferences of Solar Interior meridional flows
    The Astrophysical Journal, 2012
    Co-Authors: Junwei Zhao, A G Kosovichev, Kaori Nagashima, Richard S Bogart, T L Duvall
    Abstract:

    We report on a systematic center-to-limb variation in measured helioseismic travel times, which must be taken into account for an accurate determination of Solar Interior meridional flows. The systematic variation, found in time-distance helioseismology analysis using SDO/HMI and SDO/AIA observations, is different in both travel-time magnitude and variation trend for different observables. It is not clear what causes this systematic effect. Subtracting the longitude-dependent east-west travel times, obtained along the equatorial area, from the latitude-dependent north-south travel times, obtained along the central meridian area, gives remarkably similar results for different observables. We suggest this as an effective procedure for removing the systematic center-to-limb variation. The subsurface meridional flows obtained from inversion of the corrected travel times are approximately 10 m s−1 slower than those obtained without removing the systematic effect. The detected center-to-limb variation may have important implications in the derivation of meridional flows in the deep Interior and needs to be better understood.

  • systematic center to limb variation in measured helioseismic travel times and its effect on inferences of Solar Interior meridional flows
    arXiv: Solar and Stellar Astrophysics, 2012
    Co-Authors: Junwei Zhao, A G Kosovichev, Kaori Nagashima, Richard S Bogart, T L Duvall
    Abstract:

    We report on a systematic center-to-limb variation in measured helioseismic travel times, which must be taken into account for an accurate determination of Solar Interior meridional flows. The systematic variation, found in time-distance helioseismology analysis using SDO/HMI and SDO/AIA observations, is different in both travel-time magnitude and variation trend for different observables. It is not clear what causes this systematic effect. Subtracting the longitude-dependent east-west travel times, obtained along the equatorial area, from the latitude-dependent north-south travel times, obtained along the central meridian area, gives remarkably similar results for different observables. We suggest this as an effective procedure for removing the systematic center-to-limb variation. The subsurface meridional flows obtained from inversion of the corrected travel times are approximately 10 m/s slower than those obtained without removing the systematic effect. The detected center-to-limb variation may have important implications in the derivation of meridional flows in the deep Interior, and needs a better understanding.

  • computational acoustics in spherical geometry steps toward validating helioseismology
    The Astrophysical Journal, 2006
    Co-Authors: Shravan M Hanasoge, T L Duvall, J Schou, J Christensendalsgaard, M L Derosa, R M Larsen, N Hurlburt, Markus Roth, Sanjiva K Lele
    Abstract:

    Throughout the past decade, detailed helioseismic analyses of observations of Solar surface oscillations have led to advances in our knowledge of the structure and dynamics of the Solar Interior. Such analyses involve the decomposition of time series of the observed surface oscillation pattern into its constituent wave modes, followed by inversion procedures that yield inferences of properties of the Solar Interior. While this inverse problem has been a major focus in recent years, the corresponding forward problem has received much less attention. We aim to rectify this situation by taking the first steps toward validating and determining the efficacy of the helioseismic measurement procedure. The goal of this effort is to design a means to perform differential studies of various effects such as flows and thermal perturbations on helioseismic observables such as resonant frequencies, travel-time shifts, etc. Here we describe our first efforts to simulate wave propagation within a spherical shell, which extends from 0.2 to about 1.0004 R☉ (where R☉ is the radius of the Sun) and which possesses a Solar-like stratification. We consider a model containing no flows that will serve as a reference model for later studies. We discuss the computational procedure, some difficulties encountered in a simulation of this kind, and the means to overcome them. We also present techniques used to validate the simulation.

A C Birch - One of the best experts on this subject based on the ideXlab platform.

  • seismic probes of Solar Interior magnetic structure
    Physical Review Letters, 2012
    Co-Authors: Shravan M Hanasoge, L Gizon, A C Birch, Jeroen Tromp
    Abstract:

    Sun spots are prominent manifestations of Solar magnetoconvection, and imaging their subsurface structure is an outstanding problem of wide physical importance. Travel times of seismic waves that propagate through these structures are typically used as inputs to inversions. Despite the presence of strongly anisotropic magnetic waveguides, these measurements have always been interpreted in terms of changes to isotropic wave speeds and flow-advection-related Doppler shifts. Here, we employ partial-differential-equation-constrained optimization to determine the appropriate parametrization of the structural properties of the magnetic Interior. Seven different wave speeds fully characterize helioseismic wave propagation: the isotropic sound speed, a Doppler-shifting flow-advection velocity, and an anisotropic magnetic velocity. The structure of magnetic media is sensed by magnetoacoustic slow and fast modes and Alfven waves, each of which propagates at a different wave speed. We show that even in the case of weak magnetic fields, significant errors may be incurred if these anisotropies are not accounted for in inversions. Translation invariance is demonstrably lost. These developments render plausible the accurate seismic imaging of magnetoconvection in the Sun.

  • helioseismology challenges models of Solar convection
    Proceedings of the National Academy of Sciences of the United States of America, 2012
    Co-Authors: L Gizon, A C Birch
    Abstract:

    Convection is the mechanism by which energy is transported through the outermost of the sun (1). Solar turbulent convection is notoriously difficult to model across the entire convection zone, where the density spans many orders of magnitude. In PNAS, Hanasoge et al. (2) use recent helioseismic observations to derive stringent empirical constraints on the amplitude of large-scale convective velocities in the Solar Interior. They report an upper limit that is far smaller than predicted by a popular hydrodynamic numerical simulation.

  • high resolution mapping of flows in the Solar Interior fully consistent ola inversion of helioseismic travel times
    Solar Physics, 2008
    Co-Authors: Jason Jackiewicz, L Gizon, A C Birch
    Abstract:

    To recover the flow information encoded in travel-time data of time – distance helioseismology, accurate forward modeling and a robust inversion of the travel times are required. We accomplish this using three-dimensional finite-frequency travel-time sensitivity kernels for flows along with a (2+1)-dimensional (2+1D) optimally localized averaging (OLA) inversion scheme. Travel times are measured by ridge filtering MDI full-disk Doppler data and the corresponding Born sensitivity kernels are computed for these particular travel times. We also utilize the full noise-covariance properties of the travel times, which allow us to accurately estimate the errors for all inversions. The whole procedure is thus fully consistent. Because of ridge filtering, the kernel functions separate in the horizontal and vertical directions, motivating our choice of a 2+1D inversion implementation. The inversion procedure also minimizes cross-talk effects among the three flow components, and the averaging kernels resulting from the inversion show very small amounts of cross-talk. We obtain three-dimensional maps of vector Solar flows in the quiet Sun at horizontal spatial resolutions of 7−10 Mm using generally 24 hours of data. For all of the flow maps we provide averaging kernels and the noise estimates. We present examples to test the inferred flows, such as a comparison with Doppler data, in which we find a correlation of 0.9. We also present results for quiet-Sun supergranular flows at different depths in the upper convection zone. Our estimation of the vertical velocity shows good qualitative agreement with the horizontal vector flows. We also show vertical flows measured solely from f-mode travel times. In addition, we demonstrate how to directly invert for the horizontal divergence and flow vorticity. Finally we study inferred flow-map correlations at different depths and find a rapid decrease in this correlation with depth, consistent with other recent local helioseismic analyses.

  • high resolution mapping of flows in the Solar Interior fully consistent ola inversion of helioseismic travel times
    arXiv: Astrophysics, 2008
    Co-Authors: Jason Jackiewicz, L Gizon, A C Birch
    Abstract:

    To recover the flow information encoded in travel-time data of time-distance helioseismology, accurate forward modeling and a robust inversion of the travel times are required. We accomplish this using three-dimensional finite-frequency travel-time sensitivity kernels for flows along with a 2+1 dimensional (2+1D) optimally localized averaging (OLA) inversion scheme. Travel times are measured by ridge filtering MDI full-disk Doppler data and the corresponding Born sensitivity kernels are computed for these particular travel times. We also utilize the full noise covariance properties of the travel times which allow us to accurately estimate the errors for all inversions. The whole procedure is thus fully consistent. Due to ridge filtering, the kernel functions separate in the horizontal and vertical directions, motivating our choice of a 2+1D inversion implementation. The inversion procedure also minimizes cross-talk effects among the three flow components, and the averaging kernels resulting from the inversion show very small amounts of cross-talk. We obtain three-dimensional maps of vector Solar flows in the quiet Sun at spatial resolutions of 7-10 Mm using generally 24 h of data. For all of the flow maps we provide averaging kernels and the noise estimates. We present examples to test the inferred flows, such as a comparison with Doppler data, in which we find a correlation of 0.9. We also present results for quiet-Sun supergranular flows at different depths in the upper convection zone.

  • sensitivity of acoustic wave travel times to sound speed perturbations in the Solar Interior
    The Astrophysical Journal, 2004
    Co-Authors: A C Birch, A G Kosovichev, T L Duvall
    Abstract:

    For time-distance helioseismology, it is important to establish the relationship between the travel times of acoustic waves propagating between different points on the Solar surface through the Solar Interior and local perturbations to the sound speed in the propagation region. We use the Born approximation to derive a general expression for the linear sensitivity of travel times to local sound-speed perturbations in plane-parallel Solar models with stochastic wave sources. The results show that the sensitivity of time-distance measurements to perturbations in sound speed depends on the details of the measurement procedure, such as the phase-speed filter used in typical time-distance data analysis. As a result, the details of the measurement procedure should be taken into account in the inversion of time-distance data. Otherwise, the inferred depths of perturbations may be incorrect.

Junwei Zhao - One of the best experts on this subject based on the ideXlab platform.

  • detection of equatorward meridional flow and evidence of double cell meridional circulation inside the sun
    The Astrophysical Journal, 2013
    Co-Authors: Junwei Zhao, Alexander G. Kosovichev, R.s. Bogart, T L Duvall, Thomas Hartlep
    Abstract:

    Meridional flow in the Solar Interior plays an important role in redistributing angular momentum and transporting magnetic flux inside the Sun. Although it has long been recognized that the meridional flow is predominantly poleward at the Sun's surface and in its shallow Interior, the location of the equatorward return flow and the meridional flow profile in the deeper Interior remain unclear. Using the first 2 yr of continuous helioseismology observations from the Solar Dynamics Observatory/Helioseismic Magnetic Imager, we analyze travel times of acoustic waves that propagate through different depths of the Solar Interior carrying information about the Solar Interior dynamics. After removing a systematic center-to-limb effect in the helioseismic measurements and performing inversions for flow speed, we find that the poleward meridional flow of a speed of 15 m s–1 extends in depth from the photosphere to about 0.91 R ☉. An equatorward flow of a speed of 10 m s–1 is found between 0.82 and 0.91 R ☉ in the middle of the convection zone. Our analysis also shows evidence of that the meridional flow turns poleward again below 0.82 R ☉, indicating an existence of a second meridional circulation cell below the shallower one. This double-cell meridional circulation profile with an equatorward flow shallower than previously thought suggests a rethinking of how magnetic field is generated and redistributed inside the Sun.

  • detection of equatorward meridional flow and evidence of double cell meridional circulation inside the sun
    arXiv: Solar and Stellar Astrophysics, 2013
    Co-Authors: Junwei Zhao, Alexander G. Kosovichev, R.s. Bogart, T L Duvall, Thomas Hartlep
    Abstract:

    Meridional flow in the Solar Interior plays an important role in redistributing angular momentum and transporting magnetic flux inside the Sun. Although it has long been recognized that the meridional flow is predominantly poleward at the Sun's surface and in its shallow Interior, the location of the equatorward return flow and the meridional flow profile in the deeper Interior remain unclear. Using the first two years of continuous helioseismology observations from the Solar Dynamics Observatory / Helioseismic Magnetic Imager, we analyze travel times of acoustic waves that propagate through different depths of the Solar Interior carrying information about the Solar Interior dynamics. After removing a systematic center-to-limb effect in the helioseismic measurements and performing inversions for flow speed, we find that the poleward meridional flow of a speed of 15 m/s extends in depth from the photosphere to about 0.91 R_sun. An equatorward flow of a speed of 10 m/s is found between 0.82 to 0.91 R_sun in the middle of the convection zone. Our analysis also shows evidence of that the meridional flow turns poleward again below 0.82 R_sun, indicating an existence of a second meridional circulation cell below the shallower one. This double-cell meridional circulation profile with an equatorward flow shallower than previously thought suggests a rethinking of how magnetic field is generated and redistributed inside the Sun.

  • response to comment on detection of emerging sunspot regions in the Solar Interior
    Science, 2012
    Co-Authors: Stathis Ilonidis, Junwei Zhao, A G Kosovichev
    Abstract:

    Braun claims that his analysis using helioseismic holography does not confirm the detection of emerging sunspot regions. We examine his measurement procedure and explain why his method has different sensitivity than our method. We also discuss possible physical processes that may cause the detected phase travel-time shifts.

  • systematic center to limb variation in measured helioseismic travel times and its effect on inferences of Solar Interior meridional flows
    The Astrophysical Journal, 2012
    Co-Authors: Junwei Zhao, A G Kosovichev, Kaori Nagashima, Richard S Bogart, T L Duvall
    Abstract:

    We report on a systematic center-to-limb variation in measured helioseismic travel times, which must be taken into account for an accurate determination of Solar Interior meridional flows. The systematic variation, found in time-distance helioseismology analysis using SDO/HMI and SDO/AIA observations, is different in both travel-time magnitude and variation trend for different observables. It is not clear what causes this systematic effect. Subtracting the longitude-dependent east-west travel times, obtained along the equatorial area, from the latitude-dependent north-south travel times, obtained along the central meridian area, gives remarkably similar results for different observables. We suggest this as an effective procedure for removing the systematic center-to-limb variation. The subsurface meridional flows obtained from inversion of the corrected travel times are approximately 10 m s−1 slower than those obtained without removing the systematic effect. The detected center-to-limb variation may have important implications in the derivation of meridional flows in the deep Interior and needs to be better understood.

  • systematic center to limb variation in measured helioseismic travel times and its effect on inferences of Solar Interior meridional flows
    arXiv: Solar and Stellar Astrophysics, 2012
    Co-Authors: Junwei Zhao, A G Kosovichev, Kaori Nagashima, Richard S Bogart, T L Duvall
    Abstract:

    We report on a systematic center-to-limb variation in measured helioseismic travel times, which must be taken into account for an accurate determination of Solar Interior meridional flows. The systematic variation, found in time-distance helioseismology analysis using SDO/HMI and SDO/AIA observations, is different in both travel-time magnitude and variation trend for different observables. It is not clear what causes this systematic effect. Subtracting the longitude-dependent east-west travel times, obtained along the equatorial area, from the latitude-dependent north-south travel times, obtained along the central meridian area, gives remarkably similar results for different observables. We suggest this as an effective procedure for removing the systematic center-to-limb variation. The subsurface meridional flows obtained from inversion of the corrected travel times are approximately 10 m/s slower than those obtained without removing the systematic effect. The detected center-to-limb variation may have important implications in the derivation of meridional flows in the deep Interior, and needs a better understanding.

Sarbani Basu - One of the best experts on this subject based on the ideXlab platform.

  • Understanding the Internal Chemical Composition and Physical Processes of the Solar Interior
    Space Science Reviews, 2015
    Co-Authors: Sarbani Basu, Nicolas Grevesse, Stephane Mathis, Sylvaine Turck-chièze
    Abstract:

    The Sun, the closest and most well studied of stars, is generally used as a standard that other stars are compared to. Models of the Sun are constantly tested with helioseismic data. These data allow us to probe the internal structure and dynamics of the Sun. Among the main sources of the data is the SOHO spacecraft that has been continuously observing the Sun for more than a Solar cycle. Current Solar models, although good, do not include all the physical processes that are present in the Sun. In this chapter we focus on specific inputs to Solar models and discuss generally neglected dynamical physical processes whose inclusion could result in models that are much better representatives of the Sun.

  • Helioseismology as a diagnostic of the Solar Interior
    Astrophysics and Space Science, 2009
    Co-Authors: Sarbani Basu
    Abstract:

    Helioseismology has given us a unique window into the Solar Interior. Helioseismic data have enabled us to study the internal structure and dynamics with unprecedented detail. This has also allowed us to use the Sun as a laboratory to study the basic properties of stellar matter. We describe how helioseismology is used to determine Solar structure and what we have learned about the Sun so far. We also describe how knowledge of the Solar structure can be used to constrain the physics inputs.

  • a comparison of Solar p mode parameters from the michelson doppler imager and the global oscillation network group splitting coefficients and rotation inversions
    The Astrophysical Journal, 2002
    Co-Authors: J Schou, Sarbani Basu, J Christensendalsgaard, T Corbard, R Howe, F Hill, R Komm, R M Larsen, M C Rabellosoares, M J Thompson
    Abstract:

    Using contemporaneous helioseismic data from the Global Oscillation Network Group (GONG) and Michelson Doppler Imager (MDI) onboard SOHO, we compare frequency-splitting data and resulting inversions about the Sun's internal rotation. Helioseismology has been very successful in making detailed and subtle inferences about the Solar Interior. But there are some significant differences between inversion results obtained from the MDI and GONG projects. It is important for making robust inferences about the Solar Interior that these differences are located and their causes eliminated. By applying the different analysis pipelines developed by the projects not only to their own data but also to the data from the other project, we conclude that the most significant differences arise not from the observations themselves but from the different frequency estimation analyses used by the projects. We find that the GONG pipeline results in substantially fewer fitted modes in certain regions. The most serious systematic differences in the results, with regard to rotation, appear to be an anomaly in the MDI odd-order splitting coefficients around a frequency of 3.5 mHz and an underestimation of the low-degree rotational splittings in the GONG algorithm.

  • temporal variations of the rotation rate in the Solar Interior
    The Astrophysical Journal, 2000
    Co-Authors: H M Antia, Sarbani Basu
    Abstract:

    The temporal variations of the rotation rate in the Solar Interior are studied using frequency splittings from Global Oscillations Network Group (GONG) data obtained during the period 1995-1999. We find alternating latitudinal bands of faster and slower rotation that appear to move toward the equator with time—similar to the torsional oscillations seen at the Solar surface. This flow pattern appears to persist to a depth of about 0.1 R☉, and in this region its magnitude is well correlated with Solar activity indices. We do not find any periodic or systematic changes in the rotation rate near the base of the convection zone.

  • large scale flows in the Solar Interior effect of asymmetry in peak profiles
    arXiv: Astrophysics, 1999
    Co-Authors: Sarbani Basu, H M Antia
    Abstract:

    Ring diagram analysis can be used to study large scale velocity fields in the outer part of the Solar convection zone. All previous works assume that the peak profiles in the Solar oscillation power spectrum are symmetric. However, it has now been demonstrated that the peaks are not symmetric. In this work we study how the explicit use of asymmetric peak profiles in ring-diagram analysis influences the estimated velocity fields. We find that the use of asymmetric profiles leads to significant improvement in the fits, but the estimated velocity fields are not substantially different from those obtained using a symmetric profile to fit the peaks. The resulting velocity fields are compared with those obtained by other investigators.

Thomas Hartlep - One of the best experts on this subject based on the ideXlab platform.

  • detection of equatorward meridional flow and evidence of double cell meridional circulation inside the sun
    The Astrophysical Journal, 2013
    Co-Authors: Junwei Zhao, Alexander G. Kosovichev, R.s. Bogart, T L Duvall, Thomas Hartlep
    Abstract:

    Meridional flow in the Solar Interior plays an important role in redistributing angular momentum and transporting magnetic flux inside the Sun. Although it has long been recognized that the meridional flow is predominantly poleward at the Sun's surface and in its shallow Interior, the location of the equatorward return flow and the meridional flow profile in the deeper Interior remain unclear. Using the first 2 yr of continuous helioseismology observations from the Solar Dynamics Observatory/Helioseismic Magnetic Imager, we analyze travel times of acoustic waves that propagate through different depths of the Solar Interior carrying information about the Solar Interior dynamics. After removing a systematic center-to-limb effect in the helioseismic measurements and performing inversions for flow speed, we find that the poleward meridional flow of a speed of 15 m s–1 extends in depth from the photosphere to about 0.91 R ☉. An equatorward flow of a speed of 10 m s–1 is found between 0.82 and 0.91 R ☉ in the middle of the convection zone. Our analysis also shows evidence of that the meridional flow turns poleward again below 0.82 R ☉, indicating an existence of a second meridional circulation cell below the shallower one. This double-cell meridional circulation profile with an equatorward flow shallower than previously thought suggests a rethinking of how magnetic field is generated and redistributed inside the Sun.

  • detection of equatorward meridional flow and evidence of double cell meridional circulation inside the sun
    arXiv: Solar and Stellar Astrophysics, 2013
    Co-Authors: Junwei Zhao, Alexander G. Kosovichev, R.s. Bogart, T L Duvall, Thomas Hartlep
    Abstract:

    Meridional flow in the Solar Interior plays an important role in redistributing angular momentum and transporting magnetic flux inside the Sun. Although it has long been recognized that the meridional flow is predominantly poleward at the Sun's surface and in its shallow Interior, the location of the equatorward return flow and the meridional flow profile in the deeper Interior remain unclear. Using the first two years of continuous helioseismology observations from the Solar Dynamics Observatory / Helioseismic Magnetic Imager, we analyze travel times of acoustic waves that propagate through different depths of the Solar Interior carrying information about the Solar Interior dynamics. After removing a systematic center-to-limb effect in the helioseismic measurements and performing inversions for flow speed, we find that the poleward meridional flow of a speed of 15 m/s extends in depth from the photosphere to about 0.91 R_sun. An equatorward flow of a speed of 10 m/s is found between 0.82 to 0.91 R_sun in the middle of the convection zone. Our analysis also shows evidence of that the meridional flow turns poleward again below 0.82 R_sun, indicating an existence of a second meridional circulation cell below the shallower one. This double-cell meridional circulation profile with an equatorward flow shallower than previously thought suggests a rethinking of how magnetic field is generated and redistributed inside the Sun.