DETECTION OF EQUATORWARD MERIDIONAL FLOW AND EVIDENCE OF DOUBLE-CELL MERIDIONAL CIRCULATION INSIDE THE SUN

Meridional flow inside the Sun plays an important role in redistributing rotational angular momentum and transporting magnetic flux (Wang et al. 1989), and is crucial to our understanding of the strength and duration of sunspot cycles (Hathaway & Rightmire 2010; Dikpati et al. 2010) according to flux-transport dynamo theories (Choudhuri et al. 1995; Dikpati & Charbonneau 1999). At the Sun's surface and in its shallow interior to at least 30 Mm in depth, the meridional flow is predominantly poleward with a peak speed of approximately 20 m s⁻¹, as measured by tracer tracking (e.g., Komm et al. 1993; Švanda et al. 2007; Hathaway & Rightmire 2010), direct Doppler-shift observations (e.g., Ulrich 2010), and local helioseismology analyses (e.g., Giles et al. 1997; Haber et al. 2002; Zhao & Kosovichev 2004; González Hernández et al. 2008). The poleward plasma flow transports the surface magnetic flux from low latitudes to the polar region, causing the periodic reversals of the global magnetic field, a process important to the prediction of the solar cycles (Dikpati et al. 2010). The speed and variability of the meridional flow also play an important role in determining the strength and duration of the solar cycles, and the unusually long activity minimum at the end of Solar Cycle 23 during 2007–2010 was thought to be associated with an increase of the meridional flow speed during the declining phase of the previous cycle (Hathaway & Rightmire 2010). Therefore, an accurate determination of the meridional flow profile is crucial to our understanding and prediction of solar magnetic activities.

Although the poleward meridional flow at the solar surface and in shallow depths has been well studied, the depth and speed profile of the equatorward return flow, which is expected to exist inside the solar convection zone to meet the mass conservation, largely remains a puzzle. It is generally assumed that the return flow is located near the base of the convection zone, although no convincing evidence has been reported. Earlier helioseismic analyses of Solar Heliospheric Observatory/Michelson Doppler Imager (SOHO/MDI; Scherrer et al. 1995) data were unable to directly detect an equatorward flow, but estimated that the return flow had a speed of 2 m s⁻¹ near the bottom of the convection zone after applying a mass-conservation constraint (Giles 1999). This single-cell circulation profile has been later widely employed in the flux-transport dynamo simulations and solar cycle prediction models (e.g., Dikpati et al. 2010; Jiang et al. 2007). A later helioseismic frequency-shift analysis put the equatorward flow at a much shallower depth of 40 Mm (Mitra-Kraev & Thompson 2007), but this was questioned by Gough & Hindman (2010). More recently, an analysis based on tracking of photospheric supergranulation gave an estimate of the return flow depth below 50 Mm (Hathaway 2012), however, this analysis was unable to give an unambiguous profile of the meridional circulation as a function of both latitude and depth inside the Sun. A more robust analysis utilizing a well-established helioseismology technique, e.g., time–distance helioseismology (Duvall et al. 1993), is needed to examine the deep meridional circulation profile.

The continuous Doppler observations by the Helioseismic and Magnetic Imager (HMI; Scherrer et al. 2012; Schou et al. 2012) onboard the recently launched Solar Dynamics Observatory mission (SDO; Pesnell et al. 2012) allow us to measure and detect the long-sought equatorward flow. Our analysis, which takes into account the systematic center-to-limb effect that was recently found in the local helioseismology analysis techniques (Zhao et al. 2012), gives a two-dimensional cross-section picture of the meridional flow inside the nearly entire solar convection zone, and reveals a double-cell circulation with the equatorward flow located near the middle of the convection zone. In this Letter, we describe our analysis procedure in Section 2, present measurements and inversion results in Section 3, and then discuss these results in Section 4.

The SDO/HMI provides continuous full-disk Doppler-shift observations of the Sun with a 45 s cadence for helioseismology studies. Time–distance helioseismology (Duvall et al. 1993) measures travel times of acoustic waves, which propagate through the solar interior, by cross-correlating oscillation signals observed at different locations on the surface. The measured travel-time anomalies are usually interpreted in terms of wave-speed perturbations and mass flows along the wave path. This analysis technique has already provided rich information about the solar interior structures and dynamics (Gizon et al. 2010).

Determining the internal meridional flow is one important task in solar physics and yet one difficult challenge due to the low speed of the flow, which requires a careful analysis of potential systematic errors. In particular, recent studies have revealed a previously unreported systematic center-to-limb effect in the acoustic travel times measured by the time–distance technique (Zhao et al. 2012). The systematic travel-time variation depends on the angular distance from the solar disk center, and exhibits different magnitude, sometimes even opposite signs, when measured using different HMI observables and using different measurement distances. It is not quite clear what causes this systematic effect, and a recent study suggested that it might be partially due to the interactions of acoustic waves with the vertical flows in solar granules (Baldner & Schou 2012). Zhao et al. (2012) suggested that this systematic effect should be removed before inverting the measured acoustic travel times for interior meridional flow, and proposed to use the travel-time shifts measured in the east–west direction along the equator as proxies of the systematic effect. Their inversion results, after removal of this effect following their suggested method, showed a reduction of ∼10 m s⁻¹ in the inverted meridional flow speed (Zhao et al. 2012). We believe that this systematic effect was responsible for many past helioseismology study failures to reliably detect the equatorward meridional flow, and that the removal of this effect will play an important role in studying the meridional flow in the solar interior.

We use the HMI Doppler-shift data covering its first 2 yr period from 2010 May 1 through 2012 April 30, during which the solar magnetic activity was generally low. For each observing day, we track the data with a uniform Carrington rotation rate, remap the tracked data onto the heliographic coordinate using Postel's projection with a sampling scale of 018 pixel⁻¹, and then apply a running-difference filter to remove solar convection and low-frequency signals. Note that no other filtering is applied in our analysis in order to avoid any complications in the Fourier domain when dealing with very large spatial scales. A deep-focusing time–distance measurement scheme (shown in Figure 1), which was described and validated by Hartlep et al. (2013), is utilized. For each measurement, the solar oscillation signals are first averaged inside two 30°-long single-pixel-wide concentric arcs, located opposite to each other in the north and south directions, and then cross-correlated to extract acoustic wave packets traveling between these arcs along the wave paths through the solar interior. In order to make a robust center-to-limb effect correction, we limit the selection of oscillation signals within 15° from the central meridian. The center-to-limb variations are estimated from the east–west travel-time measurements along an equatorial band following the same geometry as used in the north–south measurements along the meridian band. The same procedure is repeated for each of the 60 measurement distances ranging from 216 to 4464, covering a radial range from approximately 0.7 R_☉ to the surface according to the acoustic ray theory. The cross-correlation functions are averaged for the same latitudes, and then averaged again over one month intervals. The Gabor wavelet fitting (Kosovichev & Duvall 1997) is performed to derive the acoustic travel times for all the measurement distances. For each distance, the travel times are averaged again over the whole 2 yr period to obtain the final results. The standard errors after the systematic effect correction for each measurement distance, estimated from the 24 measurement periods, are displayed as error bars in Figures 2 and 3. The errors of the center-to-limb effect follow a similar pattern as in δτ_SN.

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3.1. Results of Travel-time Measurements

3.2. Results from Inversion

We then invert the corrected δτ_SN from HMI for the interior meridional flow speed as a function of latitude and depth. Ray-approximation sensitivity kernels are utilized in the inversion, and they are prepared following the same geometry and averaging procedures as in the measuring. Three-dimensional kernels are first computed in spherical coordinates, and then collapsed into one meridional plane. Basically, the sensitivity kernels show thin curves of the ray path, with the strongest sensitivity located near the lower turning points. We linearize the equation that links the travel-time variations with the interior flow field: $\delta \tau _\mathrm{diff} = -2 \int _\Gamma (\mathbf {n \cdot v})/c^2 {d} \,s$, where Γ is acoustic ray path, v is flow velocity, c is sound speed, and s is distance along the ray path (Kosovichev 1996). The linearized equations are then solved in a sense of least squares using the LSQR algorithm, an iterative linear equation solver (Paige & Saunders 1982). In our inversions, the radial component of the flow is not taken into account but it is not expected that this will affect our inversion results significantly because the flows are predominantly horizontal near the deep-focus points where our measurement is more sensitive. However, an inversion procedure including the radial flow will be developed in our future studies.

We carry out two sets of inversions with and without the mass-conservation constraint. For the results inverted from only the helioseismic measurements without applying the mass-conservation constraint, a two-dimensional cross-section view of the meridional flow velocity and flow profiles at some selected depths and latitudes are displayed in Figure 4. The δτ_SN calculated from a forward procedure, which utilizes the same equation as given above that links travel time and interior flows, using the inverted velocity are overplotted in Figures 2 and 3(a) to compare with the measured δτ_SN. It can be found that they are in good agreement, demonstrating that our inversion results fit the measurement quite well. Basically, our inversion results show that the poleward flow of 15 m s⁻¹ extends from the surface to a depth of approximately 65 Mm, i.e., about 0.91 R_☉. Below this, the flow direction turns equatorward with a maximum speed of about 10 m s⁻¹. Both the depth and the thickness of the zone of return flow are clearly latitude dependent. The equatorward flow shows a significant hemispheric asymmetry, stronger in the northern hemisphere and weaker in the southern. Below about 0.82 R_☉, the flow again becomes poleward, also with a substantial hemispheric asymmetry. Errors from the inversion are typically 1 m s⁻¹ near the surface, and are as large as 10 m s⁻¹ below 0.80 R_☉. Our inversion stops at about 0.75 R_☉ because the noise prevents reliable inferences in the deeper layers. Longer observations are required to increase the signal-to-noise ratio (S/N).

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Another set of inversion with the mass-conservation constraint (results are not shown in a figure) demonstrates that the basic flow profile remains similar to that without applying the mass constraint. The major difference is that the zone of equatorward flow becomes thicker, and the poleward flow below 0.82 R_☉ becomes slower.

The averaging kernels from our inversions for some selected target depths are displayed in Figure 5. It can be seen that the kernel is well localized in the shallow areas, and becomes broader with the increase of depth, but are still localized in the latitudinal direction. The negative side lobes above and below the targeted area in the radial direction also become stronger in amplitude and larger in size with the depth. The averaging kernels remain the same for the same depth but different latitudes.

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Our analysis reveals a new picture of the Sun's interior meridional circulation, with poleward flows from the surface to 0.91 R_☉ and from 0.82 R_☉ to at least 0.75 R_☉, and an equatorward flow located between these in a layer of about 0.09 R_☉ thick. This seems to form two meridional circulation cells, one beneath the other in the radial direction (Figure 1). Not being able to invert the flow profile beneath 0.75 R_☉ and above the latitude of 60°, we cannot exclude the possibility of more circulation cells in both radial and latitudinal directions.

The interior meridional flow profile reported in this Letter is obtained after the removal of the systematic center-to-limb effect, therefore, a precise determination of this flow profile relies largely on a precise determination of that systematic effect. We follow the empirical approach of using the east–west travel-time measurements along the equator to represent this systematic effect, however, without knowing the exact cause of this effect (as already pointed out in Section 2), a small deviation of the real systematic effect from this representation can result in a significant change of the inverted meridional flow profile shown in Figure 4. However, the comparison of MDI and HMI results, which carry different amount of systematic effects, gives us confidence that our effect correction procedure is reasonable (see Figure 3). Still, we believe it is necessary to develop a different systematic-effect correction procedure in the future, after the cause of the center-to-limb effect is better known, to give a more robust inference of the deep meridional flow profile.

Based on a single-cell circulation model with the equatorward flow, peaking at 3 m s⁻¹, located near the bottom of the convection zone, Braun & Birch (2008) estimated that more than one decade of continuous observations is required for a reliable detection of the return flow, which is expected to cause an acoustic travel-time shift of about 0.01 s. However, the meridional flow profile determined from our measurements differs from the model used in their estimation. Furthermore, Figure 3 shows that the travel-time shift caused by the shallow poleward flow is partly offset by the equatorward flow in the middle of the convection zone, leaving the flow near the bottom easier to measure. This explains why 2 yr of helioseismic observations is able to probe the deep interior meridional flow. Certainly, longer observations will enable us to reliably invert the flow beneath 0.75 R_☉ and enhance the S/N through the entire convection zone, and the capability of the shorter-time measurement allows us to study the temporal evolution of the deep meridional flow with lower S/N.

This new picture of the solar interior meridional circulation differs substantially from the previously widely believed picture of a single-cell circulation with the equatorward flow near the bottom of the convection zone. Through removing a systematic center-to-limb effect that was only recently identified, our analysis corrects and improves the previous solar interior meridional flow profile given by Giles (1999) using a similar analysis procedure. The new meridional circulation profile poses a challenge to the flux-transport dynamo models (Charbonneau 2010), but provides more physical constraints to these models creating a new opportunity to further understand how magnetic field is generated and how magnetic flux is transported inside the Sun. Past dynamo simulations have already demonstrated that a meridional circulation profile with multiple cells might not be able to reproduce the butterfly diagram and the phase relationship between the toroidal and poloidal fields as observed, unless the dynamo model was reconsidered (Jouve & Brun 2007). However, on the other hand, solar convection simulations have shown the possibility of multi-cell circulation with a shallow equatorward flow (e.g., Miesch et al. 2006; Käpylä et al. 2012; Guerrero et al. 2013), demonstrating that our analysis results are reasonable. Moreover, a recent dynamo simulation, with the double-cell meridional circulation profile incorporated, showed that the solar magnetic properties could be robustly reproduced after taking into consideration of turbulent pumping, turbulent diffusivity, and other factors (Pipin & Kosovichev 2013). All these studies, together with our observational results, suggest a rethinking of how the solar magnetic flux is generated and transported inside the Sun.

We thank the two anonymous referees whose comments help to improve the presentation and quality of this Letter. SDO is a NASA mission, and HMI project is supported by NASA contract NAS5-02139 to Stanford University.