Benjamin J. Greer1,2, Bradley W. Hindman1,2, Nicholas A. Featherstone1, Juri Toomre1,2
(1) JILA, University of Colorado
(2) Department of Astrophysical and Planetary Sciences, University of Colorado
Ring-diagram helioseismology deduces subsurface flows within the Sun through the measurement of Doppler shifts of the Sun’s acoustic wave modes. We observe these waves using full-disk, line of sight Dopplergrams produced by the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO). Using a new implementation of ring-diagram helioseismology, we are able to ascertain the strength and spatial scale of convective flows throughout the near-surface shear layer. We use highly overlapped analysis regions coupled with an efficient inversion procedure to recover high-resolution flow maps from the photosphere to a depth of 30 Mm. Previous measurements of convective flows at these depths have shown the velocities to be low compared to many numerical simulations. The large discrepancy has cast doubt in both directions, implying that either the dynamical balance achieved in many simulations is far from the one that holds in the Sun, or that existing helioseismic methods underestimate velocities at depth.
Figure 1 | (a) Vector map for a subsection of the full horizontal flow map at a depth of 0.25 Mm overlaid on a map of the average magnetic field strength. Darker colors indicate stronger magnetic field, and the color table saturates at 25 Gauss. We see a strong correspondence between the flow structures found through our analysis and the advection of magnetic field at the photosphere. (b) Vector map for a larger subsection of the horizontal flow map at a depth of 10 Mm. The gray box in (b) indicates the position and size of the subsection in panel (a).
Figure 1 demonstrates the ability for this new implementation of ring-diagram helioseismology to recover convective flows. The prominent scale seen in Figure 1a is due to supergranulation. Near the surface, the scales and amplitudes of convective velocities we see are consistent with other measures of supergranulation[3,4]. Deeper into the sun, we see a trend towards larger horizontal scales. Figure 2 shows the velocity spectrum at a few depths spanning our analysis region. The flows near the surface show a peak at around l=120, consistent with the signal of supergranulation. The flows at a depth of 30 Mm are predominantly at larger scales (l < 40), and have an rms velocity of around 100 m/s. This value is much larger than the previous observations by , but are roughly consistent (over the relevant scales) with simulations. The source of the discrepancy between these observations and those in  is not currently known, but may have to do with differences in the treatment of uncorrelated noise.
Figure 1 | Velocity spectrum of horizontal flow velocities at four depths. Solid lines indicate the azimuthally integrated spectra, and the dashed lines indicate our sensitivity to each horizontal scale at each depth. The inversion technique is not able to recover all spatial scales perfectly, so we use the sensitivity at each l to understand what we can measure and what we can’t. The sensitivity at l=0 is unity by definition, but the dashed lines here have been scaled for clarity.
These measurements of the convective velocities throughout the near-surface shear layer provide useful observational constraints to numerical simulations. Using the length scales and velocity amplitudes seen here, we can infer a Rossby number at each depth. The Rossby number gives an estimate of the influence of the Coriolis force against the advection of momentum. Near the surface, we find Ro=2.2, implying weak rotational influence. At 30 Mm we find Ro=0.1, implying convective flows that do feel the effects of rotation.
This analysis not only provides a robust measure of the horizontal convective velocities in the near-surface shear layer, but also a proof-of-concept for further work in high-resolution ring-diagram helioseismology.
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