Global Rotation Rachel Howe, NSO

How deep is the tachocline, how wide is the shear? With almost a whole cycle of observations from GONG and MDI, we can look at the stationary part of the rotation. Forward-modeling exercises help to establish robustness of results.

The Questions How well can we measure the near-surface shear? Is the slant in the convection-zone rotation real? How well can we measure the shape of the tachocline?

The Data 106 overlapping 108-day sets from GONG, covering 10.5 years 1995-2006. 0≤l≤150, coefficients up to a16 49 72-day sets from MDI, starting May 1996. 0≤l≤300, coefficients up to a36

Analysis Fit 11yr sinusoid to each coefficient Use stationary part of fit 2dRLS and 2dOLA inversions Convolve averaging kernels with test profiles to simulate inversions.

Analysis – the inversion problem Kernel Averaging Kernel Aim of inversion is to go from a set of coefficients, each of which samples the rotation rate in a slightly different region, to a linear combination of those coefficients that gives a localized estimate of the rotation rate at a given location. The averaging kernel is a linear combination of the data kernels that describes the way the region over which the rotation estimate is averaged.

Coefficients

Results: profiles GONG MDI 7,3 RLS 6,2 RLS OLA

Results: profiles GONG MDI 6,2 RLS 7,3 RLS OLA

Global Rotation Profile Dashed lines inclined at 25 degrees to rotation axis.

Slope of Isorotation Contours Dashed line shows slope of radial lines. Gilman & Howe, 2003 (BB proceedings).

Results: Synthetic Profiles GONG MDI 7,3 RLS 6,2 RLS OLA

Results: Synthetic Profiles GONG MDI 7,3 RLS 6,2 RLS OLA

Results: Synthetic Profiles GONG MDI 7,3 RLS 6,2 RLS OLA

Results: Synthetic Profiles GONG MDI 7,3 RLS 6,2 RLS OLA

Discussion Slope in convection zone looks robust Near-surface shear already resolved in single-set data But reversal at high latitudes may be MDI(CA) artefact. Some sensitivity to different tachcocline thickness.

Calibrating the Tachocline Charbonneau et al (1999) used fits with error function model convolved with 1d averaging kernel Tried this using OLA inversions, checking against synthetic profiles.

Fit Results (MDI OLA)

But … We know rotation isn’t quite depth-independent in convection zone. What does technique do with tilted-contour model and no thickness?

Aha! Fits to tilted-contour model Fits to real data Fits to dashed-contour model

So … Try fitting model with slope in convection zone taken into account, combined with error-function tachocline.

And we get this …

From which we conclude Deconvolution fitting does not work perfectly. Forward modeling is only useful if the model is appropriate! The tachocline could be quite thin, (0.03±0.04)Rsun once the slanted rotation contours are taken into account. However, this still needs more study.