Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Shape of the Solar Tachocline

Sarbani Basu, Sylvain G. Korzennik

TL;DR

This paper probes the solar tachocline’s shape using long time-series helioseismic data to lift prior cos^2-based constraints. By modeling the tachocline as a latitude-dependent sigmoid in radius and fitting to $c_1$, $c_3$, and $c_5$ splittings with a simulated-annealing approach, the authors reveal a mid-latitude bulge and a latitude-driven migration of the tachocline center, from the radiative zone at low latitudes to the convection zone at intermediate latitudes and back toward radiative depths at high latitudes. A three-term latitudinal expansion improves fits over a two-term model, while a four-term expansion yields similar goodness-of-fit but larger uncertainties at high latitudes, indicating the shape is more intricate than a simple prolate cos^2 form. These findings have implications for interfacial dynamo theories and underscore the need for long time-series data to robustly constrain tachocline geometry across latitudes.

Abstract

Early helioseismic results have shown that the tachocline has a prolate shape. However, the models used in those studies constrained the tachocline to be either prolate or oblate. We use helioseismic data obtained from long time series (2304 and 4608 days) to determine the shape of the solar tachocline. Like previous work, we use forward modeling methods for this work; however, we allow more flexibility for the shape of the tachocline. We find that the tachocline does indeed deviate from a simple prolate structure and bulges out at mid latitudes. The center of the tachocline lies in the radiative zone at low latitudes, in the convection zone at intermediate latitudes, and back in the radiative zone at high latitudes. The high-latitude ($ > 60^\circ$) behavior is, however, uncertain and model dependent. Models that allow more variation of the shape indicate that the tachocline at high latitudes is almost coincident with the base of the convection zone.

The Shape of the Solar Tachocline

TL;DR

This paper probes the solar tachocline’s shape using long time-series helioseismic data to lift prior cos^2-based constraints. By modeling the tachocline as a latitude-dependent sigmoid in radius and fitting to , , and splittings with a simulated-annealing approach, the authors reveal a mid-latitude bulge and a latitude-driven migration of the tachocline center, from the radiative zone at low latitudes to the convection zone at intermediate latitudes and back toward radiative depths at high latitudes. A three-term latitudinal expansion improves fits over a two-term model, while a four-term expansion yields similar goodness-of-fit but larger uncertainties at high latitudes, indicating the shape is more intricate than a simple prolate cos^2 form. These findings have implications for interfacial dynamo theories and underscore the need for long time-series data to robustly constrain tachocline geometry across latitudes.

Abstract

Early helioseismic results have shown that the tachocline has a prolate shape. However, the models used in those studies constrained the tachocline to be either prolate or oblate. We use helioseismic data obtained from long time series (2304 and 4608 days) to determine the shape of the solar tachocline. Like previous work, we use forward modeling methods for this work; however, we allow more flexibility for the shape of the tachocline. We find that the tachocline does indeed deviate from a simple prolate structure and bulges out at mid latitudes. The center of the tachocline lies in the radiative zone at low latitudes, in the convection zone at intermediate latitudes, and back in the radiative zone at high latitudes. The high-latitude () behavior is, however, uncertain and model dependent. Models that allow more variation of the shape indicate that the tachocline at high latitudes is almost coincident with the base of the convection zone.

Paper Structure

This paper contains 8 sections, 10 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Data used
  3. The tachocline model
  4. Results
  5. The shape of the tachocline
  6. The extent of the tachocline
  7. A comparison with 1D fits
  8. Discussion and Conclusions

Figures (7)

  • Figure 1: The model of the tachocline. The tachocline parameters used in this figure are marked at the top of the figure.
  • Figure 2: Top: A sigmoid fitted to the $c_3$ splitting coefficient for the HMI $64\times72$-day set. Bottom: a sigmoid fitted to the $c_5$ splitting coefficient of the same set. The background cyan points with error-bars are the observed coefficients plotted as a function of their lower turning point. The red points show the coefficients resulting from our best-fit sigmoid model. The $c_5$ component of the $32\times72$-day sets can also be fitted with a sigmoid. This splitting coefficient is very noisy in shorter sets.
  • Figure 3: The position of the tachocline plotted as a function of latitude for all the data sets. The solid gray horizontal line shows the position of the convection-zone base, with the gray dotted lines showing the 1$\sigma$ uncertainty. Panel (a) shows the results for the $32\times72$-day sets, while panel (b) shows the results for the $64\times72$-day sets. In each panel the solid lines show the results for the three-term case, while the dot-dashed lines are the results when using the two-term latitudinal model. Note how they agree at low latitudes. We show the 1$\sigma$ error limit only for the GONG Set 1, and the HMI (Project) results for the sake of clarity. These are marked as dotted lines for the two-term case and dashed lines for the three-term one. The uncertainties are similar for the three other data sets obtained with the SGK pipeline. It should be noted that the results close to the pole are essentially an extrapolation, since the data do not have sensitivity there. Also note that the results from the HMI project's pipeline and the SGK pipeline agree well within $1\sigma$ uncertainties.
  • Figure 4: The extent of the tachocline, defined as the region between $r_d-w_d$ and $r_d+w_d$ as obtained with the HMI $64\times72$-day set. The region between the red dot-dashed lines shows the result of the two-term case, with the dotted lines indicating $1\sigma$ uncertainties. The region between the blue solid lines shows the results of the three-term case, with the dashed lines showing $1\sigma$ uncertainties.
  • Figure 5: The position of the tachocline obtained by fitting the 1D model shown in Eq. \ref{['eq:1d']} to the HMI $64\times 72$-day set is plotted as points with 1$\sigma$ error bars; the points below and above $25^\circ$ have been connected separately with a dotted line to guide the eye. The red dot-dashed line is the result of the two-term 2D fit; $1\sigma$ uncertainties are shown as red dotted line. The blue solid line is the result of the three-term 2D fit, with the blue dashed line marking $1\sigma$ uncertainties.
  • ...and 2 more figures