Measuring Center-to-Limb Effect and A New Strategy to Measure Deep Meridional Flow Junwei Zhao 1 & Ruizhu Chen 2,1 1.W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA Department of Physics, Stanford University, Stanford, CA94305

SH Session: New Windows on Solar Meridional Circulation: Observations, Models, Data-assimilation and Dynamo Implications AGU Fall Meeting San Francisco, December 15 – 19, 2014 Conveners: Junwei Zhao, Mausumi Dikpati, & Mark Miesch We need your support, and we welcome your abstracts! Abstract deadline: August 6, 2014

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Motivation The systematic center-to-limb effect (Zhao et al ApJL) in helioseismic measurements is crucial in deriving the meridional- flow profiles in the deep solar interior. What has caused this effect is not yet fully clear (Baldner & Schou 2012 ApJL). Most of the recent studies use east-west measurements along the solar equator as a proxy of CtoL effect. Is this the best approach? The main purpose of this study is to provide comprehensive measurements of the CtoL effect as functions of disk location, measurement distance, measurement angle, and acoustic frequency using different observables. Hopefully these measurements can sparkle a thorough understanding of this systematic effect. The new measurement strategy is expected to provide results more robust than the previous method (e.g., Zhao et al ApJL).

Center-to-Limb Effect The W-E acoustic travel times show systematic variations, although they are expected to be uniform along a same latitude. Zhao et al. 2012, ApJL

New Measurement Strategy Previous methods used measurements from east-west direction along equator (α=0°) and north-south measurements along the central meridian (α=90°). Here, we vary the angle of α. For each measurement, we have Through solving a set of equations in a sense of least squares, we are able to disentangle CtoL and To cancel the effects caused by rotation, two sets of measurements with opposite α are required.

Data and Measurements We used two months of data for this analysis: May 22 - Jun 21, 2010 and Nov 22 – Dec 21, These two periods are quiet with little magnetic activities. These two periods also have the solar B-angle close to 0°. In this study, we selected the angle α to be 0°, 30°, 45°, 60°, and 90°. In this study, we used HMI Doppler, line-depth, and continuum intensity for measurements. Running-difference data are used in our calculation. Other than that, no other filtering is used to avoid complications by filtering.

Study of Acoustic Travel Time

Measurements from Dopplergrams

CtoL from Dopplergrams, Obtained by Solving the Equation

Is the CtoL Effect Anisotropic? Our preliminary results show that, for the measurements from Dopplergrams, the center-to-limb effect is anisotropic relative to the azimuth angle α.

Measurements from Line-depth Data

CtoL from Line-depth Data, Obtained by Solving the Equation

Is the CtoL Effect Anisotropic? The measurements from line-depth data show that the center-to-limb effect is isotropic within measurement errors.

Measurements from Continuum Intensity

CtoL from Ic Data, Obtained by Solving the Equation

Is the CtoL Effect Anisotropic? The measurements from continuum-intensity data show that the center-to- limb effect is isotropic within measurement errors.

Comparing the CtoL Effects from Doppler, Ld, and Ic Data Measurements from Dopplergrams have the smallest effects. The CtoL effect from line-depth data are opposite to that from Doppler and Ic. The CtoL effect from intensity data can be up to 300 sec, making this type of data not useful for studying deep meridional flow, which causes a travel- time shift of less than 1 sec.

Study of Frequency-Dependent Phase Shifts

From Time-Distance Diagram to Phase Diagram

A Random Example of Phase Diagram The differences of two phase diagrams, corresponding to opposite traveling waves, give a diagram of phase shifts. This greatly expands our previous information of travel times to frequency-dependent travel times.

Frequency-Dependent Travel-Time Shifts, Measured from Dopplergrams This calculation used the CtoL data obtained after solving the least- square equations.

Frequency-Dependent Travel-Time Shifts

Frequency-Dependent Travel-Time Shifts, Measured from Line-Depth Data This calculation used the CtoL data obtained after solving the least- square equations.

Frequency-Dependent Travel-Time Shifts

Frequency-Dependent Travel-Time Shifts, Measured from Ic Data This calculation used the CtoL data obtained after solving the least- square equations.

Frequency-Dependent Travel-Time Shifts

Summary We are in the process of developing a new strategy to study the systematic CtoL effect and to infer the interior deep meridional flow. Our preliminary analysis from two months data shows that the new strategy is promising. It shows that the CtoL effect MAY be anisotropic for different measurement directions. Whether this anisotropy undermines our previous results remain to be seen, but it seems that our new measurement strategy will provide more robust results. The method of measuring frequency-dependent phase shifts provides us more information, which will be very useful when solving the least-square equations for the deep meridional flow.