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, CA94305-4085 2.Department of Physics, Stanford
University, Stanford, CA94305
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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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We need your support, and we welcome your contribution!
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Motivation The systematic center-to-limb effect (Zhao et al.
2012 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. 2013 ApJL).
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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
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New Measurement Strategy Previous methods used measurements
from east-west direction along equator (=0) and north-south
measurements along the central meridian (=90). Here, we vary the
angle of . 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 are required.
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Data and Measurements We used two months of data for this
analysis: May 22 - Jun 21, 2010 and Nov 22 Dec 21, 2010. 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 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.
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Study of Acoustic Travel Time
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Measurements from Dopplergrams
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CtoL from Dopplergrams, Obtained by Solving the Equation
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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 .
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Measurements from Line-depth Data
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CtoL from Line-depth Data, Obtained by Solving the
Equation
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Is the CtoL Effect Anisotropic? The measurements from
line-depth data show that the center-to-limb effect is isotropic
within measurement errors.
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Measurements from Continuum Intensity
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CtoL from Ic Data, Obtained by Solving the Equation
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Is the CtoL Effect Anisotropic? The measurements from
continuum-intensity data show that the center-to- limb effect is
isotropic within measurement errors.
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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.
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Study of Frequency-Dependent Phase Shifts
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From Time-Distance Diagram to Phase Diagram
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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.
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Frequency-Dependent Travel-Time Shifts, Measured from
Dopplergrams This calculation used the CtoL data obtained after
solving the least- square equations.
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Frequency-Dependent Travel-Time Shifts
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Frequency-Dependent Travel-Time Shifts, Measured from
Line-Depth Data This calculation used the CtoL data obtained after
solving the least- square equations.
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Frequency-Dependent Travel-Time Shifts
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Frequency-Dependent Travel-Time Shifts, Measured from Ic Data
This calculation used the CtoL data obtained after solving the
least- square equations.
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Frequency-Dependent Travel-Time Shifts
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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.