Title: 
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Phase Relations Between Variations in Solar Surface Velocity  and Magnetic Fields

Lead Investigator:
=======
 R.K. Ulrich

Team Members:
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A.A. Norton		     

Local Coordinator:
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Lead Programmer:
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Technical Summary:
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We propose to determine the phase relations between variations
in velocities and magnetic fields in the solar photosphere.  
The observed phase relations will provide information about 
the generation and propogation of Alfven waves in the solar 
atmosphere and the consequent energy flux.  The study will 
utilize SOI-MDI high resolution campaign data and possible
some high-rate continuing observing sequences which return 
near simultaneous images of surface velocity and magnetic
fields.

Proposal Text:
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MDI Data To Be Utilized:

This investigation utilizes simultaneous or near simultaneous
surface velocity and magnetic field measurements.  We hope to 
utilize already existing SOI-MDI data.  More specifically, 
the high resolution weak active region polarized line profile 
campaigns designated as DPC 400c3100 seem to be appropriate.  
We have unsuccessfully been trying to identify other 4 - 5 hour 
data sets containing near simultaneous velocity and magnetic
field observables.  Aid in finding these data sets would 
be appreciated. If none of the above-mentioned data proves 
suitable, a campaign will be designed specifically for this
investigation.


Scientific Premise:

Acoustic waves interacting with magnetic fields in the 
photosphere are either compressional and/or bending in 
nature.  We can differentiate between the compressional 
and bending mechanisms observationally by deterining 
the phase angle between the line of sight velocity 
and magnetic field variations.  We expect a zero degree 
phase angle for the bending mechanism and a ninety degree
phase angle for the compressional mechanism.

As the horizontal component of an acoustic wave compresses 
matter,  we see solar surface velocity increase in 
our line of sight.  The surface is being displaced upward 
because a horizontal velocity component has compressed 
the material directly below the surface.  This would also 
correspond to an increase in the magnetic field strength 
because we assume a field 'frozen into' the material.
In this manner, the compressional mechanism changes the 
magnetic field strength.

Alternatively, a bending mechanism will alter the field 
strength if the field is being bent toward the observers 
line of sight since the magnetic field measurements are 
based on the longitudinal zeeman effect.  Therefore, 
observations of the bending mechanism will be better 
observed towards the solar limb.

Data Analysis:

The velocity and magnetic field variations will be 
cross-correllated in order to obtain a temporal lag between 
the signals.  This temporal lag is easily converted into 
a phase angle if we assume the variations are caused by the 
acoustic waves with a 5 minute period, i.e. (2*pi*delta t/period) 
= phase angle in radians.  Associated energy flux can be 
calculated using the poynting vector and assuming that only 
the Alfven, or bending mechanism, is causing energy transport.
 

MDI Science Objectives Fulfilled:

The investigation falls under the SOI associated science 
objective of understanding of the importance of magneto-
hydrodynamics in the solar atmosphere. 

See Also:
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