Faraday Rotation: Expected Possible Analyses from Polarized Radio Sources and Other Matters

1. Faraday Rotation: Expected Possible Analyses from Polarized Radio Sources and Other Matters P.P. Hick, B.V. Jackson, M.M. Bisi, J.M. Clover, and A. Buffington (mmbisi@ucsd.edu) Center for Astrophysics and Space Sciences, University of California at San Diego, 9500 Gilman Drive #0424La Jolla, CA 92093-0424 USA http://ips.ucsd.edu/

2. Faraday rotation forward modeling Faraday rotation Background Field, 3D UCSD Density

3. Forward Modeling Forward modeling (how a rotation measure sky map is made) proceeds using an IDL program provided in SolarSoft from the UCSD SMEI software tree program: /ucsd/sat/idl/util/vupack/vu_earthskymap.pro.The entry point is vu_los_faraday_rm, and depending on the display selected (Hammer-Aitoff or Fisheye) provides a sky map from UCSD’s nv3 and bbt (magnetic field wso or nso) files, linearly-interpolating in time to the specific time of interest. Both nv3 and bbt files are used in the real-time IPS analysis found on the UCSD Website: http://ips.ucsd.edu/.An nv3 file is a volumetric ascii file with a header and speed and density provided in Carrington heliographic coordinates of longitude, latitude, and solar distance. A bbt file is a volumetric ascii file containing radial and tangential magnetic fields of the same coordinates.

4. The UCSD 3D-reconstruction program The UCSD 3D-reconstruction program is a “brute force” LSTQR iterative tomography routine that was first developed by B.V. Jackson and colleagues in a time-dependent version in 1999 to use IPS data. This program iterates in 3-dimensions – longitude, latitude, and time to provide the time-dependent source surface boundary for a kinematic solar wind model that provides the 4-dimensional volumes needed to match observations. An earlier version of this same model developed in 1996 is “corotating” in that it reconstructs the source surface boundary for a kinematic solar wind model in 2-dimensions – longitude and latitude.The time-dependent kinematic solar wind model (that preserves mass and mass flux) proceeds to provide a “traceback matrix” that in 4-dimensions locates the origin of every position and time within the volume at the source surface.

5. The UCSD 3D-reconstruction program In fall 2008 B.V. Jackson announced the development of a version of the time-dependent 3D reconstruction code that first iterates to provide time-dependent densities and velocities from IPS lines of sight (LOS) from STELab, and then iterates to determine 3-component magnetic fields present from Faraday rotation measurements along the same LOS input as a test pattern. The tests converged within noise limits to the original LOS values present in the solar wind as the volumetric data expanded outward. A simple directed magnetic-field vector was input at the source surface and was propagated outward over time. In these tests, the kinematic model that preserves mass and mass flux and the velocities derived by the 3D-reconstruction code were used (as in the forward modeling) to propagate the fields outward. The UCSD kinematic model only allows a frozen-field approximation of solar wind fields to be propagated outward. The 4D traceback matrix tells at any point, the 3D origin and original strength of the magnetic field vector at the source surface.

6. Where to go from here 1) To be effective, real polarization data and its change with time from one day to the next from the heliosphere needs to be obtained to provide information to be used to reconstruct 3 component fields.2) Until EISCAT data at high frequency with very few LOS were shown to provide good 3D reconstructions, B.V. Jackson was very afraid that ionospheric FR noise would overwhelm a smaller heliospheric FR signal. 3) It now becomes more important to be absolutely certain of the higher-frequency velocity and IPS scintillation-level proxy for heliospheric density. If it is impossible to use a scintillation-level proxy for density, then a coronagraph Thomson-scattering brightness proxy for density makes more sense as long as a coronagraph still operates from near-Earth when these measurements are made.

7. Where to go from here 4) One difficulty for the inversion technique used for the IPS is the line-of-sight weighting used (eq. 2) from Jackson et al. (1998). In an experiment producing LOS from the weak-scattering integral IPS approximation (Fig. 1) and demonstrated that the shape of the weighting (without regard to the LOS scintillation-level) varied significantly. In previous programming a standard source size approximation of 0.1 arc seconds was used in (eq. 2) for 327 MHz sources. This approximation becomes less secure when few sources and high-frequency data are used in the 3D reconstructions.If information on source size is available for the source frequency it should be used. 81.5 MHz 0.1 arc sec 1000 MHz 0.05 arc sec 327 MHz 0.1 arc sec 81.5 MHz 0.3 arc sec 1000 MHz 0.1 arc sec

8. Where to go from here 5) Another better approach to the UCSD 3D reconstruction program inversion would be for the program to fit observed and modeled IPS correlations to velocity. For the inversion to work in the UCSD inversion scheme, the model and observed measurement would need to come up with a single difference between the model and the observation that linearly describes the amount the velocity ensemble provided by the correlation that needs to be changed to correct the model. This would remove the need for worries about peak- and mid-velocity measurements (EISCAT) of the correlation ensemble, and would probably show the several-stream components indicated by current LOS correlation observations. 6) A similar procedure could be used to fit modeled and observed scintillation-level spectra to obtain a proxy for density directly from the data rather than going through the conversion of scintillation level to g-level. This, however is a somewhat more difficult process.

9. And finally some more on EISCAT… We leave you with still another development in the UCSD time-dependent 3D reconstruction code that B.V. Jackson implemented in the last few weeks, and has used the EISCAT analysis to demonstrate.More work is needed on this than time available in the next few days. Wonderful there is a positive correlation whatsoever! Circular reasoning, but even a better correlation from the 3D-reconstruction model (see slide 7)!