Creating a “Faraday Ghost” inside the Rotation Measure Synthesis Technique, through a Wide Observational “Gap” in Wavelength Coverage

Jacques P. Vallée

National Research Council Canada, National Science Infrastructure Portfolio, Victoria, Canada.

DOI: 10.4236/ijaa.2013.32011                

Abstract

Several recently published Faraday rotation measures (RM) derived using the novel RM synthesis technique are likely in error. If a set of polarimetric observations contains a large gap in the wavelength coverage, the rotation measure determination is sometimes ambiguous; this is also true even when two long wavelength ranges are observed but are separated by a wide gap. Essentially, there are 180° ambiguities in the observed Position Angle of the electric polarisation vector between the two wavelength ranges; these ambiguities are not resolved because the extent of wavelengths² covered, within each of the two ranges, is too small to uniquely determine the RM in isolation. We find that unphysical “Faraday ghosts” can be mathematically constructed with a np ambiguity (±180° times an integer) at predictable polarization position angles when using only two wavelength ranges separated by a gap, as a function of the width of the gap (Equation (4)). Our computations suggest an empirical correlation between an observational gap between two wavelength ranges and the appearance of “Faraday ghosts”.

Keywords

Magnetic Fields; Radio Polarization; Galactic Magnetic Fields; Spiral Galaxies

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. P. Vallée, “Magnetic Fields in the Nearby Universe, as Observed in Solar and Planetary Realms, Stars, and Interstellar Starforming Nurseries,” New Astronomy Reviews, Vol. 55, No. 3-4, 2011, pp. 23-90. doi:10.1016/j.newar.2011.01.001
[2]	J. P. Vallée, “Magnetic Fields in the Galactic Universe, as Observed in Supershells, Galaxies, Intergalactic and Cosmic Realms,” New Astronomy Reviews, Vol. 55, No. 3-4, 2011, pp. 91-154. doi:10.1016/j.newar.2011.01.002
[3]	N. W., Broten, J. M. MacLeod and J. P. Vallée, “Catalogue of Unambiguous (Faraday-Thin, One-Component, Spectrum-Selected) Rotation Measures for Galaxies and Quasars,” Astrophysics and Space Science, Vol. 141, No. 2, 1988, pp. 303-331. doi:10.1007/BF00639497
[4]	J. C. Brown and A. R. Taylor, “The Structure of the Magnetic Field in the Outer Galaxy from Rotation Measure Observations through the Disk,” Astronomical Journal, Vol. 563, No. 1, 2001, pp. L31-L34. doi:10.1086/338358
[5]	M. R. Bell, H. Junklewitz and T. A. Ensslin, “Faraday Caustics. Singularities in the Faraday Spectrum and Their Utility as Probes of Magnetic Field Properties,” Astronomy and Astrophysics, Vol. 535, No. A85, 2011, pp. 1-14.
[6]	R. Braun, G. Heald and R. Beck, “The Westerbork SINGS Survey. III. Global Magnetic Field Topology,” Astronomy and Astrophysics, Vol. 514, No. A42, 2010, pp. 1-19.
[7]	G. Heald, R. Braun and Edmonds, “The Westerbork SINGS Survey. II Polarization, Faraday Rotation, and Magnetic Fields,” Astronomy and Astrophysics, Vol. 503, No. 2, 2009, pp. 409-435. doi:10.1051/0004-6361/200912240
[8]	J. P. Vallée, “A Study of the Linear Polarization of Radio Galaxies and Quasars,” Ph.D. Thesis, University of Toronto, Toronto, 1973.
[9]	J. P. Vallée and P. P. Kronberg, “The Rotation Measures of Radio Sources and Their Interpretation,” Astronomy & Astrophysics, Vol. 43, No. 2, 1975, pp. 233-242.
[10]	J. P. Vallée, “The Rotation Measures of Radio Sources and Their Data Processing,” Astronomy and Astrophysics, Vol. 86, No. 1, 1980, pp. 251-253.
[11]	S. Sarala and P. Jain, “A Circular Statistical Method for Extracting Rotation Measures,” Monthly Notices of the Royal Astronomical Society, Vol. 328, No. 2, 2001, pp. 623-634. doi:10.1046/j.1365-8711.2001.04932.x
[12]	K. Dolag, C. Vogt and T. A. Ensslin, “PACERMAN-I. A New Algorithm to Calculate Faraday Rotation Maps,” Monthly Notices of the Royal Astronomical Society, Vol. 358, No. 3, 2005, pp. 726-731. doi:10.1111/j.1365-2966.2005.08851.x
[13]	A. A Ruzmaikin and D. D. Sokoloff, “The Calculation of Faraday Rotation Measures of Cosmic Radio Sources,” Astronomy and Astrophysics, Vol. 78, No. 1, 1979, pp. 1-6.
[14]	D. Farnsworth, L. Rudnick and S. Brown, “Integrated Polarization of Sources at λ ~ 1 m and New Rotation Measure Ambiguities,” Astronomical Journal, Vol. 141, No. A191, 2011, pp. 1-28.
[15]	P. Frick, D. Sokoloff, R. Stepanov and R. Beck, “Wavelet-Based Faraday Rotation Measure Synthesis,” Monthly Notices of the Royal Astronomical Society, Vol. 401, No. 1, 2010, pp. L24-L28. doi:10.1111/j.1745-3933.2009.00778.x
[16]	P. Frick, D. Sokoloff, R. Stepanov and R. Beck, “Faraday Rotation Measure Synthesis for Magnetic Fields of Galaxies,” Monthly Notices of the Royal Astronomical Society, Vol. 414, No. 3, 2011, pp. 2540-2549. doi:10.1111/j.1365-2966.2011.18571.x
[17]	M. Andrecut, J. M. Stil and A. R. Taylor, “Sparse Faraday Rotation Measure Synthesis,” Astronomical Journal, Vol. 143, No. A33, 2012, pp. 1-12.
[18]	B. J. Burn, “On the Depolarization of Discrete Radio Sources by Faraday Dispersion,” Monthly Notices of the Royal Astronomical Society, Vol. 133, No. 1, 1966, pp. 67-83.
[19]	S. A. Mao, B. M. Gaensler, M. Haverkorn, E. G. Zweibel, G. J. Madsen, N. M. McClure-Griffiths, A. Shukurov and P. P. Kronberg, “A Survey of Extragalactic Faraday Rotation at High Galactic Latitude: The Vertical Magnetic Field of the Milky Way toward the Galactic Poles,” Astronomical Journal, Vol. 714, No. 2, 2010, pp. 1170-1186. doi:10.1088/0004-637X/714/2/1170
[20]	C. L. Van Eck, J. C. Brown, J. M. Stil, K. Rae, S. A. Mao, B. M. Gaensler, A. Shukurov, A. R. Taylor, M. Haverkorn, P. P. Kronberg and N. M. McClure-Griffiths, “Modeling the Magnetic Field in the Galactic Disk Using New Rotation Measure Observations from the Very Large Array,” Astronomical Journal, Vol. 728, No. A97, 2011, pp. 1-14.
[21]	S. A. Mao, N. M. McClure-Griffiths, B. M. Gaensler, J. C. Brown, C. L. van Eck, M. Haverkorn, P. P. Kronberg, J. M. Still, A. Shukurov and A. R. Taylor, “New Constraints on the Galactic Halo Magnetic Field Using Rotation Measures of Extragalactic Sources toward the Outer Galaxy,” Astronomical Journal, Vol. 755, No. A21, 2012, pp. 1-15.
[22]	P. R. Bevington, “Data Reduction and Error Analysis for the Physical Sciences,” McGraw-Hill, New York, 1969, pp. 310-311.
[23]	M. A. Brentjens and A. G. de Bruyn, “Faraday Rotation Measure Synthesis,” Astronomy and Astrophysics, Vol. 441, No. 3, 2005, pp. 1217-1228. doi:10.1051/0004-6361:20052990
[24]	D. Farnsworth, L. Rudnick and S. Brown, “Integrated Polarization of Sources at λ ~ 1 m and New Rotation Measure Ambiguities,” Astronomical Journal, Vol. 141, No. A191, 2011, pp. 1-18.