Non-Zeeman Circular Polarization of CO rotational lines in SNR IC 443

1. Introduction

• Dust polarization vectors trace the plane-of-sky magnetic-field orientation because nonspherical grains emit linearly polarized radiation perpendicular to field lines.Source: §1 · p. 1

1.1. The Goldreich-Kylafis Effect

• Molecular spectral lines can be linearly polarized by magnetic-field alignment and anisotropic excitation, with polarization either parallel or perpendicular to the field.Source: §1.1 · p. 1

1.2. The Zeeman Effect

• Zeeman circular polarization arises from magnetic splitting or broadening of molecular lines and can measure the line-of-sight field component in weak-field molecular clouds.Source: §1.2 · p. 1

1.3. This work

• Anisotropic resonant scattering can convert linear molecular-line polarization into circular polarization when foreground molecules scatter background emission through a magnetic-field-dependent phase shift.Source: §1.3 · p. 2
• The paper presents dust and 12CO polarization maps near IC 443's western molecular shell edge and quantifies linear-to-circular conversion against the scattering model.Source: §1.3 · p. 2

2. Source Description

• IC 443 lies about 1.5 kpc away, is approximately 20,000 years old, and has two shells of different radii interacting with surrounding molecular material.Source: §2 · p. 2
• IC 443-G is the most massive of eight identified molecular clumps, with an estimated mass of approximately 2 × 10^3 M⊙ at the western edge of the clump ring.Source: §2 · p. 2
• Models of Clump G allow either mixed J-type and C-type shocks or a tilted molecular-ring geometry with the shock transverse to the line of sight.Source: §2 · p. 2
• Previous radio, maser, and H I observations indicate a magnetized shocked environment but leave the field geometry and line-of-sight strength incompletely constrained.Source: §2 · p. 2

3.1. IRAM 30-m Observations

• CO (J = 1 →0) at 115.271 GHz and CO (J = 2 →1) at 230.538 GHz were mapped simultaneously with the EMIR dual-polarization receiver and XPOL backend.Source: §3.1 · p. 2
• XPOL derives Stokes parameters from the time-averaged horizontal and vertical electric fields and their relative phase difference.Source: §3.1 · pp. 2–3
• Stokes I and Q come from total-power measurements, whereas U and V come from cross-correlated intermediate-frequency signals transformed into the equatorial reference frame.Source: §3.1 · p. 3
• The campaign acquired 24 paired on-the-fly maps covering 200′′ × 140′′ and Mercury maps to characterize instrumental polarization and beam sidelobes.Source: §3.1 · p. 3

3.2. IRAM 30-m Data Calibration

• Temperature calibration used hot and cold loads, while phase calibration corrected optical and electronic delays between the orthogonally polarized signal paths.Source: §3.2 · p. 3
• A wire grid measured the instrumental phase shift, and XPOL calibration software assigned Stokes-parameter signs according to the IAU convention.Source: §3.2 · p. 3

• CO Stokes data were integrated over blue- and red-shifted wings separately to avoid the self-absorption feature from about −7 to −2 km s−1.Source: §3.3 · p. 3
• The dominant instrumental effect was leakage from Stokes I into the other Stokes parameters, while higher-order mixing among Q, U, and V was also considered.Rotation from the Nasmyth to equatorial frame can mix Q and U, affecting polarization-angle accuracy.Source: §3.3 · p. 3
• Residual phase errors can mix Stokes U and V, but a measured phase error of 0.02 radians implies only about 2% leakage from intrinsic U into V, which was considered negligible.Source: §3.3 · pp. 3–4
• Instrumental polarization was modeled through convolution of the target Stokes I map with Mercury’s measured Stokes maps, then subtracted from the target maps.The corrected Q, U, and V maps had degraded spatial resolutions of 30.3 arcsec and 15.4 arcsec before deconvolution to the original CO-beam resolutions.Source: §3.3 · p. 4
• The correction rotated Mercury’s Nasmyth-frame Stokes maps to the target elevation and parallactic angles before subtraction, assuming instrumental Q and U remained stationary during mapping.The rotation-angle differences ranged from 3° to 34°, averaging 16°, and the resulting subtraction was indistinguishable within 1σ instrumental-polarization limits.Source: §3.3 · p. 4

• PolKa was used with LABOCA at APEX to observe the continuum polarization of IC 443-G using a reflection-type rotating halfwave plate.The wave plate modulates the polarized signal at four times its angular speed.Source: §3.4 · p. 4
• The observations were performed at 345 GHz with a 60 GHz bandwidth and 4.2 hours of on-source integration across December 2011 and November 2012.Average precipitable water vapor was 0.8 mm, corresponding to τ225 ≃ 0.035.Source: §3.4 · p. 4
• OTF compact raster-spiral mapping produced uniform coverage over LABOCA’s 11′ × 11′ field of view, with modulation set to 6.24 Hz above typical atmospheric fluctuations.Source: §3.4 · p. 4

3.5.1. Demodulation of the Polarized Signal

• Stokes Q and U were extracted after calibrating the rotating-halfwave-plate angles with generalized synchronous demodulation.A harmonic modulation proportional to total intensity was removed with a Fourier filter before demodulation, preserving the polarization signal.Source: §3.5.1 · p. 5

3.5.2. Calibration of the Total Power and Linear Polarization

• Total intensity was calibrated with standard flux calibrators, while polarized flux and fractional polarization were calibrated with the Crab nebula and checked against OMC-1.The analyzing polarizers cause about 50% flux loss, so the Stokes I calibration factor differs by about a factor of two from the usual LABOCA factor.Source: §3.5.2 · p. 5
• After calibrating total power and polarization, characterizing and subtracting instrumental polarization, the polarization angles were obtained directly from reduced Stokes Q and U.Source: §3.5.2 · p. 5

3.5.3. Instrumental Polarization

• Uranus tests measured an upper limit of 0.1% linear polarization at the planet’s center, while edge polarization reached 3% from weak Stokes I and sidelobe contributions.The Uranus Stokes maps were convolved with the IC 443-G maps to account for polarized sidelobes.Source: §3.5.3 · p. 5

4.1. Linear polarization maps of CO

• The CO linear polarization maps average velocity-wing measurements while excluding the self-absorption interval from −7 to −2 km s−1.Vectors are retained for pixels with p ≥3σp, and the CO (J = 1 →0) maps use comparable polarization uncertainties.Source: §4.1 · p. 5

4.2. Circular Polarization in CO Spectral lines

• Intrinsic circular polarization reaches 0.5–1% across both CO transitions and can exceed the measured linear polarization.The two transitions have similar linear polarization profiles but different Stokes V behavior, including higher circular polarization across CO (J = 2 →1).Source: §4.2 · pp. 5–6
• CO circular polarization is non-Zeeman because CO’s Zeeman splitting is negligible compared with that of CN, the molecule routinely used for Zeeman measurements.The approximate CO splitting factor is 0.2 mHz µG−1, versus approximately 2 Hz µG−1 for CN at 113 and 226 GHz.Source: §4.2 · p. 6

4.3. Anisotropic Resonance Scattering

• Anisotropic resonant scattering converts Stokes U into Stokes V when a phase shift develops between orthogonal scattered components.Without this scattering and phase shift, Stokes V is zero while the linear polarization state remains unchanged; the foreground molecules may have a different field orientation from the background.Source: §4.3 · p. 6

4.4. Linear Polarization Map of Dust Emission

• The dust map reaches polarization levels up to 10%, with the inferred magnetic field oriented perpendicular to the source’s long axis.Analyzed vectors have p ≥3σp and polarization-angle uncertainties below 10°.Source: §4.4 · p. 6

4.5. Estimating the Magnetic Field Orientation in the Foreground

• 73% of CO (J = 2 →1) vectors and 76% of CO (J = 1 →0) vectors deviate less than 10° from corresponding dust vectors after correction.For deviations below 5°, the fractions are 53% and 47%, respectively; the lower-resolution J = 1 →0 map provides fewer vectors.Source: §4.5 · p. 7
• Corrected CO polarization maps for both transitions agree closely with the dust polarization map across blue- and red-shifted wings.The best foreground-field orientation is east–west in the plane of the sky; the corrected maps show consistent polarization patterns and excellent agreement with dust.Source: §4.5 · p. 7

Data reduction

• Instrumental polarization was removed by convolving target maps with Stokes maps of Mercury, yielding credible intrinsic CO linear polarization of ≃0.5–0.8% and circular polarization up to ≃1%.The authors identify this correction as necessary for recognizing the polarization conversion.Source: §5 · p. 7

Physical assumptions

• The adopted foreground-cloud interpretation assumes an optically thin cloud whose thickness does not approximately exceed the effective mean free path for resonant scattering and absorption.Under this assumption, background photons can undergo multiple resonant scattering events before escaping.Source: §5 · p. 7

Polarization conversion

• After instrumental correction and reverse transformation of circularly polarized power, CO and dust linear polarization maps show consistent alignment across both CO transitions.The resulting blue- and red-shifted wing maps are similar between transitions, supporting the inferred foreground magnetic-field direction.Source: §5 · p. 7

Physical interpretation

• The phase-shift magnitude depends on excitation temperature, molecular number density, and the square of the plane-of-sky magnetic-field strength, among other physical parameters.The relevant expression also incorporates CO density, interaction-region size, transition frequencies, and observed polarization quantities.Source: §5 · p. 7

Limitations

• A detailed analysis of the polarization transformation requires temperature and density profiles that the authors defer to a follow-up paper.Consequently, the present discussion does not fully determine the transformation’s physical dependence in this source.Source: §5 · p. 8

Comparison with OH maser polarization

• At the OH maser position, corrected CO polarization angles of 29° ± 2° and 32° ± 3° agree with the dust angle of 20° ± 8° and support emission from shocked gas in IC 443-G.These measurements are also consistent with the earlier OH maser result of 21° polarization angle.Source: §5 · p. 8

Summary

• After flux correction, both CO transitions’ reconstructed polarization vectors align with the dust vectors, supporting linear-to-circular polarization conversion.The measured circular polarization reaches up to 1% in the ^12CO (J = 2 →1) and (J = 1 →0) lines.Source: §6 · p. 8
• The study measures linear and non-Zeeman circular polarization up to 1% in ^12CO (J = 2 →1) and (J = 1 →0) emission from a shocked molecular clump around IC 443.The observations combine CO data from the IRAM 30-m telescope with a dust polarization map from APEX.Source: §6 · p. 8

Future work

• A future paper is needed to establish definitively whether the circular polarization arises from the anisotropic resonant scattering model.If established, the technique could enable magnetic-field measurements using abundant molecules such as CO, which is not sensitive to the Zeeman effect.Source: §6 · p. 8