[Paper Review] Do pulsars rotate clockwise or counterclockwise?

Renaud Gueroult, Yuan Shi+2 more|arXiv (Cornell University)|Mar 4, 2019

Pulsars and Gravitational Waves Research45 references4 citations

TL;DR

This paper demonstrates that rotation-induced polarisation rotation in pulsar magnetospheres—distinct from interstellar Faraday rotation—can be detected in sub-GHz observations, enabling unambiguous determination of pulsar rotation sense (clockwise vs. counterclockwise). The key contribution is a novel method to resolve rotational direction using wavelength-dependent polarisation shifts, offering new constraints on magnetospheric physics and emission mechanisms.

ABSTRACT

Pulsars are rotating neutron stars which emit lighthouse-like beams. Owing to their unique properties, pulsars are a unique astrophysical tool to test general relativity, inform on matter at extreme densities, and probe galactic magnetic fields. Understanding pulsars physics and emission mechanisms is critical to these applications. Here we uncover that mechanical-optical rotation in the pulsars' magnetosphere affects polarisation in a way which is indiscernible from Faraday rotation in the interstellar medium for typical GHz observations frequency, but which can be distinguished in the sub-GHz band. Besides being essential to correct for possible systematic errors in interstellar magnetic field estimates, our novel interpretation of pulsar polarimetry data offers a unique means to determine whether pulsars rotate clockwise or counterclockwise, providing new constraints on magnetospheric physics and possible emission mechanisms. Combined with the ongoing development of sub-GHz observation capabilities, our finding promises new discoveries, such as the spatial distributions of clockwise rotating or counterclockwise rotating pulsars, which could exhibit potentially interesting, but presently invisible, correlations or features.

Motivation & Objective

• To resolve the ambiguity in pulsar rotation direction (clockwise vs. counterclockwise) using polarimetric observations.
• To identify and isolate the contribution of mechanical-optical rotation in the pulsar magnetosphere from interstellar Faraday rotation.
• To correct for systematic errors in interstellar magnetic field measurements caused by unaccounted magnetospheric rotation effects.
• To provide a new diagnostic tool for probing magnetospheric composition and particle acceleration mechanisms in pulsars.
• To enable future studies of spatial distributions of rotation-sense-specific pulsars using emerging sub-GHz radio facilities.

Proposed method

• Model the pulsar magnetosphere as a rotating, gyrotropic plasma with relativistic electron-positron pairs, using a dielectric susceptibility tensor formalism.
• Apply the Maxwell equations in a rotating frame to derive wave propagation characteristics, including refractive indices for left- and right-circularly polarised waves.
• Use the susceptibility tensor components derived from classical and quantum electrodynamics (QED) models to compute polarisation rotation in strong magnetic fields.
• Compare the wavelength dependence of polarisation rotation from magnetospheric rotation (scaling as ω⁻² near cut-off) with Faraday rotation (λ² scaling) to distinguish the two effects.
• Incorporate realistic plasma parameters: B₀ = 10⁸ T, n = 10²⁰ m⁻³, Ω = 10 s⁻¹, and test cases with charge asymmetry (f = 0.49) and QED corrections.
• Utilize vector calculus identities to handle the non-uniform susceptibility tensor in the rotating frame, ensuring consistency with electromagnetic wave propagation laws.

Experimental results

Research questions

• RQ1 Can the rotation sense of a pulsar (clockwise or counterclockwise) be determined from single-dish polarimetric observations?
• RQ2 How does mechanical-optical rotation in the pulsar magnetosphere affect polarisation angle differently than interstellar Faraday rotation?
• RQ3 What is the impact of plasma density asymmetry (e.g., nₑ ≠ nₚ) and QED corrections on polarisation rotation in pulsar magnetospheres?
• RQ4 Can sub-GHz observations resolve the distinct spectral signature of magnetospheric rotation from the λ² scaling of Faraday rotation?
• RQ5 How does the cut-off frequency for wave propagation depend on magnetospheric parameters like density and rotation rate?

Key findings

• The polarisation rotation induced by the rotating magnetosphere scales as ω⁻² near the cut-off frequency, differing from the λ² (or ω⁻²) scaling of Faraday rotation, enabling unambiguous distinction.
• Even with QED corrections and electron-positron density asymmetry (e.g., f = 0.49), the deviation from λ² scaling persists, confirming the robustness of the diagnostic method.
• The cut-off frequency for the left-handed circularly polarised wave increases due to enhanced plasma frequency, shifting the spectral signature of magnetospheric rotation.
• A polarisation jump of Δφₗc ≈ (ωₚ²Ω/√2)¹ᐟ³ l/c occurs at the cut-off frequency, providing a measurable signature in sub-GHz observations.
• The sign of Ω·B determines the handedness of the polarisation rotation, allowing inference of rotation direction without multi-epoch or multi-directional observations.
• Correcting for magnetospheric rotation effects is essential to avoid systematic errors in interstellar magnetic field measurements using rotation measure (RM) techniques.