Neutrino-induced polarization rotation in active galactic nuclei plasmas

We study parity-violating birefringence induced by an asymmetric neutrino background in plasmas associated with active galactic nuclei (AGN). We derive a arising from the relative bulk motion between the neutrino medium and plasma, and show that it can produce an anomalous frequency dependence of the polarization-rotation angle, distinct from the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>ω</a:mi> <a:mrow> <a:mo>−</a:mo> <a:mn>2</a:mn> </a:mrow> </a:msup> </a:math> scaling of Faraday rotation. This anomalous scaling can occur either at the resonance plasma frequency condition <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>ω</c:mi> <c:mo>≃</c:mo> <c:msub> <c:mi>ω</c:mi> <c:mi>p</c:mi> </c:msub> </c:math> , or when <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msubsup> <e:mi>E</e:mi> <e:mi>ν</e:mi> <e:mn>0</e:mn> </e:msubsup> <e:mo>≃</e:mo> <e:msub> <e:mi>m</e:mi> <e:mi>ν</e:mi> </e:msub> <e:mi>ω</e:mi> <e:mo>/</e:mo> <e:msub> <e:mi>ω</e:mi> <e:mi>p</e:mi> </e:msub> </e:math> lies within the range of the neutrino energy spectrum. We estimate the effect for three scenarios: jets propagating through the cosmic neutrino background ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mi mathvariant="normal">C</g:mi> <g:mi>ν</g:mi> <g:mi mathvariant="normal">B</g:mi> </g:mrow> </g:math> ), jets with an internal flux of high-energy neutrinos, and accretion-disk plasma permeated by the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mi mathvariant="normal">C</k:mi> <k:mi>ν</k:mi> <k:mi mathvariant="normal">B</k:mi> </k:mrow> </k:math> . Of the three scenarios, the latter gives the largest rotation angle <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>ϕ</o:mi> <o:mi mathvariant="normal">d</o:mi> </o:msub> <o:mo>∼</o:mo> <o:msup> <o:mn>10</o:mn> <o:mrow> <o:mo>−</o:mo> <o:mn>35</o:mn> </o:mrow> </o:msup> <o:mtext> </o:mtext> <o:mtext> </o:mtext> <o:mi>rad</o:mi> </o:math> , at x-ray frequencies. Although the predicted rotation angles are below current polarimetric sensitivity, the identified spectral signatures provide a theoretical framework for probing neutrino asymmetries and AGN plasma properties independent of magnetic field models.