Hyperfine-Resolved Quantum Alignment of Interstellar Ortho-H2: Framework and Predicted Signal Magnitude

Molecular hydrogen dominates the cold interstellar medium (ISM) mass budget, but ground-state H₂ is optically invisible due to its lack of a permanent electric dipole. We present the first hyperfine-resolved treatment of ortho-H₂ (J = 1) alignment in the ISM and apply it to Interstellar Quantum Magneto-Birefringence (IQMB): the conversion of linear to circular polarization via the Cotton-Mouton effect of aligned ortho-H₂. We show that the correct quantum basis at typical cloud field strengths is the hyperfine basis (F, m_F) with F = 0, 1, 2, not (J, M_J). This “ultrafine” interaction scales as μ_N², and projecting J onto the hyperfine eigenstates dilutes the alignment by κ_F = 1/2. We solve the non-LTE quantum master equation including m_F-resolved FUV pumping, phenomenological multi-channel collisions calibrated to state-resolved H₂–H₂ rates, and depth-dependent H₂ photodissociation. Our rigorous Clebsch-Gordan treatment reveals that the alignment parameter 𝓐 flips sign across the magic angle (θ ≈ 54.7°), acting as a geometric diagnostic of the radiation field. Under nominal assumptions and a depth-dependent ortho-to-para ratio, the peak signal is |V/I| ≈ 7.4 × 10⁻⁴ in the illuminated PDR skin. While this is a factor of ~25 below the threshold of current sub-millimeter circular polarimetry (1.8 × 10⁻² for ALMA), the limitation is purely engineering. The fundamental physical limitation is the FUV–H₂ anti-correlation, meaning IQMB probes the illuminated molecular interface rather than the dark interior. While the signal at ALMA wavelengths is currently below engineering thresholds, scaling to CMB wavelengths and accounting for the partial linear polarization of the CMB yields an induced circular polarization of ~10⁻⁵. This places IQMB orders of magnitude above the primordial V-mode floor, identifying it as a potential astrophysical foreground for future CMB experiments like LiteBIRD and CLASS.