Interstellar Polarization Survey III: Relation Between Optical Polarization and Reddening in the General Interstellar Medium

Optical starlight can be partially polarized while propagating through the dusty, magnetized interstellar medium. The polarization efficiency describes the polarization intensity fraction per reddening unit, P$_V$/E($B-V$), related to the interstellar dust grains and magnetic field properties. The maximum value observed, [P$_V$/E$(B-V)]_{max}$, is thus achieved under optimal polarizing conditions of the interstellar medium. Therefore, the analysis of polarization efficiency observations across the Galaxy contributes to the study of magnetic field topology, small-scale magnetic fluctuations, grain-alignment efficiency, and composition. Infrared observations from $Planck$ satellite have set [P$_V$/E$(B-V)]_{max}$ to 13$\%$ mag$^{-1}$. However, recent optical polarization observations in $Planck$'s highly polarized regions showed polarization efficiency values between 13.6$\%$ mag$^{-1}$ and 18.2$\%$ mag$^{-1}$ (depending on the extinction map used), indicating that [P$_V$/E$(B-V)]_{max}$ is not well constrained yet. We used $V$-band polarimetry of the Interstellar Polarization Survey (consisting of $\sim$10500 high-quality observations distributed in 34 fields of $0.3^{\circ}\times0.3^{\circ}$) to accurately estimate the polarization efficiency in the interstellar medium. We estimated the upper limit of P$_V$/E($B-V$) with the weighted $99th$ percentile of the field. In five regions, the polarization efficiency upper limit is above 13$\%$ mag$^{-1}$. Furthermore, we found [P$_V$/E$(B-V)]_{max} = 15.8^{+1.3}_{-0.9}\%$ mag$^{-1}$ using diffuse intermediate latitude ($|b|>7.5^{\circ}$) regions with apparently strong regular Galactic magnetic field in the plane-of-sky. We studied the variations of P$_V$/E($B-V$) across the sky and tested toy models of polarization efficiency with Galactic longitude that showed some correspondence with a uniform spiral magnetic field.