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A novel diagnostic of cosmic-ray modified shocks by polarimetry of H $\alpha$emissions is suggested. In a cosmic-ray modified shock, the pressure of cosmicrays is sufficiently high compared to the upstream ram pressure to force thebackground plasma to decelerate (measured in the shock rest frame).Simultaneously, a fraction of the hydrogen atoms co-existing in the upstreamplasma collide with the decelerated protons and undergo charge-exchangereactions. As a result, hydrogen atoms with the same bulk velocity of thedecelerated protons are generated. We show that when the shock is observed fromedge-on, the H $\alpha$ radiated by these upstream hydrogen atoms is linearlypolarized with a sizable degree of a few per cent as a result of resonantscattering of Ly $\beta$. The polarization direction depends strongly on thevelocity modification; the direction is parallel to the shock surface for thecase of no modification, while the direction is parallel to the shock velocityfor the case of a modified shock.

Diagnosing Cosmic Ray Modified Shocks with H {\alpha} Polarimetry