In many astrophysical environments the plasma is only partially ionized, and therefore the interaction of charged and neutral particles may alter both the triggering of reconnection and its subsequent dynamical evolution. We derive the tearing mode maximum growth rate for partially ionized plasmas in the cases of weak and strong coupling between the plasma and the neutrals. In addition, critical scalings for current sheet aspect ratios are presented in terms of Lundquist number and ion-neutral collision frequencies. In the decoupled regime the standard tearing mode is recovered with a small correction depending on the ion-neutral collision frequency; in the intermediate regime collisions with neutrals are shown to stabilize current sheets, resulting in larger critical aspect ratios for ideal tearing to occur. Nonetheless, the additional electron-neutral collisions, hidden in the definition of the Lundquist number, can shrink the critical aspect ratios below the fully ionized case. In the coupled regime, the growth rate depends on the density ratio between ions and neutrals through the collision frequency between these two species. These provide critical aspect ratios for which the tearing mode instability transitions from slow to ideal, that depend on the neutral-ion density ratio.
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