Erratum: Sound-wave instabilities in dilute plasmas with cosmic rays: Implications for cosmic ray confinement and the Perseus X-ray ripples (Monthly Notices of the Royal Astronomical Society (2020) 493 (5323) DOI: 10.1093/mnras/staa535)

This is an erratum to Kempski, Quataert & Squire (2020). In the original paper, the expression for the Alfven velocity (equation 10) was not correct. The correct form is (formula presented) where B is the magnetic field, ? is the gas density and-p is the pressure anisotropy of the thermal gas. In the original paper, the 1/2 exponent in the-p termwas by accident omitted. Ourmain results do not change qualitatively, but there are moderate quantitative changes. The minimum cosmic ray (CR) pressure required for instability increases by a factor of ?2 and instability growth rates at any given CR pressure decrease by a factor of ?2, at fixed other parameters. The factor of 2 difference comes from Taylor expanding (1) to linear order. The main conclusion is still valid: small CR pressures are required for instability at high β. The corrected perturbed CR pressure equation is then (equation 36 in Kempski et al. 2020), (formula presented) and the corrected 1D dispersion relation is (equation 40 in Kempski et al. 2020) (formula presented) i.e.Terms ωB/ωa (which drive the instability and come from-p in the CR pressure equation) are reduced by a factor of 2. Note that the damping term in (3) (=4/3iωBω, which comes from damping by-p in the momentum equation) has not changed. The parameters and frequencies we use here are defined in Section 2.3 of Kempski et al. (2020). Figs 2, 3, 4, 5 and A1 in Kempski et al. (2020) (with ? ? pc/pg on the x-Axis) should be shifted to the right (factor of roughly 2).