Constraints on parallel temperature in bi-nonextensive space plasmas driven by unstable proton firehose mode

Solar wind environments, featuring different charged particle distributions, are replete with various plasma instabilities driven by temperature anisotropies. This study unveils the effect of bi-nonextensive proton distributions on the proton firehose (PFH) instability, which plays an important role in regulating the proton parallel temperature in the solar wind. To this end, a q-dependent effective temperature model of bi-nonextensive distribution is utilized, encompassing both superextensive and subextensive regimes. To analyze the behavior of real frequency and the growth rate of PFH mode, a transverse dielectric function is derived for superextensive and subextensive dilute plasmas and solved numerically for different values of temperature anisotropy and plasma beta pertinent to the solar wind environment. It is observed that the PFH instability demonstrates a heightened sensitivity to the superextensivity and temperature anisotropy of protons. A comprehensive comparison of the current findings is made with the other plasma models, including bi-kappa and bi-Maxwellian. One notable divulgence of the present study is that, in contrast to the bi-kappa protons, the bi-nonextensive distributed protons (within the superextensive limit) consistently support the instability growth of the PFH mode, regardless of whether the anisotropy ratio is small or large.