# Effects of the Non-Equipartition of Electrons and Ions in the Outskirts of Relaxed Galaxy Cluster

#### Abstract

We have studied the effects of electron-ion non-equipartition in the outer regions of relaxed clusters for a wide range of masses in the ΛCDM cosmology using one-dimensional hydrodynamic simulations. The effects of the non-adiabatic electron heating efficiency, β, on the degree of non-equipartition are also studied. Using the gas fraction *f* _{gas} = 0.17 (which is the upper limit for a cluster), we give a conservative lower limit of the non-equipartition effect on clusters. We have shown that for a cluster with a mass of *M* _{vir} ~ 1.2 **×** 10^{15} *M* _{☉}, electron and ion temperatures differ by less than a percent within the virial radius *R* _{vir}. The difference is ≈20% for a non-adiabatic electron heating efficiency of β ~ 1/1800 to 0.5 at ~1.4*R* _{vir}. Beyond that radius, the non-equipartition effect depends rather strongly on β, and such a strong dependence at the shock radius can be used to distinguish shock heating models or constrain the shock heating efficiency of electrons. With our simulations, we have also studied systematically the signatures of non-equipartition on X-ray and Sunyaev-Zel'dovich (SZ) observables. We have calculated the effect of non-equipartition on the projected temperature and X-ray surface brightness profiles using the MEKAL emission model. We found that the effect on the projected temperature profiles is larger than that on the deprojected (or physical) temperature profiles. The non-equipartition effect can introduce a ~10% bias in the projected temperature at *R* _{vir} for a wide range of β. We also found that the effect of non-equipartition on the projected temperature profiles can be enhanced by increasing metallicity. In the low-energy band 1 keV, the non-equipartition model surface brightness can be higher than that of the equipartition model in the cluster outer regions. Future X-ray observations extending to ~*R* _{vir} or even close to the shock radius should be able to detect these non-equipartition signatures. For a given cluster, the difference between the SZ temperature decrements for the equipartition and the non-equipartition models, δΔ*T* _{SZE}, is larger at a higher redshift. For the most massive clusters at *z* ≈ 2, the differences can be δΔ*T* _{SZE} ≈ 4-5 μK near the shock radius. We also found that for our model in the ΛCDM universe, the integrated SZ bias, *Y* _{non-eq }/*Y* _{eq}, evolves slightly (at a percentage level) with redshift, which is in contrast to the self-similar model in the Einstein-de Sitter universe. This may introduce biases in cosmological studies using the *f* _{gas} technique. We discussed briefly whether the equipartition and non-equipartition models near the shock region can be distinguished by future radio observations with, for example, the Atacama Large Millimeter Array.

*This paper has been withdrawn.*