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 \Lambda CDM cosmology using one-dimensional hydrodynamic simulations .
The effects of the non-adiabatic electron heating efficiency , \beta , 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 } \sim 1.2 \times 10 ^ { 15 } M _ { \odot } , electron and ion temperatures differ by less than a percent within the virial radius R _ { vir } .
The difference is \approx 20 \% for a non-adiabatic electron heating efficiency of \beta \sim 1 / 1800 to 0.5 at \sim 1.4 R _ { vir } .
Beyond that radius , the non-equipartition effect depends rather strongly on \beta , 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 \sim 10 \% bias in the projected temperature at R _ { vir } for a wide range of \beta .
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 \lesssim 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 \sim 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 , \delta \Delta T _ { SZE } , is larger at a higher redshift .
For the most massive clusters at z \approx 2 , the differences can be \delta \Delta T _ { SZE } \approx 4–5 ~ { } \mu K near the shock radius .
We also found that for our model in the \Lambda CDM universe , the integrated SZ bias , Y _ { non { \text { - } } 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 .