We present new limits on the graviton Compton wavelength in a Yukawa potential using a sample of 12 relaxed galaxy clusters , for which the temperature and gas density profiles were derived by Vikhlinin et al ( ) using Chandra X-ray observations . These limits can be converted to a bound on the graviton mass , assuming a non-zero graviton mass would lead to a Yukawa potential at these scales . For this purpose , we first calculate the total dynamical mass from the hydrostatic equilibrium equation in Yukawa gravity and then compare it with the corresponding mass in Newtonian gravity .
We calculate a 90 % c.l .
lower/upper limit on the graviton Compton wavelength/ mass for each of the 12 clusters in the sample .
The best limit is obtained for Abell 2390 , corresponding to \lambda _ { g } > 3.58 \times 10 ^ { 19 } km or m _ { g } < 3.46 \times 10 ^ { -29 } eV . This is the first proof of principles demonstration of setting a limit on the graviton mass using a sample of related galaxy clusters with X-ray measurements and can be easily applied to upcoming X-ray surveys such as eRosita .