Table A.1.

Prior distribution, inferred median and difference with 16^th-84^th percentiles for the density fluctuation parameters, and deduced parameters, for each cluster in the X-COP sample and for a joint fit over the whole sample. The first section represents the density fluctuation parameters defined in Sec. 2.5. The second section corresponds to the parameters deduced from the density fluctuations, namely, the clumping factor (Sect. 4.2), Mach number ℳ (Sect. 4.3) and ratio of non-thermal pressure to total pressure P_NTH/P_TOT (Sect. 4.4). The parameters of the density fluctuations as well as the inferred parameters are calculated in the four regions defined in Table (1) and within R₅₀₀. We ensured the proper convergence of the MCMC sampling by assessing that for each parameter.

Name	Prior	A1644	A1795	A2029	A2142	A2255	A2319	A3158	A3266	A644	A85	RXC1825	ZW1215	Joint
σδ (I)	10𝒰(−2,1)
σδ (II)	10𝒰(−2,1)
σδ (III)	10𝒰(−2,1)
σδ (IV)	10𝒰(−2,1)
σδ in R500	10𝒰(−2,1)
ℓinj[R500] (I)	10𝒰(−2,1)
ℓinj[R500] (II)	10𝒰(−2,1)
ℓinj[R500] (III)	10𝒰(−2,1)
ℓinj[R500] (IV)	10𝒰(−2,1)
ℓinj[R500] in R500	10𝒰(−2,1)
α (I)	𝒰(0,7)
α (II)	𝒰(0,7)
α (III)	𝒰(0,7)
α (IV)	𝒰(0,7)
α in R500	𝒰(0,7)
(I)
(II)
(III)
(IV)
in R500
ℳ (I)
ℳ (II)
ℳ (III)
ℳ (IV)
ℳ in R500
PNTH/PTOT (I)
PNTH/PTOT (II)
PNTH/PTOT (III)
PNTH/PTOT (IV)
PNTH/PTOT in R500