Galaxy clusters in Milgromian dynamics: Missing matter, hydrostatic bias, and the external field effect

We study the mass distribution of galaxy clusters in Milgromian dynamics, or modified Newtonian dynamics (MOND). We focus on five galaxy clusters from the X-COP sample, for which high-quality data are available on both the baryonic mass distribution (gas and stars) and internal dynamics (from the hydrostatic equilibrium of hot gas and the Sunyaev-Zeldovich effect). We confirm that galaxy clusters require additional `missing matter' in MOND, although the required amount is drastically reduced with respect to the non-baryonic dark matter in the context of Newtonian dynamics. We studied the spatial distribution of the missing matter by fitting the acceleration profiles of the clusters with a Bayesian method, finding that a physical density profile with an inner core and an outer $r^{-4}$ decline (giving a finite total mass) provide good fits within $\sim$1 Mpc. At larger radii, the fit results are less satisfactory but the combination of the MOND external field effect and hydrostatic bias (quantified as 10$\%$-40$\%$) can play a key role. The missing mass must be more centrally concentrated than the intracluster medium (ICM). For relaxed clusters (A1795, A2029, A2142), the ratio of missing-to-visible mass is around $1-5$ at $R\simeq200-300$ kpc and decreases to $0.4-1.1$ at $R\simeq2-3$ Mpc, showing that the total amount of missing mass is smaller than or comparable to the ICM mass. For clusters with known merger signatures (A644 and A2319), this global ratio increases up to $\sim$5 but may indicate out-of-equilibrium dynamics rather than actual missing mass. We discuss various possibilities regarding the nature of the extra mass, in particular `missing baryons' in the form of pressure-confined cold gas clouds with masses of $<10^5$ M$_\odot$ and sizes of $< 50$ pc.