RAGAGNIN, ANTONIOANTONIORAGAGNINSARO, ALEXANDROALEXANDROSAROSINGH, PRIYANKAPRIYANKASINGHDolag, KlausKlausDolag2025-03-172025-03-1720210035-8711http://hdl.handle.net/20.500.12386/36841We employ a set of Magneticum cosmological hydrodynamic simulations that span over 15 different cosmologies, and extract masses and concentrations of all well-resolved haloes between z = 0 and 1 for critical overdensities $\Delta _\textrm {vir}, \Delta _{200c}, \Delta _{500c}, \Delta _{2500c}$ and mean overdensity ∆<SUB>200m</SUB>. We provide the first mass-concentration (Mc) relation and sparsity relation (i.e. M<SUB>∆1</SUB> - M<SUB>∆2</SUB> mass conversion) of hydrodynamic simulations that is modelled by mass, redshift, and cosmological parameters Ω<SUB>m</SUB>, Ω<SUB>b</SUB>, σ<SUB>8</SUB>, h<SUB>0</SUB> as a tool for observational studies. We also quantify the impact that the Mc relation scatter and the assumption of Navarro-Frank-White (NFW) density profiles have on the uncertainty of the sparsity relation. We find that converting masses with the aid of an Mc relation carries an additional fractional scatter ( $\approx 4{{\ \rm per\ cent}}$ ) originated from deviations from the assumed NFW density profile. For this reason, we provide a direct mass-mass conversion relation fit that depends on redshift and cosmological parameters. We release the package HYDRO_MC, a PYTHON tool that perform all kind of conversions presented in this paper....STAMPAenArticle10.1093/mnras/staa35232-s2.0-85099695692http://arxiv.org/abs/2011.05345v1https://academic.oup.com/mnras/article/500/4/5056/59797992021MNRAS.500.5056RFIS/05 - ASTRONOMIA E ASTROFISICAERC sectors::Physical Sciences and Engineering::PE9 Universe sciences: astro-physics/chemistry/biology; solar systems; stellar, galactic and extragalactic astronomy, planetary systems, cosmology, space science, instrumentation