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The most massive protoclusters virialize to become clusters at $z\sim 2$,which is also a critical epoch for the evolution of their member galaxies.XLSSC 122 is a $z=1.98$ galaxy cluster with 37 spectroscopically confirmedmembers. We aim to characterize their star formation histories and to put themin the context of the cluster accretion history. We measure their photometry in12 bands and create a PSF-matched catalogue of the cluster members. We employBAGPIPES to fit star formation histories characterized by exponentiallydecreasing star-forming rates. Stellar masses, metal and dust contents are alsotreated as free parameters. The oldest stars in the red-sequence galaxiesdisplay a range of ages, from 0.5 Gyr to over $\sim$3 Gyrs. Characteristictimes are between $\sim$0.1 and $\sim$0.3 Gyr, and the oldest members presentthe longest times. Using MultiDark Planck 2 dark matter simulations, wecalculate the assembly of XLSSC 122-like haloes, weighted by the age posteriorsof the oldest members. We found that 74% of these haloes were less than 10%assembled at the onset of star formation, declining to 67% of haloes when suchgalaxies had formed 50% of their z=1.98 stellar masses. When 90% of theirstellar masses were formed, 75% of the haloes were less than 30% assembled. Thestar formation histories of the red-sequence galaxies seem consistent withepisodes of star formation with short characteristic times. Onset and cessationof star formation in the oldest galaxies are both likely to precede XLSSC 122virialization.

The XXL survey. XLIX. Linking the members star formation histories to the cluster mass assembly in the z=1.98 galaxy cluster XLSSC 122