tokens: M V ∼ −13.5 and Carina M V ∼ −9.5) merit a special mention. Although both dwarf galaxies have been quenched fairly recently (∼2.5–3 Gyr ago), there are suggestions that these dwarf galaxies have been orbiting the MW for a much longer time (e.g. Pasetto et al. 2011 ; Rocha et al. 2012 ; Patel et al. 2020 ; Rusakov et al. 2020 ). However, the results are dependent upon a number of model uncertainties and are much debated in the literature (Jahn et al. 2019 ; Pardy et al. 2019 ). We choose to retain Fornax and Carina in our sample. This leaves us with a sample of 13 and 28 satellites for the MW and M31, respectively (see Table 1 ). The lookback time of shutdown in star formation of these dwarf galaxies has been drawn from the literature, and has been estimated from data of varying quality. For 6 M31 dwarfs drawn from the ISLAandS project (Skillman et al. 2017 ), the shutdown time has been estimated from deep CMDs reaching down to the oldest main-sequence turn-off (MSTO). The shutdown time for the vast majority of the M31 dwarfs have been estimated from resolved HST data reaching fainter than the horizontal branch (Weisz et al. 2019b ). A sizeable fraction of the satellites of the MW have their time of their shutdown in star formation estimated from HST data reaching down to the MSTO (Weisz et al. 2014 ). For a few of the nearer MW dwarfs, the star formation has been estimated using ground-based data (e.g. Torrealba et al. 2016 ; Bettinelli et al. 2018 ). In Table 1 , we have included both the systematic and statistical uncertainties of τ 90 . The constraints on τ 90 as well as the ancient star formation history of M31 dwarfs will dramatically improve with observations from the upcoming Cycle 27 HST Treasury survey as part of HST -GO-15902 (PI D. Weisz). Table 1. Star formation shutdown time. Note . Distance of M31 satellites is taken from Conn et al. ( 2012 ) and Weisz et al. ( 2019a ). τ 90 is taken Weisz et al. ( 2014 ), Weisz et al. ( 2019b ), Brown et al. ( 2014 ), Bettinelli et al. ( 2018 ), and Torrealba et al. ( 2016 ). M V taken from McConnachie ( 2012 ). 5.1 Temporal clustering of star formation shutdown The lookback time of shutdown in star formation in the satellites of the MW and M31 is strongly clustred. We demonstrate this by employing a kernel density estimator (KDE) to estimate the mean lookback quenching time of these clusters. In the bottom panel of Fig. 21 , we estimate the probability density function (pdf) of the lookback quenching time. To do this, we select the ‘bandwidth’ (smoothing parameter) for each KDE, such as to to optimize the bias-variance tradeoff (1.29 and 0.98 for the MW and M31, respectively). The pdf of the MW is double humped with prominent peaks at ∼2.5 and ∼11 Gyr ago. The pdf of M31 has a single prominent peak ∼6 Gyr ago. These prominent peaks continue to be significant and stable, even after taking into account the uncertainties in the lookback quenching time of the satellites. The inclusion of the
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