tokens: with the MW (Mayer et al. 2006 ; see also Section 4 ). Crucial to the identification of t sat through features of Δ F ( t ) are the uncertainties in ψ( t ). Ideally, the permitted smooth ψ( t ) should be obtained from the raw observational data by taking into account correlated errors in each time bin. Such an analysis is beyond our scope here. Upon advice from T. J. L. de Boer, we give instead an approximate treatment as follows. We first make a Monte Carlo realization of the data by sampling for each time bin according to a Gaussian distribution with the mean and standard deviation specified by the corresponding mean and 1σ uncertainty shown in Fig. 1 . The realization is accepted only if it gives (3.12 ± 0.05) × 10 7 M ⊙ for the total mass of stars formed (personal communications from T. J. L. de Boer). Out of a total of 10 4 realizations, only 3806 satisfy the constraint. For each accepted realization, we obtain a quadratic-spline fit to ψ( t ) and use it to calculate M g ( t ) and Δ F ( t ) from equations ( 15 ) and ( 16 ), respectively. 3.1 Baseline case We first discuss our baseline case of α = 1.5 and λ * ( t sat ) = 10 − 14 M ⊙ yr −1 . The M g ( t ) calculated from the smooth ψ( t ) shown in Fig. 1 assuming that λ * ( t ) = λ * ( t sat ) is shown as the top curve in Fig. 2 . The corresponding Δ F ( t ) is shown as the curve in Fig. 3 (a). The shaded region in this figure indicates the 68 per cent confidence interval for Δ F ( t ) estimated from the Monte Carlo simulations constrained by the total mass of stars formed. Figure 2. Total mass M g for cold gas in Fornax's star-forming disc as a function of time t derived from equation ( 15 ) and the smooth ψ( t ) shown in Fig. 1 for the baseline case of α = 1.5 and λ * ( t sat ) = 10 − 14 M ⊙ yr −1 . The top curve assumes a disc of fixed size with λ * ( t ) = λ * ( t sat ). The middle (bottom) curve is for a disc growing until t sat ≈ 4.8 (7.8) Gyr. The middle and top (bottom) curves have the same M g ( t ) for t > 4.8 (7.8) Gyr. Note that all curves reach M g = 0 at t ≈ 13.6 Gyr, the end of star formation in Fornax. Figure 3. Rate Δ F of net gas flow to or from Fornax's star-forming disc as a function of time t estimated from equations ( 15 ) and ( 16 ) and the data shown in Fig. 1 for the baseline case of α = 1.5 and λ * ( t sat ) = 10 − 14 M ⊙ yr −1 . A net inflow or outflow corresponds to Δ F > 0 and 0, respectively. In each panel, the curve is calculated from the smooth ψ( t ) shown in Fig. 1 and the shaded region indicates the 68 per cent confidence interval. Panel (a) assumes a disc of fixed size with λ * ( t ) = λ * ( t sat ). Panels (b) and (c) are for a disc growing until t sat ≈ 4.8 and 7.8 Gyr, respectively. We attribute the onset of suppression of the net gas inflow at t ≈ 4.8 or 7.8 Gyr to effects from Fornax's becoming an MW satellite. See text for details. We take t sat to coincide with the onset of suppression of the net gas inflow. Based on the Δ F ( t ) shown in Fig. 3
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