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We use the new Modular Open Source Fitter for Transients (MOSFiT) to model 38hydrogen-poor superluminous supernovae (SLSNe). We fit their multicolour lightcurves with a magnetar spin-down model and present the posterior distributionsof magnetar and ejecta parameters. The colour evolution can be well matchedwith a simple absorbed blackbody. We find the following medians (1$\sigma$ranges): spin period 2.4 ms (1.2-4 ms); magnetic field $0.8\times 10^{14}$ G(0.2-1.8 $\times 10^{14}$ G); ejecta mass 4.8 Msun (2.2-12.9 Msun); kineticenergy $3.9\times 10^{51}$ erg (1.9-9.8 $\times 10^{51}$ erg). Thissignificantly narrows the parameter space compared to our priors, showing thatalthough the model is flexible, the parameter space relevant to SLSNe is wellconstrained by existing data. The requirement that the instantaneous enginepower is $\sim 10^{44}$ erg at the light curve peak necessitates either a largerotational energy (P<2 ms), or more commonly that the spin-down and diffusiontimescales be well-matched. We find no evidence for separate populations offast- and slow-declining SLSNe, which instead form a continuum both in lightcurve widths and inferred parameters. Variations in the spectra are wellexplained through differences in spin-down power and photospheric radii atmaximum-light. We find no correlations between any model parameters and theproperties of SLSN host galaxies. Comparing our posteriors to stellar evolutionmodels, we show that SLSNe require rapidly rotating (fastest 10%) massive stars(> 20 Msun), and that this is consistent with the observed SLSN rate. Highmass, low metallicity, and likely binary interaction all serve to maintainrapid rotation essential for magnetar formation. By reproducing the full set ofSLSN light curves, our posteriors can be used to inform photometric searchesfor SLSNe in future survey data.

The magnetar model for Type I superluminous supernovae I: Bayesian analysis of the full multicolour light curve sample with MOSFiT