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The VLT-FLAMES Tarantula Survey - XI. A census of the hot luminous stars and their feedback in 30 Doradus

We compile the first comprehensive census of hot luminous stars in the 30 Doradus (30 Dor) star forming region of the LMC. The census extends to a radius of 10arcmin (150pc) from the central cluster, R136. Stars were selected photometrically and combined with the latest spectral types. 1145 candidate hot luminous stars were identified of which >700 were considered genuine early type stars that contribute to feedback. We assess the spectroscopic completeness to be 85% in outer regions (>5pc) but fall to 35% in the vicinity of R136, giving a total of 500 hot luminous stars with spectroscopy. Stellar calibrations and models were used to obtain their physical parameters before integrated values were compared to global observations and the population synthesis code, Starburst99. The 31 W-R and Of/WN stars made large contributions to the total ionising and wind luminosities of ~40% and ~50%, respectively. Stars with Minit>100Msun also showed high contributions to the global feedback, ~25% in both cases. Such massive stars are not accounted for by the current Starburst99 code, which underestimated the ionising and wind luminosities of R136 by factors of ~2 and ~9, respectively. The census inferred a SFR of 0.073+/-0.04Msun/yr for 30 Dor, typically higher than results from popular SFR calibrations. However, it remained consistent with a far-UV luminosity tracer and a combined Halpha and mid-infrared tracer, but only after correcting for Halpha extinction. The global ionising output exceeded measurements from the associated gas and dust, suggesting ~6(+55/-6)% of ionising photons escape the region. When studying very luminous star forming regions, it is therefore essential to include the most massive stars to ensure a reliable energy budget. If 30 Dor is typical of other large star forming regions, estimates of the SFR will be underpredicted if this escape fraction is not accounted for.(abridged)