In this paper we present an extended set of nonlinear convective pulsation models at varying the metallicity and ∆Y /∆Z ratio. The predicted instability strip and bolometric light curves are discussed by comparing the new models with our previous ones. In particular, the dependence on both metal and helium abundances is investigated. By transforming the bolometric light curves into the observational bands we are able to derive both Period-Color-Luminosity and Wesenheit relations for each selected chemical composition. Synthetic Period-Luminosity relations are obtained by populating the instability strip according to specific assumptions on the number of pulsators and the mass distribution. These theoretical results are compared with recent accurate data by Sandage et al. and Kervella et al., in order to test the predictive capabilities of the models. We confirm our previous results that the theoretical metallicity correction to the Key Project Cepheid distance scale depends both on the period range and ∆Y /∆Z ratio, becoming important for periods longer than 20 days and ∆Y /∆Z > 1.5.

We investigate how a different calibration of the Cepheid period–luminosity (PL) relation, taking into account metallicity corrections, affects the absolute magnitude calibration of Type Ia supernovae (SNe Ia) and, in turn, the determination of the Hubble constant H0. We use SN Ia light curves from the literature and previously unpublished data to establish the MB–Δm15(B) relation, and calibrate the zero point by means of nine SNe Ia with Cepheid‐measured distances. This relation is then used to establish the Hubble diagram, and in turn to derive H0. In the attempt to correct for the host‐galaxy extinction, we find that the data suggest a value for the total to selective absorption ratio of RB= 3.5, which is smaller than the standard value for our own Galaxy of RB= 4.315. Depending on the metallicity correction for the Cepheid PL relation, the value of RB, and SN sample selection criteria, the value of the Hubble constant H0 takes a value in the range 68–74 km s−1 Mpc−1, with associated uncertainties of the order of 10 per cent. Unpublished photometry is also presented for 18 SNe of our sample (1991S, 1991T, 1992A, 1992K, 1993H, 1993L, 1994D, 1994M, 1994ae, 1995D, 1995ac, 1995bd, 1996bo, 1997bp, 1997br, 1999aa, 1999dk, 2000cx). These data are the results of a long‐standing effort in supernova monitoring at ESO – La Silla and Asiago observatories.

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We report on a superdense star-forming region with an effective radius (R e ) smaller than 13 pc identified at z=6.143 and showing a star-formation rate density Σ SF R ∼ 1000 M yr −1 kpc −2 (or conservatively > 300 M yr −1 kpc −2 ). Such a dense region is detected with S/N 40 hosted by a dwarf extending over 440 pc, dubbed D1. D1 is magnified by a factor 17.4(±5.0) behind the Hubble Frontier Field galaxy cluster MACS J0416 and elongated tangentially by a factor 13.2±4.0 (including the systematic errors). The lens model accurately reproduces the positions of the confirmed multiple images with a r.m.s. of 0.35 . D1 is part of an interacting star-forming complex extending over 800 pc. The SED−fitting, the very blue ultraviolet slope (β −2.5, F λ ∼ λ β ) and the prominent Lyα emission of the stellar complex imply that very young (< 10 − 100Myr), moderately dust-attenuated (E(B-V)<0.15) stellar populations are present and organised in dense subcomponents. We argue that D1 (with a stellar mass of 2 × 10 7 M ) might contain a young massive star cluster of M 10 6 M and M U V −15.6 (or m U V = 31.1), confined within a region of 13 pc, and not dissimilar from some local super star clusters (SSCs). The ultraviolet appearance of D1 is also consistent with a simulated local dwarf hosting a SSC placed at z=6 and lensed back to the observer. This compact system fits into some popular globular cluster formation scenarios. We show that future high spatial resolution imaging (e.g., E−ELT/MAORY-MICADO and VLT/MAVIS) will allow us to spatially resolve light profiles of 2-8 pc.