The VISTA Magellanic Cloud ( VMC , PI M.-R. L. Cioni ) survey is collecting deep K _ { \mathrm { s } } -band time-series photometry of the pulsating variable stars hosted by the system formed by the two Magellanic Clouds ( MCs ) and the Bridge connecting them .
In this paper we present the first results for Classical Cepheids , from the VMC observations of two fields in the Large Magellanic Cloud ( LMC ) , centred on the South Ecliptic Pole and the 30 Doradus star forming regions , respectively .
The VMC K _ { \mathrm { s } } -band light curves of the Cepheids are well sampled ( 12 epochs ) and of excellent precision ( typical errors of \sim 0.01 mag ) .
We were able to measure for the first time the K _ { \mathrm { s } } magnitude of the faintest Classical Cepheids in the LMC ( K _ { \mathrm { s } } \sim 17.5 mag ) , which are mostly pulsating in the First Overtone ( FO ) mode , and to obtain FO Period–Luminosity ( PL ) , Period-Wesenheit ( PW ) , and Period–Luminosity–Colour ( PLC ) relations , spanning the full period range from 0.25 to 6 day .
Since the longest period Cepheid in our dataset has a variability period of 23 day , we have complemented our sample with literature data for brighter F Cepheids .
On this basis we have built a PL relation in the K _ { \mathrm { s } } band that , for the first time , includes short period - hence low luminosity - pulsators , and spans the full range from 1.6 to 100 day in period .
We also provide the first ever empirical PW and PLC relations using the ( V - K _ { \mathrm { s } } ) colour and time-series K _ { \mathrm { s } } photometry .
The very small dispersion ( \sim 0.07 mag ) of these relations makes them very well suited to study the three-dimensional ( 3D ) geometry of the Magellanic system .
The use of “ direct ” ( parallax- and Baade–Wesselink- based ) distance measurements to both Galactic and LMC Cepheids , allowed us to calibrate the zero points of the PL , PW , and PLC relations obtained in this paper , and in turn to estimate an absolute distance modulus of ( m - M ) _ { 0 } = 18.46 \pm 0.03 mag for the LMC .
This result is in agreement with most of the latest literature determinations based on Classical Cepheids .