Observing the gas temperature drop in the high-density nucleus of L 1544

Context. The thermal structure of a starless core is crucial for our understanding of the physics in these objects and hence for our understanding of star formation. Theory predicts a gas temperature drop in the inner similar to 5000 AU of the pre-stellar core L 1544, but there has been no observational proof of this. Aims. We performed VLA observations of the NH3 (1,1) and (2,2) transitions towards L 1544 in order to measure the temperature gradient between the high density core nucleus and the surrounding core envelope. Our VLA observation for the first time provide measurements of gas temperature in a core with a resolution smaller than 1000 AU. We have also obtained high resolution Plateau de Bure observations of the 110 GHz 1(11) - 1(01) para-NH2D line in order to further constrain the physical parameters of the high density nucleus. Methods. We combine our interferometric NH3 and NH2D observations with available single dish measurements in order to estimate the effects of flux loss from extended components upon our data. We have estimated the temperature gradient using a model of the source to fit our data in the u, v plane. As the NH3 (1, 1) line is extremely optically thick, this also involved fitting a gradient in the NH3 abundance. In this way, we also measure the [NH2D]/[NH3] abundance ratio in the inner nucleus. Results. We find that indeed the temperature decreases toward the core nucleus from 12 K down to 5.5 K resulting in an increase of a factor of 50% in the estimated density of the core from the dust continuum if compared with the estimates done with constant temperature of 8.75 K. Current models of the thermal equilibrium can describe consistently the observed temperature and density in this object, simultaneously fitting our temperature profile and the continuum emission. We also found a remarkably high abundance of deuterated ammonia with respect to the ammonia abundance (50% +/- 20%), which proves the persistence of nitrogen bearing molecules at very high densities (2 x 10(6) cm(-3)) and shows that high-resolution observations yield higher deuteration values than single-dish observations. The NH2D observed transition, free of the optical depth problems that affect the NH3 lines in the core center, is a much better probe of the high-density nucleus and, in fact, its map peak at the dust continuum peak. Our analysis of the NH3 and NH2D kinematic fields shows a decrease of specific angular momentum from the large scales to the small scales.