$\eta$ Carinae: high angular resolution continuum, H30$\alpha$ and
  He30$\alpha$ ALMA images
  We present images of $\eta$ Carinae in the recombination lines H30$\alpha$
and He30$\alpha$ and the underlying continuum with 50~mas resolution (110 AU),
obtained with ALMA. For the first time, the 230 GHz continuum image is resolved
into a compact core, coincident with the binary system position, and a weaker
extended structure to the NW of the compact source. Iso-velocity images of the
H30$\alpha$ recombination line show at least 16 unresolved sources with
velocities between -30 and -65 km s$^{-1}$ distributed within the continuum
source. A NLTE model, with density and temperature of the order $10^7$
cm$^{-3}$ and $10^4$ K, reproduce both the observed H30$\alpha$ line profiles
and their underlying continuum flux densities. Three of these sources are
identified with Weigelt blobs D, C and B; estimating their proper motions, we
derive ejection times (in years) of 1952.6, 1957.1, and 1967.6, respectively,
all of which are close to periastron passage. Weaker H30$\alpha$ line emission
is detected at higher positive and negative velocities, extending in the
direction of the Homunculus axis. The He30$\alpha$ recombination line is also
detected with the same velocity of the narrow H30$\alpha$ line. Finally, the
close resemblance of the H30$\alpha$ image with that of an emission line that
was reported in the literature as HCO$^+$(4-3) led us to identify this line as
H40$\delta$ instead, an identification that is further supported by modeling
results. Future observations will enable to determine the proper motions of all
the compact sources discovered in the new high-angular resolution data of
$\eta$ Carinae.
