Deeply Buried Nuclei in the Infrared-Luminous Galaxies NGC 4418 and Arp
  220: I. ALMA Observations at $\lambda = $1.4-0.4 mm and Continuum Analysis
  We observed with ALMA three deeply buried nuclei in two galaxies, NGC 4418
and Arp 220, at $\sim$0.2$''$ resolution over a total bandwidth of 67 GHz in
$f_{\rm rest}$ = 215 - 697 GHz. Here we (1) introduce our program, (2) describe
our data reduction method for wide-band, high-resolution imaging spectroscopy,
(3) analyze in visibilities the compact nuclei with line forests, (4) develop a
continuum-based estimation method of dust opacity and gas column density in
heavily obscured nuclei, which uses the BGN (buried galactic nuclei) model and
is sensitive to $\log(N_{\rm H_2}/{\rm cm}^{-2}) \sim $ 25 - 26 at $\lambda
\sim 1$ mm, and (5) present the continuum data and diagnosis of our targets.
The three continuum nuclei have major-axis FWHM of $\sim$0.1$''$-0.3$''$
(20-140 pc) aligned to their rotating nuclear disks of molecular gas. However,
each nucleus is described better with two or three concentric components than
with a single Gaussian. The innermost cores have sizes of 0.05$''$-0.10$''$
(8-40 pc), peak brightness temperatures of ~100-500 K at 350 GHz, and more
fractional flux at lower frequencies. The intermediate components correspond to
the nuclear disks. They have axial ratios of $\approx$0.5 and hence
inclinations $\stackrel{>}{\sim} 60$ deg. The outermost elements include the
bipolar outflow from Arp 220W. We estimate 1 mm dust opacity of $\tau_{\rm
d,1mm} \approx 2.2$, $1.2$, and $\stackrel{<}{\sim} 0.4$ respectively for NGC
4418, Arp 220W, and Arp 220E. The first two correspond to $\log(N_{\rm H}/{\rm
cm}^{-2}) \sim 26$ for conventional dust-opacity laws, and hence the nuclei are
highly Compton thick.
