  Images of dust continuum and carbon monoxide (CO) line emission are powerful
tools for deducing structural characteristics of galaxies, such as disk sizes,
H$_2$ gas velocity fields and enclosed H$_2$ and dynamical masses. We report on
a fundamental constraint set by the cosmic microwave background (CMB) on the
observed structural and dynamical characteristics of galaxies, as deduced from
dust continuum and CO-line imaging at high redshifts. As the CMB temperature
rises in the distant Universe, the ensuing thermal equilibrium between the CMB
and the cold dust and H$_2$ gas progressively erases all spatial and spectral
contrasts between their brightness distributions and the CMB. For high-redshift
galaxies, this strongly biases the recoverable H$_2$ gas and dust mass
distributions, scale lengths, gas velocity fields and dynamical mass estimates.
This limitation is unique to mm/submm wavelengths and unlike its known effect
on the global dust continuum and molecular line emission of galaxies, it cannot
be addressed simply. We nevertheless identify a unique signature of
CMB-affected continuum brightness distributions, namely an increasing rather
than diminishing contrast between such brightness distributions and the CMB
when the cold dust in distant galaxies is imaged at frequencies beyond the
Raleigh-Jeans limit. For the molecular gas tracers, the same effect makes the
atomic carbon (CI) lines maintain a larger contrast than the CO lines against
the CMB.
