  A first adiabatic core is a transient object formed in the early phase of
star formation. The observation of a first core is believed to be difficult
because of its short lifetime and low luminosity. On the basis of radiation
hydrodynamic simulations, we propose a novel theoretical model of first cores,
Exposed Long-lifetime First core (ELF). In the very low-mass molecular core,
the first core evolves slowly and lives longer than 10,000 years because the
accretion rate is considerably low. The evolution of ELFs is different from
that of ordinary first cores because radiation cooling has a significant effect
there. We also carry out radiation transfer calculation of dust-continuum
emission from ELFs to predict their observational properties. ELFs have
slightly fainter but similar SEDs to ordinary first cores in radio wavelengths,
therefore they can be observed. Although the probabilities that such low mass
cores become gravitationally unstable and start to collapse are low, we still
can expect that a considerable number of ELFs can be formed because there are
many low-mass molecular cloud cores in star-forming regions that can be
progenitors of ELFs.
