  The low-mass star formation evolutionary sequence is relatively well-defined
both from observations and theoretical considerations. The first hydrostatic
core is the first protostellar equilibrium object that is formed during the
star formation process. Using state-of-the-art radiation-magneto-hydrodynamic
3D adaptive mesh refinement calculations, we aim to provide predictions for the
dust continuum emission from first hydrostatic cores. We investigate the
collapse and the fragmentation of magnetized one solar mass prestellar dense
cores and the formation and evolution of first hydrostatic cores using the
RAMSES code. We use three different magnetization levels for the initial
conditions, which cover a large variety of early evolutionary morphology, e.g.,
the formation of a disk or a pseudo-disk, outflow launching, and fragmentation.
We post-process the dynamical calculations using the 3D radiative transfer code
RADMC-3D. We compute spectral energy distributions and usual evolutionary stage
indicators such as bolometric luminosity and temperature. We find that the
first hydrostatic core lifetimes depend strongly on the initial magnetization
level of the parent dense core. We derive, for the first time, spectral energy
distribution evolutionary sequences from high-resolution
radiation-magneto-hydrodynamic calculations. We show that under certain
conditions, first hydrostatic cores can be identified from dust continuum
emission at 24 microns and 70 microns. We also show that single spectral energy
distributions cannot help to distinguish between the formation scenarios of the
first hydrostatic core, i.e., between the magnetized and non-magnetized models.
Spectral energy distributions are a first useful and direct way to target first
hydrostatic core candidates but high-resolution interferometry is definitively
needed to determine the evolutionary stage of the observed sources.
