Deciphering an evolutionary sequence of merger stages in
  infrared-luminous starburst galaxies at z ~ 0.7
  Based on optical/near-IR Magellan FIRE spectra of 25 starburst galaxies at
0.5 < z < 0.9, Calabr\`o et al.(2018) showed that their attenuation properties
can be explained by a single-parameter sequence of total obscurations ranging
from A(V)=2 to A(V)=30 towards the starburst core centers in a mixed stars and
dust configuration. We investigate here the origin of this sequence for the
same sample. We show that total attenuations anti-correlate with the starburst
sizes in radio (3 GHz) with a significance larger than 5sigma and a scatter of
0.26 dex. More obscured and compact starbursts also show enhanced N2
(=[NII]/Halpha) ratios and larger line velocity widths that we attribute to an
increasing shock contribution toward later merger phases, driven by deeper
gravitational potential wells at the coalescence. Additionally, the attenuation
is also linked to the equivalent width (EW) of hydrogen recombination lines,
which is sensitive to the luminosity weighted age of the relatively unobscured
stellar populations. Overall, the correlations among A(V), radio size, line
width, N2 and EW of Balmer/Paschen lines converge towards suggesting an
evolutionary sequence of merger stages: all of these quantities are likely to
be good time-tracers of the merger phenomenon, and their large spanned range
appears to be characteristic of the different merger phases. Half of our sample
at higher obscurations have radio sizes approximately 3 times smaller than
early type galaxies at the same redshift, suggesting that, in analogy with
local Ultraluminous Infrared galaxies (ULIRGs), these cores cannot be directly
forming elliptical galaxies. Finally, we detect mid-IR AGN torus for half of
our sample and additional X-ray emission for 6 starbursts; intriguingly, the
latter have systematically more compact sizes, suggestive of emerging AGNs
towards later merger stages, possibly precursors of a later QSO phase.
