  To date, various formation channels of merging events have been heavily
explored with the detection of nearly 100 double black hole (BH) merger events
reported by the LIGO-Virgo-KAGRA (LVK) Collaboration. We here systematically
investigate an alternative formation scenario, i.e., binary BHs (BBHs) formed
through double helium stars (hereafter double-core evolution channel). In this
scenario, the two helium stars (He-rich stars) could be the outcome of the
classical isolated binary evolution scenario involving with and without
common-envelope phase (i.e., CE channel and stable mass transfer channel), or
alternatively of massive close binaries evolving chemically homogeneously
(i.e., CHE channel). We perform detailed stellar structure and binary evolution
calculations that take into account internal differential rotation and mass
loss of He-rich stars, as well as tidal interactions in binaries. For double
He-rich stars with equal masses in binaries, we find that tides start to be at
work on the Zero Age Helium Main Sequence (ZAHeMS: the time when a He-rich star
starts to burn helium in the core, which is analogous to ZAMS for core hydrogen
burning) for initial orbital periods not longer than 1.0 day, depending on the
initial metallicities. Besides the stellar mass loss rate and tidal
interactions in binaries, we find that the role of the angular momentum
transport efficiency in determining the resulting BH spins, becomes stronger
when considering BH progenitors originated from a higher metal-metallicity
environment. We highlight that double-core evolution scenario does not always
produce fast-spinning BBHs and compare the properties of the BBHs reported from
the LVK with our modeling.
