Forming supermassive black holes by accreting dark and baryon matter

7 pages, 2 figures. accepted by MNRASGiven a large-scale mixture of self-interacting dark matter (SIDM) particles and baryon matter distributed in the early Universe, we advance here a two-phase accretion scenario for forming supermassive black holes (SMBHs) with masses around $\sim 10^9 M_{\odot}$ at high redshifts $z (\gsim 6)$. The first phase is conceived to involve a rapid quasi-spherical and quasi-steady Bondi accretion of mainly SIDM particles embedded with baryon matter onto seed black holes (BHs) created at redshifts $z\lsim 30$ by the first generation of massive Population III stars; this earlier phase rapidly gives birth to significantly enlarged seed BH masses of $M_{\hbox{\tiny BH},t_1}\backsimeq 1.4\times 10^6\ M_\odot \sigma_0/(1\hbox{cm}^2\hbox{g}^{-1})(C_s/30\hbox{km s}^{-1})^4$ during $z\sim 20-15$, where $\sigma_0$ is the cross section per unit mass of SIDM particles and $C_s$ is the velocity dispersion in the SIDM halo referred to as an effective "sound speed". The second phase of BH mass growth is envisaged to proceed primarily via baryon accretion, eventually leading to SMBH masses of $M_{\hbox{\tiny BH}}\sim 10^9 M_\odot$; such SMBHs may form either by $z\sim 6$ for a sustained accretion at the Eddington limit or later at lower $z$ for sub-Eddington mean accretion rates. We intend to account for the reported detections of a few SMBHs at early epochs, e.g., SDSS 1148+5251 and so forth, without necessarily resorting to either super-Eddington baryon accretion or very frequent BH merging processes. Only extremely massive dark SIDM halos associated with rare peaks of density fluctuations in the early Universe may harbour such early SMBHs or quasars. Observational consequences are discussed