Given 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 ( \lower 4.0 pt \hbox { $ { \buildrel \displaystyle > \over { \sim } } $ } 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 \lower 4.0 pt \hbox { $ { \buildrel \displaystyle < \over { \sim } } $ } 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 .
In between these two phases , there is a transitional yet sustained diffusively limited accretion of SIDM particles which in an eventual steady state would be much lower than the accretion rates of the two main phases .
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 .
During the final stage of accumulating a SMBH mass , violent feedback in circumnuclear environs of a galactic nucleus leads to the central bulge formation and gives rise to the familiar empirical M _ { \hbox { \tiny BH } } - \sigma _ { b } correlation inferred for nearby normal galaxies with \sigma _ { b } being the stellar velocity dispersion in the galactic bulge ; in our scenario , the central SMBH formation precedes that of the galactic bulge .