T. R. MONGAN 53
at , as self-similar large scale structure develop-
ed, supermassive black holes formed within lower struc-
tural levels, and almost all systems composed of stars or
star aggregations developed central supermassive black
holes.
6z
5. Central Black Hole Develop ment
Development of visible large scale structures within
isothermal spherical halos of dark matter with 2
ar
R
R
density distributions resulted in the commonly observed
flat tangential speed distribution of sub-elements. In the
holographic model of large scale structure, black holes
near the center of nascent large scale structures are pro-
genitors of supermassive black holes. Any sub-element
passing within a distance from the central black hole that
is less than the holographic radius of the sub-element is
disrupted and drawn into the central black hole. So, the
mass within a core radius c is drawn into in the cen-
tral black hole. The core radius c is the holographic
radius of the lowest mass sub-element of the large scale
structure because no sub-element can exist as an isolated
system closer to the central black hole than the holo-
graphic radius of the lowest mass sub-element without
being disrupted and drawn into the central black hole. In
consequence, the upper bound on the mass of the central
black hole within in the
c
R
2
1
4
s
s
M
Rr
r
density
distribution of the large scale structure is c
s
R
R
R
. Again,
the upper bound is reached when the central black hole
has accumulated all of the matter within the central
volume inside .
c
Stars with masses >100
developed at .
They had very short lives and many of them collapsed to
black holes [20]. It has been claimed that black holes
resulting from collapse of stars in the 100
10z
range
might not suffice as seeds for supermassive black holes,
so supermassive stars in the 5
10
range should be
considered as seeds for supermassive black holes [21].
That scenario is consistent with the holographic model
for large scale structure [2]. When photon decoupling
took place, at , “hydrogen gas was free to col-
lapse under its own self-gravity (and the added gravita-
tional attraction of the dark matter)” [22]. The extended
holographic principle used in the holographic model of
large scale structure [2] indicates the information de-
scribing a structure of mass
1100z
is encoded on a holo-
graphic screen with radius cm
0.16
s
M
s
R, if the Hub-
ble constant 0. Consider the escape
velocity of protons on the holographic screen for a mass
71HkmsecMpc
with radius
R at , and set it equal to the
average velocity of protons in equilibrium with CMB
radiation outside the screen. Then the holographic model
for large scale structure [2] identifies 10
1100z
5
as the
mass of systems in thermal equilibrium with the CMB,
since there is no heat transfer between a system with
mass s
5
10
M1100z
and the CMB at . At z =
1100, protons outside the holographic screen with radius
cm
0.16
s
s
M
R
5
10
that are in equilibrium with the CMB
cannot transfer heat (and energy) across the holographic
screen surrounding a system with mass s
M
1100z
at
. The free fall time [23] for systems with mass
s
5
10
M1100z
with the matter density at
is
about 2.6 million years, so there is sufficient time for
those systems to ignite as supermassive stars and subse-
quently collapse to seed black holes with masses near
5
10
[24] leading to formation of supermassive black
holes in the 800 million years before emissions as-
sociated with the 4 × 1042 g black hole in the quasar
ULAS J112001.48 + 064124.3 observed at redshift
7.085z
[19]. Anyway, the first stars apparently pro-
duced seed black holes for subsequent development of
large scale structures.
In the earliest phase of development of large scale
structure, at 6z
, there was only one Jeans’ mass struc-
ture level in the holographic model for large scale struc-
ture [2]. These earliest large scale structures, home of the
earliest quasars, then developed around a seed black hole
near their center. Sub-elements of the earliest large scale
structures were early stars with masses in the
to 10
100
range, resulting in the estimated mass for super-
massive black holes in the range mentioned above.
As additional self-similar large scale structure levels de-
veloped, remaining seed black holes at the center of each
emerging large scale structure grew by disrupting and
entraining lowest mass sub-elements of the self-similar
large scale structure.
6z
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