Quasar formation and energy emission in black hole universe.
Quasars are quasi-stellar objects, from which light is extremely shifted toward the red [1-5]. If their large redshifts are cosmological, quasars should be extremely distant and thus very luminous such that a single quasar with the scale of the solar system can emit the amount of energy comparable to that emitted by dozens of normal galaxies [6-7]. A highly charged quasar may also have significant electric redshift .
Quasars are generally believed to be extremely luminous galactic centers powered by supermassive black holes with masses up to billions of solar masses [9-13]. It is usually suggested that the material (e.g., gas and dust) falling into a supermassive black hole is subjected to enormous pressure and thus heated up to millions of degrees, where a huge amount of thermal radiation including waves, light, and X-rays give off [14-16]. However, the density of the falling material, if it is less dense than the supermassive black hole, is only about that of water. In other words, the pressure of the falling gas and dust may not go such high required for a quasar to emit energy as amount of that emitted by hundred billions of the Sun.
According to the Einsteinian general theory of relativity  and its Schwarzschild solution , the gravitational field (or acceleration) at the surface of a black hole is inversely proportional to its mass or radius. For a supermassive black hole with one billion solar masses, the gravitational field at the surface is only about 1.5 x 104 m/[s.sup.2]. Although this value is greater than that of the Sun (~ 270 m/[s.sup.2]), it is about two-order smaller than that of a white dwarf with 0.8 solar masses and 0.01 solar radii (~ 2.2 x [10.sup.6] m/[s.sup.2]), eightorder smaller than that of a neutron star with 1.5 solar masses and 10 km in radius (~ 2.0 x [10.sup.12] m/[s.sup.2]), and eight-order smaller than that of a star-like black hole with 3 solar masses (~ 5 x [10.sup.12] m/[s.sup.2]). Table 1 shows the gravitational field at the surface of these typical objects. A black hole becomes less violent and thus less power to the ambient matter and gases as it grows. Therefore, a supermassive black hole may not be able to extremely compress and heat the falling matter by such relative weak gravitational field. It is still unclear about how a quasar is powered by a supermassive black hole.
The Chandra X-ray observations of quasars 4C37.43 and 3C249.1 have provided the evidence of quasar ignition with an enormous amount of gas to be driven outward at high speed or a galactic superwind . The observation of quasar Q0957+561 has shown the existence of an intrinsic magnetic moment, which presents an evidence that the quasar may not have a closed event horizon . In addition, the observations of the distant quasars have shown that some supermassive black holes were formed when the universe was merely 1-2 billion years after the big bang had taken place [5, 21]. How the supermassive black holes with billions of solar masses were formed so rapidly during the early universe is a great mystery raised by astronomers recently . Theoretically, such infant universe should only contain hydrogen and helium, but observationally scientists have found a lot of heavy elements such as carbon, oxygen, and iron around these distant quasars, especially the large fraction of iron was observed in quasar APM 08279+5255 , which has redshift Z = 3.91. If the heavy ions, as currently believed, are produced during supernova explosions when stars runs out of their fuel supplies and start to end their lives, then quasars with heavy elements should be much elder than the main sequence stars and normal galaxies.
Recently, in the 211th AAS meeting, Zhang proposed a new cosmological model called black hole universe . In Paper I , Zhang has fully addressed the origin, structure, evolution, and expansion of black hole universe (see also ). In Paper II , Zhang has quantitatively explained the cosmic microwave background radiation of black hole universe (see ), an ideal black body. Zhang  summarized the observational evidences of black hole universe. According to this new cosmological model, the universe originated from a hot star-like black hole with several solar masses, and gradually grew through a supermassive black hole with billions of solar masses to the present state with hundred billion-trillions of solar masses by accreting ambient material and merging with other black holes. The entire space is hierarchically structured with infinite layers. The innermost three layers are the universe in which we live, the outside space called mother universe, and the inside star-like and supermassive black holes called child universes. The outermost layer is infinite in radius and limits to zero for both the mass density and absolute temperature, which corresponds to an asymptotically flat spacetime without an edge and outside space and material. The relationship among all layers or universes can be connected by the universe family tree. Mathematically, the entire space can be represented as a set of all black hole universes. A black hole universe is a subset of the entire space or a subspace and the child universes are null sets or empty spaces. All layers or universes are governed by the same physics, the Einsteinian general theory of relativity with the Robertson-Walker metric of spacetime, and expand physically in one way (outward). The growth or expansion of a black hole universe decreases its density and temperature but does not alter the laws of physics.
In the black hole universe model, the observed distant quasars are suggested to be donuts from the mother universe. They were formed in the mother universe from star-like black holes rather than formed inside our universe. In other words, the observed distant quasars actually were child universes of the mother universe, i.e., little sister universes of our universe. After they were swallowed, quasars became child universes of our universe. In general, once a star-like black hole is formed in a normal galaxy, the black hole will eventually inhale, including merge with other black holes, most matter of the galaxy and grow gradually to form a supermassive black hole. Therefore, quasars are supposed to be much elder than the normal stars and galaxies, and thus significantly enriched in heavy elements as measured. Some smaller redshift quasars might be formed in our universe from the aged galaxies that came from the mother universe before the distant quasars entered. Nearby galaxies will form quasars after billions of years and enter the new universe formed from the observed distant quasars as donuts. The entire space evolves iteratively. When one universe expands out, a new similar universe is formed from its inside star-like or supermassive black holes. This study as Paper III develops the energy mechanism for quasars to emit a huge amount of energy according to the black hole universe model.
2 Energy Mechanism for Quasars
As a consequence of the Einsteinian general theory of relativity, a main sequence star, at the end of its evolution, will become, in terms of its mass, one of the follows: a dwarf, a neutron star, or a stellar black hole. A massive star ends its life with supernova explosion and forms a neutron star or a black hole. Recently, Zhang  proposed a new mechanism called gravitational field shielding for supernova explosion. For the evolution of the entire galaxy, many details have been uncovered by astronomers, but how a galaxy ends its life is still not completely understood. In the black hole universe, all galaxies are suggested to eventually evolve to be supermassive black holes. Galaxies with different sizes form supermassive black holes with different masses. Quasars are formed from normal galaxies through active galaxies as shown in Figure 1.
Once many stars of a galaxy have run out of their fuels and formed dwarfs, neutral stars, and black holes, the galaxy shrinks its size and collapses toward the center, where a massive black hole with millions of solar masses may have already existed, by the gravity. During the collapse, the dwarfs, neutron stars, and stellar black holes are merging each other and gradually falling into the massive black hole at the center to form a supermassive black hole with billions of solar masses. When stellar black holes merge and collapse into a supermassive black hole, a huge amount of energies are released. In this situation, the galaxy is activated and a quasar is born.
In a normal galaxy, such as our Milky Way, most stars are still active and bright because they have not yet run out of their fuels to form dwarfs, neutron stars, and black holes. In the disk of a normal galaxy, there should be not much of such hardly observed matter as shown by the measurements [31-32]. In the center of a normal galaxy, a quiet massive black hole with millions of solar masses may exist. Once many stars have run out of their fuels and evolved into dwarfs, neutron stars, and black holes, the disk of the galaxy becomes dim, though intensive X-rays can emit near the neutron stars and black holes, and starts to shrink and collapse. As the galaxy collapses, the black holes fall towards (or decrease of orbital radius) the center and merge with the massive black hole at the center, where huge amounts of energies leak out of the black holes through the connection region, where the event horizons are broken. The galaxy first activates with a luminous nucleus and then becomes a quasar in a short period at the evolution end.
The inside space of a black hole is a mystery and can never be observed by an observer in the external world. It is usually suggested that when a star forms a Schwarzschild black hole its matter will be collapsed to the singularity point with infinite density. Material falling into the black hole will be crunched also to the singularity point. Other regions under the event horizon of the black hole with radius R = 2GM/[c.sup.2] are empty. The inside space of the black hole was also considered to be an individual spacetime with matter and field distributions that obeys the Einsteinian general theory of relativity. Gonzalez-Diaz  derived a spacetime metric for the region of nonempty space within the event horizon from the Einsteinian field equation.
In the black hole universe model, we have considered the inside space of the Schwarzschild black hole as an individual spacetime, which is also governed by the Friedmann equation with the Robertson-Walker metric of spacetime and where matter is uniformly distributed rather than crunched into a single point. Highly curved spacetime sustains the highly dense matter and strong gravity. A black hole governed by the Einsteinian general theory of relativity with the Robertson-Walker metric of spacetime is usually static with a constant mass-radius ratio called M-R relation or a constant density when it does not eat or accrete matter from its outside space . The density of the matter is given by
[rho] = M/V = 3[c.sup.2]/8[pi]G[R.sup.2] = 3[c.sup.6]/32[pi][G.sup.3][M.sup.2] (1)
where V = 4[pi][R.sup.3]/3 is the volume. Figure 2 shows the density of black hole as a function of its radius or mass. It is seen that the density of the black hole universe is inversely proportional to the square of radius or mass. At the present time, the mass and radius of the universe are 9 x [10.sup.51] kg and 1.3 x [10.sup.26] m, respectively, if the density of the universe is chosen to be [[rho].sub.0] = 9 x [10.sup.-27] kg/[m.sup.3].
The total radiation energy inside a black hole, an ideal black body, is given by
U = 4/3 [pi][beta][R.sup.3][T.sup.4] = [mu][R.sup.3] [T.sup.4], (2)
where T is the temperature and [beta] is a constant . The constant u is given by
[mu] = 4/3 [pi][beta] = 32[[pi].sup.6][k.sup.4.sub.B]/45[h.sup.3][c.sup.3], (3)
where [k.sub.B] is the Boltzmann constant, h is the Planck constant, and c is the light speed. Using the Robertson-Walker metric with the curvature parameter k = 1 to describe the black hole spacetime, we have obtained in Paper I, from the Einsteinian field equation, that the black hole is stable dR/dt = 0 if no material and radiation enter, otherwise the black hole enlarges or expands its size at a rate dR/dt = RH and thus decrease its density and temperature. Here H is the Hubble parameter.
When two black holes merge, their event horizons first break and then reconnect to form a single enveloping horizon and therefore a larger black hole. Brandt et al.  simulated the merge and collision of black holes. During the period of the reconnection of the event horizons, a huge amount of radiation energy leak/emit out from the black holes through the connection region, where the formed event horizon is still concave and has negative curvature. As many star-like black holes merge, a supermassive black hole or a quasar forms.
To illustrate the energy emission of a quasar, we first consider two black holes with mass [M.sub.1], [M.sub.2] (or radius [R.sub.1], [R.sub.2]) and temperature [T.sub.1], [T.sub.2] to merge into a larger black hole with mass [M.sub.3] = [M.sub.1] + [M.sub.2] (or radius [R.sub.3] = [R.sub.1] + [R.sub.2] because of the M-R relation) and temperature T3. Figure 3 show a schematic sketch for the merging of two black holes and the energy emission from them. This is somewhat similar to the energy release by fusion of two light nuclei. The total energy radiated from the collision region can be estimated as
E = [mu][R.sup.3.sub.1] [T.sup.4.sub.1] + [mu][R.sup.3.sub.2] [T.sup.4.sub.2] - [mu][R.sup.3.sub.3] [T.sup.4.sub.3] . (4)
It can be positive if the merged black hole is colder than the merging black holes (i.e., E > 0, if [T.sub.3] < [T.sub.1], [T.sub.2]).
For N star-like black holes and one massive black hole to merge into a supermassive black hole, the total radiation energy that is emitted out can be written as
[E.sub.total] = [mu] [N.summation over (j=0)][R.sup.3.sub.j][T.sup.4.sub.j] - [mu][R.sup.3.sub.Q] [T.sup.4.sub.Q], (5)
where [R.sub.j] and [T.sub.j] are the radius and temperature of the jth stellar black hole (j = 0 for the massive black hole existed at the center), [R.sub.Q] and T[.sub.Q] are the radius and temperature of the supermassive black hole formed at the end, and N is the number of the star-like black holes formed in the galaxy. The radius of the supermassive black hole can be estimated as
[R.sub.Q] = [N.summation over (j=0)] [R.sub.j]. (6)
Considering all the star-like black holes to have the same size and temperature (for simplicity or in an average radius and temperature), we have
[E.sub.total] = E[R.sup.3.sub.0][T.sup.4.sub.0] + [mu]N[R.sup.3.sub.j][T.sup.4.sub.j] - [mu][N.sup.3][R.sup.3.sub.j] [T.sup.4.sub.Q] . (7)
Here we have also considered that [R.sub.Q] [much greater than] [R.sub.0] and
[R.sub.Q] = [R.sub.0] + N[R.sub.j] [equivalent] N[R.sub.j]. (8)
Paper II has shown that the temperature of a black hole including our black hole universe depends on its size or radius. For a child universe (i.e., star-like or supermassive black hole), the relation is approximately power law,
T [varies] -1/[R.sup.[delta]], (9)
where [delta] is a power law index less than about 3/4. Applying this temperature-radius relation into Eqs. (8) and (7), we have,
[T.sub.Q] = [T.sub.j] [N.sup.-[delta]], (10)
[E.sub.total] = [mu][R.sup.3.sub.j] [T.sup.4.sub.j]N(1 - [N.sup.2-4[delta]]]). (11)
The average luminosity of a collapsing galaxy (or quasar) can be written as
L [equivalent to] [E.sub.total]/[tau] (12)
where [tau] is the time for all star-like black holes in a galaxy to merge into a single supermassive black hole.
It is seen that the luminosity of a quasar increases with [delta], N, [R.sub.j], and [T.sub.j], but decreases with t. As an example, choosing [R.sub.j] = 9 km (or [M.sub.j] [equivalent] 3[M.sub.s]), [T.sub.j] = [10.sup.12] K, N = [10.sup.9], and [tau] = [10.sup.9] years, we obtain L [equivalent] 7.3 x [10.sup.37] W, which is ~ 2 x [10.sup.11] times that of the Sun and therefore about the order of a quasar's luminosity . The formed supermassive black hole will be three billion solar masses. Here [delta] is chosen to be greater enough (e.g., 0.55). For a hotter [T.sub.j], a shorter [tau], or a larger N, the luminosity is greater. Therefore, if quasars are collapsed galaxies at their centers that star-like black holes are merging into supermassive black holes, then the huge luminosities of quasars can be understood. The extremely emitting of energy may induce extensive shocks and produce jet flows of matter outward along the strong magnetic field lines.
To see how the luminosity of a quasar depends on the parameters N, [delta], [T.sub.j], and [tau], we plot the luminosity of a collapsing galaxy (merging black holes or an ignited quasar) in Figure 4 as a function of [delta] and in Figure 5 as a function of [tau] with different N. In Figure 4, we let [delta] vary from 0.5 to 0.6 as the x-axis and N be equal to 108, 2 x [10.sup.8], 5 x [10.sup.8], and [10.sup.9], where other parameters are fixed at [R.sub.j] = 9 km, [T.sub.j] = [10.sup.12] K, and t = 109 years. In Figure 5, we let t vary from [10.sup.8] years to [10.sup.10] years as the x-axis and [T.sub.j] equal to 5 x [10.sup.11], [10.sup.12], 2 x [10.sup.12], and 4 x [10.sup.12]K, where other parameters are fixed at [R.sub.j] = 9 km, N = [10.sup.9], and [delta] = 0.55.
It is seen from Figure 4 that the luminosity of a quasar increases with [delta] and N, and saturates when [delta] [??] 0.52. For a supermassive black hole to emit energy, 6 must be greater than about 0.5. Paper II has shown [delta] [??] 3/4 = 0.75. From Figure 5, we can see that the luminosity decreases with the collapsing time t and increases with [T.sub.j].
Corresponding to the possible thermal history given by Paper II, 6 varies as the black hole universe grows. Figure 6 plots the parameters y defined in Paper II and [delta] as functions of the radius R. It is seen that when a supermassive black hole grows up to R [??] [10.sup.14] km (or M [??] 3 x [10.sup.5] billion solar masses) it does not emit energy when it merges with other black holes because [delta] < 0.5. In the observed distant voids, it is possible to have this kind of objects called mini-black-hole universes. The observed distant quasars may have grown up to this size or mass now and so that quite at present. A cluster, when most of its galaxies become supermassive black holes or quasars, will merge into a mini-black-hole universe.
3 Discussions and Conclusions
If there does not pre-exist a massive black hole at the center of a galaxy, a supermassive black hole can also be formed from the galaxy. As the galaxy shrinks it size, a hot star-like black hole enlarges its size when it swallows dwarfs or neutron stars, which may also collapse to form black holes  or merges with other black holes and forms a supermassive black hole at the end.
As a summary, we proposed a possible explanation for quasars to ignite and release a huge amount of energy in accord with the black hole universe model. General relativity tells us that a main sequence star will, in terms of its mass, form a dwarf, a neutron star, or a black hole. After many stars in a normal galaxy have run out of their fuels and formed dwarfs, neutron stars, and black holes, the gravity cause the galaxy to eventually collapse and form a supermassive black hole with billions of solar masses. It has been shown that this collapse can lead to the extremely hot stellar black holes to merge each other and further into the massive black hole at the center and release intense thermal radiation energy as great as a quasar emits. When the stellar black holes of a galaxy collapse and merge into a supermassive black hole, the galaxy is activated and a quasar is born. The observed distant quasars were donuts from the mother universe. They were actually formed in the mother universe as little sisters of our universe. After the quasars entered our universe, they became our universe's child universes. The results from this quasar model are consistent with observations.
Department of Physics, Alabama A & M University, Normal, Alabama. E-mail: email@example.com
This work was supported by the NASA EPSCoR grant (NNX-07AL52A), NSF CISM and MRI grants, AAMU Title III program, and National Natural Science Foundation of China (G40890161).
Submitted on July 17, 2012 / Accepted on July 22, 2012
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Table 1: Mass, radius, and gravitational field at the surface of the Sun, white dwarf, neutron star, star-like black hole (BH), and super-massive black hole. Object M ([M.sub.Sun]) R (m) Sun 1 7 x [10.sup.8] White Dwarfs 0.8 7 x [10.sup.6] Nneutron Stars 1.5 1 x [10.sup.4] Black Holes (BH) 3 3 x [10.sup.3] Spermassive BH [10.sup.9] 3 x [10.sup.12] [g.sub.R] Object (m/[s.sup.2]) Sun 270 White Dwarfs 2 x [10.sup.4] Nneutron Stars 2 x [10.sup.12] Black Holes (BH) 5 x [10.sup.12] Spermassive BH 1.5 x [10.sup.4]
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