HIGH-z QUASARS IN THE R_h = ct UNIVERSE

Quasars are the most powerful objects in the universe. The efficient extraction of gravitational energy from matter falling onto their central supermassive black hole is sufficient to make them identifiable out to very large redshifts (z ≳ 7), where they can be studied to probe black hole growth (e.g., Kauffmann & Haehnelt 2000; Wyithe & Loeb 2003; Hopkins et al. 2005; Croton et al. 2006) and the formation of large-scale structure in the early universe (Fan 2006). For example, it is now believed that supermassive black holes played an active role in galaxy evolution, e.g., through their feedback on the interstellar medium, by heating and expelling gas that would otherwise have formed stars (see also Silk & Rees 1998; Di Matteo et al. 2005). However, the impact of studying high-z quasars is not limited to just these few examples; they can also provide crucial information on the re-ionization of the intergalactic medium (IGM) several hundred Myr after recombination.

One of the most useful observations of these sources has been the reverberation mapping of broad-lines, yielding the distance of the line-emitting gas from the central ionizing source. The measurement of the velocity of this plasma, e.g., via its Doppler-broadened line width, can therefore yield the gravitational mass of the central black hole to within a factor of three or so (e.g., Wandel et al. 1999). This method has made it possible to determine black hole masses for quasars beyond z ∼ 6 (Willott et al. 2003; Jiang et al. 2007; Kurk et al. 2007, 2009) and, combined with a measurement of the source spectrum, has helped us conclude that the most luminous high-z quasars contain black holes with mass M ≳ 10⁹ M_☉, accreting at close to the Eddington limit.

But the discovery of such massive objects so early in the universe's history (corresponding to an age of only ∼800 Myr in the context of ΛCDM), and the apparent constancy of the observed quasar broad-line region properties with redshift (e.g., Pentericci et al. 2002), is quite surprising and difficult to understand in the context of the standard model. Indeed, the early appearance of supermassive black holes has developed into one of the most important unsolved mysteries in astronomy.

Their existence has resulted in diverse attempts to explain how such objects could have formed so quickly in the rapidly expanding early universe. If one invokes standard Eddington-limited accretion, the e-folding time (i.e., the so-called Salpeter timescale) for black hole growth is ∼45 Myr, assuming an efficiency of 10%. Thus, reaching an observed mass of 10⁹ M_☉ from a supernova-produced seed black hole of 5 M_☉ would have taken at least 860 Myr, longer than the short cosmic time available since the big bang.

Some workers have therefore suggested that super-Eddington accretion must have occurred at very high redshifts (e.g., Volonteri & Rees 2005). Others have proposed that rapidly spinning black holes accrete with higher efficiency (when the disk is spinning with a retrograde orbit), thereby lowering the Salpeter timescale (Shapiro 2005). It has also been demonstrated that Eddington-limited accretion can still account for these black holes, but only if the seeds were ≫5 M_☉. However, to produce high-z quasars in only ∼400 Myr, the initial black hole masses would have had to have been greater than ∼10⁴–10⁵ M_☉ (Yoo & Miralda-Escudé 2004).

All the proposals thus far appear to be contrived for one reason or another. Unless some exotic mechanism involving self-interacting dark matter was responsible, the resolution to this problem ultimately relies on an enhanced accretion rate, or the creation of a seed mass much larger than we can currently explain. Observations of the local universe indicate that seed black holes could have formed during supernova explosions following the Dark Ages (see Section 2 below), but probably not with masses exceeding ∼5–20 M_☉. And now that we have detected over 50 high-z quasars, we also know that none of them appear to be accreting at greatly super-Eddington rates (see, e.g., Figure 5 in Willott et al. 2010a).

In the context of the standard model, the only viable alternative now appears to be the role played by mergers in the early universe, which may also be relevant—perhaps even essential—to creating the correlation between black hole mass and host bulge mass observed nearby (see, e.g., Tanaka & Haiman 2009; Lippai et al. 2009; Hirschmann et al. 2010). However, in order to make this work, the black hole seeds would have had to form well before the currently understood beginning of the period of re-ionization, and their creation would have had to cease by a redshift of ∼20–30 in order to not overproduce the mass density in lower-mass (i.e., between a few × 10⁵ M_☉ and a few × 10⁷ M_☉) black holes. We will continue our discussion of this possibility in the conclusions in Section 4.

In this paper, we advance an alternative viewpoint—that the difficulty faced by ΛCDM in accounting for the high-z quasars is actually more evidence against it being the correct cosmology. We show that the problems faced by ΛCDM disappear when we instead interpret the origin and evolution of the high-z quasars in the context of the R_h = ct universe. In particular, we will demonstrate that in this cosmology, high-z quasars appeared only after the beginning of the Epoch of Re-ionization (EoR), as one would expect if their 5–20 M_☉ seeds were created from the deaths of Pop II and III stars.

The explanation for how and when the high-z quasars came into existence is necessarily woven into the history of the Dark Ages and the EoR that followed. In the context of ΛCDM, the universe became transparent roughly 0.4 Myr after the big bang, ushering in a period of darkness that ended several hundred Myr later, when the first stars and galaxies started forming and emitting ionizing radiation. The current constraints delimit the EoR to the redshift range z ∼ 6–15 (Zaroubi 2012), which (again in the context of ΛCDM) corresponds to a cosmic time t ∼ 400–900 Myr.

The IGM was neutral at the beginning of the EoR, but an evolving patchwork of neutral (H i) and ionized hydrogen (H ii) unfolded as the re-ionization progressed. The temperature and ionized fraction of the gas increased rapidly as the number of ultraviolet sources formed, until the ionized regions eventually permeated the whole universe (Barkana & Loeb 2001; Bromm & Larson 2004). Some of the best probes of this re-ionization process are actually the high-z quasars themselves. High-resolution spectra of Sloan Digital Sky Survey (SDSS) high-z quasars show a complete absence of structure blueward of the quasar Lyα rest-frame emission, especially those with redshift ≳ 6 (Fan et al. 2006). This is interpreted as due to an increase in the Lyα optical depth resulting from the decrease in the ionized fraction along the line of sight. The fact that the trend is not monotonic with redshift may also be an indication that we are witnessing the aforementioned patchwork of ionization at these redshifts. The main conclusion from the Lyα optical depth measurements is that the universe was highly ionized at z ≲ 6, but its neutral fraction increased with increasing redshift, presumably reaching a value ∼1 by z ∼ 15. Support for these results is also provided by the Wilkinson Microwave Anisotropy Probe (Bennett et al. 2003) mission, whose measurements suggest that the universe may have been ∼50% neutral at z ≳ 10, and that re-ionization did not start before z ∼ 14 (Page et al. 2007).

Hydrogen is ionized by photons with energy ≳ 13.6 eV. Obvious candidate sources are Pop II and III stars. The constraints on decaying or self-annihilating dark matter particles, or decaying cosmic strings, make it unlikely that these could re-ionize the universe on their own (see, e.g., Ripamonti et al. 2007). Accreting supermassive black holes also produce large quantities of UV and X-radiation, but their mass distribution in the early universe is not fully known, rendering the role played by quasars during re-ionization somewhat uncertain (see, e.g., Meiksin 2005). We can therefore reasonably conclude that the EoR was brought about by a combination of Pop II and III stars in star-forming galaxies and the ionizing radiation produced by the high-z quasars that formed during this period. The latter may have become more important toward the end of the EoR, though it is not clear if they, by themselves, could have caused the universe to become fully ionized by redshift z ≲ 6 (Jiang et al. 2006).

Let us now examine how the high-z quasars observed thus far impact this basic picture when viewed from the perspective of ΛCDM. In Table 1 we list many of the objects for which a reliable determination of mass has been made. This is not a complete sample, but is probably quite representative of the overall distribution. The columns in this table are as follows: (2) the quasar's measured redshift, (3) its inferred mass, quoted as a range when the uncertainty is well defined, (4) the quasar's age, calculated from its redshift, using the universe's expansion history according to ΛCDM, (5) the quasar's age (for the same redshift) calculated using R_h = ct, (6) the cosmic time at which a 5 M_☉ seed must have formed in order to grow into the observed quasar, assuming Eddington-limited accretion in the context of R_h = ct, and (7) the same as column (6), except for a seed mass of 20 M_☉.

Our analysis in this paper is based strictly on the premise that black hole seeds are produced in supernova events, which observations in the local universe indicate result in ∼5–20 M_☉ remnant cores. We further avoid any possible exotic mechanism that might have enhanced their accretion rate above the Eddington limit, defined from the maximum luminosity attainable due to outward radiation pressure acting on highly ionized infalling material (see, e.g., Melia 2009). This power depends somewhat on the gas composition, but for hydrogen plasma is given as L_Edd ≈ 1.3 × 10³⁸ (M/M_☉) erg s⁻¹, in terms of the accretor's mass, M. The accretion rate $\dot{M}$ is inferred from L_Edd, once the fractional efficiency η of converting rest mass energy into radiation is identified. Matter spiraling inward toward the event horizon releases a minimum of ∼6% of its rest energy for a Schwarzschild black hole, but η may be as high as 0.3 (or more) when the black hole is spinning (and the disk is on a prograde orbit), permitting frictional dissipation to continue down to radii smaller than ∼3 Schwarzschild radii (e.g., Melia 2009). Most workers adopt the "fiducial" value η = 0.1, reasonably close to the Schwarzschild limit, but also allowing for some influence from a possible black hole spin. This is the value we will assume here.

For simplicity, we will also ignore the contribution to black hole growth from mergers, which almost certainly must have occurred at some level and, as we have already indicated in the introduction, may have been necessary in order to produce their final distribution and intrinsic scatter in black hole versus galaxy mass relations (Hirschmann et al. 2010). The constraints we will derive below should therefore be viewed with this important caveat in mind. In particular, mergers may still make it feasible for supermassive black holes to form by z ∼ 6, even in the context of ΛCDM.

Under these conditions, the maximum accretion rate experienced by quasars at high redshift was then $\dot{M}=L_{\rm Edd}/\eta c^2$, which grew their mass at a rate $\dot{M}\approx 0.022\,(M/M_\odot)\;M_\odot /$Myr. Solving for the mass as a function of cosmic time then produces the Salpeter relation,

$$\begin{equation} M(t)=M_0 \exp \left({t-t_{\rm seed}\over 45\;{\rm Myr}}\right), \end{equation} \tag{ 1 }$$

where M₀ is the seed mass produced at time t_seed. We have calculated the time t_seed for each of the quasars in Table 1, using the universe's expansion history in ΛCDM, for two values of the seed mass, M₀ = 5 M_☉ and 20 M_☉. In each case, the possible range of "birth" times (between these two limits) is shown against the redshift of the observed quasar in Figure 1, for the assumed cosmological parameters H₀ = 72 km s⁻¹ Mpc⁻¹, Ω_m = 0.28, and a dark-energy equation of state p_de = −ρ_de.

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In this figure, we also show the period of Dark Ages and the EoR, the latter identified from its measured redshift range (z ∼ 6–15). The evident problems with this diagram are well known by now and we do not need to dwell on them. We simply point out the rather obvious flaws with this model, in which all of the quasars in this sample had to begin their evolution from seeds formed around the time of the big bang, well before the EoR even started. Worse, as quasars continue to be discovered at greater and greater redshifts, the model becomes completely untenable. Already, ULAS J1120 + 0641 (discovered at redshift 7.085; Mortlock et al. 2011) and SDSS J1148 + 5251 (discovered at redshift 6.419; Fan et al. 2002) must both have started their growth phase well before the big bang, which makes no physical sense.

These are the reasons, of course, why investigators have been motivated to propose exotic methods of greatly enhancing the accretion rate and/or starting from much bigger seed masses. But as we have already suggested in the introduction, our proposal in this paper is that the black hole birth and evolution were in fact quite standard (as we understand these from observations in the local universe), and that the answer lies instead with the assumed cosmology. Next, we will move to a consideration of how the observations are interpreted in the context of the R_h = ct universe.

Whereas ΛCDM is an empirical cosmology, deriving many of its traits from observations, the R_h = ct universe is a Friedmann–Robertson–Walker (FRW) cosmology whose basic principles follow directly from a strict adherence to the cosmological principle and Weyl's postulate (Melia 2007; Melia & Shevchuk 2012; see also Melia 2012a for a more pedagogical treatment). By now, these two expansion scenarios have been compared with each other, and with the various cosmological measurements, both at low and high redshifts. The evidence suggests that R_h = ct is a better match to the data, particularly the cosmic microwave background (CMB), whose fluctuations are so different from the predictions of ΛCDM that its probability of being the correct description of nature has been assessed at <0.03% (Copi et al. 2009). On the other hand, the R_h = ct universe explains the CMB angular correlation function very well, particularly the observed absence of any correlation at angles greater than ∼60° (Melia 2012b). A short summary of the current status of this cosmology appears in Melia (2012c).

Insofar as accounting for the high-z quasars is concerned, the essential feature of the R_h = ct universe that distinguishes it from ΛCDM is its expansion factor, a(t)∝t. Therefore, the cosmological redshift is given as

$$\begin{equation} 1+z={t_0\over t_e}{,} \end{equation} \tag{ 2 }$$

where t₀ is the current age of the universe and t_e is the cosmic time at which the light with redshift z was emitted. In addition, the gravitational horizon R_h is equivalent to the Hubble radius c/H(t), and therefore one has t₀ = 1/H₀. These equations are sufficient for us to produce a diagram like that shown in Figure 1, except this time for the R_h = ct universe, and this is illustrated in Figure 2. Note that the EoR redshift range z ∼ 6–15 here corresponds to the cosmic time t ∼ 830–1890 Myr, and so the Dark Ages did not end until ∼830 Myr after the big bang.

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The most striking feature of this diagram, however, is that not only did all the high-z quasars have time to grow after the big bang, but all of the 5–20 M_☉ seeds that grew into these sources formed after the EoR had started. This is exactly what one would have expected if these seeds were produced from Pop II and III supernovae, which presumably occurred after these stars had time to evolve and begin re-ionizing the universe. To be clear, what these results are telling us is that in the R_h = ct universe, all of the high-z quasars listed in Table 1 started their growth at redshift z ≲ 15, and developed into M ∼ 10⁹ M_☉ supermassive black holes by redshift z ≳ 6. And all of this happened with standard astrophysical principles, as we know them. There was no need for anomalously high accretion rates, nor the exotic creation of very large seed black holes.

It is difficult to understand how ∼10⁹ M_☉ black holes appeared so quickly after the big bang without invoking non-standard accretion physics and the formation of massive seeds, both of which are not seen in the local universe. The more recent data have compounded the problem by demonstrating that most (if not all) of the high-z quasars appear to be accreting at the Eddington limit.

Within the framework of the standard model, it therefore appears that mergers must have played a key role, not only in producing the observed correlations between black hole mass and host bulge mass in the local universe (Hirschmann et al. 2010), but perhaps also in assembling the 10⁹ M_☉ black holes seen at z ∼ 6–7. However, the former outcome does not necessarily guarantee the latter. An important finding of detailed merger simulations is that, irrespective of the initial seed profile, the black hole population always converges toward a Gaussian distribution. Observations of supermassive black holes locally therefore allow for quite some flexibility in the initial conditions.

Of course, this is quite useful for ΛCDM because the merger hypothesis offers a viable mechanism by which the high-z quasars could have formed by z ∼ 6. However, in order to comply with all of the available data, certain conditions must have prevailed at z ≫ 6. The simulations (see, e.g., Tanaka & Haiman 2009) show that ∼100 M_☉ seeds must have started forming by z ∼ 40, well before the EoR, and must have stopped being created, or accreted at severely diminished rates, by z ∼ 20–30, in order to not overproduce the mass density observed in lower-mass (a few × 10⁵ M_☉ to a few × 10⁷ M_☉) black holes. Without this cutoff, these lower-mass black holes would have been overproduced by a factor of ∼10²–10³.

These are all interesting possibilities and are permitted by the lack of any direct observational constraints on black hole mergers. In principle, the Laser Interferometer Space Antenna (LISA) might have been able to detect such mergers, or place limits on them, in the mass range ∼(10⁴–10⁷) M_☉/(1 + z) out to z ∼ 30 (Tanaka & Haiman 2009). But LISA may not become a reality unless a reprogrammed mission can eventually be approved by ESA. Unfortunately, the question of whether mergers could have assembled the high-z quasars in under 800 Myr since the big bang may therefore not be resolved any time soon.

There is also the question of whether the formation of black hole seeds in ΛCDM would be consistent with our improved understanding of the EoR. It appears that seeds would have formed quite early in the universe's history, well before re-ionization started at z ∼ 15. Additional work would have to be carried out to demonstrate that a sufficient number of seeds could have been produced by Population III stars shortly after the big bang, without any evidence of re-ionization appearing until much later, past the point where the creation of seeds stopped (at z ∼ 20–30). It may not be possible to completely reconcile these opposing trends.

In this paper, we have suggested that the disparity between the predictions of ΛCDM and the observations is further evidence against this being the correct cosmology. We have shown that the high-z quasar data may instead be interpreted much more sensibly in the context of the R_h = ct universe, for which standard 5–20 M_☉ seeds forming after re-ionization had begun (at z ≲ 15) could have grown to ≳ 10⁹ M_☉ supermassive black holes by redshift z ≳ 6, merely by accreting at the observed Eddington rate. Together with similarly compelling evidence from the CMB and the large-scale matter distribution, this comparison suggests that R_h = ct is the correct cosmology and that ΛCDM is, at best, simply an empirically derived approximation to it that nonetheless fails at high redshifts.

I am grateful for helpful and enjoyable discussions with Xiaoui Fan and Andrew Shevchuk. I am also grateful to Amherst College for its support through a John Woodruff Simpson Lectureship. This work was partially supported by grant 2012T1J0011 from The Chinese Academy of Sciences Visiting Professorships for Senior International Scientists, and grant GDJ20120491013 from the Chinese State Administration of Foreign Experts Affairs.