On the Detection of High Redshift Black Holes with ALMA through CO and H2 Emission
Many present-day galaxies are known to harbor supermassive, , black holes. These central black holes must have grown through accretion from less massive seeds in the early universe. The molecules CO and H can be used to trace this young population of accreting massive black holes through the X-ray irradiation of ambient gas. The X-rays drive a low-metallicity ion-molecule chemistry that leads to the formation and excitation of CO and H in K gas. H traces very low metallicity gas, solar or less, while some pollution by metals, solar or more, must have taken place to form CO. Strong CO and H S(0) & S(1) emission is found that allows one to constrain ambient conditions. Comparable line strengths cannot be produced by FUV or cosmic ray irradiation. Weak, but perhaps detectable, H (2,2)(1,1) emission is found and discussed. The models predict that black hole masses larger than can be detected with ALMA, over a redshift range of 5-20, provided that the black holes radiate close to Eddington.
Central to the study of galaxy evolution is the formation and evolution of the supermassive black holes in their nuclei. Accretion onto these black holes can provide the energy source for active galactic nuclei, which in turn impact the evolution of galaxies (Silk 2005). The processes believed to play a role in the formation of seed black holes, from which large black holes may form through accretion, involve 1) dynamical friction and collision processes in dense young stellar clusters (Portegies Zwart et al. 2004); 2) seeds as the remnants of popIII stars (e.g., Bromm et al. 1999, Abel et al. 2000, Yoshida et al. 2003); 3) accretion of low angular momentum material and gravitational instability in primordial disks (e.g., Koushiappas, Bullock & Dekel 2004; Lodato & Natarajan 2007); and 4) the (singular) collapse of massive pre-galactic halos (Bromm & Loeb 2003; Spaans & Silk 2006).
The growth of these seed black holes to larger sizes involves accretion that roughly follows an Eddington rate and requires the incorporation of feedback effects (Silk & Rees 1998, Wyithe & Loeb 2003, Di Matteo, Springel & Hernquist 2005). See Pelupessy, Di Matteo & Ciardi (2007) for an asessment on the difficulties that seed black holes have to grow at the Eddingtion rate. Understanding the growth of these black holes is also important because there appears to be a scaling relation between bulge and black hole mass, with about of the bulge mass tied up in the central black holes (Magorrian et al. 1998, Ferrarese & Merritt 2000, Häring & Rix 2004). In this work, it is investigated how one can observe a population of these putative black holes in the early universe, at redshifts , through high temperature molecular lines that are driven by X-rays and that are accessible to the Atacama Large Millimeter Array (ALMA), which covers the 300 m to 3 mm wavelength range.
2 Model Description
We consider a high redshift halo which already contains, by assumption, a seed black hole. Suppose further that an initially metal-free hydrogen gas is cooled by Lyman to K and settles in the center of a halo close to the black hole. Part of the gas is likely to experience a period of popIII star formation. If popIII star formation occurs, then the short life times of primordial stars ensure that the accreted gas is quickly polluted by a modest amount of dust and metals. If no star formation takes place, then the gas will remain metal-free. In either case, the accretion process will lead to the emission of X-rays that impact the thermal, ionization an chemical balance of the gas in the halo, leading to an X-ray dominated region (XDR, Maloney et al. 1996; Meijerink & Spaans 2005). For simplicity the black hole is taken to radiate at the Eddington luminosity.
For a baryonic number density cm today, hydrogen mass , halo masses of and a characteristic size scale of , one has a typical mean density and column of cm and cm, respectively. The work of Mo, Mao & White (1988) shows that the subsequent formation of a disk occurs, with a collapse factor of . This yields densities that exceed cm within 1 kpc. The above cosmology provides the boundary conditions for the ambient density and column density of individual models, and the metallicity is put in by hand.
The models of Meijerink & Spaans (2005) and Meijerink et al. (2007) are used to compute the thermal, chemical and ionization balance of the irradiated gas self-consistently, for one-dimensional constant density slabs of gas. The multi-zone escape probability method of Poelman & Spaans (2005, 2006) has been used to compute the line intensities presented here. The same radiative transfer is performed in relevant atomic (fine-structure) and molecular (rotational and vibrational) cooling lines. Cloud type “A” from Meijerink et al. (2007, their Table 1) is adopted, which is 1 pc in size. The interested reader is referred to the cited papers for a detailed description of all physical processes involved. There are four free parameters in the models: hydrogen density, hydrogen column density, metallicity and X-ray flux. The latter parameterizes unknowns like the accretion rate, turbulent viscosity and the spectral shape of the X-ray radiation. For definiteness, a power law radiation field with is adopted for energies between 1 and 100 keV, appropriate for a self-absorbed Seyfert nucleus. This slope, if it is between and does not significantly impact the chemistries of H, CO and H; see also Meijerink & Spaans (2005) for the case of a 1 keV thermal spectrum. Solar elemental abundance ratios are adopted. As long as [O/C] this does not influence the CO results. Chemical equilibrium is assumed. At densities of cm and for high X-ray fluxes, collisional and radiative time scales are short compared to the free-fall time. The chemical network comprises a few thousand reactions between 154 species with sizes up to 4 atoms (Woodall et al. 2006). Polycyclic aromatic hydrocarbons and small grains are included in the charge balance and are assumed to scale with the elemental carbon abundance.
Following the above cosmology, we consider column densities of cm and densities of cm. The X-ray flux takes values of erg s cm. Results are shown in the Figures 1, 2 and 3 for a density of cm. Values below this density but above cm were found to lead to similar signal strengths for H and H. For CO, line intensities smaller by a factor of were found. Recall that the Eddington luminosity is erg s. So erg s cm corresponds to a black hole that emits erg s through a surface with a radius of about 100 pc. The level to which popIII star formation pollutes the center of the primodial galaxy with metals through supernova explosions is a free parameter. Metallicities between and 1.0 solar are considered since solar is quite like a zero-metallicity gas as far as H and CO are concerned, and supersolar values appear unlikely for the bulk of the very high redshift gas. Dust grains, with standard Milky Way properties (Mathis et al. 1977), are included and their abundance is assumed to scale with the overall metallicity. The velocity dispersion of the gas has a thermal contribution, equal to km/s, and a turbulent contribution, equal to km/s, for individual gas clouds on the scale of 1 pc. In the dense gas considered here, turbulence is expected to be maintained at a level similar to that in active galaxies.
The main goal is to compute the expected columns of H, CO and H, and their associated emission strengths. For simplicity, a fiducial column of cm is adopted for the predicted line emissivities. This is driven by the theoretical considerations above, but also by recent observations of massive galaxies at (Daddi et al. 2007a,b). A significant fraction (20-30%) of the systems appear to contain heavily obscured AGN with columns in excess of cm. These massive systems appear to be a somewhat later stage of the concurrent bulge-black hole mass forming systems studied here. The X-ray luminosities of these lower redshift counterparts is erg s in the 2-8 keV band. The precise value of the total obscuring hydrogen column does not impact our emissivity results as long as it exceeds cm, i.e., includes all K gas.
3.1 H and H
In the absence of dust grains, H is formed in the gas phase through the H route, H+HH+e. This leads to high abundances of H, , even for low metallicities (Figure 1). So, contrary to far-ultraviolet (FUV, 6-13.6 eV) illumination, X-ray irradiation constitutes a form of positive feedback for H (Haiman et al. 1997). The models with a modest metallicity of , and thus dust grains, follow the H formation prescription as in Cazaux & Spaans (2004), which includes both physisorbed and chemisorbed hydrogen atoms. The columns of H that are reached at low metallicities are as large as cm. This while temperatures exceed 100 K over the bulk of this column, and reach K at its edge, sufficient to excite the K S(0) line at 28 m and K S(1) line at 17 m. The S(1) line is typically weaker than the S(0) line, while both lines are optically thin and in LTE. High molecular gas temperatures are reached in XDRs because of efficient ionization and Coulomb heating, rather than photo-electric heating from dust grains (Meijerink & Spaans 2005). Interestingly, an increase in metallicity decreases the H line strength. This is a direct consequence of enhanced cooling in fine-structure lines and a lower resulting temperature. Hence, the pure rotational H lines are particularly well suited to detect the earliest stages of black hole accretion, prior to significant metal pollution by star formation. Metallicities below were found to lead to quite similar H emissivities since all H is formed in the gas phase and fine-structure cooling is modest.
Figure 2 (see Section 4 for its details) shows rest frame line intensities of erg s cm sr at a metallicity of solar. For the numbers below, the ALMA sensitivity tool on the ESO website has been used and the concordance model, with the latest WMAP3 results, is adopted. With a source size of , or 600 pc at , this yields a S(0) flux density of Jy, for a fiducial galaxy center velocity dispersion of 20 km/s ( pc from a central mass). For the S(0) line from , so at 0.45 mm, and for 10 km/s spectral resolution, this is detectable with ALMA (50 antennas, beam size = source size) at the level in 4 hours of integration. Hence, despite the fact that the line falls in the less sensitive band 9, spectrally resolved detection is possible. The pure rotational H lines are intrinsically very bright, because of the strong contribution from the X-ray driven H route, and are accessible to ALMA for redshifts above 10, for S(0) 28 m, and above 16 for S(1) 17 m.
Figure 1, for a density of cm, shows that the H abundance increases with ionization parameter for metallicities below of solar. A higher X-ray ionization rate leads to a larger H abundance, through H secondary ionizations, and boosts the formation rate H+HH. The H abundance is thus key since no H can be formed without it. Too large values of lead to a decrease in the H abundance, driven by dissociative recombination.
The best candidate for an H detection is the optically thin (2,2)(1,1) line at 95 m, as suggested by Pan & Oka (1986). The critical density of the (2,2)(1,1) transition is about cm and the excitation energy K. Collisions between H and electrons have been included in the non-thermal rotational excitation of H (Faure et al. 2006). In all, Figure 2 shows that one reaches a maximum rest frame intensity of erg s cm sr, at low metallicity and strong X-ray irradiation, with typical abundances of . With a source size of , or about 1.8 kpc at , this yields a flux density of mJy, for a fiducial galaxy center velocity dispersion of 20 km/s. For at 1 mm (from 95 m), this is barely detectable with ALMA at the level, in 48 hours of integration (50 antennas, beam size = source size), and only if the line is unresolved.
Any metallicity larger than solar leads to significant, , abundances of CO. X-rays, because of their large energy, do not dissociate CO directly. FUV photons are produced through collisional excitation of H and H by electrons, followed by radiative decay. This UV flux is generally modest and thus CO can survive even in strong X-ray radiation fields. Given the high molecular gas temperatures in XDRs, K, rotational levels with are excited (Meijerink et al. 2006, 2007). This very high CO emission requires densities cm because the critical densities of these lines are about cm. Metallicities in excess of of solar further raise the CO emissivities, even though the higher abundances of C, O, Si and Fe also enhance the cooling of the gas (Santoro & Shull 2006). The CO emissivities below solar are negligible.
One finds from Figure 2 that, at a metallicity solar, rest frame CO line intensities reach erg cm s sr, which yields a flux density of Jy for a source size, or 850 pc at , and a fiducial galaxy center velocity dispersion of 20 km/s. For the rest frame peak in the CO line spectral energy distribution (SED) at 3000 GHz (see Figure 2), 10 km/s velocity resolution and for , ALMA detects such a source at in 8 hours of integration (50 antennas, beam size = source size). Spectrally resolved detection is possible. ALMA covers 0.3 to 3.0 mm, fortuitously matching most of the X-ray driven CO line SED for .
Figure 2 shows how the rest frame spectral line distribution of CO, pure rotational H and H evolves with irradiation and metallicity for an ALMA beam that is filled with 1 pc clouds at cm. These clouds are in Keplerian orbit around the central black hole and are randomly distributed over a spherical region with a linear size of 1 kpc in such a way that there is about one cloud along each line of sight. This central region is slowly enriched in metals as indicated. The total column density is on average cm along each line of sight. The total intensity is then found by a ray-trace on the level populations of the individual clouds. More complicated geometries are not an issue as long as the cloud covering factor is of the order of unity and the bulk of the emitted X-rays are absorbed.
Overall, X-ray fluxes of erg s cm, corresponding to black hole masses of and a region with a size of pc yield detectable lines, provided the black hole is radiating at its Eddington luminosity. This mass value is comparable to that of black holes present in in cosmological simulations of halos collapsing at (Peluppessy et al. 2007). Black holes that are emitting below the Eddington luminosity by a factor of are detectable with ALMA only if their masses exceed . Also, the Eddington time of yr is 25% of the Hubble time at , yielding a fair probability for detection of these systems in the ALMA frequency window. Finding sources is best done in the continuum (e.g. the James Webb Space Telescope), with ALMA follow-up. Since the molecular lines are optically thin, they trace the kinematics of all irradiated gas. Multiple CO and H lines further allow one to determine the ambient density, temperature and X-ray flux.
[OI] 63 m and [CII] 158 m fine-structure lines can be important coolants of X-ray irradiated gas as well. At a metallicity of , fine-structure line cooling contributes about half of the total cooling. These lines could also be observed with ALMA, but FUV or cosmic ray irradiation boosts them as well (Meijerink et al. 2007), diminishing their diagnostic value for tracing black hole accretion. In addition, the 149 m (, ) rotational line of HeH is shown in Figure 2, because it was suggested by Maloney et al. (1996) as a useful XDR tracer. It is found that this line is typically much weaker than the H and CO lines, and HeH abundances do not exceed .
Fast ( km/s) shocks can lead to similar CO and H emissivities, albeit over much smaller regions so that beam dilution would be an issue. Also, shocks should produce CO line profiles with strong non-Gaussian wings. At redshifts of a few, CO emission with upper levels from massive tori in active galaxies is also accessible to ALMA. This has been studied by Kawakatu et al. (2007) for the case where FUV photons drive the chemistry. Narayanan et al. (2008a) look at simulations of quasars in halos and find that the CO is highly excited by starbursts, peaking at . Narayanan et al. (2008b) further find that AGN-driven winds may leave signatures in the CO line emission profile in the form of high velocity peaks at a few times the circular velocity. Also, Lintott & Viti (2006) and Meijerink et al. (2007) find an increase in HCN emission with X-ray flux, but this effect is suppressed at low metallicity and for densities cm. The X-ray driven lines presented here complement these efforts. Finally, Figure 3 shows a CO comparison between an AGN (XDR) and a starburst (PDR = photon dominated region) model, for the same impinging flux by energy of 100 erg s cm, typical of a erg s Seyfert nucleus or B0 stars within a 200 pc region. Solar metallicity is assumed, merely because it favors the PDR. It is obvious that star formation can never compete with an XDR, for the same illuminating flux by energy, in terms of the very high CO line intensities that are produced.
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