Te

Here A = 2.85 x 10-15 s-1 is the spontaneous emission rate and CH, Ce, and Cp are the de-excitation rates of the triplet due to collisions with neutral atoms, electrons, and protons. A fourth term must be added in the presence of ambient Lya radiation, since intermediate transitions to the 2p level can mix the spin states and couple Ts to Te, the "Wouthuysen-Field" effect (Wouthuysen 1952; Field 1958; Hirata 2006). In the absence of Lya photons, to unlock the spin temperature of a neutral medium with (say) Te = 500 K from the CMB requires a collision rate CH > AT/T*, corresponding to a baryon over-density > 5[(1 + z)/20]-2. Not only dense gas within virialized minihalos but also intergalactic filamentary structure heated by adiabatic compression or shock-heating may then be observable in 21-cm emission. A population of X-ray sources ("miniquasars") turning on at early stages (e.g. Madau et al. 2004; Ricotti et al. 2005) may make even the

Figure 3.20. The two-dimensional distribution of spin temperature versus baryonic over-density at z = 17.5. The shading indicates the fraction of the simulated volume at a given (Sb,TS). Left: the NS run. The volume- and mass-averaged spin temperatures are 48.6 and 67.5 K, respectively. Right: MQ run. Only gas with neutral fraction >90% is shown in the figure. The volume- and mass-averaged spin temperatures are 82.6 and 138.0 K, respectively. The horizontal line marks the temperature of the CMB at that redshift.

Figure 3.20. The two-dimensional distribution of spin temperature versus baryonic over-density at z = 17.5. The shading indicates the fraction of the simulated volume at a given (Sb,TS). Left: the NS run. The volume- and mass-averaged spin temperatures are 48.6 and 67.5 K, respectively. Right: MQ run. Only gas with neutral fraction >90% is shown in the figure. The volume- and mass-averaged spin temperatures are 82.6 and 138.0 K, respectively. The horizontal line marks the temperature of the CMB at that redshift.

low-density IGM visible in 21-cm emission as structures develop in the pre-reionization era.

In Kuhlen et al. (2006) we used the same hydrodynamic simulations of early structure formation in a ACDM universe as discussed in Section 1.4.2 to investigate the spin temperature and 21-cm brightness of the diffuse IGM prior to the epoch of cosmic reion-ization, at 10 < z < 20. The two-dimensional distribution of gas over-density and spin temperature at z = 17.5 is shown in Figure 3.20 for a simulation with no radiation sources ("NS") and one ("MQ") in which a miniquasar powered by a 150M0 black hole turns on at redshift 21 within a host halo of mass 2 x 106M0. The miniquasar shines at the Eddington rate and emits X-ray radiation with a power-law energy spectrum <x E-1 in the range 0.2-10 keV. The color coding in this phase diagram indicates the fraction of the simulated volume at a given (6b,TS). In both runs we have assumed that there is no Lya mixing, so that the visibility of hydrogen at 21 cm is entirely determined by collisions. Only gas with neutral fraction >90% is shown in the figure. The low-density IGM in the NS run lies on the yellow TS = T = 50.4-K line: this is gas cooled by the Hubble expansion to Te ^ T that cannot unlock its spin states from the CMB and therefore remains invisible. At over-densities between a few and ^200, H-H collisions become efficient and adiabatic compression and shocks from structure formation heat up the medium to well above the radiation temperature. The coupling coefficient during this epoch is y ~ SbT-0'64: gas in this regime has T <TS ~ yTe < Te and appears in emission against the CMB (red and green swath). Some residual hydrogen with over-density up to a few tens, however, is still colder than the CMB, and is detectable in absorption. At higher densities, y ^ 1 and TS ^ Te: the blue cooling branch follows the evolutionary tracks in the kinetic temperature-density plane of gas shock-heated to virial values, Te = 2000-104 K, which is subsequently cooling down to ^100 K because of H2 line emission.

Figure 3.21. Projected (mass-weighted) spin temperature (upper panels, logarithmic scale) and 21-cm differential brightness temperature (lower panels, composite linear scale) in a 0.5-Mpc simulation box for runs "NS" (left) and "MQ" (right) at z = 17.5. The location of the miniquasar is indicated by crosses in the right panels.

Figure 3.21. Projected (mass-weighted) spin temperature (upper panels, logarithmic scale) and 21-cm differential brightness temperature (lower panels, composite linear scale) in a 0.5-Mpc simulation box for runs "NS" (left) and "MQ" (right) at z = 17.5. The location of the miniquasar is indicated by crosses in the right panels.

The effect of the miniquasar on the spin temperature is clearly seen in the right panel of Figure 3.20. X-ray radiation drives the volume-averaged temperature and electron fraction (xe) within the simulation box from (8K, 1.4 x 10—4) to (2800K, 0.03), therefore producing a warm, weakly ionized medium (Kuhlen & Madau 2005). The H-H-collision term for spin exchange in the low-density IGM increases on average by a factor of 3500 36 ~ 8, while the e-H-collision term grows to Ce ~ 0.5CH. Gas with (Sb,Te,xe) = (1, 2800 K, 0.03) has coupling efficiency y = 0.008 and spin temperature TS =73K >T, and can now be detected in emission against the CMB. Within 150 comoving kiloparsecs from the source, the volume-averaged electron fraction rises above 10%, and e-H collisions dominate the coupling.

A beam of 21-cm radiation passing through a neutral-hydrogen patch having optical depth t and spin temperature TS causes absorption and induces emission. In the comoving frame of the patch, the radiative-transfer equation yields for the brightness temperature through the region Tb = Te—T + TS(1 — e—T). We have used our numerical simulations to perform 21-cm-radiation transport calculations, including the effect of peculiar velocities and local changes in spin temperature, gas density, and neutral-hydrogen fraction. The resulting 21-cm radio signal is shown in Figure 3.21 (lower panels), together with an image of the projected hydrogen spin temperature (upper panels): the latter highlights the abundance of structure within our simulation box on scales up to hundreds of kiloparsecs. Owing to Hubble and peculiar velocity shifts not all of this structure contributes to the 6Tb map. In the NS simulation, coherent features in the IGM can be discerned in emission (TS > T, 6Tb > 0): this filamentary shock-heated structure is typically surrounded by mildly over-dense gas that is still colder than the CMB and appears in absorption (TS < T, 6Tb < 0). The covering factor of material with 6Tb < —10 mK is 1.7%, which is comparable to that of material with 6Tb > + 10mK: only about 1% of the pixels are brighter than +40 mK. While low-density gas (black color in the left-lower panel) remains invisible against the CMB in the NS run, the entire box glows in 21-cm emission after being irradiated by X-rays. The fraction of sky emitting with 6Tb > (+10, +20, +30, +50, +100) mK is now (0.57, 0.31, 0.19, 0.1, 0.035).

The above calculations show that, even in the absence of external heating sources, spin exchange by H-H collisions can make filamentary structures in the IGM (heated by adiabatic compression or shock-heating) observable in 21-cm emission at redshifts z < 20. Some cold gas with over-densities in the range 5-100 is still detectable in absorption at a level of 6Tb < —10 mK, with a signal that grows as T—1 and covers a few percent of the sky. X-ray radiation from miniquasars preheats the IGM to a few thousand kelvins and increases the electron fraction: this boosts both the H-H and the e-H collisional coupling between TS and Te, making even low-density gas visible in 21-cm emission well before the Universe is significantly reionized. Any absorption signal has disappeared, and as much as 30% of the sky is now shining with 6Tb > +20 mK. As pointed out by Nusser (2005), the enhanced e-H coupling makes the spin temperature very sensitive to the free-electron fraction: the latter is also a tracer of the H2 molecular fraction in the IGM.

3.4.4 Concluding remarks Since hierarchical clustering theories provide a well-defined framework in which the history of baryonic material can be tracked through cosmic time, probing the reionization epoch may then help constrain competing models for the formation of cosmic structures. Quite apart from uncertainties in the primordial power spectrum on small scales, however, it is the astrophysics of baryons that makes us unable to predict when reionization actually occurred. Consider the following illustrative example.

Photoionization of hydrogen requires more than one photon above 13.6 eV per hydrogen atom: of order t/trec — 10 (where trec is the volume-averaged hydrogen-recombination timescale) extra photons appear to be needed to keep the gas in over-dense regions and filaments ionized against radiative recombinations (Gnedin 2000; Madau et al. 1999). A "typical" stellar population produces during its lifetime about 4000 Lyman-continuum (ionizing) photons per stellar proton. A fraction f — 0.25% of cosmic baryons must then condense into stars to supply the requisite UV flux. This estimate assumes a standard (Salpeter) IMF, which determines the relative abundance of hot, high-mass stars versus cold, low-mass ones. The very first generation of stars ("Population III") must have formed, however, out of unmagnetized metal-free gas: characteristics, these, which may have led to a "top-heavy" IMF biased toward very massive stars (i.e. stars a few hundred times more massive than the Sun), quite different from the present-day Galactic case. Population III stars emit about 105 Lyman-continuum photons per stellar baryon (Bromm et al. 2001), approximately 25 times more than a standard stellar population. A correspondingly smaller fraction of cosmic baryons would have to collapse then into Population III stars to reionize the Universe, f — 10—4. There are of course further complications. Since, at zero metallicity, mass loss through radiatively driven stellar winds is expected to be negligible, Population III stars may actually die losing only a small fraction of their mass. If they retain their large mass until death, stars with masses

140M0 < m* < 26OM0 will encounter the electron-positron-pair instability and disappear in a giant nuclear-powered explosion (Fryer et al. 2001), leaving no compact remnants and polluting the Universe with the first heavy elements. In still-heavier stars, however, oxygen and silicon burning is unable to drive an explosion, and complete collapse to a black hole will occur instead (Bond et al. 1984). Thin-disk accretion onto a Schwarzschild black hole releases about 50MeV per baryon. The conversion of a trace amount of the total baryonic mass into early black holes, f ~ 3 x 10-6, would then suffice to at least partially ionize and reheat the Universe.

The above discussion should make it clear that, despite much recent progress in our understanding of the formation of early cosmic structure and the high-redshift Universe, the astrophysics of first light remains one of the missing links in galaxy formation and evolution studies. We are left very uncertain about the whole era from 108 to 109 yr - the epoch of the first galaxies, stars, supernovae, and massive black holes. Some of the issues reviewed here are likely to remain a topic of lively controversy until the launch of the James Webb Space Telescope (JWST), which will be ideally suited to image the earliest generation of stars in the Universe. If the first massive black holes form in pregalactic systems at very high redshifts, they will be incorporated through a series of mergers into larger and larger halos, sink to the center owing to dynamical friction, accrete a fraction of the gas in the merger remnant to become supermassive, and form binary systems (Volonteri et al. 2003). Their coalescence would be signaled by the emission of low-frequency gravitational waves detectable by the planned Laser Interferometer Space Antenna (LISA). An alternative way to probe the end of the dark ages and discriminate between different possible reionization histories is through 21-cm tomography. Prior to the epoch of full reionization, 21-cm spectral features will display angular structure as well as structure in redshift space due to inhomogeneities in the gas-density field, ionized fraction of hydrogen, and spin temperature. Radio maps will show a patchwork (both in angle and in frequency) of emission signals from HI zones modulated by HII regions where no signal is detectable against the CMB (Ciardi & Madau 2003). The search at 21 cm for the epoch of first light has become one of the main science drivers for the next generation of radio arrays.

While many of the cosmological puzzles we have discussed can be tackled directly by studying distant objects, it has also become clear that many of today's "observables" within the Milky Way and nearby galaxies relate to events occurring at very high redshifts, during and soon after the epoch of reionization. In this sense, studies of galaxies in the Local Group ("near-field cosmology") can provide a crucial diagnostic link to the physical processes that govern structure formation and evolution in the early Universe ("far-field cosmology"). It is now well established, for example, that the hierarchical mergers that form the halos surrounding galaxies are rather inefficient, leaving substantial amounts of stripped-halo cores or "subhalos" orbiting within these systems (see Figure 3.22). Small halos collapse at high redshift when the Universe is very dense, so their central densities are correspondingly high. When these merge into larger hosts, their high densities allow them to resist the strong tidal forces that act to destroy them. Gravitational interactions appear to unbind most of the mass associated with the merged progenitors, but a significant fraction of these small halos survives as distinct substructure.

The Via Lactea simulation has recently shown that, in the standard CDM paradigm, galaxy halos should be filled with tens of thousands of subhalos that appear to have no optically luminous counterpart: this is more than an order of magnitude more than found in previous simulations. Their cumulative mass function is well fit by N(>Msub) x M-Ub down to Msub = 4 x 106M0. Sub-substructure is apparent in all the larger satellites, and

Figure 3.22. A projected dark-matter density-squared map of the Via Lactea halo at the present epoch. The image covers an area of 800 kpc x 600 kpc, and the projection goes through a 600-kpc-deep cuboid containing a total of 110 million particles. The logarithmic color scale covers 20 decades in density squared.

Figure 3.22. A projected dark-matter density-squared map of the Via Lactea halo at the present epoch. The image covers an area of 800 kpc x 600 kpc, and the projection goes through a 600-kpc-deep cuboid containing a total of 110 million particles. The logarithmic color scale covers 20 decades in density squared.

a few dark-matter lumps are now resolved even in the Solar vicinity. In Via Lactea, the number of dark satellites with peak circular velocities above 5 km s_1 (10 km s_1) exceeds 800 (120). As shown in Figure 3.23, such a finding appears to exacerbate the so-called "missing-satellite problem," the large mismatch between the 20 or so dwarf satellite galaxies observed around the Milky Way and the predicted large number of CDM

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