4.2 21 cm Emission, Absorption and Tomography
The 21 cm line of HI at redshift z would contribute to the
background spectrum at a wavelength of 21(1 + z) cm. This
contribution depends on the spin temperature Ts and the CMB
temperature Tbb. It amounts to a brightness
temperature of only 0.01 h-1
(
b
h2 /0.02) ((1 +
z)/10)1/2 (Ts -
Tbb) / Ts K - very small compared
with the 2.7K of the present CMB;
and even smaller compared to the galactic synchrotron radiation that
swamps the CMB, even at high galactic latitudes, at the long
wavelengths where high-z HI should show up.
Nonetheless, inhomogeneities in the HI may be detectable because they would give rise not only to angular fluctuations but also to spectral structure. (Madau, Meiksin and Rees 1997, Tozzi et al. 1999) If the same strip of sky were scanned at two radio frequencies differing by (say) 1 MHz, the temperature fluctuations due to the CMB itself, to galactic thermal and synchrotron backgrounds, and to discrete sources would track each other closely. Contrariwise, there would be no correlation between the 21 cm contributions, because the two frequencies would be probing `shells' in redshift space whose radial separation would exceed the correlation length. It may consequently be feasible to distinguish the 21 cm background, utilizing a radio telescope with large collecting area. The fact that line radiation allows 3-dimensional tomography of the high-z HI renders this a specially interesting technique.
For the 21 cm contribution to be observable, the spin temperature Ts must of course differ from Tbb. The HI would be detected in absorption or in emission depending on whether Ts is lower or higher than Tbb. During the `dark age' the hyperfine levels of HI are affected by the microwave background itself, and also by collisional processes. Ts will therefore be a weighted mean of the CMB and gas temperatures. Since the diffuse gas is then cooler than the radiation (having expanded adiabatically since it decoupled from the radiation), collisions would tend to lower Ts below Tbb , so that the 21 cm line would appear as an absorption feature, even in the CMB. At the low densities of the IGM, collisions are however ineffectual in lowering Ts substantially below Tbb (Scott and Rees 1990). When the first UV sources turn on, Lyman alpha (whose profile is itself controlled by the kinetic temperature) provides a more effective coupling between the spin temperature and the kinetic temperature. If Lyman alpha radiation penetrates the HI without heating it, it can actually lower the spin temperature so that the 21 cm line becomes a stronger absorption feature. However, whatever objects generate the Lyman alpha emission would also provide a heat input, which would soon raise Ts above Tbb.
When the kinetic temperature rises above Tbb, the 21 cm feature appears in emission. The kinetic temperature can rise due to the weak shocking and adiabatic compression that accompanies the emergence of the first (very small scale) non-linear structure (cf section 2). When photoionization starts, there will also, around each HII domain, be a zone of predominantly neutral hydrogen that has been heated by hard UV or X-ray photons (Tozzi et al. (1999). This latter heat input would be more important if the first UV sources emitted radiation with a power-law (rather than just exponential) component.
In principle, one might be able to detect incipient large-scale structure, even when still in the linear regime, because it leads to variations in the column density of HI, per unit redshift interval, along different lines of sight (Scott and Rees (1990)).
Because the signal is so weak, there is little prospect of detecting high-z 21 cm emission unless it displays structure on (comoving) scales of several Mpc (corresponding to angular scales of several arc minutes) According to CDM-type models, the gas is likely to have been already ionized, predominantly by numerous ionizing sources each of sub-galactic scale, before such large structures become conspicuous. On the other hand, if the primordial gas were heated by widely-spaced quasar-level sources, each of these would be surrounded by a shell that could feasibly be revealed by 21cm tomography using, for instance, the new Giant Meter Wave Telescope (GMRT) (Swarup (1994)). With luck, effects of this kind may be detectable. Otherwise, they will have to await next-generation instruments such as the Square-Kilometer Array.