When? (Reionisation)
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When?
Gunn and Peterson made the first measurements in 1965 using 3C9 at z = 2.012 as a source (ApJ 142 1633). They, and others, found no absorption, indicating no neutral hydrogen between us and 3C9. Over time, as more distant QSOs were found, the redshift by which reionisation was complete was pushed further up. Currently, it is accepted that reionisation was complete by z = 6: Becker01, Fan02, WBFS03. (Refs from SFP04) At what redshift would we finally see some absorption in the spectra?
The evidence indicates reionisation was completed by z∼6.5 (Fen02 & He04). More recently, spectra from distant QSOs have finally been observed which have absorption. Becker01 reports Lyα absorption systems towards high-z quasars indicate reionisation occured around z = 6. Observed quasars at z = 5.82, 5.99, 6.28. Observed a Gunn-Peterson trough toward the z = 6.28 quasar. The HI optical depth rises dramatically from z = 5.5 to 6.0. Their Fig. 1 shows the spectra and Ly limit.
Mesinger05 argues the neutral fraction, xHI, is >0.2 at z = 6.
So can we agree that the epoch of reionisation was around z∼6? Nope! Lyα emission has been observed from galaxies beyond z∼6. This simply should not be possible if the gas was ionised. More damning, measurements of the CMB polarisation indicate a column density of ionised gas stretching out to z∼14 or more.
Lyα emission has been observed from galaxies beyond z = 6.5 (Hu et al 2002, Kodaira et al 2003, Rhoads et al 2004, Kurk et al 2004, Stern et al 2004) The line should be heavily absorbed by the red damping wing of resonant Lyα in the surrounding IGM. If the HII region around a galaxy is increased in size, the optical depth from the red damping wing of resonant Lyα is reduced. (Gnedin & Prada 2004, Furlanetto Hernquist & Zaldariaga 2004) Lyα photons can sneek out from redshifts before reionisation. WL04b show that faint undetected sources clustered around observed galaxies can generate an HII region big enough to be seen, even if it is prior to reionisation. Unseen and short-lived quasars also contribute to the formation of the HII region.
MR04 show that reinionisation was complete before z = 6.5 by finding no evolution in the luminosity function of Lyα emitters between z = 6.5 and z = 5.7. This test is sensitive to a neutral fraction of ∼0.1 instead of ∼0.01 for the Gunn-Peterson effect. Their luminosity functions have a pretty large scatter and suffer from lack of data points.
Similar to MR04, but using one galaxy, Stern04 declares reionisation occured at z > 6.5. Lyα emission from a galaxy at z = 6.545 is found to not be attenuated.
Djorgovski et al (2001) found an abrupt increase in optical depth in Lyα at 
. From the sizes of HII regions around QSOs, it can be inferred that the neutral fracion of the IGM is > 0.1 (Mesinger & Haiman 2004, WL04a).
Kogut03 (Primary paper) & Spergel03 (a few more details): WMAP data suggests a higher redshift, but is poorly constrained. Kogut et al found correlations between the temperature and polarization map. For scales < 5°, data consistent with adiabatic perturbations. For scales > 10°, the data are inconsistent with adiabatic perturbations. They are consistent with reionization at z between 11 and 30. The reionization optical depth is found to be τ = 0.17±0.04.
CMB polarization arises at the scattering surface from the quadropole moment of the local temperature distribution around a scatterer. If the scatterer sees a bit warmer (hence brighter) photons coming from above and below compared to from the sides, then the scatterered light will be polarized. (Kogut03) At this time, the acoustic horizon is a degree.
At reionisation, additional polarisation is create. Thomson scattering damps the temperature anisotropy and regenerates a polarized signal on scales comparable to the horizon. The scales of the observed polarization excess are > 5°. (Kogut03)
Kogut03 (their Figure 7) shows the polarisation power spectrum matches the predictions of purely adiabatic processes for l>20. There is one data point at lower l (l<10) that disagrees significantly from prediction. The excess is attributed to reionisation.
The optical depth due to Thomson scattering can be estimated from the polarisation measurements. High optical depth, and the signal at small scales would be dominated by Thomson scattering. Low optical depth, and the CMB polarisation would be insensitive to reionisation. Since Thomson scattering (and Compton scattering) are due to photons interacting with free electrons, the larger the optical depth, the earlier the reionisation. An optical depth of τ=0.17±0.04 is found from the WMAP data. (Kogut03)
Note, there seems to be a bit of confusion in the literature (or at least, I find the literature confusing and inconsistent). Some papers say the WMAP result is due to Compton scattering, while Kogut says Thomson scattering. From Lang, "Astrophysical Formulae": "In the case of Thomson scattering, there is no change in the frequency of the radiation . For Compton scattering, the incident radiation transfers energy to the electron, and the scattered photon has less energy and a longer wavelength than the incident one. Thomson scattering applies for photon energies much less than the rest mass energy of the electron, or hν « mc2, whereas the Compton effect becomes important for larger incident photon energies. In the inverse Compton effect, high energy electrons scatter low energy photons so that in the Compoton interaction the photons now gain energy and the electrons lose energy."
In either case, what is observed is polarisation on the angular scales of the horizon at reionisation (θ > 5°). The polarisation leads to excess power in the temperature-polarization power spectrum. The Thomson optical depth can be interpreted and is found to be τ∼0.17. However, this is sensitive to the model. MCSF05 found the data to be consistent with τ = 0.3 (a more disturbing scenario) and letting τ free more than doubles the errors on cosmological parameters. Hence, understanding reionisation will permit stronger constraints on cosmological constants.
Conversion of CMB polarisation optical depth to redshift requires a model. Assuming step-function ionisation at a given redshift, the data imply z=17±4 as the epoch of reionisation. I'm confused about this model, since the gas will by clumpy and the model doesn't say anything about the assumed clumpiness (if any) of the gas. If reionisation is permitted to occur gradually over a period of time, then it started as long ago as z=30. (Kogut03)
FHZ04 cites other papers to point out: 4 quasars with z > 6.2, observed with SDSS, show complete Gunn-Peterson absorption over substantial path lengths in their spectrum, implying a rapid change in the ionizing background at this redshift with reionisation being completed by about z∼6. This is inconsistent with the CMB polarisation results, and the observations of the Ly-a forest temperature which imply reionisation at z ≤ 10.
Are the data contradictory? Not really. It does not take a large nutral fraction to lead to strong absorption. Indeed, most of the gas can be ionised and still appear opaque. The WMAP data say there is ionised gas up to at least z∼14. The QSO spectral data say all the gas (or nearly all) must be ionised by z∼6. Between z∼6 and 14 a partly ionised medium is consistent with both sets of data.
Gnedin04 shows that the WMAP result (high Thomson optical depth to the surface of reionisation ⇒ zr∼14) and SDSS results (zr∼6) are consistent. The SDSS results can simply be a drop in the ionising temperature, not an indication that reionisation was complete at zr∼6 since only a small amount of HI (
fraction at an overdentity of 0.1) is required for a high optical depth. This leads to Gnedin's question, "What does the redshift of reionisation mean?" He identifies 3 phases: 1) Pre-overlap; 2) Overlap; 3) Post-overlap. Gnedin identifies the completion of reionisation as when the mean free path of ionising radiation is determined fully by Lyman-limit systems. Gnedin defines the redshift of reionisation as the redshift at which the rate of change of the neutral fraction reaches a maximum, corresponding in his simulations to a fraction of about 
. He uses his SLH code combined with the Optically Thin Eddington Variable Tensor (OTVET) approximation for modeling radiative transfer insead of a "crude Local Optical Depth approximation."
By this point, it should be obvious that the ionisation history of the IGM is complex (Loeb & Barkana 2001, Barkana & Loeb 2001, Miralda-Escudé 2003). There may have been more than one ionisation period (Wyithe & Loeb 2003, Cen03b, Haiman & Holder 2003, Somerville, Bullock, & Livio 2003, Bromm 2004). A first reionisation at z∼20 due to massive Pop III stars, followed by a period of partial recombination, and finally the reionisation at z∼6.
FZH04b: Show that the statistical properties of observations of the 21 cm line at high redshift can distinguish various ionisation histories. Specifically, ionisation by discrete bubbles versus partial ionisation by a diffuse background can be distinguished by the power spectrum. Also, certain aspects of double reionisation are distinguishable, as is ionisation of the voids first. 21 cm has the advantage that saturation is not a problem. But this is also a problem, since foreground objects predominate. But foreground objects will have smooth continuum in the frequency regime of redshifted 21 cm (100 - 200 cm) allowing removal of the contaminating signal.
The highest redshift QSO so far is at z = 6.42. It shows G-P troughs in Lyα and Lyβ, but there is also emission in those troughs. OF04 show that this emission must be coming from the QSO which puts an upper limit on the Lyα optical depth at z∼6.2 of τeff < 14.3(2σ). WBFS04 concur, claiming the leakage is through two transparent windows at z∼6 and 5.
PS04 perform hydro simulations to show that the mean transission (given by the effective optical depth, τeff) ramps up with a slope of 4.16±0.02 up to reionisation.
The HI opacity in the range 1.6 ≤ z ≤ 3.2 is described by A(z + 1)γ where A = 0.0062 and γ=2.75 (Kirkman05).
Lyα photons will be absorbed if the gas is neutral. The statistics of high-redshift Lyα sources put limits on the ionisation volume fraction. Using conservative estimates of the number density of sources and the size of the Stromgren spheres around the sources, MR05 find a lower limit to the ionised volume fraction of 20-50% at z=6.5.
Generally, there are two possible reionisation epochs: an Early Reionisation Model (ERM) and a Late Reionisation Model (LRM) which are distiguished by early (z∼14) or late (z∼6). In principal, the choice of sources is not dictated by the model. But physically-motivated models typically have Pop III stars as the sources in ERMs and QSOs and galaxies as the sources in LRMs. Other options exist, such as miniquasars for ERMs. Distinguishing between ERMs and LRMs is a goal of many studies. Using semi-analytic ERMs and LRMs, GCF05 find QSO absorption sepctra are unable to distiguish ERMs from LRMs if the QSOs lie at z < 6. However, as is expected, if the QSO lies at z > 6, its spectra can distinguish the models. Specifically, the dark gap and peak width distributions are the statistics to use.
However you interpret it, the low-density medium of the universe changed dramatically around z∼6. Using 19 QSO spectra, Fan05 find the evolution of the Gunn-Peterson optical depth went from a z4 dependency to a z11 one at z∼5.7. The mean size of dark gaps went from about <10 Mpc to >80 Mpc. Also the UV fluctuations became more significant, as implied by the dispersion of IGM properties. The sizes of HII regions around quasars increased by a factor of 14 between z=6.4 and z=5.7. All the statistics point to the ionisation voids merging around z=6.
All the controversy coming from the WMAP measurement of τ = 0.17± 0.08 was dispelled by the 3-year polarization data, which dropped it down to τ = 0.09±0.03, at the lower edge of the 1-year data. The drop came about from σ8 dropping from 0.92±0.1 to 0.74±0.06 and the spectral index dropping from n = 0.98±0.03 to 0.95±0.01 (Spergel06).
The drop in σ8 from the WMAP1 to WMAP3 data implies a delay in structure formation. On the face of it, this may be enough to delay reionisation and account for the reduction in τ between the two data sets. Popa06 argues this is not enough. Assuming ionisation by supermassive PopIII stars, he finds the required mass of the stars also drops, from 1000 Mo to 80 Mo. I think his conclusion can be made more general: the WMAP3 data need softer spectra of a lower intensity. But the paper is confusing because it talks about star clusters, with no definition of how the star clusters change in the number of stars when the mass of the stars is changed.
TM06 show that the order in which gas is ionised (helium first versus hydrogen first) has a profound effect since the mean molecular weight drops by 45% during hydrogen ionisation while it drops only 7% during helium ionisation. Since ionising helium produces temperatures much cooler than observed, this makes a strong case for hydrogen ionisation occuring prior to helium ionisation.
Up to now, we have looked at measurements of when reionisation occured. Auxilliary to this is understanding the timing of structure formation that leads to reionisation. If reionisation was complete by z=10 but structures hadn't formed until z=8, then there is a problem.
Structures grow from the primordial density fluctuations parametrized by the Power Spectrum. The Power Spectrum at different scales is constrained by different observations. The CMB constrains the largest scales. The Lyα forest and clusters the intermediate scales, and galaxy distributions the smaller scales. The power spectrum on even smaller scales is unknown since growth quickly becomes non-linear and the primordial power spectrum is erased.
Cosmic strings create perturbations in the primordial density field around which structures can form. Enhanced early structure formation can alter the timing of reionisation, pushing it earlier (OV06).
According to BSNL05, star formation in high-z galaxies can match all the WMAP (2nd year) data. Indeed, their model can fit pretty much anything set by WMAP, particularly if you let the escape fraction vary.
Standard reionisation scenarios cannot form enough sources to reionize by high redshifts. This used to be a problem until WMAP's latest results were released. Still, if primordial magnetic fields were larger than 
Gauss, then fluctuations induced by primordial magnetic fields would trigger early structure formation (TS05).
Gallerani, Ferrara, Fan, & Choudhury (2007) show that the data are consistent with everything between an Early Reionization Model (f* = 0.1; fesc = 0.07) and a Late Reionization Model (f* = 0.08; fesc = 0.04) where f* is the star-formation efficiency and fesc is the escape fraction. The electron scattering optical depth, τ, is exceeded for earlier models while the Gunn-Peterson optical depth is exceeded for later models.
Gallerani, Ferrara, Fan, & Choudhury (2007) also show that xHI evolves from 10-4.4 to 10-4.2 between z=5.3 and 5.6 while finding xHI < 0.36 at z=6.3.
Etittley 14:42, 9 October 2007 (BST)
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