Optical Depth to Reionization, τ

As discussed in the ΛCDM Theory section, the "Dark Ages" following recombination are brought to an end by an epoch of reionization. Although there is at present no firm scenario that describes the detailed history and mechanisms by which the intergalactic medium (IGM) evolves from a largely neutral state (post-recombination) to one of being largely ionized, the existence of reionization introduces key observational consequences. The history of the reionization process is important for its relevance to how and when the first stars and galaxies formed, since these objects are presumed to be sources for most of the ionizing photons. Reionization affects our ability to measure the CMB radiation propagating through the IGM: Thomson scattering of CMB photons by the free electrons produced by reionization serves as an opacity source that suppresses the amplitude of the observed primordial anisotropies. Additionally, electron scattering associated with reionization induces large-scale polarization of the CMB radiation above that produced earlier during recombination.

In the context of CMB observations, the optical depth to reionization, τ, is a unitless quantity which provides a measure of the line-of-sight free-electron opacity to CMB radiation. Under the assumption of instantaneous, complete reionization at redshift zreion, τ is computed as the integral of the electron density times the Thomson cross section over the geometrical path length computed between z=0 (i.e., today) and zreion (see e.g. Griffiths et al. 1999, Venkatesan 2000, Shull & Venkatesan 2007). Assuming a fixed dependence of electron density on redshift, a larger value of τ implies a larger value of zreion and thus an earlier onset of star and galaxy formation; τ = 0 implies no reionization at all.

Prior to WMAP, there was no detection of τ available. Upper limits had been derived based on the detection of microwave background temperature anisotropies in DMR, QMAP and other data (Griffiths et al. 1999), indicating τ < 1. Lower limits have been derived based on the lack of the Gunn-Peterson trough (Gunn & Peterson 1965) in the spectra of distant quasars and galaxies at redshifts z ≈ 6. This absorption feature is attributed to complete Lyα absorption by the neutral IGM, and is thus an indicator of ionization fraction. Estimates based on these data indicate τ > 0.03 (Pryke et al. 2002, Fan et al. 2005). Conservative theoretical priors chosen by e.g. Boomerang and DASI placed τ somewhere between 0 and 0.5. In the figure, we plot the Boomerang prior as representative of the state of knowledge at that time.

The first year WMAP release in 2003 contained both temperature information and a first-cut polarization dataset, allowing a τ detection. Since then, inclusion of multiple datasets and additional polarization data in evaluation of ΛCDM models has tightened constraints.Results which include pixel-based polarization likelihoods at low multipoles, in combination with other data, are represented by those of WMAP9++(WMAP9+eCMB+BAO+H0) and Planck_PR2++ 2015 (Planck XIII 2015). Planck Collaboration PR3 analyses resulted in smaller uncertainties (Planck V 2018, Planck VI 2018) using higher sensitivity 100 and 143 GHz polarization observations and a power-spectrum based quadratic maximum likelihood method. Additional reprocessings of Planck data have returned roughly 10% uncertainties (Pagano et al. 2020, Planck Int LVII 2020, Tristram et al. 2023). Analyses which exclude the use of polarization data and use only temperature and large-scale structure observations serve as a valuable independent check on these findings, but as yet do not achieve the lower uncertainties obtained through the addition of polarization data (Planck XIII 2015, Weiland et al. 2018).

Improved constraints on τ are expected from future high sensitivity observations of CMB polarization signals. In addition, future observations of 21 cm emission from neutral hydrogen may prove useful for tracking a more detailed reionization history and structure (Fialkov & Loeb 2016). Deep-field observations continue to discover new galaxies at high redshifts (e.g. z>10, Oesch et al. 2016), and the James Webb Space Telescope will provide even greater detection sensitivity for distant galaxies near the beginning of the reionization era.

Universe Age 2016

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The optical depth to reionization, τ, serves as a means of quantifying the era when emitting sources first began forming and reionizing the neutral gas that existed after recombination. The optical depth can be related to an approximate redshift, or range of redshifts, during which reionization occured: larger values imply an earlier onset of reionization. Lower limits based on lack of continuous Lyα absorption (by a neutral IGM) in the spectra of the most distant quasars and galaxies at redshifts z ≈ 6 suggest τ > 0.03 (Pryke et al. 2002, Fan et al. 2005). The detection of polarized CMB signal by WMAP in 2003 (Spergel et al. 2003) allowed the first determination of τ. Since that time, determinations of τ from CMB polarization data have improved in precision and accuracy, and polarized observations of the CMB are currently the best determinants of τ. Ongoing efforts seek to place even stricter limits on τ in order to constrain early galaxy formation models and inflation scenarios. The gray vertical line, representing the weighted average of WMAP and Planck data points, is positioned at τ = 0.0580.

Contributed by the NASA / LAMBDA Archive Team.

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