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[0803.0586] Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP data
Authors:J. Dunkley, E. Komatsu, M. R. Nolta, D. N. Spergel, D. Larson, G. Hinshaw, L. Page, C. L. Bennett, B. Gold, N. Jarosik, J. L. Weiland, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, G. S. Tucker, E. Wollack, E. L. Wright
Abstract:This paper focuses on cosmological constraints derived from analysis of WMAP data alone. A simple LCDM cosmological model fits the five-year WMAP temperature and polarization data. The basic parameters of the model are consistent with the three-year data and now better constrained: Omega_b h^2 = 0.02273+-0.00062, Omega_c h^2 = 0.1099+-0.0062, Omega_L = 0.742+-0.030, n_s = 0.963+0.014- 0.015, tau = 0.087+-0.017, sigma_8 = 0.796+-0.036. With five years of polarization data, we have measured the optical depth to reionization, tau>0, at 5 sigma significance. The redshift of an instantaneous reionization is constrained to be z_reion = 11.0+-1.4 with 68% confidence. This excludes a sudden reionization of the universe at z=6 at more than 3.5 sigma significance, suggesting that reionization was an extended process. Using two different methods for polarized foreground cleaning, and foreground marginalization, we get consistent estimates for the optical depth. This cosmological model also fits small-scale CMB data, and a range of astronomical data measuring the expansion rate and clustering of matter in the universe. We find evidence for the first time in the CMB power spectrum for a non-zero cosmic neutrino background, or a background of relativistic species, with the standard three light neutrino species preferred over the best-fit LCDM model with N_eff=0 at >99.5% confidence, and N_eff > 2.3 (95% CL) when varied. The five-year WMAP data improve the upper limit on the tensor-to-scalar ratio to r < 0.43 (95% CL), for power-law models. With longer integration we find no evidence for a running spectral index, with dn_s/dlnk = -0.037+-0.028.
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Antony Lewis

Joined: 23 Sep 2004
Posts: 1181
Affiliation: University of Sussex

PostPosted: March 11 2008  Reply with quote

One of the main improvements in parameter constraints in year 5 seems to be the significantly better constraint on the optical depth. Reassuringly τ~0.09 is fully consistent with the previous result, though moves around by ~0.01 in the alternative low-l polarization analysis presented (but not used) in this paper, indicating a non-negligible (but not large) systematic error.

Having constrained the optical depth, you can then try to infer the reionization redshift; they quote zre ~ 11.0 ± 1.4 assuming reionization is sharp. They also claim to rule out sharp reionization at z=6−7 at ~3 sigma which is an interesting result.

Now my question is this: what happens with helium reionization? If helium singly ionized at the same time as hydrogen, this potentially shifts τ by ~ 10% (or equivalently zre by ~ 6%). In the reionization literature it seems people often assume that this was the case (due to the relatively closeness of the ionization energies); does anyone know any evidence? More practically, should we all be assuming xe ~1.08 if we are going to assume sharp reionization?

(the effect of the second reionization of helium at z~3−4 corresponds to only an extra τ ~ 0.001)
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Ilian Iliev

Joined: 17 Aug 2006
Posts: 8
Affiliation: University of Sussex

PostPosted: March 14 2008  Reply with quote

To a good approximation helium does become singly-ionized at the same time and places as hydrogen. This is not just an assumption, but is shown by simulations. See e.g.:

This paper has a different goals, but it does show this point as well (I am
sure there are many other examples). See e.g. Figs. 7 and 8 - the H II and He II ionization fronts are in all cases at very similar positions and their ionization levels are similar, as well. There are, however, some minor differences between the two, which are also dependent on the ionizing source spectrum.
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