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[0803.0586]
FiveYear 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 fiveyear WMAP
temperature and polarization data. The basic parameters of the model are
consistent with the threeyear 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 smallscale 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 nonzero cosmic neutrino
background, or a background of relativistic species, with the standard three
light neutrino species preferred over the bestfit LCDM model with N_eff=0 at
>99.5% confidence, and N_eff > 2.3 (95% CL) when varied. The fiveyear WMAP
data improve the upper limit on the tensortoscalar ratio to r < 0.43 (95%
CL), for powerlaw 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: 1239 Affiliation: University of Sussex

Posted: March 11 2008 


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 lowl polarization analysis presented (but not used) in this paper, indicating a nonnegligible (but not large) systematic error.
Having constrained the optical depth, you can then try to infer the reionization redshift; they quote z_{re} ~ 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 z_{re} 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 x_{e} ~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

Posted: March 14 2008 


To a good approximation helium does become singlyionized at the same time and places as hydrogen. This is not just an assumption, but is shown by simulations. See e.g.:
http://adsabs.harvard.edu/abs/2004MNRAS.348..753S
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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