MEDIDAS PREVENTIVAS EN LOS MEDIOS DE DIFUSIÓN

If metals remain ionized, they can contribute an additional residual free-electron fraction at late times, ∆xe∼xM+. In fact we have ∆x_e=1

2xM+, as we show below. At late times the evolution of

the free-electron fraction is given by

˙

xe≈ −nHαBxexp=−nHαBxe(xe−xM+). (6.15)

Eq. (6.15) is valid because the free electron fraction is many orders of magnitude above the Saha equilibrium value at late time (for a discussion, see Section 2.2.2). If x0

e is the unperturbed free

electron fraction (i.e., obtained withxM+= 0) andx_e=x0_e+ ∆x_e, we obtain

˙

∆xe=−nHαBxe0(2∆xe−xM+), (6.16)

which asymptotes to ∆xe = 1₂xM+. The Planck satellite will be sensitive to fractional changes

∆xe/xe ∼ 1% at late times. Since xe ≈ 0.3−1×10−3 for 200 ∼< z ∼< 700, we conclude that a

potential detection byPlanck requires a fractional abundance of metalsxM_∼>10−5(in the case that

metals remain fully ionized). Note that for a given Ωb, the presence of metals also modifies the total

abundance of hydrogen, nH, throughout the recombination history. However these modifications

are degenerate with a mere change of Ωb ofYHe at the level of a few times 10−5 and are therefore

undetectable.

6.5

Conclusions

We have investigated whether a primordial metal content could sufficiently affect the recombination history to be detectable in upcoming CMB data from Planck. We first considered the effect of photoionization of neutral metals by Lyαphotons. We showed that although a very small abundance of neutral metals would be enough to significantly affect the net decay rate in Lyα, metals with ionization threshold below Lyαare mostly ionized atz∼1100, and therefore undetectable. We also considered the Bowen resonance-fluorescence mechanism if primordial oxygen is present. This effect leads to an enhanced escape rate of Lyβ photons and a speed up of recombination. We showed that it could lead to detectable changes for a primordial oxygen abundance of a couple hundredths of solar xO ∼10−5. Finally, we pointed out that metals that stay ionized until late times provide

additional free electrons and therefore change the late-time Thomson scattering optical depth. A fractional abundancexM∼10−5 of primordial metals could be detectable through this effect. As a

reference, the most abundant metal in the solar photosphere is oxygen (xO = 4.9×10−4), followed

(xMg= 3.4×10−5), silicon (xSi= 3.2×10−5), iron (xFe= 3.2×10−5) and sulfur (xS= 1.3×10−5).

Other metals have fractional abundancesxM<10−5 in the Sun [122]. As carbon, nitrogen, oxygen

and neon are neutral at late times (due to their high ionization potential), we conclude thatPlanck

could potentially detect primordial metals with an abundance at least a few tenths of solar. This is moreover an optimistic estimate, as the effect of metals is likely to be degenerate with the redshift of reionization or other cosmological parameters.

Given that Lyman-alpha-forest measurements and ultra-metal-poor halo stars suggest a primor- dial metallicity much smaller than one hundredth solar, we conclude that the CMB can unfortunately not usefully constrain the abundance of primordial metals. At the same time, we also conclude that the CMB predictions for thePlancksatellite are robust to a primordial metallicity allowed by current empirical constraints.

Part II

Chapter 7

Introduction

7.1

Motivations

Observational cosmology has entered an era of high precision, exemplified by the most recent temper- ature results from sensitive cosmic microwave background (CMB) experiments [123, 124, 125, 126]. However, foreground separation and removal remains a major challenge for any CMB measure- ment (see e.g. Refs. [127, 128]). In addition to the standard Galactic foregrounds, free-free, syn- chrotron and thermal dust emission (for a description see Box 2 below), an unknown “anomalous” dust-correlated emission has been observed over the last decade, in the microwave region of the spectrum. The anomalous emissions was first interpreted as free-free emission from shock-heated gas in Ref. [129], but Draine & Lazarian [7] showed that this would require an extremely high plasma temperature and a corresponding unrealistic energy injection rate. They proposed instead two possible mechanisms to explain the anomalous microwave emission. One of them is the mag- netic dipole emission from thermal fluctuations in the magnetization of interstellar dust grains [130]. The other possible mechanism, on which the present work focuses, is electric dipole radiation from the smallest carbonaceous grains, described in Ref. [8], hereafter DL98b. The physical principle is quite straightforward: dust grains are presumably asymmetric, and thus will have a nonzero elec- tric dipole moment. These grains will spin due to interaction with the ambient interstellar medium (ISM) and radiation field, and thus radiate electromagnetic waves due to the rotation of their electric dipole moment. To get the electric dipole radiation spectrum, one thus needs three ingredients: the quantity of small grains, then their dipole moment, and finally their rotation rates.

Although the observational interest in electric dipole radiation from spinning dust grains has only grown in the last decade, there is a long standing history of theoretical work on the subject. Ref. [131] was the first to consider the possibility that rotating dust grains could be the source of non-thermal radio-noise. Ref. [132] showed that this process was dominated by grains with radius a_∼<10−6 _{cm and could lead to radio emission around 10 GHz. Ref. [133] estimated the spinning}

rotational excitation of small grains was Ref. [134], where the effect of collisions with gas atoms and absorption and emission of radiation were considered. Ref. [135] evaluated the effect of collisions with ions and “plasma drag” (torques due to the electric field of passing ions).

DL98b provided the first comprehensive study of the rotational dynamics of small grains, in- cluding all the previous effects. They evaluated, as a function of grain radius and environmental conditions, rotational damping and excitation rates through collisions, “plasma drag”, infrared emis- sion, emission of electric dipole radiation, photoelectric emission and formation of H2 molecules.

The spectra they provided are now widely used in interpreting ISM microwave emission (see for example Refs. [136, 137, 138, 139, 140, 141, 142, 143]) and for CMB foreground analyses (e.g. Refs. [144, 145, 146, 147, 148]). Given that the DL98b models are now a decade old, and the recent surge in interest in anomalous emission, it is timely to revisit the theory of spinning dust emission, including the approximations made in DL98b. This is the purpose of the second part of this thesis.