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Issue A&A
Volume 495, Number 2, February IV 2009
Page(s) 389 - 405
Section Cosmology (including clusters of galaxies)
DOI 10.1051/0004-6361:200810757
Published online 04 December 2008

A&A 495, 389-405 (2009)
DOI: 10.1051/0004-6361:200810757

The simulated 21 cm signal during the epoch of reionization: full modeling of the Ly-$\alpha$ pumping

S. Baek1, P. Di Matteo1, 2, B. Semelin1, F. Combes1, and Y. Revaz1, 3

1  LERMA, Observatoire de Paris, UPMC, CNRS, 61 Av. de l'Observatoire, 75014 Paris, France
    e-mail: sunghye.baek@obspm.fr
2  GEPI, Observatoire de Paris, section de Meudon, CNRS, Place Jules Janssen, 92190 Meudon, France
3  Laboratoire d'Astrophysique, École Polytechnique Fédérale de Lausanne (EPFL), Switzerland

Received 6 August 2008 / Accepted 3 November 2008

Abstract
The $21\,\rm {cm}$ emission of neutral hydrogen is the most promising probe of the epoch of reionization (EoR). In the next few years, the SKA pathfinders will provide statistical measurements of this signal, such as its power spectrum. Within one decade, SKA should produce a full tomography of the signal. Numerical simulations predicting these observations are necessary to optimize the design of the instruments and help in the interpretation of the data. Simulations are reaching a reasonable level in terms of scale range, but still often rely on simplifications to compute the strength of the signal. The main difficulty is the computation of the spin temperature of neutral hydrogen which depends on the gas kinetic temperature and on the level of the local Lyman-$\alpha$ flux (The Wouthuysen-Field effect). A $T_{\rm S} \gg T_{\rm CMB}$ assumption is usual. However, this assumption does not apply early in the reionization history, or even later in the history as long as the sources of X-rays are too weak to heat the intergalactic medium significantly. This work presents the first EoR numerical simulations including, beside dynamics and ionizing continuum radiative transfer, a self-consistent treatment of the Ly-$\alpha$ radiative transfer. This allows us to compute the spin temperature more accurately. We use two different box sizes, $20\,h^\,\rm {Mpc}$ and $100\,h^\,\rm {Mpc}$, and a star source model. Using the redshift dependence of average quantities, maps, and power spectra, we quantify the effect of using different assumptions to compute the spin temperature and the influence of the box size. The first effect comes from allowing for a signal in absorption (i.e. not making the $T_{\rm S} \gg T_{\rm CMB}$ approximation). The magnitude of this effect depends on the amount of heating by hydrodynamic shocks and X-rays in the intergalactic medium (IGM). With our source model we have little heating so regions seen in absorption survive almost until the end of reionization. The second effects comes from using the real, local, Lyman-$\alpha$ flux. This effect is important for an average ionization fraction of less than ~$ 10\%$: it changes the overall amplitude of the $21\,\rm {cm}$ signal, and adds its own fluctuations to the power spectrum.


Key words: radiative transfer -- methods: numerical -- ISM: HII regions -- ISM: bubbles -- cosmology: early Universe



© ESO 2009


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