Observational constraints on key-parameters of cosmic reionisation
  history
  We discuss constraints on cosmic reionisation and their implications on a
cosmic SFR density $\rho_\mathrm{SFR}$ model; we study the influence of
key-parameters such as the clumping factor of ionised hydrogen in the
intergalactic medium (IGM) $C_{H_{II}}$ and the fraction of ionising photons
escaping star-forming galaxies to reionise the IGM $f_\mathrm{esc}$. Our
analysis uses SFR history data coming from luminosity functions, assuming that
star-forming galaxies were sufficient to lead the reionisation process at high
redshift. We add two other sets of constraints: measurements of the IGM ionised
fraction and the most recent result from Planck Satellite about the integrated
Thomson optical depth of the Cosmic Microwave Background (CMB)
$\tau_\mathrm{Planck}$. We also consider various possibilities for the
evolution of these two parameters with redshift, and confront them with
observational data cited above. We conclude that, if the model of a constant
clumping factor is chosen, the fiducial value of $3$ often used in papers is
consistent with observations; even if a redshift-dependent model is considered,
the resulting optical depth is strongly correlated to $C_{H_{II}}$ mean value
at $z>7$, an additional argument in favour of the use of a constant clumping
factor. Besides, the escape fraction is related to too many astrophysical
parameters to allow us to use a complete and fully satisfactory model. A
constant value with redshift seems again to be the most likely expression:
considering it as a fit parameter, we get from the maximum likelihood (ML)
model $f_\mathrm{esc}=0.24\pm0.08$; with a redshift-dependent model, we find an
almost constant evolution, slightly increasing with $z$, around
$f_\mathrm{esc}=0.23$. Last, our analysis shows that a reionisation beginning
as early as $z\geq14$ and persisting until $z\sim6$ is a likely storyline.
