A Monte Carlo Implementation of Galactic Free-Free Emission for the EoR
  Foreground Models
  The overwhelming foreground causes severe contamination on the detection of
21-cm signal during the Epoch of Reionization (EoR). Among various foreground
components, the Galactic free-free emission is less studied, so that its impact
on the EoR observation remains unclear. To better constrain this emission, we
perform the Monte Carlo simulation of H$\alpha$ emission, which comprises
direct and scattered H$\alpha$ radiation from HII regions and warm ionized
medium (WIM). The positions and radii of HII regions are quoted from the WISE
HII catalog, and the WIM is described by an axisymmetric model. The scattering
is off dust and free electrons that are realized by applying an exponential
fitting to the HI4PI HI map and an exponential disk model, respectively. The
simulated H$\alpha$ intensity, the Simfast21 software, and the latest SKA1-Low
layout configuration are employed to simulate the SKA "observed" images of
Galactic free-free emission and the EoR signal. By analyzing the
one-dimensional power spectra, we find that the Galactic free-free emission can
be about $10^{5.4}$-$10^{2.1}$, $10^{5.0}$-$10^{1.7}$, and
$10^{4.3}$-$10^{1.1}$ times more luminous than the EoR signal on scales of
$0.1~{\rm Mpc^{-1}} < k < 2~{\rm Mpc^{-1}}$ in the 116-124, 146-154, and
186-194 MHz frequency bands, respectively. We further calculate the
two-dimensional power spectra inside the EoR window and show that the power
leaked by Galactic free-free emission can still be significant, as the power
ratios can reach about $110\%$-$8000\%$, $30\%$-$2400\%$, and $10\%$-$250\%$ on
scales of $0.5~{\rm Mpc^{-1}} \lesssim k \lesssim 1~{\rm Mpc^{-1}}$ in three
frequency bands. Therefore, we indicate that the Galactic free-free emission
should be carefully treated in future EoR detections.
