#import "importer/main.typ": *
#import "@preview/physica:0.9.5": *
#import "@preview/touying:0.6.1": *


= Simulating the Epoch of Reionization
== The Epoch of Reionization
- Marks the universe’s last major phase transition: from neutral to ionized hydrogen.

- Shapes the large-scale structure of the intergalactic medium (IGM).

- Is strongly linked to the formation and growth of the first galaxies and black holes.

- Sets the stage for many observables: CMB secondary anisotropies, 21-cm signal, high-z galaxy surveys.
// reformulate

== The 21cm signal

The brigthtness temperature describes the difference between the CMB temperature and the spin temperature of neutral hydrogen
#grid[
  #image("assets/cmb_black_body_spectrum.svg", height: 1fr, fit: "contain") @cmb_spectrum
][
  Removing the contribution from the black body spectrum of the CMB yields the explicit 21-cm signal:
  #image("assets/cmb_black_body_spectrum.svg", height: 1fr, fit: "contain")

]



#align(center)[
  #image("assets/evolution_of_dtb.png", fit: "contain")
]
@Pritchard2012

#pagebreak()

$
  d T_"b" (bold(x), z) tilde.eq T_0 (z) dot x_"HI" (bold(x), z)  dot (1 + delta_b (bold(x), z)) dot (x_alpha (bold(x), z)) / (1 + x_alpha (bold(x), z) ) dot ((1 - T_"CMB" (z)) / (T_"gas" (bold(x), z)))
$ <eq:dTb>
(e.g @Pritchard2012)



== The halo model of reionization



Following @Schneider_2021 @schneider2023cosmologicalforecast21cmpower:

$
  rho_alpha (r bar M, z) = (1 + z)^2 / (4 pi r^2) dot sum_(n=2)^(n_m)f_n dot epsilon_alpha (nu prime) dot f_star dot dot(M)(z prime bar M, z)
$
#line(
  length: 100%
)
$
  3/2 dot derivative(rho_h (r bar M, z), z) = (3 rho_h (r bar M, z)) / (1 + z) - (rho_"xray" (r bar M, z)) /(k_B (1 + z) H(z))
$
#line(
  length: 100%
)
$
  x_("HII")(r bar M, z) = theta_"H" lr([R_b (M, z) - r], size: #150%)
$



== The current state of simulations
#lorem(20)

- slow and big
- radiative transfer // what are the downsides


$==>$ semi-numerical approaches such as `BEoRN` @Schaeffer_2023


#link(<backup_validation>, "validation")

== `BEoRN`