#import "globals.typ": *


= 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 21-cm signal


The brigthtness temperature describes the difference between the CMB temperature and the spin temperature of neutral hydrogen

#v(1em)

#grid(columns: 2, align: center, column-gutter: 1em)[
  #image("assets/cmb_and_dtb.jpeg", height: 1fr, fit: "contain")   #text(size: 0.8em)[from @cmb_spectrum]
][
  #pause
  #set text(size: 0.8em)
  remove contribution from the BB spectrum:

  _differential brightness temperature_

  $==>$ the actual 21-cm signal

  #image("assets/brighness_temperature.png", fit: "contain")
  from @Schaeffer_2023
]

#pagebreak()



#align(center)[
  #image("assets/evolution_of_dtb.png", height: 85%, fit: "contain")
  #text(size: 0.8em)[from @Pritchard2012]
]

// COMMENTS:



== Expression the 21-cm signal
Expressing the _differential brightness temperature_ (e.g @Pritchard2012):

$
  d T_"b" (bold(x), z) tilde.eq T_0 (z) dot
  #pin(1) x_"HI" (bold(x), z) #pin(2) dot
  (1 + delta_b (bold(x), z)) dot
  (x_alpha (bold(x), z)) / (#pin(3)  1 + x_alpha (bold(x), z) #pin(4) ) dot
  ((1 - T_"CMB" (z)) / (#pin(5) T_"gas" (bold(x), z) #pin(6)))
$ <eq:dTb>

// Explanation
- further modulation by _RSD_


== The current state of simulations


#layouts.contained(
  [
    *Traditional approaches*
    // From first principles
    - need to cover large dynamic range
    // small scales to resolve sources + sinks + feedback
    // large scales to capture statistics
    - hydrodynamics & radiative transfer
    - hard to scale

    $=>$ no reproducibility
    #pause
  ],
  [
    #pad(1em)[
      #align(left)[
        #text(weight: "bold")[semi-numerical approaches]

        such as #beorn @Schaeffer_2023, `21cmFAST` @21cmfast

        // IF ASKED: difference with `21cmFAST`:
        // based on excursion formalistm -> only valid >= 1Mpc, which is ideal for large volumes + statistics => 21-cm forecasts

        $->$ approximative treatment

        $->$ link

        $->$ scalable + efficient

        $=>$ reproducible and flexible
        // interesting to build emulators for instance
      ]

    ]
  ]
)