fleshed out the introductory sections

procedure.typ

@@ -1,6 +1,73 @@
-= Overview of the BEoRN simulation procedure
-This section describes the full procedure for a single simulation run of the BEoRN simulation suite, as well as the necessary adaptations to reflect the refined underlying model.
+#import "importer/main.typ": *
+#import "helpers.typ": *
+#import "@preview/physica:0.9.5": *
+
+= Overview of the #beorn framework <procedure>
+
+This section describes the procedure for a full simulation run of the #beorn simulation suite, including the underlying modelling of the radiation sources. The code of #beorn as well as usage instructions are publicly available under #link("https://github.com/cosmic-reionization/BEoRN", "https://github.com/cosmic-reionization/BEoRN")#footnote[
+  For an explicit overview of the changes referenced here, please refer to #link("https://github.com/moll-re/BEoRN")
+].
+
+
+
+== The halo mass model of reionization <hmreio>
+
+The central action
+// don't like that word
+performed by #beorn is the parametrization of sources of ionizing radiation through the properties of their host dark matter halos. This approach is based on the model presented by @schneider2023cosmologicalforecast21cmpower and gives a description
+// bad word
+of the $21 "cm"$ signal through the treatment of flux profiles around sources. Using these overlying profiles allows to efficiently compute the ionization state of the intergalactic medium (IGM) without the need for computationally expensive radiative transfer simulations.
+
+The model assumes that the radiation sources are hosted by dark matter halos and expresses the star formation and radiation properties as a function of the halo mass $M_"h"$ and mass accretion rate $dot(M_"h")$. The modelling of the halo mass evolution is subject to a detailed discussion in section @halo_mass_history, for the purpose of the model an arbitrary halo mass accretion history $M_"h" (z)$ is assumed to be known.
+
+star formation rate
+$
+  dot(M)_star = f_star (M_"h") dot dot(M_"h")
+$ <eq:star_formation_rate>
+The star formation efficiency $f_star$ is explained by @Schaeffer_2023
+
+
+=== Expression of the profiles
+$
+  derivative(V, t) = dot(N)_"ion"(t) / overline(n)_H^0 - alpha_B dot C / a^3 dot overline(n)_H^0 dot V
+$
+
+Lyman-alpha photons induce a coupling between the spin temperature and the kinetic temperature of the gas. This effect, known as the Wouthuysen-Field effect
+#cite(<Wouthuysen>, form: "normal")
+#cite(<Field>, form: "normal")
+causes absorption of $21 "cm"$ photons before reionization. This is reflected in the absorption expected in the global signal before reionization.
+$
+  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)
+$
+
+
+
+The temperature around the sources is described
+// bad word
+by the cooling temperature of the adiabatically expanding universe and the heating due to X-ray photons emitted by the newly formed stars. The temperature profile follows
+
+$
+  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))
+$
+which is based on ????
+
+
+
+Ionizing photons, i.e. photons with energies above $13.6 "eV"$ experience a large optical depth which justifies the expression
+$
+x_("HII")(r bar M, z) = theta_"H" (R_b (M, z) - r) = theta_"H" (root(3, 3/ (4pi) V(M,z))
+ -r )
+$
+
+// introduced inaccuracies
+// e.g. papers like "2309...." suggest a revised halo mass growth.
+// e.g. bursty star formation as presented by Romain Teyssier
 
 == Simulation steps
 
-The code of BEoRN as well as a comprehensive documentation are publicly available under #link("https://github.com/cosmic-reionization/BEoRN", "https://github.com/cosmic-reionization/BEoRN").
+=== Halo catalog - n body simulations
+
+=== Computation of radiation profiles
+
+=== Optimized painting with the parallel+binned approach
+