nearly fully fleshed out now

halo_model.typ

@@ -3,7 +3,7 @@
 
 
 == The halo model of reionization
-Following @Schneider_2021 @schneider2023cosmologicalforecast21cmpower:
+Following @Schneider_2021 @schneider2023cosmologicalforecast21cmpower, the halo model describes (#link(<backup_full_profiles>, "derivation")):
 #line(length: 100%, stroke: color.white.transparentize(100%))
 #pause
 
@@ -16,7 +16,11 @@ $
 $
   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))
 $
-
+// From the xray emission
+// primordial + heating term
+// expansion + deposition by xrays
+// => xrays are assumed to be the only source of heating
+//
 #pause
 $
   derivative(V_b, t) = dot(N)_"ion"(t) / overline(n)_H^0 - alpha_B dot C / a^3 dot overline(n)_H^0 dot V_b
@@ -26,8 +30,15 @@ $
 // $
 
 #pagebreak()
+Visually:
 
+#image("assets/profiles.png")
+// COMMENTS:
+// - contribution from the lyman lines
+// - 1/r^2 decrease from spreading photons
+// - more steep outwards + sharp drop due to redshifting out of line
 
+#pagebreak()
 
 
 == Revisiting the 21cm signal