starting to take shape

halo_model.typ

@@ -0,0 +1,52 @@
+#import "globals.typ": *
+
+
+
+== The halo model of reionization
+Following @Schneider_2021 @schneider2023cosmologicalforecast21cmpower:
+#line(length: 100%, stroke: color.white.transparentize(100%))
+#pause
+
+$
+  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)
+$
+
+#pause
+
+$
+  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))
+$
+
+#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
+$
+// $
+//   x_("HII")(r bar M, z) = theta_"H" lr([R_b (M, z) - r], size: #150%)
+// $
+
+#pagebreak()
+
+
+
+
+== Revisiting the 21cm signal
+$
+  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>
+
+#pause
+// #pinit-highlight(1, 20)
+#pinit-point-from((1, 2))[from $x_"HII"$]
+#pause
+
+#pinit-point-from((3, 4))[From $rho_alpha$]
+#pause
+
+#pinit-point-from((5, 6))[From $rho_"h"$]
+
+#pagebreak()