#import "globals.typ": *


= Halo growth

== Motivation
#layouts.contained(
  [
    Crucial dependence on the *star formation rate*

    - assumed to be directly linked to halo growth rate $dot(M)$:
    $
      dot(M)_star = f_star (M_"h") dot dot(M_"h")

    $
    - growth according to the exponential model:
    $
      M_"h" (z) = M_"h" (z_0) dot exp[-alpha (z - z_0)]
    $
    with $alpha = dot(M_"h")/M_"h"$ the _specific growth rate_
    #pause
  ],
  [
    $->$ inaccurate when applied to all halos

    $->$ #text(weight: "bold")[inconsistent] with the N-body output

    #pause
    $->$ how to implement #text(weight: "bold")[consistent] growth?
  ]
)


== Effect on the flux profiles
#let notebook = json("../workdir/11_visualization/alpha_dependence_of_profiles.ipynb")

#image_cell(notebook, cell_id: "profile_plot_alpha_dependence")

$M_"h" = 6.08 dot 10^11 M_dot.circle$ (fixed)

$==>$ correction up to $times 5$

// COMMENTS
// That will be directly affect the global signal as well
// shifting
//
// Yu-Siu already investigated the more nuanced effect of stochasticity but the approach we propose should supersede that

#pagebreak()

== Inferring growth from #smallcaps[Thesan] data
- already includes precomputed merger trees @Springel2005
// ideal for rapid iterations

- follow main progenitor branch back in time

- fit the exponential model to main progrenitor branch
// in a parallelized fashion => want to stay fast
// fix the original mass for max. consistency
// fix the allowed dynamic range

- use *individual growth* to select profile
// this sort of "breaks the degeneracy" between halos of the same mass but different growth histories

- *self-consistent*#pause$*$#meanwhile treatment of halo growth leveraging the snapshots


#pagebreak()

#let notebook = json("../workdir/11_visualization/show_trees.ipynb")
#[
  #set image(width: 100%, fit: "contain")
  #image_cell(notebook, cell_id: "merger_tree_and_fitting")
]
// COMMENTS:
// no clear trend between mass and growth rate