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final adjustments before the hand in

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Remy Moll
2025-09-15 11:50:00 +00:00
parent 221bdcda07
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8 changed files with 48 additions and 27 deletions
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halo_mass_history.typ
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@@ -78,7 +78,7 @@ while still allowing us to iterate quickly and test the refined model without ex
Growth of structure in #lambdacdm is hierarchical: Small structures form first and merge to form larger structures. The growth of halos can be represented using merger trees. These tree-like structures describe the halo history in terms of the mergers of its smaller progenitors. A merger tree is constructed by linking halos in consecutive snapshots of the simulation where each halo as a single descendant but potentially multiple progenitors.
// As described in ... THESAN
The main progenitor serves as a tracer of the halo mass history if we assume that the halo mass growth is dominated by mergers.
The main progenitor is the most massive progenitor and serves as a tracer of the halo mass history if we assume that the halo mass growth is dominated by mergers.
// Has this been explicitlyshown somewhere?
Beyond that, we expect the main progenitor to be most representative of the baryonic conditions inside and outside the halo as the merger occurs.
// Might need to reformulate
@@ -100,9 +100,9 @@ The restriction to the main progenitor corresponds to a reduction of the dimensi
) <fig:merger_tree_and_fitting>
We use a linear regression in log-space to obtain estimates of the accretion rate $alpha$ for each halo. This is implemented in a vectorized fashion to allow for efficient processing of the full dataset. For this fit we enforce the current halo mass as a boundary condition. This prevents inconsistent fits where the latest fitted mass deviates from the actual current halo mass. As a visualization of the fitting procedure @fig:merger_tree_and_fitting shows a collection of normalized main progenitor branches starting at $z=10.3$ and looking back over $n=10$ snapshots. After fitting we overlay the estimated exponential growth history for a selection of halos. The right panel shows the distribution of best-fit accretion rates $alpha$ for all halos at $z=10.3$. Even given the relative low mass of the halos we observe a strong clustering of accretion rates around a value of $alpha approx 0.5$. Outliers with significantly deviating values appear nevertheless and are not linked to a specific mass range.
We use a linear regression in log-space to obtain estimates of the accretion rate $alpha$ for each halo. This is implemented in a vectorized fashion to allow for efficient processing of the full dataset. For this fit we enforce the current halo mass as a boundary condition. This prevents inconsistent fits where the latest fitted mass deviates from the actual current halo mass. As a visualization of the fitting procedure @fig:merger_tree_and_fitting shows a collection of normalized main progenitor branches starting at $z=8.29$ and looking back over $n=10$ snapshots. After fitting we overlay the estimated exponential growth history for a selection of halos. The right panel shows the distribution of best-fit accretion rates $alpha$ for all halos at $z=8.29$. Given the relative low mass of the halos we observe a strong clustering of accretion rates around a value of $alpha approx 0.5$. Outliers with significantly deviating values appear nevertheless and are not linked to a specific mass range.
Similarly to the halo mass itself the accretion rate can then be taken into account during the painting procedure by selecting a profile corresponding to the halo mass and accretion rate of each halo. Consequently, the accretion rate is binned as well and the range that is covered during the painting is finite. We leave this as a free parameter to be specified at runtime.
Similarly to the halo mass itself, the accretion rate can then be taken into account during the painting procedure by selecting a profile corresponding to the halo mass and accretion rate of each halo. Consequently, the accretion rate is binned as well and the range that is covered during the painting is finite. We leave this as a free parameter to be specified at runtime.
@@ -118,7 +118,7 @@ Similarly to the halo mass itself the accretion rate can then be taken into acco
In order to obtain a sensible range of $alpha$ values to cover during the painting procedure, we investigate the global result of the fitting procedure. Our method of fitting trades speed and convenience for absolute precision: Not all halos are well represented in the merger tree and no further processing is done beyond the consideration of the tree. Additionally, we need to account for unphysical or incomplete histories due to limitations of the halo finder. We discuss this step in @implementation. For the current investigation we disregard these halos and only consider well-behaved, fully resolved trees. @fig:alpha_evolution_vs_redshift shows how the fitted accretion rate evolves when starting from the different snapshots. We plot the mean and $1 sigma$ standard deviation of the resulting distribution of $alpha$ values. We consider different lookback lengths with the goal of assessing the stability of the fitting procedure.
We observe a clear stabilization of the mean accretion for longer lookbacks. Not only does it make sense to consider longer lookbacks because of their causal connection, but also because it helps to absorb short-term fluctuations most likely introduced by the halo finder. This is especially noticeable in the first few snapshots where the $1 sigma$ uncertainty is significantly higher. This is probably due to the overabundance of low mass halos whose mass history is more erratic and harder to reconstruct.
We observe a clear stabilization of the mean accretion for longer lookbacks. Not only does it make sense to consider longer lookbacks because of their causal connection, but also because it helps to absorb short-term fluctuations most likely introduced by the halo finder. This is especially noticeable in the first few snapshots where mean and $1 sigma$ uncertainty are significantly higher. This is probably due to the overabundance of low mass halos whose mass history is more erratic and harder to reconstruct.
Numerically, the advantage of longer lookbacks is the stabilization of the fit leading to reduced scatter in the resulting distribution. We note that these behaviors stabilize once we consider around $n = 10$ snapshots of lookback. Both the mean and standard deviation follow a stable trend and the mean settles at $alpha approx 0.6$.
We attribute the slight offset of the means to the fact that discarding incomplete trees favors more massive halos at higher lookbacks. These halos are more stable in terms of detection by the halo finder and are expected to have fewer fluctuations.