with compiled pdf

.gitignore

@@ -1,3 +1,7 @@
 *.pdf
 # but keep the pdfs in the "assets" folder
 !assets/*
+
+# finally - allow the main.pdf to be commited for completeness
+!main.pdf
+

conclusion.typ

@@ -11,7 +11,7 @@ It uses flux profiles to express the emission of radiation by sources in terms o
 
 We have presented an extension to #beorn that improves the physical accuracy by implementing a more consistent growth of galaxies based on the individual mass accretion histories of their host dark matter halo. We use the fact that the input data from the underlying #nbody simulation already includes constraints on the growth from the halo properties at different snapshots. Disregarding this information and instead assuming a fixed accretion rate for all halos is an oversimplification. The proof-of-concept implementation presented here leverages the halo history encoded in the merger trees of the #thesan simulation. More broadly, the updated framework is now better suited to incorporate more detailed growth simulations and can be easily extended to other simulations. We also refactored the simulation procedure and achieved a faster execution time by a factor of two. This further enhances the usability of #beorn for large parameter studies.
 
-After validating the new procedure we have shown that the consistent modeling of halo growth produces simulation outputs which have distinct features compared to simpler models. We compared map outputs direcly and also analyzed global quantities and their derived signal. The results are sensitive to the distribution of accretion rates, highlighting the importance of careful modeling of the halo growth.
+After validating the new procedure we have shown that the consistent modeling of halo growth produces simulation outputs which have distinct features compared to simpler models. We compared map outputs directly and also analyzed global quantities and their derived signal. The results are sensitive to the distribution of accretion rates, highlighting the importance of careful modeling of the halo growth.
 
 
 Works going beyond this proof-of-concept implementation should utilize more sophisticated history tracking that ensures the consistency of halo properties across mutlitple timesteps (e.g. the `rockstar` halo finder by @Behroozi_2012). We also highlighted the limitations incurred by the coarse mass resolution of the #thesan simulation, which is why subsequent research should be based on higher resolution simulations in order to benefit from accurate accretion rate matching down to the lowest halo masses.

halo_mass_history.typ

@@ -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.

implementation.typ

@@ -9,8 +9,7 @@ For each halo we require a flux profile that matches the halo properties which n
 // Maybe reformulate
 Since the dynamic range of accretion rates is large, the resulting parameter space rapidly expands. The computation of the profiles therefore utilizes vectorized operations to achieve reasonable runtimes.
 
-// TODO - reformulate
+Note that the precomputation of the profiles introduces another "second degree" inconsistency: The flux profile attributes a radiative behavior to the halo that is motivated by its history. This is repeated for each snapshot creating possibly conflicting histories. In the case of stable halo growth this is not a problem but in the case of erratic growth (e.g. major mergers) this can lead to unphysical behavior. A more consistent approach would be to assume a more flexible mass growth model that distinguishes different regimes of growth. This would require a much more complex handling of the precomputed profiles and is beyond the scope of this work. The current approach remains a good approximation for the majority of halos.
-Note that this introduces another "second degree" inconsistency: The flux profile attributes a radiative behavior to the halo that is motivated by its history. This is repeated for each snapshot creating possibly conflicting histories. In the case of stable halo growth this is not a problem but in the case of erratic growth (e.g. major mergers) this can lead to unphysical behavior. A more consistent approach would be to assume a more flexible mass growth model that distinguishes different regimes of growth. This would require a much more complex handling of the precomputed profiles and is beyond the scope of this work. The current approach remains a good approximation for the majority of halos.
 
 
 == Parallel painting of profile bins
@@ -40,4 +39,4 @@ In addition to the changes directly linked to the new accretion model we impleme
 We improve the input/output handling by implementing proper `HDF5` support and caching of intermediate results. This allows for a more efficient usage of disk space and faster loading times. It also enables the resumption of interrupted simulations.
 The import of data from the original #nbody simulation has been generalized to a reference class to ensure modularity and easy adaptation to other simulations. This has been part of a larger overhaul of the codebase to improve modularity and readability. #beorn aims to be a flexible framework that produces fast results that the end user can customize to reflect their parameter choices. Usability is therefore a key aspect of the code design.
 
-A general speedup from the cumulated effect of the above changes and code optimizations results in a faster painting procedure. A contribution to that speedup comes from the usage of `Pylians` by @Pylians. It provides efficient implementations of the grid mapping of the individual particles. This additionally allows for a rigorous implementation of redshift space distortions (RSD) by utilizing the exact velocity information of each dark matter particle individually. Previous implementations of RSD in #beorn were based on approximations of the velocity field derived from the density field. The impact of RSD on the 21-cm signal has been discussed e.g. by @Ross_2021 but is not the focus of this work.
+A general speedup from the cumulated effect of the above changes and code optimizations results in a faster painting procedure. A contribution to that speedup comes from the usage of the `pylians` package by @Pylians. It provides efficient implementations of the grid mapping of the individual particles. This additionally allows for a rigorous implementation of redshift space distortions (RSD) by utilizing the exact velocity information of each dark matter particle individually. Previous implementations of RSD in #beorn were based on approximations of the velocity field derived from the density field. The impact of RSD on the 21-cm signal has been discussed e.g. by @Ross_2021 but is not the focus of this work.

introduction.typ

@@ -1,7 +1,7 @@
 #import "helpers.typ": *
 = Introduction
 
-The earliest cosmological events such as the formation of the first astrophysical objects, e.g. stars, galaxies, black holes, have a profound influence on the evolution of the universe. Though poorly understood, these events have shaped the characteristics of our current universe, including the structure and distribution of matter itself.
+The formation of the earliest astrophysical objects, such as stars, galaxies, and black holes, have a profound influence on the evolution of the universe. Though poorly understood, these events have shaped the characteristics of our current universe, including the structure and distribution of matter itself.
 // Citation about an overview paper on ionization vs structure formation.
 Despite the milestones achieved in observational cosmology, many aspects of the early universe and its dark ages remain difficult to probe. While traditional measurements provide insights into relatively recent epochs, and the cosmic microwave background (CMB) serves as an early snapshot of the universe, the dark ages are incompatible with direct observations. They represent a critical link between the late-time universe and the primordial conditions that has remained largely unexplored.
 
@@ -21,7 +21,7 @@ The dark ages of the universe refer to the period after recombination where the
 The formation of the first stars marks the end of the dark ages. These so-called population III stars have zero metallicity and very distinct characteristics compared to later generations of stars. Their existence has not been confirmed observationally but they are thought to have shaped the subsequent formation of stars and galaxies and to have played a crucial role in the reionization of the universe (e.g. @Mebane_2020).
 
 // Paragraph talking about the evolution of the IGM and the formation of ionized bubbles around sources.
-Driven by the newly formed stars and galaxies, reionization is explained as an inside-out process expanding from within the halos that host the first galaxies. The ionizing radiation emitted by these sources reaches the intergalactic medium (IGM), creating ionized bubbles that grow and eventually overlap.
+Driven by the newly formed stars and galaxies, reionization is explained as an inside-out process (e.g. @10.1111-j.1365-2966.2006.10502.x) expanding from within the halos that host the first galaxies. The ionizing radiation emitted by these sources reaches the intergalactic medium (IGM) and creates ionized bubbles that grow and eventually overlap to fully ionize the universe again.
 
 While reionization marks the gradual disappearance of neutral hydrogen, the preceeding abundance during the dark ages and cosmic dawn allows for an additional mode of observation: the 21-cm line. Due to the hyperfine transition of neutral hydrogen there is a characteristic emission or absorption of photons at a frequency of $1420 "MHz"$. The strength of this signal depends on the local conditions, encoded by the spin temperature. The redshifting of the photons allows to probe different epochs through the observed frequency.
 
@@ -30,9 +30,9 @@ Square Kilometer Array #cite(<SKAlow>, form: "normal", supplement: "SKA")
 or the Hydrogen Epoch of Reionization Array #cite(<HERA>, form: "normal", supplement: "HERA")
 . These instruments are expected to detect the power spectrum of the 21-cm signal, providing further insights into the dynamics of the early universe. In particular the low-frequency component SKA-Low is expected to have the sensitivity to image the 21-cm signal directly and to produce maps of the ionization field during the EOR.
 
-Beyond observations, an additional pillar of understanding the EOR is the modeling and simulation of the universe during that time. The main purpose of simulations is to constrain these EOR observables. Combined with the first observations, simulations will generate a wealth of information about the early universe at a range of redshifts that has previously been inaccessible. With the highest sensitivity and resolution forecasted for these observations, the simulations must be able to capture the full dynamic range of the interactions from the small-scale physics of star formation and feedback to the large-scale structure of the universe.
+Beyond observations, an additional pillar of understanding the EOR is the modeling and simulation of the universe during that time. The main purpose of simulations is to constrain the EOR observables. Combined with the first observations, simulations will generate a wealth of information about the early universe at a range of redshifts that has previously been inaccessible. With the highest sensitivity and resolution forecasted for these observations, the simulations must be able to capture the full dynamic range of the interactions from the small-scale physics of star formation and feedback to the large-scale structure of the universe.
 
-State of the art simulations need to implement a range of physical processes, including gravitational interactions, hydrodynamics, radiative transfer, and feedback mechanisms. Prominent examples include for instance the #thesan simulations
+State-of-the-art simulations need to implement a range of physical processes, including gravitational interactions, hydrodynamics, radiative transfer, and feedback mechanisms. Prominent examples include for instance the #thesan simulations
 #cite(<Kannan_2021>, form: "normal")
 #cite(<Garaldi_2022>, form: "normal")
 #cite(<Smith_2022>, form: "normal")
@@ -42,11 +42,10 @@ Another approach is to use ray-tracing algorithms which give detailed descriptio
 These simulations are computationally expensive and cannot be used to to repeatedly explore the parameter space of reionization.
 
 
-
+This work presents #beorn, the _Bubbles during the Epoch of Reionization Numerical simulator_ by @Schaeffer_2023. In its simplest description #beorn is the implementation of the "halo model of reionization" by @schneider2023cosmologicalforecast21cmpower. In this model the radiative interactions are described through spherically symmetric profiles around sources embedded in dark matter halos. This effectively reduces the dimensionality of the radiative transfer problem. #beorn uses the one-dimensional (1-d) profiles generated by this model to paint the 3-d space around halos which are obtained from a large-scale #nbody simulation. A distinguishing feature of #beorn is the self-consistent treatment of the expansion of the affected regions around the sources. This approach allows for simulations at the largest scales while still taking into account the core processes of reionization. The computational efficiency of #beorn makes it suitable to explore the underlying parameters.
-This work presents #beorn, the _Bubbles during the Epoch of Reionization Numerical simulator_ by @Schaeffer_2023. In its simplest description #beorn is the implementation of the "halo model of reionization" by @schneider2023cosmologicalforecast21cmpower. In this model the radiative interactions are treated as spherically symmetric around a halo-scale source. This effectively reduces the dimensionality of the radiative transfer problem. #beorn uses the one-dimensional (1-d) profiles generated by this model to paint the 3-d space around dark matter halos which are obtained from a large-scale #nbody simulation. A distinguishing feature of #beorn is the self-consistent treatment of the expansion of the affected regions around the sources. This approach allows for simulations at the largest scales while still taking into account the core processes of reionization. The computational efficiency of #beorn makes it suitable to explore the underlying parameters.
 
 // growth of individual sources over the course of the simulation.
-The first iteration of #beorn focused on the impact of parameters related to the emission of photons whereas this work focuses on the effects of gravitational mass accretion. We show that the radiation profiles are sensitive to the growth rate and that the mass accretion history provdied by #nbody simulations is too complex to be captured by simple parametrizations. Our improved version of #beorn permits a more consistent treatment by considering the individual mass accretion history of each source. We demonstrate the effect on the 21-cm observables when compared to the simpler models.
+The first iteration of #beorn focused on the impact of parameters related to the emission of photons whereas this work focuses on the effects of gravitational mass accretion. We show that the radiation profiles are sensitive to the growth rate and that the mass accretion history provdied by #nbody simulations is too complex to be captured by simple parametrizations. Our improved version of #beorn permits a more consistent treatment by considering the individual mass accretion history of each source. We demonstrate the resulting measurable effects on the 21-cm observables when compared to the simpler models.
 
 This report is structured as follows: @procedure describes the details of the simulation procedure, including the underlying model. @halo_mass_history explains how mass evolution is modeled and its impact on the flux profiles used by #beorn.
 In @implementation we give an overview of the implementation and changes required by the refined modeling.

procedure.typ

@@ -13,7 +13,7 @@ This section presents the model describing the sources of radiation that drive r
 
 The distinguishing feature
 // don't like that word
-of #beorn is the parametrization of sources of radiation through the properties of their host dark matter halos. This approach is based on the model presented by @schneider2023cosmologicalforecast21cmpower and gives a description
+of #beorn is the parametrization of sources of radiation through the properties of their host dark matter halo. 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 profiles and allowing them to overlap enables efficient computations of the ionization state of the IGM without the need for detailed radiative transfer simulations. The following description follows the derivation made by @schneider2023cosmologicalforecast21cmpower @Schneider_2021 and we refer to these works for components that are not defined here.
 
@@ -35,7 +35,7 @@ with $M_"p"$ the pivot mass where the efficiency peaks, and $gamma_1$, $gamma_2$
 
 === Expression of the profiles
 Derived from the star formation rate the halo model predicts the production and distribution of photons in three distinct energy bands:
-Lyman-$alpha$ photons, ionizing UV photons, and X-ray photons. Each of these bands has a different effect on the IGM and is treated separately.
+Lyman-$alpha$ photons, x-ray photons, and ionizing UV photons. Each of these bands has a different effect on the IGM and is treated separately.
 // Not really sure that's true
 ==== Lyman-$alpha$ flux profile
 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
@@ -69,7 +69,7 @@ The comoving ionized volume around a source of ionizing photons satisfies the di
 $
   derivative(V, t) = dot(N)_"ion"(t) / overline(n)_H^0 - alpha_B dot C / a^3 dot overline(n)_H^0 dot V
 $
-where $alpha_B$ is the recombination coefficient, $C$ is the clumping factor, $a$ is the scale factor, and $overline(n)_H^0$ is the mean density of hydrogen.
+where $alpha_B$ is the recombination coefficient, $C$ is the clumping factor, $a$ is the scale factor, and $overline(n)_H^0$ is the mean density of hydrogen. We expressed this volume in terms of $dot(N)_"ion"$ the rate of change of the total number of ionizing photons per baryon. This description is not dependent on the frequency since we simply consider the contribution of all photons above the ionization threshold.
 
 Ionizing photons, i.e. photons with energies above $13.6 "eV"$, experience a large optical depth, which justifies the sharp cutoff of the ionization profile at the bubble radius $R_b = root(3, 3/ (4pi) V(M,z))$. The radial dependence of the ionized fraction is expressed through the Heaviside step function $theta_"H"$ and reads
 $
@@ -80,14 +80,14 @@ $
 
 The above profiles express the local effect of radiation around a single halo as a 1-d simplification. A representation of a typical profile can be seen in @fig:alpha_evolution_vs_redshift. Using an estimate of the spatial distribution of halos, these profiles can be applied to generate a full 3-d map if we assume spherical symmetry.
 
-The observable signal of the 21-cm line is obtained from a combination of the mapped quantities. It is expressed as the differential brightness temperature $d T_"b"$ which describes the contrast between the foreground and the CMB background.
+The observable signal of the 21-cm line is now a spatially dependent quantity obtained from a combination of the mapped quantities. It is expressed as the differential brightness temperature $d T_"b"$ which describes the contrast between the foreground and the background radiation emitted by the CMB.
 // might want to rephrase that
 Following e.g. @Pritchard2012 an expression for $d T_"b"$ is given by
 $
   d T_"b" (bold(x), z) tilde.eq T_0 (z) dot x_"HI" (bold(x), z)  dot (1 + delta_b (bold(x), z)) dot (x_alpha (bold(x), z)) / (1 + x_alpha (bold(x), z) ) dot ((1 - T_"CMB" (z)) / (T_"gas" (bold(x), z)))
 $ <eq:dTb>
 // where $T_0 (z) = 27 "mK" sqrt((1 + z)/10 (0.15 / (Omega_m h^2))) (Omega_b h^2 / 0.023)$, $x_"HI"$ is the neutral hydrogen fraction, $delta_b$ is the baryonic overdensity, $x_alpha$ is the coupling coefficient introduced by the Wouthuysen-Field effect, $T_"CMB"$ is the temperature of the CMB, and $T_"gas"$ is the kinetic temperature of the gas. The expression assumes that the spin temperature is closely coupled to the kinetic temperature which is valid in most regimes of interest during reionization.
-where the background radiation originates from the CMB. The above considerations give us the values of $x_"HI"$, $x_alpha$, and $T_"gas"$. The baryonic overdensity $delta_b$ is assumed to trace the dark matter overdensity $delta_"dm"$ which is obtained from the underlying #nbody simulation. The amplitude of the signal is given by
+where the background radiation originates from the CMB. The previous considerations allow us to infer the values of $x_"HI"$, $x_alpha$, and $T_"gas"$ from $x_"HII"$, $rho_alpha$, and $rho_h$ respectively. The baryonic overdensity $delta_b$ is assumed to trace the dark matter overdensity $delta_"dm"$ which is obtained from the underlying #nbody simulation. The amplitude of the signal is given by
 $
   T_0 (z) = 27 dot (Omega_b h^2) / 0.023 dot sqrt((1 + z)/10 0.15 / (Omega_m h^2)) "mK"
 $
@@ -112,10 +112,11 @@ In accordance with the astrophysical parameters set by the user, radiation profi
 The last step consists of applying the ionization and temperature distributions defined by the profiles onto a 3-d grid. This is done by iterating over the halos in the catalog and using their corresponding profile. For a given profile a 3-d kernel is generated and mapped onto the grid via convolution using the fast fourier transform implemented by the `astropy` #cite(<astropy:2022>, form: "normal") package. We refer to this procedure as "painting" since the addition of the contributions of each halo allows us to sequentially build up the final map. In general, contributions from multiple halos can overlap without any restrictions. The ionization map is treated specially: In order to conserve the overall number of ionizing photons, we ensure that each cell is only ionized once.
 // If multiple halos contribute to the ionization of a cell, the excess photons are redistributed to neighboring cells until they are either used up or reach the edge of the simulation box.
 
+This final step ensures consistent painting: While the contributions to the temperature and coupling maps can be simply added, the ionization map requires a binary treatment. Cells cannot be ionized past a value of $x_"HII" = 1$. Discarding the excesses would violate photon conservation. A redistribution of the excess photons to neighboring cells is performed to ensure that the total number of ionizations matches the total number of emitted photons.
+
 The usage of precomputed profiles is crucial to the efficiency of the simulation but it introduces a discretization in halo mass since each halo is assigned the profile of the closest mass bin. The effect of this simplification has been shown to converge for a sufficient number of mass bins by @Schaeffer_2023.
 
-One final step is required to ensure consistent painting: While the contributions to the temperature and coupling maps can be simply added, the ionization map requires a binary treatment. Cells cannot be ionized past a value of $x_"HII" = 1$. Discarding the excesses would violate photon conservation. A redistribution of the excess photons to neighboring cells is performed to ensure that the total number of ionizations matches the total number of emitted photons.
 
 
 === Derivation of global quantities
-The global signal as well as the power spectrum are derived from the map data and compared to other models or observations. Being derived from a full 3-d #nbody simulation, the results are sensitive to the underlying cosmology and the detailed profile modeling. This means that the results depend on the underlying astrophysical model.
+The global signal as well as the power spectrum are derived from the map data to be compared to other models or observations. Being derived from a full 3-d #nbody simulation, the results are sensitive to the underlying cosmology and the detailed profile modeling. This means that the results also depend on the underlying astrophysical model.

references.bib

@@ -74,7 +74,7 @@
 archivePrefix = {arXiv},
        eprint = {astro-ph/0504097},
  primaryClass = {astro-ph},
-       adsurl = {https://ui.adsabs.harvard.edu/abs/2005Natur.435..629S},
+       url = {https://ui.adsabs.harvard.edu/abs/2005Natur.435..629S},
       adsnote = {Provided by the SAO/NASA Astrophysics Data System}
 }
 
@@ -415,3 +415,25 @@ archivePrefix = {arXiv},
        url = {https://ui.adsabs.harvard.edu/abs/2022ApJ...935..167A},
       adsnote = {Provided by the SAO/NASA Astrophysics Data System}
 }
+
+
+
+# evidence for inside out reionization
+@article{10.1111-j.1365-2966.2006.10502.x,
+    author = {Iliev, I. T. and Mellema, G. and Pen, U.-L. and Merz, H. and Shapiro, P. R. and Alvarez, M. A.},
+    title = {Simulating cosmic reionization at large scales – I. The geometry of reionization},
+    journal = {Monthly Notices of the Royal Astronomical Society},
+    volume = {369},
+    number = {4},
+    pages = {1625-1638},
+    year = {2006},
+    month = {07},
+    abstract = {We present the first large-scale radiative transfer simulations of cosmic reionization, in a simulation volume of (100 h−1 Mpc)3. This is more than a two orders of magnitude improvement over previous simulations. We achieve this by combining the results from extremely large, cosmological, N-body simulations with a new, fast and efficient code for 3D radiative transfer, c2-ray, which we have recently developed. These simulations allow us to do the first numerical studies of the large-scale structure of reionization which at the same time, and crucially, properly take account of the dwarf galaxy ionizing sources which are primarily responsible for reionization. In our realization, reionization starts around z∼ 21, and final overlap occurs by z∼ 11. The resulting electron-scattering optical depth is in good agreement with the first-year Wilkinson Microwave Anisotropy Probe (WMAP) polarization data. We show that reionization clearly proceeded in an inside-out fashion, with the high-density regions being ionized earlier, on average, than the voids. Ionization histories of smaller-size (5–10 comoving Mpc) subregions exabit a large scatter about the mean and do not describe the global reionization history well. This is true even when these subregions are at the mean density of the universe, which shows that small-box simulations of reionization have little predictive power for the evolution of the mean ionized fraction. The minimum reliable volume size for such predictions is ∼30 Mpc. We derive the power spectra of the neutral, ionized and total gas density fields and show that there is a significant boost of the density fluctuations in both the neutral and the ionized components relative to the total at arcmin and larger scales. We find two populations of H ii regions according to their size, numerous, mid-sized (∼10-Mpc) regions and a few, rare, very large regions tens of Mpc in size. Thus, local overlap on fairly large scales of tens of Mpc is reached by z∼ 13, when our volume is only about 50 per cent ionized, and well before the global overlap. We derive the statistical distributions of the ionized fraction and ionized gas density at various scales and for the first time show that both distributions are clearly non-Gaussian. All these quantities are critical for predicting and interpreting the observational signals from reionization from a variety of observations like 21-cm emission, Lyα emitter statistics, Gunn–Peterson optical depth and small-scale cosmic microwave background secondary anisotropies due to patchy reionization.},
+    issn = {0035-8711},
+    doi = {10.1111/j.1365-2966.2006.10502.x},
+    url = {https://doi.org/10.1111/j.1365-2966.2006.10502.x},
+    eprint = {https://academic.oup.com/mnras/article-pdf/369/4/1625/3799304/mnras0369-1625.pdf},
+}
+
+
+

results.typ

@@ -65,7 +65,7 @@ The maps resemble each other closely and we focus on the residual maps
 // rename?
 that highlight specific deviations produced when changing the accretion model. They show that fixing the mean accretion rate is not sufficient to fully represent the complex reionization behavior.
 
-The coupling coefficient map sees a increase in all regions which is explained by the stronger emission of Lyman-$alpha$ photons at these late stages. At the considered redshift, the mean model uses $alpha approx 0.51$. Regions where this reversal has not occured are in theory possible but don't seem to appear with this particular halo population.
+The coupling coefficient map sees an increase in all regions which is explained by the stronger emission of Lyman-$alpha$ photons at these late stages. At the considered redshift, the mean model uses $alpha approx 0.51$. Regions where this reversal has not occured are in theory possible but don't seem to appear with this particular halo population.
 
 As before, the kinetic temperature maps reflect the observation made for the signals. Most regions are colder than in the fiducial case due to the lower heating by fewer stars. The halos lag behind but some high accretion halos seem to catch up already, they practically vanish in the residual map.
 These differences are only visible because the mean model fails to capture this diversity of halo histories.

validation.typ

@@ -19,7 +19,7 @@ We perform several validation tests to ensure the accuracy and reliability of ou
 
 ) <fig:validation_signal_comparison_old_v_new>
 
-We ensure the consistency of the updated #beorn code with previous versions by running a series of simulations under identical conditions. We compare key outputs starting from the profiles of individual sources, to the ionization maps, and finally to the global reionization signals. This step-by-step comparison allows us to identify any discrepancy that may arise from the code changes. In @fig:validation_signal_comparison_old_v_new we present a comparison of the central observables of reionization between the previous and current versions of #beorn. The underlying simulation parameters are kept identical or updated to an equivalent setting where necessary. The results show an essentially unchanged evolution of the global brightness temperature, kinetic temperature, and ionization fraction. Note that this run uses an artifical halo catalog and an unphysically high star formation efficiency to ensure a rapid reionization within the simulation range. As such this setup is not representative of a realistic reionization scenario.
+We ensure the consistency of the updated #beorn code with previous versions by running a series of simulations under identical conditions. We compare key outputs starting from the profiles of individual sources, to the ionization maps, and finally to the global reionization signals. This step-by-step comparison allows us to identify any discrepancy that may arise from the code changes. In @fig:validation_signal_comparison_old_v_new we present a comparison of the central observables of reionization between the previous and current versions of #beorn. The underlying simulation parameters are kept identical or updated to an equivalent setting where necessary. The results show an essentially unchanged evolution of the global brightness temperature, kinetic temperature, and ionization fraction. The small changes in timing are attributed to the slightly shifted mass bins of the updated procedure. Note that this run uses an artifical halo catalog and an unphysically high star formation efficiency to ensure a rapid reionization within the simulation range. As such this setup is not representative of a realistic reionization scenario.
 
 Similarly we maintain backward compatibility with the input format used in previous #beorn runs (i.e. snapshots generated by #pkdgrav or `21cmfast`). This allows us to reproduce the earlier runs and match the results as described by @Schaeffer_2023.
 
@@ -41,7 +41,7 @@ Similarly we maintain backward compatibility with the input format used in previ
 
 To ensure that our results are not sensitive to the numerical resolution of the simulation, we perform convergence tests. We compare the following variations of resolution: Firstly, we scrutinize the impact of the grid resolution by running simulations with $128^3$ and $256^3$ cells. Secondly, we investigate how changing the mass resolution affects the results by comparing the outputs obtained from the #smallcaps[Thesan-Dark] 1 and 2 simulations, which have different particle masses, as mentioned in @procedure.
 
-@fig:validation_signal_comparison shows that there is no significant difference when using a finer grid resolution. This is expected since the ionized regions rapidly become larger than the cell size. The comparison between the different mass resolutions exhibits a deviation in the timing of reionization. This effect is expected and documented by @Kannan_2021: The lowest mass halos which are not resolved by #thesandark 2 form small bubbles quickly (as early as $z=10$) and contribute to the ionization budget at early times. We account for this by artificially increasing the lower mass cutoff during these validation runs but an imbalance between the two simulations remains. Additionally, the higher particle count per halo seems to enable a more consistent tree finding. The lack of good trees at the earliest snapshots is clearly visible as a dip in the $d T_b$ signal of the #thesandark 2 runs. When the accretion rate cannot be inferred from the tree, a fallback value is used instead. This leads to a systematic shift in the signal that abruptly appears when the fallback value is no longer needed. After observing this effect we tune the fallback value to be in line with the expected accretion rate as shown in @fig:alpha_evolution_vs_redshift. This largely removes the jump in the subsequent runs.
+@fig:validation_signal_comparison shows that there is no significant difference when using a finer grid resolution. This is expected since the ionized regions rapidly become larger than the cell size. The comparison between the different mass resolutions exhibits a deviation in the timing of reionization. This effect is expected and documented by @Kannan_2021: The lowest mass halos which are not resolved by #thesandark 2 form small bubbles quickly (as early as $z=10$) and contribute to the ionization budget at early times. We account for this by artificially increasing the lower mass cutoff during these validation runs but an imbalance between the two simulations remains. Additionally, the higher particle count per halo seems to enable a more consistent tree finding. The lack of good trees at the earliest snapshots is clearly visible as a dip in the $d T_b$ signal of the #thesandark 2 runs. When the accretion rate cannot be inferred from the tree, a fallback value is used instead. This leads to a systematic shift in the signal that abruptly becomes apparent when the fallback value is no longer needed. After observing this effect we tune the fallback value to be in line with the expected accretion rate as shown in @fig:alpha_evolution_vs_redshift. This largely removes the jump in the subsequent runs.
 
 Globally the shapes of the signals are very similar and, apart from the initially delayed cosmic dawn, the power spectra match closely after the discrepancy during the first few snapshots.