arXiv subjects

Stefan Gottlöber

Publications and source records attributed to Stefan Gottlöber.

At least 19 recordsLinked to original sources

arXiv2026

HINORA II: Testing the Existence of the Council of Giants in ΛCDM simulations

The discovery of the galaxy ring known as the Council of Giants (CoG) highlights the need to explain such structures in the Local Universe. In the first paper of this series we presented HINORA - a code to locate (ring-like) structures in 3D point sets - and used it to identify the CoG in the most complete observations of the Local Volume. Here, in Part II, we apply the same method to cosmological simulations to quantify the possible existence of such objects in the LCDM model of structure formation. We analyze DM-only simulations with random and constrained initial conditions, selecting regions that reproduce the properties of the Local Group and Volume, respectively. In order to use the same selection criteria as previsouly done for observations, we relate K-band luminosities to halo masses through semi-empirical relations. After confirming that the selected regions from the simulations match the observed mass function and density of the Local Universe, we use HINORA to search for ring-like structures in them. We find that the existence of CoGs in LCDM simulations is a rather unusual phenomenon. The observed CoG represents an anomaly of more than 2.7 sigma from what is expected in the distribution of massive galaxies in LCDM. These results hint that the CoG could either be a rare chance configuration or the imprint of physical processes at intermediate scales that standard DM-only simulations fail to capture.

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arXiv2026

Ginnungagap -- a massively parallel cosmological initial conditions generator

Ginnungagap is a fully parallel (MPI+OpenMP) code designed to generate cosmological initial conditions for simulations involving very large numbers of particles. It operates in several modes, including the creation of initial conditions with either uniform or spatially varying resolution (for "zoom-in" simulations). The initial conditions can be fully random or derived by extending the resolution of existing ones while preserving the large-scale structures. Ginnungagap is open source and modular, consisting of a collection of independent tools that can be used for a variety of tasks. In this paper, we describe the main features of Ginnungagap and present test results for different types of simulations prepared with it.

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arXiv2026

Constraining cosmological simulations with peculiar velocities: a forward-modeling approach

Numerical simulations are a key tool to decipher the dynamics of gravitation. Yet, they fail to spatially reproduce the Universe we observe, limiting comparison between observations and simulations to a statistical level. This is highly problematic for rare, faint or well studied nearby objects that are observed in a single environment. The computational cost of recovering this environment in random simulations is prohibitive. We present Hamlet-PM, a method that enables the constraining of initial conditions for cosmological simulations so as to produce evolved numerical universes that can be directly compared to observations of the Local Universe: constrained simulations. Our method implements the field-level forward modeling of the early-time density field from sparse and noisy measurements of late-time peculiar velocities. The dynamics are integrated with a particle-mesh gravity solver, thus probing the mildly non-linear regime. The code is applied to the Cosmicflows-4 compilation of peculiar velocities up to z < 0.05 (160 Mpc/h). The constrained ICs a re-simulated with a high precision N-body code. A series of one hundred dark-matter only cosmological constrained simulations with a resolution of 512^3 particles in a 500^3 [Mpc/h]3 box is presented. Special attention is given to twelve prominent nearby galaxy clusters, whose simulated counterparts are matched on criteria of mass and separation. We provide a mass estimate constrained by the dynamical environment for each cluster. Field-level forward modeling of the initial conditions produces highly constrained cosmological simulations. Currently, this method already overtakes in quality the pipeline in use in the peculiar-velocity community, although systematic biases still need to be addressed. Furthermore, improving the model is easy thanks to the inherent flexibility of the Bayesian approach.

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arXiv2025

A continuous parameterization of the cosmic web

The intrinsic properties of galaxies are influenced by their environments, underscoring the environment's critical role in galaxy formation and evolution. Traditionally, these environments are categorized into four fixed classifications: knots, filaments, walls, and voids, which collectively describe the complex organization of galaxies within large-scale structures. We propose an alternative description that complements the traditional quadripartite categorization by introducing a continuous framework, allowing for a more nuanced examination of the relationship between the intrinsic properties of galaxies and their environments. This complementary description is applied using one of the most prevalent methodologies: categorization using the eigenvalues of the Hessian matrix extracted from the matter density field. We integrated our findings into a semi-analytical model of galaxy formation, combined with cosmological numerical simulations, to analyze how the intrinsic properties of galaxies are influenced by environmental changes. In our study, we find a continuous distribution of eigenvalue ratios, revealing a clear dependence of galaxy properties on their surrounding environments. This method allowed us to identify critical values at which transitions in the behavior of key astrophysical galaxy properties become evident.

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arXiv2025

Machine Learning the Dark Matter Halo Mass of the Milky Way

Although numerous dynamical techniques have been developed to estimate the total dark matter halo mass of the Milky Way, it remains poorly constrained, with typical systematic uncertainties of 0.3 dex. In this study, we apply a neural network-based approach that achieves high mass precision without several limitations that have affected past approaches; for example, we do not assume dynamical equilibrium, nor do we assume that neighboring galaxies are bound satellites. Additionally, this method works for a broad mass range, including for halos that differ significantly from the Milky Way. Our model relies solely on observable dynamical quantities, such as satellite orbits, distances to larger nearby halos, and the maximum circular velocity of the most massive satellite. In this paper, we measure the halo mass of the Milky Way to be log_10 M_vir / M_Sun = 12.20^{+0.163}_{-0.138}. Future studies in this series will extend this methodology to estimate the dark matter halo mass of M31, and develop new neural networks to infer additional halo properties including concentration, assembly history, and spin axis.

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arXiv2025

Dust-UV offsets in high-redshift galaxies in the Cosmic Dawn III simulation

Recent observations have revealed puzzling spatial disparities between ALMA dust continuum and UV emission as seen by HST and JWST in galaxies at $z=5-7$ (e.g. ALPINE and REBELS surveys), compelling us to propose a physical interpretation of such offsets. We investigate these offsets using the Cosmic Dawn III (CoDa III) simulation, a state-of-the-art fully coupled radiation-hydrodynamics cosmological simulation, which incorporates a dynamical dust model. First of all, we find that our simulated dust masses, while calibrated to match observed ones, yield unrealistically large UV attenuations. In fact, the bright-end galaxy UV Luminosity function is best reproduced using only 7.5\% of the dust content of CoDa III galaxies. With this recalibration, we obtain populations of massive galaxies matching ALPINE and REBELS magnitudes and UV slopes, but with smaller dust masses than observed. In this framework, we also find significant dust-UV offsets in massive, UV-bright galaxies ($\mathrm{M}_\mathrm{DM}> 10^{11.5}$ M$_\odot$, M$_*>10^{10}$ M$_\odot$, M$_{\rm AB1600}<-21.5$), reaching up to $\sim 2$ pkpc for the most massive systems. Our analysis reveals that these offsets primarily result from severe dust extinction in galactic centers rather than a misalignment between dust and stellar mass distributions. At the spatial resolution of CoDa III (1.65 pkpc at z=6), the dust remains in majority well-aligned with the bulk stellar component, and we predict the dust continuum should therefore align well with the stellar rest-frame NIR component, less affected by dust attenuation. This study highlights the importance of dust in shaping the appearance of early galaxies at UV wavelengths, even as early as in the Epoch of Reionization.

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arXiv2025

Variable gravitational potential of Milky Way analogues in HESTIA suite

Investigations of trajectories of various objects orbiting the Milky Way (MW) halo with modern precision, achievable in observations by Gaia, requires sophisticated, non-stationary models of the Galactic potential. In this paper we analyze the evolution of the spherical harmonics expansion of MW analogues potential in constrained simulations of the Local Group (LG) from the HESTIA suite. We find that at distances $r\ge 100$~kpc the non-spherical part of the potential demonstrates a significant impact of the environment: ignoring the mass distribution outside the virial radius of the MW results in $>$20\% errors in the potential quadrupole at these distances. {Account of the environment results in a noticeable change of the angular momenta of objects orbiting MW analogues}. Spherical harmonics vary significantly during the last 6 Gyr. We attribute variations of the potential at $r\ge 30$~kpc to the motions of MW satellites and LG galaxies. We also predict that the non-sphericity of the real MW potential should grow with distance in the range $r_\mathrm{vir}<r<500$~kpc, since all realizations of simulated MW-like objects demonstrate such a trend.

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arXiv2025

Line Intensity Mapping Prediction from the Cosmic Dawn (CoDa) III Simulation for H$α$ from Galaxies and the Intergalactic Medium during the Epoch of Reionization

The evolution of large-scale structure, galaxies and the intergalactic medium (IGM) during the Epoch of Reionization (EoR) can be probed by upcoming Line Intensity Mapping (LIM) experiments, which sample in redshift and direction without needing to resolve individual galaxies. We predict the intensity and sources of hydrogen H$α$ emission, dominated by radiative recombination following ionization by UV from the same massive stars that caused reionization, down to redshift 4.6, using the largest fully-coupled, radiation-hydro simulation of galaxy formation and reionization to date, Cosmic Dawn (CoDa) III. We compute the mean intensity and Voxel Intensity Distribution (VID) vs. redshift, including the relative contributions of galaxies and IGM. This will provide mock data to guide and interpret LIM experiments such as NASA's SPHEREx and proposed Cosmic Dawn Intensity Mapper (CDIM).

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arXiv2025

Hermeian haloes: extreme objects with two interactions in the past

Recent studies based on numerical models of the Local Group predict the existence of field haloes and galaxies that have visited both the Milky Way and M31 in the past, called Hermeian haloes. We extend this analysis beyond the Local Group using two high-resolution dark matter-only N-body simulations from the MultiDark suite. We define Hermeian haloes as field haloes which had close interactions with two other more massive field haloes in the past, called targets. We find that Hermeian haloes are a more extreme example of field haloes with interactions in the past than the well-known backsplash haloes that experienced only one interaction. Compared to backsplashers, Hermeians have more concentrated density profiles and tend to occupy more overdense regions. They also have higher velocities relative to their target haloes and relative to their neighbours within 1~$h^{-1}\; \mathrm{Mpc}$. Hermeian haloes can be found around every halo in the simulation (if the resolution is sufficient) and make up 0.4 to 2.3 per cent of the total number of field haloes (for haloes more massive than $10^{10}\; h^{-1}\;\mathrm{M_{\odot}}$ and $3.3 \times 10^{7}\; h^{-1}\;\mathrm{M_{\odot}}$, respectively), increasing to 10 per cent in overdense regions. They tend to be distributed close to the line connecting their targets, which may help to identify Hermeian haloes in observations. We also identify Local Group analogues in the simulation and find that about one-third (15 out of 49) of them contain Hermeian haloes if the distance between the two main haloes is below 1~$h^{-1} \;\mathrm{Mpc}$.

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arXiv2024

Astraeus X: Indications of a top-heavy initial mass function in highly star-forming galaxies from JWST observations at z>10

The James Webb Space Telescope (JWST) has uncovered an abundance of $z>10$ galaxies bright in the ultraviolet (UV) that has challenged traditional theoretical models at high redshifts. Recently, various new models have emerged to address this discrepancy by refining their description of star formation. Here we investigate whether modifications to the stellar initial mass function (IMF) alone can reproduce the $z>10$ UV luminosity functions (UV LFs) when the star formation rate is used as a proxy for the fraction of massive stars. We incorporate an Evolving IMF into the {\sc astraeus} galaxy evolution and reionisation simulation framework, which becomes increasingly top-heavy as the gas density in a galaxy rises above a given threshold. Our implementation accounts for the IMF's effects on supernova (SN) feedback, metal enrichment, and the UV and ionising emissivities. For this Evolving IMF model, we find that (i) the maximum UV luminosity enhancement is twice as large in massive galaxies ($ΔM_\mathrm{UV}\simeq2.6$) than those where star formation is strongly limited by SN feedback ($ΔM_\mathrm{UV}\simeq1.3$); (ii) it successfully reproduces the observed UV LFs at $z=5-15$; (iii) galaxies with top-heavy IMFs exhibit the highest star formation rates, driven by their location in local density peaks, which facilitates higher gas accretion rates; (iv) the $1σ$ variances in the UV luminosity are only slightly higher compared to when assuming a Salpeter IMF, but the $2σ$ variances are significantly increased by a factor of $1.4-2$ boosting the abundance of UV-bright galaxies at $z>10$; (v) reionisation begins earlier with more extended large ionised regions and fewer smaller ones during its initial stages, though these differences diminish at lower redshifts, leading to a similar end of reionisation at $z\simeq5.6$.}

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arXiv2024

The Thermal Sunyaev-Zel'dovich Effect from the Epoch of Reionization

The thermal Sunyaev-Zel'dovich (tSZ) effect arises from inverse Compton scattering of low energy photons onto thermal electrons, proportional to the integrated electron pressure, and is usually observed from galaxy clusters. However, we can expect that the Epoch of Reionization (EoR) also contributes to this signal, but that contribution has not been previously evaluated. In this work we analyse a suite of fully-coupled radiation-hydrodynamics simulations based on RAMSES-CUDATON to calculate and study the tSZ signal from the Reionization Epoch. We construct lightcones of the electron pressure in the intergalactic medium for $6<z$ to calculate the resulting Compton y-parameters. We vary the box sizes, resolutions and star formation parameters to investigate how these factors affect the tSZ effect. We produce plots of maps and distributions of y, as well as angular temperature power spectra of the tSZ signal obtained from integrating the lightcones constructed for each simulation. We find that the tSZ signal from reionization is generally sub-dominant to the post-reionization one at larger scales ($\ell< 10^4$), but can contribute non-trivially and potentially contaminate the measured signals. At scales probed by current experiments like SPT ($\ell\sim10^3-10^4$), we find that the tSZ signal power spectrum from reionization contributes at roughly a percent level compared to the current templates, with the quadratic Doppler effect contributing an additional $\sim10\%$ to the tSZ signal. At smaller scales the tSZ from reionization peaks and can potentially dominate the total signal and is thus a potentially much more important contribution to take into account in any future, more sensitive experiments.

astro-ph.CO↗

arXiv2024

The impact of an evolving stellar initial mass function on early galaxies and reionisation

Observations with JWST have revealed an unexpected high abundance of bright z>10 galaxy candidates. We explore whether a stellar initial mass function (IMF) that becomes increasingly top-heavy towards higher redshifts and lower gas-phase metallicities results in a higher abundance of bright objects in the early universe and how it affects the evolution of galaxy properties compared to a constant IMF. We incorporate such an evolving IMF into the Astraeus framework that couples galaxy evolution and reionisation in the first billion years. Our implementation accounts for the IMF dependence of supernova feedback, metal enrichment, ionising and ultraviolet radiation emission. We conduct two simulations: one with a Salpeter IMF and one with the evolving IMF. Compared to a constant Salpeter IMF, we find that (i) the higher abundance of massive stars in the evolving IMF results in more light per unit stellar mass, a slower build-up of stellar mass and lower stellar-to-halo mass ratio; (ii) due to the self-similar growth of the underlying dark matter halos, the evolving IMF's star formation main sequence hardly deviates from that of the Salpeter IMF; (iii) the evolving IMF's stellar mass-metallicity relation shifts to higher metallicities while its halo mass-metallicity relation remains unchanged; (iv) the evolving IMF's median dust-to-metal mass ratio is lower due to its stronger SN feedback; (v) the evolving IMF requires lower values of the escape fraction of ionising photons and exhibits a flatter median relation and smaller scatter between the ionising photons emerging from galaxies and the halo mass. Yet, the topology of the ionised regions hardly changes compared to the Salpeter IMF. These results suggest that a top-heavier IMF alone is unlikely to explain the higher abundance of bright z>10 sources, since the lower mass-to-light ratio is counteracted by the stronger stellar feedback.

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arXiv2024

HINORA, a method for detecting ring-like structures in 3D point distributions I: application to the Local Volume Galaxy catalogue

We present a new method - called HINORA (HIgh-NOise RANdom SAmple Consensus) - for the identification of regular structures in 3D point distributions. Motivated by the possible existence of the so called Council of Giants, i.e. a ring of twelve massive galaxies surrounding the Local Group in the Local Sheet with a radius of 3.75 Mpc, we apply HINORA to the Local Volume Galaxy catalogue confirming its existence. When varying the lower limit of K-band luminosity of the galaxy entering the catalogue, we further report on the existence of another ring-like structure in the Local Volume that now contains the Milky Way and M31. However, this newly found structure is dominated by low-mass (satellite) galaxies. While we here simply present the novel method as well as its first application to observational data, follow-up work using numerical simulations of cosmic structure formation shall shed light into the origin of such regular patterns in the galaxy distribution. Further, the method is equally suited to identify similar (or even different) structures in various kinds of astrophysical data (e.g. locating the actual 'baryonic-acoustic oscillation spheres' in galaxy redshift surveys).

astro-ph.CO↗

arXiv2023

The large scale velocity field from the Cosmicflows-4 data

The reconstruction of the large scale velocity field from the grouped Cosmicflows-4 (CF4) database is presented. The lognormal bias of the inferred distances and velocities data is corrected by the Bias Gaussianization correction (BGc) scheme, and the linear density and velocity fields are reconstructed by means of the Wiener filter (WF) and constrained realizations (CRs) algorithm. These tools are tested against a suite of random and constrained Cosmicflows-3-like mock data. The CF4 data consists of 3 main subsamples - the 6dFGS and the SDSS data - and the `others'. The individual contributions of the subsamples have been studied. The quantitative analysis of the velocity field is done mostly by the mean overdensity ($Δ_L(R)$) and the bulk velocity ($V_{\mathrm{bulk}}(R)$) profiles of the velocity field out to $300\, h^{-1}{\rm Mpc}$. The $V_{\mathrm{bulk}}(R)$ and $Δ_{\mathrm L}(R)$ profiles of the CF4 data without its 6dFGS component are consistent with the cosmic variance to within $1σ$. The 6dFGS sample dominates the $V_{\mathrm{bulk}}$ ($Δ_{\mathrm L}$) profile beyond $\sim120\, h^{-1}{\rm Mpc}$, and drives it to roughly a $3.4σ$ ($-1.9σ$) excess (deficiency) relative to the cosmic variance at $R\sim250\ (190)\ \, h^{-1}{\rm Mpc}$. The excess in the amplitude of $V_{\mathrm{bulk}}$ is dominated by its Supergalactic X component, roughly in the direction of the Shapley Concentration. The amplitude and alignment of the inferred velocity field from the CF4 data is at $\sim(2\,-\,3)\,σ$ discrepancy with respect to the $Λ$CDM model. Namely, it is somewhat atypical but yet there is no compelling tension with the model.

astro-ph.CO↗

arXiv2023

Astraeus VIII: A new framework for Lyman-$α$ emitters applied to different reionisation scenarios

We use the {\sc astraeus} framework to investigate how the visibility and spatial distribution of Lyman-$α$ (Ly$α$) emitters (LAEs) during reionisation is sensitive to a halo mass-dependent fraction of ionising radiation escaping from the galactic environment ($f_\mathrm{esc}$) and the ionisation topology. To this end, we consider the two physically plausible bracketing scenarios of $f_\mathrm{esc}$ increasing and decreasing with rising halo mass. We derive the corresponding observed Ly$α$ luminosities of galaxies for three different analytic Ly$α$ line profiles and associated Ly$α$ escape fraction ($f_\mathrm{esc}^\mathrm{Lyα}$) models: importantly, we introduce two novel analytic Ly$α$ line profile models that describe the surrounding interstellar medium (ISM) as dusty gas clumps. They are based on parameterising results from radiative transfer simulations, with one of them relating $f_\mathrm{esc}^\mathrm{Lyα}$ to $f_\mathrm{esc}$ by assuming the ISM of being interspersed with low-density tunnels. Our key findings are: (i) for dusty gas clumps, the Ly$α$ line profile develops from a central to double peak profile as a galaxy's halo mass increases; (ii) LAEs are galaxies with $M_h\gtrsim10^{10}M_\odot$ located in overdense and highly ionised regions; (iii) for this reason, the spatial distribution of LAEs is primarily sensitive to the global ionisation fraction and only weakly in second-order to the ionisation topology or a halo mass-dependent $f_\mathrm{esc}$; (iv) furthermore, as the observed Ly$α$ luminosity functions reflect the Ly$α$ emission from more massive galaxies, there is a degeneracy between the $f_\mathrm{esc}$-dependent intrinsic Ly$α$ luminosity and the Ly$α$ attenuation by dust in the ISM if $f_\mathrm{esc}$ does not exceed $\sim50\%$.

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arXiv2023

On the general nature of 21cm-Lyman-$α$ emitters cross-correlations during reionisation

We explore how the characteristics of the cross-correlation functions between the 21cm emission from the spin-flip transition of neutral hydrogen (HI) and early Lyman-$α$ (Ly$α$) radiation emitting galaxies (Ly$α$ emitters, LAEs) depend on the reionisation history and topology and the simulated volume. For this purpose, we develop an analytic expression for the 21cm-LAE cross-correlation function and compare it to results derived from different Astraeus and 21cmFAST reionisation simulations covering a physically plausible range of scenarios where either low-mass ($<10^{9.5}M_\odot$) or massive ($>10^{9.5}M_\odot$) galaxies drive reionisation. Our key findings are: (i) the negative small-scale ($<2$ cMpc) cross-correlation amplitude scales with the intergalactic medium's (IGM) average HI fraction ($\langleχ_\mathrm{HI}\rangle$) and spin-temperature weighted overdensity in neutral regions ($\langle1+δ\rangle_\mathrm{HI}$); (ii) the inversion point of the cross-correlation function traces the peak of the size distribution of ionised regions around LAEs; (iii) the cross-correlation amplitude at small scales is sensitive to the reionisation topology, with its anti-correlation or correlation decreasing the stronger the ionising emissivity of the underlying galaxy population is correlated to the cosmic web gas distribution (i.e. the more low-mass galaxies drive reionisation); (iv) the required simulation volume to not underpredict the 21cm-LAE anti-correlation amplitude when the cross-correlation is derived via the cross-power spectrum rises as the size of ionised regions and their variance increases. Our analytic expression can serve two purposes: to test whether simulation volumes are sufficiently large, and to act as a fitting function when cross-correlating future 21cm signal Square Kilometre Array and LAE galaxy observations.

astro-ph.CO↗

arXiv2023

Environmental effects on associations of dwarf galaxies

We study the properties of associations of dwarf galaxies and their dependence on the environment. Associations of dwarf galaxies are extended systems composed exclusively of dwarf galaxies, considering as dwarf galaxies those galaxies less massive than $M_{\star, \rm max} = 10^{9.0}$ ${\rm M}_{\odot}\,h^{-1}$. We identify these particular systems using a semi-analytical model of galaxy formation coupled to a dark matter only simulation in the $Λ$ Cold Dark Matter cosmological model. To classify the environment, we estimate eigenvalues from the tidal field of the dark matter particle distribution of the simulation. We find that the majority, two thirds, of associations are located in filaments ($ \sim 67$ per cent), followed by walls ($ \sim 26 $ per cent), while only a small fraction of them are in knots ($ \sim 6 $ per cent) and voids ($ \sim 1 $ per cent). Associations located in more dense environments present significantly higher velocity dispersion than those located in less dense environments, evidencing that the environment plays a fundamental role in their dynamical properties. However, this connection between velocity dispersion and the environment depends exclusively on whether the systems are gravitational bound or unbound, given that it disappears when we consider associations of dwarf galaxies that are gravitationally bound. Although less than a dozen observationally detected associations of dwarf galaxies are currently known, our results are predictions on the eve of forthcoming large surveys of galaxies, which will enable these very particular systems to be identified and studied.

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arXiv2023

Simulating the LOcal Web (SLOW): I. Anomalies in the local density field

Context: Several observations of the local Universe (LU) point towards the existence of very prominent structures. The presence of massive galaxy clusters and local super clusters on the one hand, but also large local voids and under-densities on the other hand. However, it is highly non trivial to connect such different observational selected tracers to the underlying dark matter (DM) distribution. Methods (abridged): We used a 500 Mpc/h large constrained simulation of the LU with initial conditions based on peculiar velocities derived from the CosmicFlows-2 catalogue and follow galaxy formation physics directly in the hydro-dynamical simulations to base the comparison on stellar masses of galaxies or X-ray luminosity of clusters. We also used the 2668 Mpc/h large cosmological box from the Magneticum simulations to evaluate the frequency of finding such anomalies in random patches within simulations. Results: We demonstrate that haloes and galaxies in our constrained simulation trace the local DM density field very differently. Thereby, this simulation reproduces the observed 50% under-density of galaxy clusters and groups within the sphere of ~100 Mpc when applying the same mass or X-ray luminosity limit used in the observed cluster sample (CLASSIX), which is consistent with a ~1.5$σ$ feature. At the same time, the simulation reproduces the observed over-density of massive galaxy clusters within the same sphere, which on its own also corresponds to a ~1.5$σ$ feature. Interestingly, we find that only 44 out of 15635 random realizations (i.e. 0.28%) are matching both anomalies, making the LU to be a ~3$σ$ environment. We finally compared a mock galaxy catalogue with the observed distribution of galaxies in the LU, finding also a match to the observed factor of two over-density at ~16 Mpc as well as the observed 15% under-density at ~40 Mpc distance.

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