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Galaxy clusters are important cosmological probes that have helped to establish the $\mathrm{\Lambda}$CDM paradigm as the standard model of cosmology. However, recent tensions between different types of high-accuracy data highlight the need for novel probes of the cosmological parameters. Such a probe is the turnaround density: the mass density on the scale where galaxies around a cluster join the Hubble flow. To measure the turnaround density, one must locate the distance from the cluster center where turnaround occurs. Earlier work has shown that a turnaround radius can be readily identified in simulations by analyzing the 3D dark matter velocity field. However, measurements using realistic data face challenges due to projection effects. This study aims to assess the feasibility of measuring the turnaround radius using machine learning techniques applied to simulated observations of galaxy clusters. We employ N-body simulations across various cosmologies to generate galaxy cluster projections. Utilizing Convolutional Neural Networks (CNNs), we assess the predictability of the turnaround radius based on galaxy line-of-sight velocity, number density, and mass profiles. We find a strong correlation between the turnaround radius and the central mass of a galaxy cluster, rendering the mass distribution outside the virial radius of little relevance to the model's predictive power. The velocity dispersion among galaxies also contributes valuable information concerning the turnaround radius. Importantly, the accuracy of a line-of-sight velocity model remains robust even when the data within $\mathrm{R_{200}}$ of the central overdensity are absent., Comment: Submitted to A&A, 12 pages, 10 figures, 3 tables

Density profiles are important tools in galaxy cluster research, offering insights into clusters dynamical states and their relationship with the broader Universe. While these profiles provide valuable information about the matter content of the Universe, their utility in understanding its dark energy component has remained limited due a lack of tools allowing us to study the transition from cluster portions that are relaxed and infalling, to those that are merging with the Hubble flow. In this work we investigate signatures of this transition in stacked density profiles of simulated cluster-sized halos at different redshifts. To highlight the Hubble flow around clusters we use their turnaround radius to normalize stacked simulated density profiles and calculate their logarithmic slope. Then, we complement our analysis by modeling the outer portions of these profiles assuming Gaussian early Universe statistics and spherical collapse without shell-crossing. We find the logarithmic slope of median cluster density profiles beyond the turnaround radius - where the Hubble flow dominates - to be Universal and well described by our model. Importantly, we find the slope of the profiles to diverge from the SCM prediction from within the turnaround radius where the actual profiles exhibit caustics which give rise to the splashback feature. We suggest utilizing this divergence from the spherical collapse model as a method to identify the turnaround radius in stacked cluster density profiles, offering a new perspective on understanding cluster dynamics and their cosmological implications., Comment: 8 pages, 5 figures, submitted to A&A

The average matter density within the turnaround scale, which demarcates where galaxies shift from clustering around a structure to joining the expansion of the Universe, is an important cosmological probe. However, a measurement of the mass enclosed by the turnaround radius is difficult. Analyses of the turnaround scale in simulated galaxy clusters place the turnaround radius at about three times the virial radius in a \(\Lambda CDM\) universe and at a (present-day) density contrast with the background matter density of the Universe of \(\delta \sim 11\). Assessing the mass at such extended distances from a cluster's center is a challenge for current mass measurement techniques. Consequently, there is a need to develop and validate new mass-scaling relations, to connect observable masses at cluster interiors with masses at greater distances. Our research aims to establish an analytical framework for the most probable mass profile of galaxy clusters, leading to novel mass scaling relations, allowing us to estimate masses at larger scales. We derive such analytical mass profiles and compare them with those from cosmological simulations. We use excursion set theory, which provides a statistical framework for the density and local environment of dark matter halos, and complement it with the spherical collapse model to follow the non-linear growth of these halos. The profile we developed analytically shows a good agreement (better than 30\%, and dependent on halo mass) with the mass profiles of simulated galaxy clusters. Mass scaling relations are obtained from the analytical profile with offset better than 15\% from the simulated ones. This level of precision highlights the potential of our model for probing structure formation dynamics at the outskirts of galaxy clusters., Comment: 10 pages, 9 figures. Published in A&A

The mean matter density within the turnaround radius, which is the boundary that separates a nonexpanding structure from the Hubble flow, was recently proposed as a novel cosmological probe. According to the spherical collapse model, the evolution with cosmic time of this turnaround density, $\rm \rho_{ta}(z)$, can be used to determine both $\rm \Omega_m$ and $\Omega_\Lambda$, independently of any other currently used probe. The properties of $\rm \rho_{ta}$ predicted by the spherical collapse model were also shown to persist in the presence of full three-dimensional effects in $\rm \Lambda$CDM N-body cosmological simulations when considering galaxy clusters at the present time, $z=0$. However, a small offset was discovered between the spherical-collapse prediction of the value of $\rho_{ta}$ at $z=0$ and its value measured in simulations. In this letter, we explore whether this offset evolves with cosmic time; whether it differs in different cosmologies; whether its origin can be confidently identified; and whether it can be corrected. We found that the offset does evolve slightly with redshift, and that it correlates strongly with the deviation from spherical symmetry of the dark matter halo distribution inside and outside of the turnaround radius. We used an appropriate metric to quantify deviations in the environment of a structure from spherical symmetry. We found that using this metric, we can construct a sphericity-selected sample of halos for which the offset of $\rho_{ta}$ from the spherical collapse prediction is zero, independently of redshift and cosmology. We found that a sphericity-selected halo sample allows us to recover the simulated cosmology, and we conclude that the turnaround density evolution indeed encodes the cosmology in N-body simulations., Comment: 8 pages, 4 figures, accepted for publication in A&A

Spherical collapse predicts that a single value of the turnaround density (average matter density within the scale on which a structure detaches from the Hubble flow) characterizes all cosmic structures at the same redshift. It has been recently shown by Korkidis et al. that this feature persists in complex non-spherical galaxy clusters identified in N-body simulations. Here we show that the low-redshift evolution of the turnaround density constrains the cosmological parameters, and that it can be used to derive a local constraint on $\Omega_\Lambda$ alone, independent of $\Omega_m$. The turnaround density thus provides a promising new way to exploit upcoming large cosmological datasets., Comment: 5 pages, 3 figures, submitted to A&AL

We use N-body simulations to examine whether a characteristic turnaround radius, as predicted from the spherical collapse model in a $\rm {\Lambda CDM}$ Universe, can be meaningfully identified for galaxy clusters, in the presence of full three-dimensional effects. We use The Dark Sky Simulations and Illustris-TNG dark-matter--only cosmological runs to calculate radial velocity profiles around collapsed structures, extending out to many times the virial radius $R_{200}$. There, the turnaround radius can be unambiguously identified as the largest non-expanding scale around a center of gravity. We find that: (a) Indeed, a single turnaround scale can meaningfully describe strongly non-spherical structures. (b) For halos of masses $M_{200}>10^{13}M_\odot$, the turnaround radius $R_{ta}$ scales with the enclosed mass $M_{ta}$ as $M_{ta}^{1/3}$, as predicted by the spherical collapse model. (c) The deviation of $R_{ta}$ in simulated halos from the spherical collapse model prediction is insensitive to halo asphericity. Rather, it is sensitive to the tidal forces due to massive neighbors when such are present. (d) Halos exhibit a characteristic average density within the turnaround scale. This characteristic density is dependent on cosmology and redshift. For the present cosmic epoch and for concordance cosmological parameters ($\Omega_m \sim 0.7$; $\Omega_\Lambda \sim 0.3$) turnaround structures exhibit an average matter density contrast with the background Universe of $\delta \sim 11$. Thus $R_{ta}$ is equivalent to $R_{11}$ -- in a way analogous to defining the "virial" radius as $R_{200}$ -- with the advantage that $R_{11}$ is shown in this work to correspond to a kinematically relevant scale in N-body simulations., Comment: Submitted to A&A, nine pages, 10 figures