Splashback Radius Research Articles

The Uchuu-universe machine data set: galaxies in and around clusters

ABSTRACT We present the public data release of the Uchuu-UM galaxy catalogues by applying the UniverseMachine algorithm to assign galaxies to the dark matter haloes in the Uchuu N-body cosmological simulation. It includes a variety of baryonic properties for all galaxies down to ∼5 × 108 M⊙ with haloes in a mass range of 1010 < Mhalo/M⊙ < 5 × 1015 up to redshift z = 10. Uchuu-UM includes more than 104 cluster-size haloes in a volume of 8(h−1Gpc)3, reproducing observed stellar mass functions across the redshift range of z = 0−7, galaxy quenched fractions, and clustering statistics at low redshifts. Compared to the previous largest UM catalogue, the Uchuu-UM catalogue includes significantly more massive galaxies hosted by large-mass dark matter haloes. Overall, the number density profile of galaxies in dark matter haloes follows the dark matter profile, with the profile becoming steeper around the splashback radius and flattening at larger radii. The number density profile of galaxies tends to be steeper for larger stellar masses and depends on the colour of galaxies, with red galaxies having steeper slopes at all radii than blue galaxies. The quenched fraction exhibits a strong dependence on the stellar mass and increases towards the inner regions of clusters. The publicly available Uchuu-UM galaxy catalogue presented here can serve to model ongoing and upcoming large galaxy surveys.

On the kinematic morphology around haloes

ABSTRACT In this paper, we report an interesting kinematic phenomenon around the haloes’ edge related to the ‘splashback’ radius. After the shell-crossing, cosmic flow exhibits various rotational morphologies via stream-mixing. Vorticity is generated in a particular way that coincides with the large-scale structure. Notably, one specific flow morphology, which is spiralling inward and compressing in the third direction, concentrates around haloes. A detailed examination that reveals a sharp change in the logarithmic derivative of its volume fraction coincides with the location of the splashback radius Rsp defined as the outermost caustic structure. Such a feature encodes valuable phase-space information and provides a new perspective on understanding the dynamical evolution of haloes. As a volume-weighted quantity, the profile of flow morphology is purely kinematic. And unlike other related studies, the rotational flow morphologies capture the anisotropic phase structure in the multistream region.

Anisotropy and characteristic scales in halo density gradient profiles

We use a large N-body simulation to study the characteristic scales in the density gradient profiles in and around halos with masses ranging from 1012 to 1015 M⊙. We investigate the profiles separately along the major (T1) and minor (T3) axes of the local tidal tensor and how the characteristic scales depend on halo mass, formation time, and environment. We find two prominent features in the gradient profiles: a deep “valley” and a prominent “peak.” We use the Gaussian process regression to fit the gradient profiles and identify the local extrema in order to determine the scales associated with these features. Around the valley, we identify three types of distinct local minima, corresponding to caustics of particles orbiting around halos. The appearance and depth of the three caustics depend on the direction defined by the local tidal field, formation time, and environment of halos. The first caustic is located at r > 0.8R200, corresponding to the splashback feature, and is dominated by particles at their first apocenter after infall. The second and third caustics, around 0.6R200 and 0.4R200, respectively, can be determined reliably only for old halos. The three caustics are consistent with the prediction of self-similar gravitational collapse. The first caustic is always the most prominent feature along T3, but may not be true along T1 or in azimuthally averaged profiles, suggesting that caution must be taken when using averaged profiles to investigate the splashback radius. We find that the splashback feature is approximately isotropic when proper separations are made between the first and the other caustics. We also identify a peak feature located at ∼2.5R200 in the density gradient profile. This feature is the most prominent along T1 and is produced by mass accumulations from the structure outside halos. We also discuss the origins of these features and their observational implications.

Splashback Radius in a Spherical Collapse Model

It was shown several years ago that dark matter halo outskirts are characterized by very steep density profiles in a very small radial range. This feature has been interpreted as a pile-up of different particle orbits at a similar location, namely, splashback material at half an orbit after collapse. Adhikari et al. (2014) obtained the location of the splashback radius through a very simple model by calculating a dark matter shell trajectory in the secondary infall model while it crosses a growing NFW profile-shaped dark matter halo. Because they imposed a halo profile instead of calculating it from the trajectories of the shells of dark matter, they were not able to find the dark matter profile around the splashback radius. In the present paper, we use an improved spherical infall model taking into account shell crossing as well as several physical effects such as ordered and random angular momentum, dynamical friction, adiabatic contraction, etc. This allows us to determine the density profile from the inner to the outer region and to study the behavior of the outer density profile. We compare the density profiles and their logarithmic slope of with the simulation results of Diemer and Kravtsov (2014), finding a good agreement between the prediction of the model and the simulations.

Shocks in the stacked Sunyaev-Zel’dovich profiles of clusters II: Measurements from SPT-SZ + Planck Compton-y map

ABSTRACT We search for the signature of cosmological shocks in stacked gas pressure profiles of galaxy clusters using data from the South Pole Telescope (SPT). Specifically, we stack the latest Compton-y maps from the 2500 deg2 SPT-SZ survey on the locations of clusters identified in that same data set. The sample contains 516 clusters with mean mass $\langle M_{\rm 200m}\rangle = 10^{14.9} \, {\rm M}_\odot$ and redshift 〈z〉 = 0.55. We analyse in parallel a set of zoom-in hydrodynamical simulations from the three hundred project. The SPT-SZ data show two features: (i) a pressure deficit at R/R200m = 1.08 ± 0.09, measured at 3.1σ significance and not observed in the simulations, and; (ii) a sharp decrease in pressure at R/R200m = 4.58 ± 1.24 at 2.0σ significance. The pressure deficit is qualitatively consistent with a shock-induced thermal non-equilibrium between electrons and ions, and the second feature is consistent with accretion shocks seen in previous studies. We split the cluster sample by redshift and mass, and find both features exist in all cases. There are also no significant differences in features along and across the cluster major axis, whose orientation roughly points towards filamentary structure. As a consistency test, we also analyse clusters from the Planck and Atacama Cosmology Telescope Polarimeter surveys and find quantitatively similar features in the pressure profiles. Finally, we compare the accretion shock radius ($R_{\rm sh,\, acc}$) with existing measurements of the splashback radius (Rsp) for SPT-SZ and constrain the lower limit of the ratio, $R_{\rm sh,\, acc}/R_{\rm sp}\gt 2.16 \pm 0.59$.

First measurement of the characteristic depletion radius of dark matter haloes from weak lensing

ABSTRACT We use weak lensing observations to make the first measurement of the characteristic depletion radius, one of the three radii that characterize the region where matter is being depleted by growing haloes. The lenses are taken from the halo catalogue produced by the extended halo-based group/cluster finder applied to DESI Legacy Imaging Surveys DR9, while the sources are extracted from the DECaLS DR8 imaging data with the fourier_quad pipeline. We study halo masses $12 \lt \log (M_{\rm grp} \,[{\rm M_{\odot }}\, h^{-1}]) \le 15.3$ within redshifts 0.2 ≤ z ≤ 0.3. The virial and splashback radii are also measured and used to test the original findings on the depletion region. When binning haloes by mass, we find consistency between most of our measurements and predictions from the cosmicgrowth simulation, with exceptions to the lowest mass bins. The characteristic depletion radius is found to be roughly 2.5 times the virial radius and 1.7–3 times the splashback radius, in line with an approximately universal outer density profile, and the average enclosed density within the characteristic depletion radius is found to be roughly 29 times the mean matter density of the Universe in our sample. When binning haloes by both mass and a proxy for halo concentration, we do not detect a significant variation of the depletion radius with concentration, on which the simulation prediction is also sensitive to the choice of concentration proxy. We also confirm that the measured splashback radius varies with concentration differently from simulation predictions.

The impact of galaxy selection on the splashback boundaries of galaxy clusters

ABSTRACTWe explore how the splashback radius (Rsp) of galaxy clusters, measured using the number density of the subhalo population, changes based on various selection criteria using the IllustrisTNG cosmological galaxy formation simulation. We identify Rsp by extracting the steepest radial gradient in a stacked set of clusters in 0.5 dex wide mass bins, with our clusters having halo masses 1013 ≤ M200,mean/M⊙ ≤ 1015. We apply cuts in subhalo mass, galaxy stellar mass, i-band absolute magnitude, and specific star formation rate. We find that, generally, galaxies of increasing mass and luminosity trace smaller measured splashback radii relative to the intrinsic dark matter radius. We also show that quenched galaxies may be used to reliably reconstruct the dark matter splashback radius. This trend is likely due to changes in the galaxy population. Additionally, we are able to reconcile different observational predictions that Rsp based upon galaxy number counts and dark matter may either align or show significant offset (e.g. those using optically or SZ-selected clusters) through the selection functions that these studies employ. Finally, we demonstrate that changes in Rsp measured through number counts are not due to a simple change in galaxy abundance inside and outside of the cluster.

Connecting galaxy evolution in clusters with their radial profiles and phase space distribution: results from the IllustrisTNG hydrodynamical simulations

ABSTRACT We study the population of galaxies around galaxy clusters in the hydrodynamic simulation suite IllustrisTNG 300-1 to study the signatures of their evolutionary history on observable properties. We measure the radial number density profile, phase space distribution, and splashback radius for galaxies of different masses and colours over the redshift range z = 0−1. The three primary physical effects which shape the galaxy distribution within clusters are the galaxy quenching, angular momentum distribution, and dynamical friction. We find three distinct populations of galaxies by applying a Gaussian mixture model to their distribution in colour and mass. They have distinct evolutionary histories and leave distinct signatures on their distribution around cluster haloes. We find that low-mass red galaxies show the most concentrated distribution in clusters and the largest splashback radius, while high-mass red galaxies show a less concentrated distribution and a smaller splashback radius. Blue galaxies, which mostly quench into the low-mass red population, have the shallowest distribution within the clusters, with those on radial orbits quenched rapidly before reaching pericentre. Comparison with the distribution of galaxies from the Dark Energy Survey survey around Sunyaev–Zeldovich clusters from the Atacama Cosmology Telescope and South Pole Telescope surveys shows evidence for differences in galaxy evolution between simulations and data.

Probing Galaxy Evolution in Massive Clusters Using ACT and DES: Splashback as a Cosmic Clock

Abstract We measure the projected number density profiles of galaxies and the splashback feature in clusters selected by the Sunyaev–Zel’dovich effect from the Advanced Atacama Cosmology Telescope (AdvACT) survey using galaxies observed by the Dark Energy Survey (DES). The splashback radius is consistent with CDM-only simulations and is located at 2.4 − 0.4 + 0.3 Mpc h − 1 . We split the galaxies on color and find significant differences in their profile shapes. Red and green-valley galaxies show a splashback-like minimum in their slope profile consistent with theory, while the bluest galaxies show a weak feature at a smaller radius. We develop a mapping of galaxies to subhalos in simulations and assign colors based on infall time onto their hosts. We find that the shift in location of the steepest slope and different profile shapes can be mapped to the average time of infall of galaxies of different colors. The steepest slope traces a discontinuity in the phase space of dark matter halos. By relating spatial profiles to infall time, we can use splashback as a clock to understand galaxy quenching. We find that red galaxies have on average been in clusters over 3.2 Gyr, green galaxies about 2.2 Gyr, while blue galaxies have been accreted most recently and have not reached apocenter. Using the full radial profiles, we fit a simple quenching model and find that the onset of galaxy quenching occurs after a delay of about a gigayear and that galaxies quench rapidly thereafter with an exponential timescale of 0.6 Gyr.

Shock and splash: gas and dark matter halo boundaries around ΛCDM galaxy clusters

ABSTRACT Recent advances in simulations and observations of galaxy clusters suggest that there exists a physical outer boundary of massive cluster-size dark matter (DM) haloes. In this work, we investigate the locations of the outer boundaries of DM and gas around cluster-size DM haloes, by analysing a sample of 65 massive DM haloes extracted from the Omega500 zoom-in hydrodynamical cosmological simulations. We show that the location of accretion shock is offset from that of the DM splashback radius, contrary to the prediction of the self-similar models. The accretion shock radius is larger than all definitions of the splashback radius in the literature by $20-100{{\ \rm per\ cent}}$. The accretion shock radius defined using the steepest drop in the entropy and pressure profiles is approximately 1.89 times larger than the splashback radius defined by the steepest slope in the DM density profile, and it is ≈1.2 times larger than the edge of the DM phase space structure. We discuss implications of our results for multiwavelength studies of galaxy clusters.

Shocks in the stacked Sunyaev–Zel’dovich profiles of clusters – I. Analysis with the Three Hundred simulations

ABSTRACT Gas infalling into the gravitational potential wells of massive galaxy clusters is expected to experience one or more shocks on its journey to becoming part of the intracluster medium (ICM). These shocks are important for setting the thermodynamic properties of the ICM and can therefore impact cluster observables such as X-ray emission and the Sunyaev–Zel’dovich (SZ) effect. We investigate the possibility of detecting signals from cluster shocks in the averaged thermal SZ profiles of galaxy clusters. Using zoom-in hydrodynamic simulations of massive clusters from the Three Hundred Project, we show that if cluster SZ profiles are stacked as a function of R/R200m, shock-induced features appear in the averaged SZ profile. These features are not accounted for in standard fitting formulae for the SZ profiles of galaxy clusters. We show that the shock features should be detectable with samples of clusters from ongoing and future SZ surveys. We also demonstrate that the location of these features is correlated with the cluster accretion rate, as well as the location of the cluster splashback radius. Analyses of ongoing and future surveys, such as SPT-3g, AdvACT, Simons Observatory, and CMB-S4, which include gas shocks will gain a new handle on the properties and dynamics of the outskirts of massive haloes, both in gas and in mass.

Discovery of a possible splashback feature in the intracluster light of MACS J1149.5+2223

ABSTRACT We present an analysis of the intracluster light (ICL) in the Frontier Field Cluster MACS J1149.5+2223 (z = 0.544), which combines new and archival Hubble WFC3/IR imaging to provide continuous radial coverage out to 2.8 Mpc from the brightest cluster galaxy (BCG). Employing careful treatment of potential systematic biases and using data at the largest radii to determine the background sky level, we reconstruct the surface brightness profile out to a radius of 2 Mpc. This radius is the largest to which the ICL has been measured for an individual cluster. Within this radius, we measure a total luminosity of 1.5 × 1013 L⊙ for the BCG plus ICL. From the profile and its logarithmic slope, we identify the transition from the BCG to ICL at r ∼ 70 kpc. Remarkably, we also detect an apparent inflection in the profile centred in the 1.2–1.7 Mpc (0.37–0.52 r200m) radial bin, a signature of an infall caustic in the stellar distribution. Based upon the shape and strength of the feature, we interpret it as potentially being at the splashback radius, although the radius is smaller than theoretical predictions. If this is the splashback radius, then it is the first such detection in the ICL and the first detection of the splashback radius for an individual cluster. Similar analyses should be possible with the other Frontier Field clusters, and eventually with clusters observed by the Euclid and Roman missions.

The effect of finite halo size on the clustering of neutral hydrogen

Post-reionisation 21cm intensity mapping experiments target the spectral line of neutral hydrogen (HI) resident in dark matter haloes. According to the halo model, these discrete haloes trace the continuous dark matter density field down to a certain scale, which is dependent on the halo physical size. The halo physical size defines an exclusion region which leaves imprints on the statistical properties of HI. We show how the effect of exclusion due to the finite halo size impacts the HI power spectrum, with the physical boundary of the host halo given by the splashback radius. Most importantly, we show that the white noise-like feature that appears in the zero-momentum limit of the power spectrum is exactly cancelled when the finite halo size is taken into consideration. This cancellation in fact applies to all tracers of dark matter density field, including galaxies. Furthermore, we show that the exclusion due to finite halo size leads to a sub-Poissonian noise signature on large scales, consistent with the results from N-body simulations.

Evolution of splashback boundaries and gaseous outskirts: insights from mergers of self-similar galaxy clusters

ABSTRACT A self-similar spherical collapse model predicts a dark matter (DM) splashback and accretion shock in the outskirts of galaxy clusters while missing a key ingredient of structure formation – processes associated with mergers. To fill this gap, we perform simulations of merging self-similar clusters and investigate their DM and gas evolution in an idealized cosmological context. Our simulations show that the cluster rapidly contracts during the major merger and the splashback radius rsp decreases, approaching the virial radius rvir. While in the self-similar model rsp depends on a smooth mass accretion rate parameter Γs, our simulations show that in the presence of mergers, rsp responds to the changes in the total mass accretion rate Γvir, which accounts for both mergers and smooth accretion. The scatter of the Γvir − rsp/rvir relation indicates a generally low Γs ∼ 1 in clusters in cosmological simulations. In contrast to the DM, the hot gaseous atmospheres significantly expand by the merger-accelerated (MA-) shocks formed when the runaway merger shocks overtake the outer accretion shock. After a major merger, the MA-shock radius is larger than rsp by a factor of up to ∼1.7 for Γs ≲ 1 and is ∼rsp for Γs ≳ 3. This implies that (1) mergers could easily generate the MA-shock-splashback offset measured in cosmological simulations, and (2) the smooth mass accretion rate is small in regions away from filaments where MA-shocks reside. We further discuss the shapes of the DM haloes, various shocks, and contact discontinuities formed at different epochs of the merger, and the ram-pressure stripping in cluster outskirts.

Erratum: The splashback radius of optically selected clusters with Subaru HSC Second Public Data Release

Erratum: The splashback radius of optically selected clusters with Subaru HSC Second Public Data Release

A redefinition of the halo boundary leads to a simple yet accurate halo model of large-scale structure

ABSTRACT We present a model for the halo–mass correlation function that explicitly incorporates halo exclusion and allows for a redefinition of the halo boundary in a flexible way. We assume that haloes trace mass in a way that can be described using a single scale-independent bias parameter. However, our model exhibits scale-dependent biasing due to the impact of halo-exclusion, the use of a ‘soft’ (i.e. not infinitely sharp) halo boundary, and differences in the one halo term contributions to ξhm and ξmm. These features naturally lead us to a redefinition of the halo boundary that lies at the ‘by eye’ transition radius from the one-halo to the two-halo term in the halo–mass correlation function. When adopting our proposed definition, our model succeeds in describing the halo–mass correlation function with $\approx 2{{\ \rm per\ cent}}$ residuals over the radial range 0.1 h−1 Mpc < r < 80 h−1 Mpc, and for halo masses in the range 1013 h−1 M⊙ < M < 1015 h−1 M⊙. Our proposed halo boundary is related to the splashback radius by a roughly constant multiplicative factor. Taking the 87 percentile as reference we find rt/Rsp ≈ 1.3. Surprisingly, our proposed definition results in halo abundances that are well described by the Press–Schechter mass function with δsc = 1.449 ± 0.004. The clustering bias parameter is offset from the standard background-split prediction by $\approx 10{{\ \rm per\ cent}}\!-\!15{{\ \rm per\ cent}}$. This level of agreement is comparable to that achieved with more standard halo definitions.

The Corona Borealis supercluster: connectivity, collapse, and evolution

Context. Rich superclusters of galaxies represent dynamically active environments in which galaxies and their systems form and evolve. Aims. We study the dynamical properties and connectivity of the richest galaxy clusters in the Corona Borealis (CB) supercluster and of the whole supercluster, and analyse star formation of galaxies in them with the aim to understand the evolution of the supercluster and the galaxies within it. We compare it with the supercluster SCl A2142. Methods. We used the luminosity-density field to determine the high-density cores of the CB. We identified the richest galaxy clusters in them and studied the dynamical state of the clusters, analysed their substructure, and studied the star formation properties of galaxies in them using normal mixture modelling and the projected phase space diagram. We determined filaments in the supercluster to analyse the connectivity of clusters. To understand the possible future evolution of the CB, we compared the mass distribution in it with predictions from the spherical collapse model and analysed the gravitational acceleration field in the CB. Results. The richest clusters in the high-density cores of the CB are the Abell clusters A2065, A2061 (together with A2067), A2089, and Gr2064. At a radius R30 around each cluster (corresponding to the density contrast Δρ ≈ 30), the galaxy distribution shows a minimum. The R30 values for individual clusters lie in the range of 3 − 6 h−1 Mpc. The radii of the clusters (splashback radii) lie in the range of Rcl ≈ 2 − 3 Rvir. The projected phase space diagrams and the comparison with the spherical collapse model suggest that R30 regions have passed turnaround and are collapsing, forming infall regions around each cluster. Galaxies in the richest cluster of the CB, A2065, and in its infall region have on average younger stellar populations than other clusters and their environment. The cluster A2061 has the highest fraction of galaxies with very old stellar populations, similar to those in A2142. The number of long filaments that begin near clusters vary from one near A2089 to five near A2061. The total connectivity of these clusters (the number of infalling groups and filaments) varies from two to nine. Conclusions. During the future evolution, the clusters in the main part of the CB may merge and form one of the largest bound systems in the nearby Universe. Another part, with the cluster Gr2064, will form a separate system. Our study suggests that structures with a current characteristic density contrast Δρ ≈ 30 have passed turnaround and started to collapse at redshifts z ≈ 0.3 − 0.4. The comparison of the number and properties of the most massive collapsing supercluster cores from observations and simulations may serve as a test for cosmological models.

The splashback boundary of haloes in hydrodynamic simulations

ABSTRACT The splashback radius, Rsp, is a physically motivated halo boundary that separates infalling and collapsed matter of haloes. We study Rsp in the hydrodynamic and dark matter-only IllustrisTNG simulations. The most commonly adopted signature of Rsp is the radius at which the radial density profiles are steepest. Therefore, we explicitly optimize our density profile fit to the profile slope and find that this leads to a $\sim 5{{\ \rm per\ cent}}$ larger radius compared to other optimizations. We calculate Rsp for haloes with masses between 1013 and 15 M⊙ as a function of halo mass, accretion rate, and redshift. Rsp decreases with mass and with redshift for haloes of similar M200 m in agreement with previous work. We also find that Rsp/R200 m decreases with halo accretion rate. We apply our analysis to dark matter, gas, and satellite galaxies associated with haloes to investigate the observational potential of Rsp. The radius of steepest slope in gas profiles is consistently smaller than the value calculated from dark matter profiles. The steepest slope in galaxy profiles, which are often used in observations, tends to agree with dark matter profiles but is lower for less massive haloes. We compare Rsp in hydrodynamic and N-body dark matter-only simulations and do not find a significant difference caused by the addition of baryonic physics. Thus, results from dark matter-only simulations should be applicable to realistic haloes.

LoCuSS: The Splashback Radius of Massive Galaxy Clusters and Its Dependence on Cluster Merger History

Abstract We present the direct detection of the splashback feature using the sample of massive galaxy clusters from the Local Cluster Substructure Survey (LoCuSS). This feature is clearly detected (above 5σ) in the stacked luminosity density profile obtained using the K-band magnitudes of spectroscopically confirmed cluster members. We obtained the best-fit model by means of Bayesian inference, which ranked models including the splashback feature as more descriptive of the data with respect to models that do not allow for this transition. In addition, we have assessed the impact of the cluster dynamical state on the occurrence of the splashback feature. We exploited the extensive multiwavelength LoCuSS data set to test a wide range of proxies for the cluster formation history, finding the most significant dependence of the splashback feature location and scale according to the presence or absence of X-ray emitting galaxy groups in the cluster infall regions. In particular, we report for the first time that clusters that do not show massive infalling groups present the splashback feature at a smaller clustercentric radius r sp/r 200,m = 1.158 ± 0.071 than clusters that are actively accreting groups r sp/r 200,m = 1.291 ± 0.062. The difference between these two subsamples is significant at 4.2σ, suggesting a correlation between the properties of the cluster potential and its accretion rate and merger history. Similarly, clusters that are classified as old and dynamically inactive present stronger signatures of the splashback feature, with respect to younger, more active clusters. We are directly observing how fundamental dynamical properties of clusters reverberate across vastly different physical scales.

Flybys, Orbits, Splashback: Subhalos and the Importance of the Halo Boundary

Abstract The classification of dark matter halos as isolated hosts or subhalos is critical for our understanding of structure formation and the galaxy–halo connection. Most commonly, subhalos are defined to reside inside a spherical overdensity boundary such as the virial radius. The resulting host–subhalo relations depend sensitively on the somewhat arbitrary overdensity threshold, but the impact of this dependence is rarely quantified. The recently proposed splashback radius tends to be larger and to include more subhalos than even the largest spherical overdensity boundaries. We systematically investigate the dependence of the subhalo fraction on the radius definition and show that it can vary by factors of unity between different spherical overdensity definitions. Using splashback radii can yet double the abundance of subhalos compared to the virial definition. We also quantify the abundance of flyby (or backsplash) halos, hosts that used to be subhalos in the past. We show that the majority of these objects are mislabeled satellites that are naturally classified as subhalos when we use the splashback radius. We show that the subhalo fraction can be understood as a universal function of only peak height and the slope of the linear power spectrum. We provide a simple fitting function that captures our simulation results to 20% accuracy across a wide range of halo masses, redshifts, and cosmologies. Finally, we demonstrate that splashback radii significantly change our understanding of satellite and flyby galaxies in the Local Group.