arXiv subjects

Ravi K. Sheth

Publications and source records attributed to Ravi K. Sheth.

At least 55 records · Page 3Linked to original sources

arXiv2020

On the Presence of a Universal Acceleration Scale in Elliptical Galaxies

Dark matter phenomena in rotationally supported galaxies exhibit a characteristic acceleration scale of $g_\dagger \approx 1.2\times 10^{-10}$ m s$^{-2}$. Whether this acceleration is a manifestation of a universal scale, or merely an emergent property with an intrinsic scatter, has been debated in the literature. Here we investigate whether a universal acceleration scale exists in dispersion-supported galaxies using two uniform sets of integral field spectroscopy (IFS) data from SDSS-IV MaNGA and ATLAS$^{\rm 3D}$. We apply the spherical Jeans equation to 15 MaNGA and 4 ATLAS$^{\rm 3D}$ slow-rotator E0 (i.e., nearly spherical) galaxies. Velocity dispersion profiles for these galaxies are well determined with observational errors under control. Bayesian inference indicates that all 19 galaxies are consistent with a universal acceleration of $g_\dagger=1.5_{-0.6}^{+0.9}\times 10^{-10}$ m s$^{-2}$. Moreover, all 387 data points from the radial bins of the velocity dispersion profiles are consistent with a universal relation between the radial acceleration traced by dynamics and that predicted by the observed distribution of baryons. This universality remains if we include 12 additional non-E0 slow-rotator elliptical galaxies from ATLAS$^{\rm 3D}$. Finally, the universal acceleration from MaNGA and ATLAS$^{\rm 3D}$ is consistent with that for rotationally supported galaxies, so our results support the view that dark matter phenomenology in galaxies involves a universal acceleration scale.

astro-ph.GA↗

arXiv2020

Analytical thresholds for black hole formation in general cosmological backgrounds

We consider black holes which form from an initially spherically symmetric super-Hubble perturbation of a cosmological background filled by a perfect fluid $p=w ρ$ with $w\in (0,1]$. Previous work has shown that when $w = 1/3$ (radiation), there is a critical threshold for black hole formation ($δ_c$), which, to a very good approximation, only depends upon the curvature of the compaction function around its peak value. We find that this generalizes to all $w\gtrsim 1/3$; for smaller $w$s the knowledge of the full shape of the compaction function is necessary. We provide analytic approximations for $δ_c$ which are accurate for $w\in [1/3,1]$.

gr-qc↗

arXiv2020

Non-linear statistics of primordial black holes from gaussian curvature perturbations

We develop the non-linear statistics of primordial black holes generated by a gaussian spectrum of primordial curvature perturbations. This is done by employing the compaction function as the main statistical variable under the constraints that: a) the over-density has a high peak at a point $\vec{x}_0$, b) the compaction function has a maximum at a smoothing scale $R$, and finally, c) the compaction function amplitude at its maximum is higher than the threshold necessary to trigger a gravitational collapse into a black hole of the initial over-density. Our calculation allows for the fact that the patches which are destined to form PBHs may have a variety of profile shapes and sizes. The predicted PBH abundances depend on the power spectrum of primordial fluctuations. For a very peaked power spectrum, our non-linear statistics, the one based on the linear over-density and the one based on the use of curvature perturbations, all predict a narrow distribution of PBH masses and comparable abundance. For broader power spectra the linear over-density statistics over-estimate the abundance of primordial black holes while the curvature-based approach under-estimates it. Additionally, for very large smoothing scales, the abundance is no longer dominated by the contribution of a mean over-density but rather by the whole statistical realisations of it.

astro-ph.CO↗

arXiv2020

A universal threshold for primordial black hole formation

In this letter, we argue and show numerically that the threshold to form primordial black holes from an initial spherically symmetric perturbation is, to an excellent approximation, universal, whenever given in terms of the compaction function averaged over a sphere of radius $r_m$, where $r_m$ is the scale on which the compaction function is maximum. This can be understood as the requirement that, for a black hole to form, each shell of the averaged compaction function should have an amplitude exceeding the so-called Harada-Yoo-Kohri limit. For a radiation dominated universe we argued, supported by the numerical simulations, that this limit is $δ_c = 0.40$, which is slightly below the one quoted in the literature. Additionally, we show that the profile dependence of the threshold for the compaction function is only sensitive to its curvature at the maximum. We use these results to provide an analytic formula for the threshold amplitude of the compaction function at its maximum in terms of the normalised compaction function curvature at $r_m$.

gr-qc↗

arXiv2019

Probing black hole accretion tracks, scaling relations and radiative efficiencies from stacked X-ray active galactic nuclei

The masses of supermassive black holes at the centres of local galaxies appear to be tightly correlated with the mass and velocity dispersions of their galactic hosts. However, the local Mbh-Mstar relation inferred from dynamically measured inactive black holes is up to an order-of-magnitude higher than some estimates from active black holes, and recent work suggests that this discrepancy arises from selection bias on the sample of dynamical black hole mass measurements. In this work we combine X-ray measurements of the mean black hole accretion luminosity as a function of stellar mass and redshift with empirical models of galaxy stellar mass growth, integrating over time to predict the evolving Mbh-Mstar relation. The implied relation is nearly independent of redshift, indicating that stellar and black hole masses grow, on average, at similar rates. Matching the de-biased local Mbh-Mstar relation requires a mean radiative efficiency ~0.15, in line with theoretical expectations for accretion onto spinning black holes. However, matching the "raw" observed relation for inactive black holes requires a mean radiative efficiency around 0.02, far below theoretical expectations. This result provides independent evidence for selection bias in dynamically estimated black hole masses, a conclusion that is robust to uncertainties in bolometric corrections, obscured active black hole fractions, and kinetic accretion efficiency. For our fiducial assumptions, they favour moderate-to-rapid spins of typical supermassive black holes, to achieve a mean radiative efficiency ~0.12-0.20. Our approach has similarities to the classic Soltan analysis, but by using galaxy-based data instead of integrated quantities we are able to focus on regimes where observational uncertainties are minimized.

astro-ph.GA↗

arXiv2019

Linear Point and Sound Horizon as Purely Geometric standard rulers

The Baryon Acoustic Oscillations feature (BAO) imprinted in the clustering correlation function is known to furnish us cosmic distance determinations that are independent of the cosmological-background model and the primordial perturbation parameters. These measurements can be accomplished rigorously by means of the Purely Geometric BAO methods. To date two different Purely Geometric BAO approaches have been proposed. The first exploits the linear-point standard ruler. The second, called correlation-function model-fitting, exploits the sound-horizon standard ruler. A key difference between them is that, when estimated from clustering data, the linear point makes use of a cosmological-model-independent procedure to extract the ratio of the ruler to the cosmic distance, while the correlation-function model-fitting relies on a phenomenological cosmological model for the correlation function. Nevertheless the two rulers need to be precisely defined independently of any specific observable. We define the linear point and sound horizon and we characterize and compare the two rulers' cosmological-parameter dependence. We find that they are both geometrical within the required accuracy, and they have the same parameter dependence for a wide range of parameter values. We estimate the rulers' best-fit values and errors given the cosmological constraints obtained by the Planck Satellite team from the CMB measurements. We do this for three different cosmological models encompassed by the Purely Geometric BAO methods. In each case we find that the relative errors of the two rulers coincide and they are insensitive to the assumed cosmological model. Interestingly both the linear point and the sound horizon shift by $0.5σ$ when we do not fix the spatial geometry to be flat in LCDM. This points toward a sensitivity of the rulers to different cosmological models when they are estimated from the CMB.

astro-ph.CO↗

arXiv2019

Constraining black hole-galaxy scaling relations from the large-scale clustering of Active Galactic Nuclei and implied mean radiative efficiency

A supermassive black hole has been found at the centre of nearly every galaxy observed with sufficient sensitivity. The masses of these black holes are observed to increase with either the total mass or the mean (random) velocity of the stars in their host galaxies. The origin of these correlations remains elusive. Observational systematics and biases severely limit our knowledge of the local demography of supermassive black holes thus preventing accurate model comparisons and progress in this field. Here we show that the large-scale spatial distribution of local active galactic nuclei (AGN), believed to be accreting supermassive black holes, can constrain the shape and normalization of the black hole-stellar mass relation thus bypassing resolution-related observational biases. In turn, our results can set more stringent constraints on the so-called "radiative efficiency", a fundamental parameter describing the inner physics of supermassive black holes that is closely linked to their spin, geometry, and ability to release energy. The mean value of the radiative efficiency can be estimated by comparing the average total luminous output of AGN with the relic mass density locked up in quiescent supermassive black holes at galaxy centres today. For currently accepted values of the AGN obscured fractions and bolometric corrections, our newest estimates of the local supermassive black hole mass density favour mean radiative efficiencies of ~10-20\%, suggesting that the vast majority of supermassive black holes are spinning moderately to rapidly. With large-scale AGN surveys coming online, our novel methodology will enable even tighter constraints on the fundamental parameters that regulate the growth of supermassive black holes.

astro-ph.GA↗

arXiv2019

Cosmic web anisotropy is the primary indicator of halo assembly bias

The internal properties of dark matter haloes correlate with the large-scale halo clustering strength at fixed halo mass $-$ an effect known as assembly bias $-$ and are also strongly affected by the local, non-linear cosmic web. Characterising a halo's local web environment by its tidal anisotropy $α$ at scales $\sim4$ x the halo radius, we demonstrate that these multi-scale correlations represent two distinct statistical links: one between the internal property and $α$, and the other between $α$ and large-scale ( $>30h^{-1}$Mpc) halo bias $b_1$. We focus on scalar internal properties of haloes related to formation time (concentration $c_{\rm vir}$), shape (mass ellipsoid asphericity $c/a$), velocity dispersion structure (velocity ellipsoid asphericity $c_v/a_v$ and velocity anisotropy $β$) and angular momentum (dimensionless spin $λ$) in the mass range $8\times10^{11}< M_{\rm vir}/(h^{-1}M_\odot)<5\times10^{14}$. Using conditional correlation coefficients and other detailed tests, we show that the joint distribution of $α$, $b_1$ and any of the internal properties $c\in\{β,c_v/a_v,c/a,c_{\rm vir},λ\}$ is consistent with $p(α,b_1,c)\simeq p(α)p(b_1|α)p(c|α)$, at all but the largest masses. $\textit{Thus, the assembly bias trends $c-b_1$ reflect the two fundamental correlations $c-α$ and $b_1-α$.}$ Our results are unaffected by the exclusion of haloes with recent major merger events or splashback objects, although the latter are distinguished by the fact that $α$ does not explain their assembly bias trends. The overarching importance of $α$ provides a new perspective on the nature of assembly bias of distinct haloes, with potential ramifications for incorporating realistic assembly bias effects into mock catalogs of future large-scale structure surveys and for detecting galaxy assembly bias.

astro-ph.CO↗

arXiv2019

Exact enumeration approach to first-passage time distribution of non-Markov random walks

We propose an analytical approach to study non-Markov random walks by employing an exact enumeration method. Using the method, we derive an exact expansion for the first-passage time (FPT) distribution for any continuous, differentiable non-Markov random walk with Gaussian or non-Gaussian multivariate distribution. As an example, we study the FPT distribution of a fractional Brownian motion with a Hurst exponent $H\in(1/2,1)$ that describes numerous non-Markov stochastic phenomena in physics, biology and geology, and for which the limit $H=1/2$ represents a Markov process.

cond-mat.stat-mech↗

arXiv2019

Radial Acceleration Relation between Baryons and Dark or Phantom Matter in the Super-critical Acceleration Regime of Nearly Spherical Galaxies

The central regions of nearby elliptical galaxies are dominated by baryons (stars) and provide interesting laboratories for studying the radial acceleration relation (RAR). We carry out exploratory analyses and discuss the possibility of constraining the RAR in the super-critical acceleration range $(10^{-9.5},\hspace{1ex}10^{-8})$~${\rm m}~{\rm s}^{-2}$ using a sample of nearly round pure-bulge (spheroidal, dispersion-dominated) galaxies including 24 ATLAS$^{\rm 3D}$ galaxies and 4201 SDSS galaxies covering a wide range of masses, sizes and luminosity density profiles. We consider a range of current possibilities for the stellar mass-to-light ratio ($M_\star/L$), its gradient and dark or phantom matter (DM/PM) halo profiles. We obtain the probability density functions (PDFs) of the parameters of the considered models via Bayesian inference based on spherical Jeans Monte Carlo modeling of the observed velocity dispersions. We then constrain the DM/PM-to-baryon acceleration ratio $a_{\rm X}/a_{\rm B}$ from the PDFs. Unless we ignore observed radial gradients in $M_\star/L$, or assume unreasonably strong gradients, marginalization over nuisance factors suggests $a_{\rm X}/a_{\rm B} = 10^{p} (a_{\rm B}/a_{+1})^q$ with $p = -1.00 \pm 0.03$ (stat) $^{+0.11}_{-0.06}$ (sys) and $q=-1.02 \pm 0.09$ (stat) $^{+0.16}_{-0.00}$ (sys) around a super-critical acceleration $a_{+1}\equiv 1.2\times 10^{-9}~{\rm m}~{\rm s}^{-2}$. In the context of the $Λ$CDM paradigm, this RAR suggests that the NFW DM halo profile is a reasonable description of galactic halos even after the processes of galaxy formation and evolution. In the context of the MOND paradigm, this RAR favors the Simple interpolating function but is inconsistent with the vast majority of other theoretical proposals and fitting functions motivated mainly from sub-critical acceleration data.

astro-ph.GA↗

arXiv2019

Cosmic voids: a novel probe to shed light on our Universe

Cosmic voids, the less dense patches of the Universe, are promising laboratories to extract cosmological information. Thanks to their unique low density character, voids are extremely sensitive to diffuse components such as neutrinos and dark energy, and represent ideal environments to study modifications of gravity, where the effects of such modifications are expected to be more prominent. Robust void-related observables, including for example redshift-space distortions (RSD) and weak lensing around voids, are a promising way to chase and test new physics. Cosmological analysis of the large-scale structure of the Universe predominantly relies on the high density regions. Current and upcoming surveys are designed to optimize the extraction of cosmological information from these zones, but leave voids under-exploited. A dense, large area spectroscopic survey with imaging capabilities is ideal to exploit the power of voids fully. Besides helping illuminate the nature of dark energy, modified gravity, and neutrinos, this survey will give access to a detailed map of under-dense regions, providing an unprecedented opportunity to observe and study a so far under-explored galaxy population.

astro-ph.CO↗

arXiv2019

Modeling Nearly Spherical Pure-Bulge Galaxies with a Stellar Mass-to-Light Ratio Gradient under the $Λ$CDM and MOND Paradigms: II. The Orbital Anisotropy of Slow Rotators within the Effective Radius

We investigate the anisotropy of the stellar velocity dispersions within the effective radius, $R_{\rm e}$, in 24 ATLAS$^{\rm 3D}$ pure-bulge galaxies, 16 of which are kinematic slow rotators (SRs). We allow the spherical anisotropy parameter $β$ to be radially varying and allow a radial gradient in the stellar mass-to-light ratio ($M_\star/L$) through the parameter $K$ introduced earlier. The median anisotropy for SRs depends on $K$ as follows: $\langleβ_{\rm m}\rangle = a + b K$ with $a=0.19\pm 0.05$, $b=-0.13\pm 0.07$ ($Λ$CDM) or $a=0.21\pm 0.05$, $b=-0.26\pm 0.08$ (MOND), where $β_{\rm m}$ refers to the radially averaged quantity. Under the $Λ$CDM paradigm this scaling is tied to a scaling of $\langle f_{\rm DM}\rangle = (0.16\pm 0.03) +(0.31\pm 0.06) K$, where $f_{\rm DM}$ refers to the DM fraction within a sphere of $r=R_{\rm e}$. For $K=0$ (constant $M_\star/L$), we obtain radially biased results with $\langleβ_{\rm m}\rangle \approx 0.2$ consistent with previous results. However, marginalizing over $0 < K < 1.5$ yields $\langleβ_{\rm m}\rangle = 0.06 ^{+0.11}_{-0.14}$ with $\langle f_{\rm DM}\rangle = 0.35 \pm 0.08$: isotropy is preferred. This isotropy hides the fact that $β_{\rm m}$ is correlated with kinematic features such as counter rotating cores (CRCs), kinematically distinct cores (KDCs), and low-level velocities (LVs): SRs with LVs are likely to be radially biased while SRs with CRCs are likely to be tangentially biased, and SRs with KDCs are intermediate. Existing cosmological simulations allow us to understand these results qualitatively in terms of their dynamical structures and formation histories although there exist quantitative tensions. More realistic cosmological simulations, particularly allowing for $M_\star/L$ gradients, may be required to better understand SRs.

astro-ph.GA↗

arXiv2019

Black hole scaling relations of active and quiescent galaxies: Addressing selection effects and constraining virial factors

Local samples of quiescent galaxies with dynamically measured black hole masses (Mbh) may suffer from an angular resolution-related selection effect, which could bias the observed scaling relations between Mbh and host galaxy properties away from the intrinsic relations. In particular, previous work has shown that the observed Mbh-Mstar (stellar mass) relation is more strongly biased than the Mbh-sigma (velocity dispersion) relation. Local samples of active galactic nuclei (AGN) do not suffer from this selection effect, as in these samples Mbh is estimated from megamasers and/or reverberation mapping-based techniques. With the exception of megamasers, Mbh-estimates in these AGN samples are proportional to a virial coefficient fvir. Direct modelling of the broad line region suggests that fvir~3.5. However, this results in a Mbh-Mstar relation for AGN which lies below and is steeper than the one observed for quiescent black hole samples. A similar though milder trend is seen for the Mbh-sigma relation. Matching the high-mass end of the Mbh-Mstar and Mbh-sigma relations observed in quiescent samples requires fvir~15 and fvir~7, respectively. On the other hand, fvir~3.5 yields Mbh-sigma and Mbh-Mstar relations for AGN which are remarkably consistent with the expected `intrinsic' correlations for quiescent samples (i.e., once account has been made of the angular resolution-related selection effect), providing additional evidence that the sample of local quiescent black holes is biased. We also show that, as is the case for quiescent black holes, the Mbh-Mstar scaling relation of AGN is driven by velocity dispersion, thus providing additional key constraints to black hole-galaxy co-evolution models.

astro-ph.GA↗

arXiv2018

Cosmic distance inference from purely geometric BAO methods: Linear Point standard ruler and Correlation Function Model Fitting

Leveraging the Baryon Acoustic Oscillations (BAO) feature present in clustering 2-point statistics, we aim to measure cosmological distances independently of the underlying background cosmological model. However this inference is complicated by late-time non-linearities that introduce model and tracer dependencies in the clustering correlation function and power spectrum, which must be properly accounted for. With this in mind, we introduce the "Purely-Geometric-BAO," which provides a rigorous tool to measure cosmological distances without assuming a specific background cosmology. We focus on the 2-point clustering correlation function monopole, and show how to implement such an inference scheme employing two different methodologies: the Linear Point standard ruler (LP) and correlation-function model-fitting (CF-MF). For the first time we demonstrate how, by means of the CF-MF, we can measure very precisely the sound-horizon/isotropic-volume-distance ratio, $r_{d}/D_{V}(\bar{z})$, while correctly propagating all the uncertainties. Using synthetic data, we compare the outcomes of the two methodologies, and find that the LP provides up to $50\%$ more precise measurements than the CF-MF. Finally, we test a procedure widely employed in BAO analyses: fitting the 2-point function while fixing the cosmological and the non-linear-damping parameters at fiducial values. We find that this underestimates the distance errors by nearly a factor of $2$. We thus recommend that this practice be reconsidered, whether for parameter determination or model selection.

astro-ph.CO↗

arXiv2018

Density and velocity profiles around cosmic voids

We study the evolution of the cross-correlation between voids and the mass density field - i.e. of void profiles. We show that approaches based on the spherical model alone miss an important contribution to the evolution on large scales of most interest to cosmology: they fail to capture the well-known fact that the large-scale bias factor of conserved tracers evolves. We also show that the operations of evolution and averaging do not commute, but this difference is only significant within about two effective radii. We show how to include a term which accounts for the evolution of bias, which is directly related to the fact that voids move. The void motions are approximately independent of void size, so they are more significant for smaller voids that are typically more numerous. This term also contributes to void-matter pairwise velocities: including it is necessary for modeling the typical outflow speeds around voids. It is, therefore, important for void redshift space distortions. Finally, we show that the excursion set peaks/troughs approach provides a useful, but not perfect framework for describing void profiles and their evolution.

astro-ph.CO↗

arXiv2018

Modeling Nearly Spherical Pure-bulge Galaxies with a Stellar Mass-to-Light Ratio Gradient under the $Λ$CDM and MOND Paradigms: I. Methodology, Dynamical Stellar Mass, and Fundamental Mass Plane

We carry out spherical Jeans modeling of nearly round pure-bulge galaxies selected from the ATLAS$^{\rm 3D}$ sample. Our modeling allows for gradients in the stellar mass-to-light ratio ($M_\star/L$) through analytic prescriptions parameterized with a `gradient strength' $K$ introduced to accommodate any viable gradient. We use a generalized Osipkov-Merritt model for the velocity dispersion (VD) anisotropy. We produce Monte Carlo sets of models based on the stellar VD profiles under both the $Λ$CDM and MOND paradigms. Here, we describe the galaxy data, the empirical inputs, and the modeling procedures of obtaining the Monte Carlo sets. We then present the projected dynamical stellar mass, $M_{\rm \star e}$, within the effective radius $R_{\rm e}$, and the fundamental mass plane (FMP) as a function of $K$. We find the scaling of the $K$-dependent mass with respect to the ATLAS$^{\rm 3D}$ reported mass as: $\log_{10} \left[M_{\star{\rm e}}(K)/M_{\star{\rm e}}^{\rm A3D} \right] = a' + b' K$ with $a'=-0.019\pm 0.012$ and $b'=-0.18\pm 0.02$ ($Λ$CDM), or $a'=-0.023\pm 0.014$ and $b'=-0.23\pm 0.03$ (MOND), for $0\le K < 1.5$. The FMP has coefficients consistent with the virial expectation and only the zero-point scales with $K$. The median value of $K$ for the ATLAS$^{\rm 3D}$ galaxies is $\langle K\rangle =0.53^{+0.05}_{-0.04}$. We perform a similar analysis of the much larger SDSS DR7 spectroscopic sample. In this case, only the VD within a single aperture is available, so we impose the additional requirement that the VD slope be similar to that in the ATLAS$^{\rm 3D}$ galaxies. Our analysis of the SDSS galaxies suggests a positive correlation of $K$ with stellar mass.

astro-ph.GA↗

arXiv2018

The Excursion set approach: Stratonovich approximation and Cholesky decomposition

The excursion set approach is a framework for estimating how the number density of nonlinear structures in the cosmic web depends on the expansion history of the universe and the nature of gravity. A key part of the approach is the estimation of the first crossing distribution of a suitably chosen barrier by random walks having correlated steps: The shape of the barrier is determined by the physics of nonlinear collapse, and the correlations between steps by the nature of the initial density fluctuation field. We describe analytic and numerical methods for calculating such first up-crossing distributions. While the exact solution can be written formally as an infinite series, we show how to approximate it efficiently using the Stratonovich approximation. We demonstrate its accuracy using Monte-Carlo realizations of the walks, which we generate using a novel Cholesky-decomposition based algorithm, which is significantly faster than the algorithm that is currently in the literature.

astro-ph.CO↗

arXiv2018

Bimodal Formation Time Distribution for Infall Dark Matter Halos

We use a 200 $h^{-1}Mpc$ a side N-body simulation to study the mass accretion history (MAH) of dark matter halos to be accreted by larger halos, which we call infall halos. We define a quantity $a_{\rm nf}\equiv (1+z_{\rm f})/(1+z_{\rm peak})$ to characterize the MAH of infall halos, where $z_{\rm peak}$ and $z_{\rm f}$ are the accretion and formation redshifts, respectively. We find that, at given $z_{\rm peak}$, their MAH is bimodal. Infall halos are dominated by a young population at high redshift and by an old population at low redshift. For the young population, the $a_{\rm nf}$ distribution is narrow and peaks at about $1.2$, independent of $z_{\rm peak}$, while for the old population, the peak position and width of the $a_{\rm nf}$ distribution both increases with decreasing $z_{\rm peak}$ and are both larger than those of the young population. This bimodal distribution is found to be closely connected to the two phases in the MAHs of halos. While members of the young population are still in the fast accretion phase at $z_{\rm peak}$, those of the old population have already entered the slow accretion phase at $z_{\rm peak}$. This bimodal distribution is not found for the whole halo population, nor is it seen in halo merger trees generated with the extended Press-Schechter formalism. The infall halo population at $z_{\rm peak}$ are, on average, younger than the whole halo population of similar masses identified at the same redshift. We discuss the implications of our findings in connection to the bimodal color distribution of observed galaxies and to the link between central and satellite galaxies.

astro-ph.CO↗