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Refracted Gravity (RG) is a a classical theory of gravity where a gravitational permittivity $ a monotonically-increasing function of the local density rho , is introduced in the Poisson equation to mimic the effect of dark matter at astrophysical scales. We use high precision spectroscopic data of two massive galaxy clusters, MACS J1206.2-0847 at redshift z=0.44, and Abell S1063 (RXC J2248.7-4431) at z=0.35, to determine the total gravitational potential in the context of RG and to constrain the three, supposedly universal, free parameters of this model. Using an upgraded version of the MG-MAMPOSSt algorithm, we perform a kinematic analysis which combines the velocity distribution of the cluster galaxies and the velocity dispersion profile of the stars within the Brightest Cluster Galaxy (BCG). The unprecedented dataset used has been obtained by an extensive spectroscopic campaign carried out with the VIMOS and MUSE spectrographs at the ESO VLT. We found that RG describes the kinematics of these two clusters as well as Newtonian gravity, although the latter is slightly preferred. However, (i) each cluster requires a different set of the three free RG parameters, and (ii) the two sets are inconsistent with other results in the literature at different scales. We discuss the limitation of the method used to constrain the RG parameters as well as possible systematic effects which can give rise to the observed tension, notably deviations from the spherical symmetry and from the dynamical equilibrium of the clusters., Comment: 10 pages, 6 figures. Submitted to A&A

We use simulated cluster member galaxies from Illustris TNG300-1 to develop a technique for measuring the galaxy cluster mass accretion rate (MAR) that can be applied directly to observations. We analyze 1318 IllustrisTNG clusters of galaxies with $M_{200c}>10^{14}$M$_\odot$ and $0.01\leq z \leq 1.04$. The MAR we derive is the ratio between the mass of a spherical shell located in the infall region and the time for the infalling shell to accrete onto the virialized region of the cluster. At fixed redshift, an $\sim 1$ order of magnitude increase in $M_{200c}$ results in a comparable increase in MAR. At fixed mass, the MAR increases by a factor of $\sim 5$ from $z=0.01$ to $z=1.04$. The MAR estimates derived from the caustic technique are unbiased and lie within 20% of the MARs based on the true mass profiles. This agreement is crucial for observational derivation of the MAR. The IllustrisTNG results are also consistent with (i) previous merger tree approaches based on N-body dark matter only simulations and with (ii) previously determined MARs of real clusters based on the caustic method. Future spectroscopic and photometric surveys will provide MARs of enormous cluster samples with mass profiles derived from both spectroscopy and weak lensing. Combined with future larger volume hydrodynamical simulations that extend to higher redshift, the MAR promises important insights into evolution of massive systems of galaxies., Comment: 14 pagers, 13 figures, 4 tables. Accepted for publication in A&A

We show how the star formation activity of galaxies is progressively inhibited from the outer region to the center of the massive cluster A2142. From an extended spectroscopic redshift survey of 2239 galaxies covering a circular area of radius $\sim 11$~Mpc from the cluster center, we extract a sample of 333 galaxies with known stellar mass, star formation rate, and spectral index $D_n4000$. We use the Blooming Tree algorithm to identify the substructures of the cluster and separate the galaxy sample into substructure galaxies, halo galaxies and outskirt galaxies. The substructure and halo galaxies are cluster members, whereas the outskirt galaxies are only weakly gravitationally bound to the cluster. For the cluster members, the star formation rate per stellar mass decreases with decreasing distance $R$ from the cluster center. Similarly, the spectral index $D_n4000$ increases with $R$, indicating an increasingly average age of the stellar population in galaxies closer to the cluster center. In addition, star formation in substructure galaxies is generally more active than in halo galaxies and less active than in outskirt galaxies, proving that substructures tend to slow down the transition between field galaxies and cluster galaxies. We finally show that most actively star forming galaxies are within the cluster infall region, whereas most galaxies in the central region are quiescent., Comment: 11 pages, 12 figures, replaced to match the version accepted by RAA

The TNG300-1 run of the IllustrisTNG simulations includes 1697 clusters of galaxies with $M_{200c}>10^{14}$M$_\odot$ covering the redshift range $0.01-1.04$. We build mock spectroscopic redshift catalogues of simulated galaxies within these clusters and apply the caustic technique to estimate the cumulative cluster mass profiles. We compute the total true cumulative mass profile from the 3D simulation data and calculate the ratio of caustic mass to total 3D mass, $\mathcal{F}_\beta$, as a function of cluster-centric distance and identify the radial range where $\mathcal{F}_\beta$ is roughly constant. The filling factor, $\mathcal{F}_\beta=0.41\pm 0.08$, is constant on a plateau that covers a wide cluster-centric distance range, $(0.6-4.2)R_{200c}$. This calibration is insensitive to redshift. The calibrated caustic mass profiles are unbiased, with an average uncertainty of $23\%$. At $R_{200c}$, the average $M^C/M^{3D}=1.03\pm 0.22$; at $2R_{200c}$, the average $M^C/M^{3D}=1.02\pm 0.23$. Simulated galaxies are unbiased tracers of the mass distribution. IllustrisTNG is a broad statistical platform for application of the caustic technique to large samples of clusters with spectroscopic redshifts for $\gtrsim 200$ members in each system. These observations will allow extensive comparisons with weak lensing masses and will complement other techniques for measuring the growth rate of structure in the universe., Comment: 11 pages, 9 figures, 2 tables

We use the kinematic data of the stars in eight dwarf spheroidal galaxies to assess whether $f(R)$ gravity can fit the observed profiles of the line-of-sight velocity dispersion of these systems without resorting to dark matter. Our model assumes that each galaxy is spherically symmetric and has a constant velocity anisotropy parameter $\beta$ and constant mass-to-light ratio consistent with stellar population synthesis models. We solve the spherical Jeans equation that includes the Yukawa-like gravitational potential appearing in the weak field limit of $f(R)$ gravity, and a Plummer density profile for the stellar distribution. The $f(R)$ velocity dispersion profiles depend on two parameters: the scale length $\xi^{-1}$, below which the Yukawa term is negligible, and the boost of the gravitational field $\delta>-1$. $\delta$ and $\xi$ are not universal parameters, but their variation within the same class of objects is expected to be limited. The $f(R)$ velocity dispersion profiles fit the data with a value $\xi^{-1}= 1.2^{+18.6}_{-0.9}$ Mpc for the entire galaxy sample. On the contrary, the values of $\delta$ show a bimodal distribution that picks at $\bar{\delta}=-0.986\pm0.002$ and $\bar{\delta}=-0.92\pm0.01$. These two values disagree at $6\sigma$ and suggest a severe tension for $f(R)$ gravity. It remains to be seen whether an improved model of the dwarf galaxies or additional constraints provided by the proper motions of stars measured by future astrometric space missions can return consistent $\delta$'s for the entire sample and remove this tension., Comment: 11 pages, 4 figures, 2 Tables. Accepted for publication on MNRAS

We show that measuring the proper motion of ${{\sim 2000}}$ stars within a dwarf galaxy, with an uncertainty of 1 km/s at most, can establish whether the Dark Matter (DM) density profile of the dwarf has a central core or cusp. We derive these limits by building mock star catalogues similar to those expected from future astrometric {\it Theia}-like missions and including celestial coordinates, radial velocity and proper motion of the stars. The density field of the DM halo of the dwarf is sampled from an extended Navarro-Frank-White (eNWF) spherical model, whereas the number density distribution of the stars is a Plummer sphere. The velocity field of the stars is set according to the Jeans equations. A Monte Carlo Markov Chain algorithm applied to a sample of $N\gtrsim 2000$ stars returns unbiased estimates of the eNFW DM parameters within $10\%$ of the true values and with $1\sigma$ relative uncertainties $\lesssim 20$\%. The proper motions of the stars lift the degeneracy among the eNFW parameters which appears when the line-of-sight velocities alone are available. {Our analysis demonstrates that, by estimating the log-slope of the mass density profile estimated at the half-light radius, a sample of $N=2000$ stars can distinguish between a core and a cusp at more than $8\sigma$.} Proper motions also return unbiased estimates of the dwarf mass profile with $1\sigma$ uncertainties that decrease, on average, from 2.65 dex to 0.15 dex when the size of the star sample increases from $N=100$ to $N=6000$ stars. The measure of the proper motions can thus strongly constrain the distribution of DM in nearby dwarfs and provides a fundamental contribution to understanding the nature and the properties of DM., Comment: 14 pages, 10 Figures and 5 Tables. Accepted for publication on MNRAS

We show that $\varsigma$, the radial location of the minimum in the differential radial mass profile $M^\prime(r)$ of a galaxy cluster, can probe the theory of gravity. We derived $M^\prime(r)$ of the dark matter halos of galaxy clusters from N-body cosmological simulations that implement two different theories of gravity: standard gravity in the $\Lambda$CDM model, and $f(R)$. We extracted 49169 dark matter halos in 11 redshift bins in the range $0\leq z\leq 1$ and in three different mass bins in the range $0.9

Clusters of galaxies are powerful probes with which to study cosmology and astrophysics. However, for many applications an accurate measurement of a cluster's mass is essential. A systematic underestimate of hydrostatic masses from X-ray observations (the so-called hydrostatic bias) may be responsible for tension between the results of different cosmological measurements. We compare X-ray hydrostatic masses with masses estimated using the caustic method (based on galaxy velocities) in order to explore the systematic uncertainties of both methods and place new constraints on the level of hydrostatic bias. Hydrostatic and caustic mass profiles were determined independently for a sample of 44 clusters based on Chandra observations of clusters from the Hectospec Cluster Survey. This is the largest systematic comparison of its kind. Masses were compared at a standardised radius ($R_{500}$) using a model that includes possible bias and scatter in both mass estimates. The systematics affecting both mass determination methods were explored in detail. The hydrostatic masses were found to be systematically higher than caustic masses on average, and we found evidence that the caustic method increasingly underestimates the mass when fewer galaxies are used to measure the caustics. We limit our analysis to the 14 clusters with the best-sampled caustics where this bias is minimised ($\ge210$ galaxies), and find that the average ratio of hydrostatic to caustic mass at $R_{500}$ is $M_X/M_C=1.12^{+0.11}_{-0.10}$. We interpret this result as a constraint on the level of hydrostatic bias, favouring small or zero levels of hydrostatic bias (less than $20\%$ at the $3\sigma$ level). However, we find systematic uncertainties associated with both mass estimation methods remain at the $10-15\%$ level, which would permit significantly larger levels of hydrostatic bias., Comment: 15 pages plus appendices. Updated to match version accepted for publication in A&A. Updates include additional tests of systematics. Main results are unchanged

We discuss a spectroscopic survey of the strong lensing cluster A1489 that includes redshifts for 195 cluster members along with central velocity dispersions for 188 cluster members. The caustic technique applied to the redshift survey gives the dynamical parameters $M_{200} = (1.25~\pm~0.09) \times 10^{15}~M_\odot$, $r_{200} = 1.97~\pm~{0.05}$ Mpc, and a cluster line-of sight velocity dispersion $1150~\pm~{72}~$km$~$s$^{-1}$ within $r_{200}$. These parameters are very similar to those of other strong lensing systems with comparably large Einstein radii. We use the spectroscopy and deep photometry to demonstrate that A1489 is probably dynamically active; its four BCGs have remarkably different rest frame radial velocities. Like other massive strong lensing clusters, the velocity dispersion function for members of A1489 shows an excess for dispersions $\geq~250~$km$~$s$^{-1}$. The central dispersions also provide enhanced constraints on future lensing models., Comment: 20 pages, 13 figures

We propose a new method to determine the shape of the gravitational potential of the dark matter (DM) halo of the Milky Way (MW) with the galactocentric tangential velocities of a sample of hypervelocity stars (HVSs). We compute the trajectories of different samples of HVSs in a MW where the baryon distribution is axisymmetric and the DM potential either is spherical or is spheroidal or triaxial with radial-dependent axis ratios. We determine the shape of the DM potential with the distribution of the latitudinal velocity $|v_{\vartheta}|$ in axisymmetric Galactic potentials, or with the distribution of $|v_{\vartheta}|$ and of a function $\bar v_{\varphi}$ of the azimuthal velocity in non-axisymmetric Galactic potentials. We recover the correct shape of the DM potential by comparing the distribution of $|v_{\vartheta}|$ and $\bar v_{\varphi}$ against the corresponding distributions of mock samples of HVSs that traveled in DM halos of different shapes. We use the largest possible sample of $\sim 800$ HVSs of $4~M_\odot$ ejected with the Hills mechanism at a rate $\sim 10^{-4}$ yr$^{-1}$, currently outgoing, and located at more than 10 kpc from the Galactic center. In our ideal case of galactocentric velocities with null uncertainties and no observational limitations, our method recovers the correct shape of the DM potential with a success rate $S\gtrsim 89\%$ in axisymmetric Galactic potentials, and $S > 96\%$ in the explored non-axisymmetric cases. The unsuccessful cases yield axis ratios of the DM potential that are off by $\pm 0.1$. The success rate decreases with decreasing sample size: for example, for a spherical DM halo, $S$ drops from $\sim 98\%$ to $\sim 38\%$ when the sample size decreases from $\sim 800$ to $\sim 40$ HVSs. A robust determination of the shape of the DM potential thus requires the measure of the galactocentric velocity of a few hundred genuine HVSs., Comment: 29 pages, 20 figures, 5 tables. Accepted in Astronomy and Astrophysics

Sky survey telescopes and powerful targeted telescopes play complementary roles in astronomy. In order to investigate the nature and characteristics of the motions of very faint objects, a flexibly-pointed instrument capable of high astrometric accuracy is an ideal complement to current astrometric surveys and a unique tool for precision astrophysics. Such a space-based mission will push the frontier of precision astrometry from evidence of Earth-mass habitable worlds around the nearest stars, to distant Milky Way objects, and out to the Local Group of galaxies. As we enter the era of the James Webb Space Telescope and the new ground-based, adaptive-optics-enabled giant telescopes, by obtaining these high precision measurements on key objects that Gaia could not reach, a mission that focuses on high precision astrometry science can consolidate our theoretical understanding of the local Universe, enable extrapolation of physical processes to remote redshifts, and derive a much more consistent picture of cosmological evolution and the likely fate of our cosmos. Already several missions have been proposed to address the science case of faint objects in motion using high precision astrometry missions: NEAT proposed for the ESA M3 opportunity, micro-NEAT for the S1 opportunity, and Theia for the M4 and M5 opportunities. Additional new mission configurations adapted with technological innovations could be envisioned to pursue accurate measurements of these extremely small motions. The goal of this White Paper is to address the fundamental science questions that are at stake when we focus on the motions of faint sky objects and to briefly review instrumentation and mission profiles., Comment: arXiv admin note: substantial text overlap with arXiv:1910.08028, arXiv:1707.01348

We estimate the mass accretion rate (MAR) of the 346 clusters of galaxies in the HectoMAP Cluster Survey. The clusters span the redshift range $0.17-0.42$ and the $M_{200}$ mass range $\approx (0.5 - 3.5)\cdot 10^{14} M_\odot$. The MAR estimate is based on the caustic technique along with a spherical infall model. Our analysis extends the measurement of MARs for 129 clusters at $z<0.3$ from the Cluster Infall Regions in the Sloan Digital Sky Survey (CIRS) and the Hectospec Cluster Survey (HeCS) to redshift $z \sim 0.42$. Averaging over redshift, low-mass clusters with $M_{200}\sim 0.7\cdot 10^{14} M_\odot$ accrete $\sim 3\cdot 10^4 M_\odot$yr$^{-1}$; more massive clusters with $M_{200}\sim 2.8\cdot 10^{14} M_\odot$ accrete $\sim 1\cdot 10^5 M_\odot$yr$^{-1}$. Low- and high-mass clusters increase their MAR by $\sim 46\%$ and $\sim 84\%$, respectively, as the redshift increases from $z\sim 0.17-0.29$ to $z\sim 0.34-0.42$. The MARs at fixed redshift increase with mass and MARs at fixed mass increase with redshift in agreement with $\Lambda$CDM cosmological model for hierarchical structure formation. We consider the extension of MAR measurements to $z \sim 1$., Comment: 14 pages, 5 figures, 2 tables

We propose a covariant formulation of refracted gravity (RG), a classical theory of gravity based on the introduction of gravitational permittivity (GP), a monotonic function of the local mass density, in the standard Poisson equation. GP mimics dark matter (DM) phenomenology. The covariant formulation of RG (CRG) that we propose belongs to the class of scalar-tensor theories, where the scalar field $\varphi$ has a self-interaction potential $V(\varphi)=-\Xi\varphi$, with $\Xi$ a normalization constant. We show that $\varphi$ is twice the GP in the weak-field limit. Far from a spherical source of density $\rho_s(r)$, the transition between the Newtonian and the RG regime appears below the acceleration scale $a_\Xi=(2\Xi-8\pi G\rho/\varphi)^{1/2}$, with $\rho=\rho_s+\rho_{bg}$, $\rho_{bg}$ being an isotropic and homogeneous background. In the limit $2\Xi\gg 8\pi G\rho/\varphi$, we obtain $a_\Xi\sim 10^{-10}$~m~s$^{-2}$. This is comparable to the acceleration $a_0$ originally introduced in MOND. From CRG, we also derived the modified Friedmann equations for an expanding, homogeneous, and isotropic universe. We find that the same scalar field that mimics DM also drives the accelerated expansion of the Universe. From the stress-energy tensor of $\varphi$, we derived the equation of state of a redshift-dependent effective dark energy (DE) $w_{DE}=p_{DE}/\rho_{DE}$. Current observational constraints on $w_{DE}$ and distance modulus data of SNIa suggest that $\Xi$ has a comparable value to the cosmological constant $\Lambda$ in the standard model. CRG, therefore, suggests a natural explanation of the known relation $a_0\sim \Lambda^{1/2}$ and appears to describe both the dynamics of cosmic structure and the expanding Universe with a single scalar field, highlighting a possible deep connection between phenomena currently attributed to DM and DE separately., Comment: 16 pages, 6 appendices, 3 figures, matches the accepted version in A&A

We apply a friends-of-friends (FoF) algorithm to identify galaxy clusters and we use the catalog to explore the evolutionary synergy between BCGs and their host clusters. We base the cluster catalog on the dense HectoMAP redshift survey (2000 redshifts deg$^{-2}$). The HectoMAP FoF catalog includes 346 clusters with 10 or more spectroscopic members. We list these clusters and their members (5992 galaxies with a spectroscopic redshift). We also include central velocity dispersions ($\sigma_{*, BCG}$) for all of the FoF cluster BCGs, a distinctive feature of the HectoMAP FoF catalog. HectoMAP clusters with higher galaxy number density (80 systems) are all genuine clusters with a strong concentration and a prominent BCG in Subaru/Hyper Suprime-Cam images. The phase-space diagrams show the expected elongation along the line-of-sight. Lower-density systems include some false positives. We establish a connection between BCGs and their host clusters by demonstrating that $\sigma_{*,BCG}/\sigma_{cl}$ decreases as a function of cluster velocity dispersion ($\sigma_{cl}$), in contrast, numerical simulations predict a constant $\sigma_{*, BCG}/\sigma_{cl}$. Sets of clusters at two different redshifts show that BCG evolution in massive systems is slow over the redshift range $z < 0.4$. The data strongly suggest that minor mergers may play an important role in BCG evolution in these clusters ($\sigma_{cl} \gtrsim 300$ km s$^{-1}$). For systems of lower mass ($\sigma_{cl} < 300$ km s$^{-1}$), the data indicate that major mergers may play a significant role. The coordinated evolution of BCGs and their host clusters provides an interesting test of simulations in high density regions of the universe., Comment: 20 pages, 16 figures, 3 tables. Submitted to the ApJ

We show that measuring the velocity components of hypervelocity stars (HVSs) can discriminate between modified Newtonian dynamics (MOND) and Newtonian gravity. HVSs are ejected from the Galactic center on radial trajectories with a null tangential velocity component in the reference frame of the Galaxy. They acquire tangential components due to the nonspherical components of the Galactic gravitational potential. Axisymmetric potentials only affect the latitudinal components, $v_\theta$, and non-null azimuthal components, $v_\phi$, originate from non-axisymmetric matter distributions. For HVSs with sufficiently high ejection speed, $v_\phi$ is proportionate to the deviation of the gravitational potential from axial symmetry. The ejection velocity threshold is $\sim$ 750 km/s for 4 $M_{\odot}$ stars and increases with decreasing HVS mass. We determine the upper limit of $v_\phi$ as a function of the galactocentric distance for these high-speed HVSs if QUMOND, the quasi-linear formulation of MOND, is the correct theory of gravity and either the triaxial Galactic bulge or a nonspherical hot gaseous halo is the primary source of $v_\phi$. In Newtonian gravity, the HVSs within 60 kpc of the Galactic center may easily have $v_\phi$ values higher than the QUMOND upper limit if the dark matter (DM) halo is triaxial or if the DM halo and the baryonic components are axisymmetric but their two axes of symmetry are misaligned. Therefore, even a limited sample of high-speed HVSs could distinguish between QUMOND and the DM model. This test is currently limited by (i) the lack of a proper procedure to assess the HVS nature of a star in the model to be constrained; and (ii) the present uncertainties on $v_\phi$, which are a factor of $\sim 10$ too large. A proper procedure to assess the HVS nature of the stars and astrometric measurements with microarcsecond precision would make this test feasible., Comment: 16 pages, 15 figures. Minor modifications, matched with the published version

We tested whether refracted gravity, a theory of modified gravity that describes the dynamics of galaxies without the aid of dark matter, can model the dynamics of the three massive elliptical galaxies, NGC 1407, NGC 4486, and NGC 5846, out to $\sim$$10R_{\rm e}$, where the baryonic mass component fades out and dark matter is required in Newtonian gravity. We probed these outer regions with the kinematics of the globular clusters provided by the SLUGGS survey. Refracted gravity mimics dark matter with the gravitational permittivity, a monotonic function of the local mass density depending on three parameters, $\epsilon_0$, $\rho_{\rm c}$, and $Q$, which are expected to be universal. Refracted gravity satisfactorily reproduces the velocity dispersion profiles of the stars and red and blue globular clusters, with stellar mass-to-light ratios in agreement with stellar population synthesis models, and orbital anisotropy parameters consistent with previous results obtained in Newtonian gravity with dark matter. The sets of the three parameters of the gravitational permittivity found for each galaxy are consistent with each other within $\sim$2$\sigma$. We compare the mean $\{\epsilon_0,Q,\log_{10}\left[\rho_{\rm c}\left(\mathrm{g}\, \mathrm{cm}^{-3}\right)\right]\} = \{0.089^{+0.038}_{-0.035}, 0.47^{+0.29}_{-0.21}, -24.25^{+0.28}_{-0.20}\}$ found here with the means of the parameters required to model the rotation curves and vertical velocity dispersion profiles of 30 disk galaxies from the DiskMass Survey (DMS): $\rho_{\rm c}$ and $Q$ agree within 1$\sigma$ with the DMS values, whereas $\epsilon_0$ agrees within 3$\sigma$. This agreement suggests that ellipticals and disk galaxies allow for common values of the parameters of the permittivity and supports the universality of the permittivity function., Comment: 19 pages, 9 figures, 7 tables, published in Astronomy & Astrophysics in January 2022, Volume 657, Page A133, accepted for publication on 12 October 2021. v2: changes after refereeing process

The cold dark matter model successfully explains both the emergence and evolution of cosmic structures on large scales and, when we include a cosmological constant, the properties of the homogeneous and isotropic Universe. However, the cold dark matter model faces persistent challenges on the scales of galaxies. {Indeed,} N-body simulations predict some galaxy properties that are at odds with the observations. These discrepancies are primarily related to the dark matter distribution in the innermost regions of the halos of galaxies and to the dynamical properties of dwarf galaxies. They may have three different origins: (1) the baryonic physics affecting galaxy formation is still poorly understood and it is thus not properly included in the model; (2) the actual properties of dark matter differs from those of the conventional cold dark matter; (3) the theory of gravity departs from General Relativity. Solving these discrepancies is a rapidly evolving research field. We illustrate some of the solutions proposed} within the cold dark matter model, and solutions when including warm dark matter, self-interacting dark matter, axion-like particles, or fuzzy dark matter. { We also illustrate some modifications of the theory of gravity: Modified Newtonian Dynamics (MOND), MOdified Gravity (MOG), and $f(R)$ gravity., Comment: 70 pages; 27 Figures; Invited Review accepted for publication on Universe. Special Issue "Theories of Gravity: Alternatives to the Cosmological and Particle Standard Models"

We introduce a new kinematic method to investigate the structure of open star clusters. We adopt a hierarchical clustering algorithm that uses the celestial coordinates and the proper motions of the stars in the field of view of the cluster to estimate a proxy of the pairwise binding energy of the stars and arrange them in a binary tree. The cluster substructures and their members are identified by trimming the tree at two thresholds, according to the $\sigma$-plateau method. Testing the algorithm on 100 mock catalogs shows that, on average, the membership of the identified clusters is $(91.5\pm 3.5)$\% complete and the fraction of unrelated stars is $(10.4\pm 2.0)$\%. We apply the algorithm to the stars in the field of view of the Perseus double cluster from the Data Release 2 of Gaia. This approach identifies a single structure, Sub1, that separates into two substructures, Sub1-1 and Sub1-2. These substructures coincide with $h$ Per and $\chi$ Per: the distributions of the proper motions and the color-magnitude diagrams of the members of Sub1-1 and Sub1-2 are fully consistent with those of $h$ Per and $\chi$ Per reported in the literature. These results suggest that our hierarchical clustering algorithm can be a powerful tool to unveil the complex kinematic information of star clusters., Comment: 16 pages, 22 figures, accepted for publication in ApJ

We measure the central stellar velocity dispersion function for quiescent galaxies in a set of nine northern clusters in the redshift range $0.18 < z < 0.29$ and with strong lensing arcs in Hubble Space Telescope images. The velocity dispersion function links galaxies directly to their dark matter halos. From dense SDSS and MMT/Hectospec spectroscopy we identify $231 - 479$ spectroscopic members in each cluster. We derive physical properties of cluster members including redshift, $D_{n}4000$, and central stellar velocity dispersion and we include a table of these measurements for 3419 cluster members. We construct the velocity dispersion functions for quiescent galaxies with $D_{n}4000 > 1.5$ and within $R_{200}$. The cluster velocity dispersion functions all show excesses at $\sigma \gtrsim 250 km s^{-1}$ compared to the field velocity dispersion function. The velocity dispersion function slope at large velocity dispersion ($\sigma > 160 km s^{-1}$) is steeper for more massive clusters, consistent with the trend observed for cluster luminosity functions. The spatial distribution of galaxies with large velocity dispersion at radii larger than $R_{200}$ further underscores the probable major role of dry mergers in the growth of massive cluster galaxies during cluster assembly., Comment: 16 pages, 12 figures, Accepted for publication in the ApJ

We derive the distribution of the phantom dark matter in the eight classical dwarf galaxies surrounding the Milky Way, under the assumption that modified Newtonian dynamics (MOND) is the correct theory of gravity. According to their observed shape, we model the dwarfs as axisymmetric systems, rather than spherical systems, as usually assumed. In addition, as required by the assumption of the MOND framework, we realistically include the external gravitational field of the Milky Way and of the large-scale structure beyond the Local Group. For the dwarfs where the external field dominates over the internal gravitational field, the phantom dark matter has, from the star distribution, an offset of ~0.1-0.2 kpc, depending on the mass-to-light ratio adopted. This offset is a substantial fraction of the dwarf half-mass radius. For Sculptor and Fornax, where the internal and external gravitational fields are comparable, the phantom dark matter distribution appears disturbed with spikes at the locations where the two fields cancel each other; these features have little connection with the distribution of the stars within the dwarfs. Finally, we find that the external field due to the large-scale structure beyond the Local Group has a very minor effect. The features of the phantom dark matter we find represent a genuine prediction of MOND, and could thus falsify this theory of gravity in the version we adopt here if they are not observationally confirmed., Comment: 15 pages, 11 figures. This version contains minor corrections included in the published paper

We use a new spherical accretion recipe tested on N-body simulations to measure the observed mass accretion rate (MAR) of 129 clusters in the Cluster Infall Regions in the Sloan Digital Sky Survey (CIRS) and in the Hectospec Cluster Survey (HeCS). The observed clusters cover the redshift range of $0.01

We test if Refracted Gravity (RG) can describe the dynamics of disk galaxies without resorting to dark matter. RG is a classical theory of gravity where the standard Poisson equation is modified by the gravitational permittivity, $\epsilon$, a universal monotonic function of the local mass density. We use the rotation curves and the vertical velocity dispersions of 30 galaxies in the DiskMass Survey (DMS) to determine $\epsilon$. RG describes the kinematic profiles with mass-to-light ratios consistent with SPS models, and disk thicknesses in agreement with observations, once observational biases are considered. Our results rely on setting the three free parameters of $\epsilon$ for each galaxy. However, we show that the differences of these parameters from galaxy to galaxy could be ascribed to statistical fluctuations. We adopt an approximate method to find a single set of parameters that may properly describe the kinematics of the entire sample and suggest the universality of $\epsilon$. Finally, we show that the RG models of the individual rotation curves can only partly describe the radial acceleration relation (RAR). Evidently, the RG models underestimate the observed accelerations of 0.1-0.3 dex at low Newtonian accelerations. Another problem is the strong correlation, at much more than 5$\sigma$, between the residuals of the RAR models and three radially-dependent properties of galaxies, whereas the DMS data show a considerably less significant correlation, at more than 4$\sigma$, for only two of them. These correlations might originate the non-null intrinsic scatter of the RG models, at odds with the observed intrinsic scatter of galaxy samples different from DMS, which is consistent with 0. Further studies are required to assess if these discrepancies in the RAR originate from the DMS sample, which might not be ideal for deriving the RAR, or if they are genuine failures of RG., Comment: 36 pages, 22 figures, 7 tables, published in Astronomy & Astrophysics, Section 2. Astrophysical processes of Astronomy and Astrophysics; v2: minor corrections due to editorial process, notes added below the tables, arXiv references updated, italics removed from the title

We explore connections between brightest cluster galaxies (BCGs) and their host clusters. We first construct a HeCS-omnibus cluster sample including 227 galaxy clusters within $0.02 < z < 0.30$; the total number of spectroscopic members from MMT/Hectospec and SDSS observations is 52325. Taking advantage of the large spectroscopic sample, we compute physical properties of the clusters including the dynamical mass and cluster velocity dispersion ($\sigma_{cl}$). We also measure the central stellar velocity dispersion of the BCGs ($\sigma_{*,BCGs}$) to examine the relation between BCG velocity dispersion and cluster velocity dispersion for the first time. The observed relation between BCG velocity dispersion and the cluster velocity dispersion is remarkably tight. Interestingly, the $\sigma_{*, BCG} / \sigma_{cl}$ ratio decreases as a function of $\sigma_{cl}$ unlike the prediction from the numerical simulation of Dolag et al. (2010). The trend in $\sigma_{*, BCG} / \sigma_{cl}$ suggests that the BCG formation is more efficient in lower mass halos., Comment: 11 pages, 9 figures, 3 tables, submitted to ApJ, comments are welcome

Sky survey telescopes and powerful targeted telescopes play complementary roles in astronomy. In order to investigate the nature and characteristics of the motions of very faint objects, a flexibly-pointed instrument capable of high astrometric accuracy is an ideal complement to current astrometric surveys and a unique tool for precision astrophysics. Such a space-based mission will push the frontier of precision astrometry from evidence of earth-massed habitable worlds around the nearest starts, and also into distant Milky way objects up to the Local Group of galaxies. As we enter the era of the James Webb Space Telescope and the new ground-based, adaptive-optics-enabled giant telescopes, by obtaining these high precision measurements on key objects that Gaia could not reach, a mission that focuses on high precision astrometry science can consolidate our theoretical understanding of the local universe, enable extrapolation of physical processes to remote redshifts, and derive a much more consistent picture of cosmological evolution and the likely fate of our cosmos. Already several missions have been proposed to address the science case of faint objects in motion using high precision astrometry ESA missions: NEAT for M3, micro-NEAT for S1 mission, and Theia for M4 and M5. Additional new mission configurations adapted with technological innovations could be envisioned to pursue accurate measurements of these extremely small motions. The goal of this white paper is to address the fundamental science questions that are at stake when we focus on the motions of faint sky objects and to briefly review quickly instrumentation and mission profiles., Comment: White paper for the Voyage 2050 long-term plan in the ESA Science Programme. arXiv admin note: substantial text overlap with arXiv:1707.01348

We explore the structure of galaxy cluster Abell 2029 and its surroundings based on intensive spectroscopy along with X-ray and weak lensing observations. The redshift survey includes 4376 galaxies (1215 spectroscopic cluster members) within 40 arcmin of the cluster center; the redshifts are included here. Two subsystems, A2033 and a Southern Infalling Group (SIG) appear in the infall region based on the spectroscopy as well as on the weak lensing and X-ray maps. The complete redshift survey of A2029 also identifies at least 12 foreground and background systems (10 are extended X-ray sources) in the A2029 field; we include a census of their properties. The X-ray luminosities $L_{X}$ - velocity dispersions ($\sigma_{cl}$) scaling relations for A2029, A2033, SIG, and the foreground/background systems are consistent with the known cluster scaling relations. The combined spectroscopy, weak lensing, and X-ray observations provide a robust measure of the masses of A2029, A2033, and SIG. The total mass of the infalling groups (A2033 and SIG) is $\sim 60\%$ of the M200 of the primary cluster, A2029. Simple dynamical consid- erations suggest that A2029 will accrete these subsystems in next few Gyr. In agreement with simulations and with other clusters observed in a similar redshift range, the total mass in the A2029 infall region is comparable with the A2029 M200 and will mostly be accreted in the long-term future., Comment: 15 pages, 10 figures, ApJ submitted

To investigate the dynamics of the galaxy cluster A2142, we compile an extended catalog of 2239 spectroscopic redshifts of sources, including newly measured 237 redshifts, within 30 arcmin from the cluster center. With the $\sigma$-plateau algorithm from the caustic method, we identify 868 members and a number of substructures in the galaxy distribution both in the outskirts, out to $\sim$3.5 Mpc from the cluster center, and in the central region. In the outskirts, one substructure overlaps a falling clump of gas previously identified in the X-ray band. These substructures suggests the presence of multiple minor mergers, which are responsible for the complex dynamics of A2142, and the absence of recent or ongoing major mergers. We show that the distribution of the galaxies in the cluster core and in several substructures are consistent with the mass distribution inferred from the weak lensing signal. Moreover, we use spatially-resolved X-ray spectroscopy to measure the redshift of different regions of the intracluster medium within $\sim$3 arcmin from the cluster center. We find a ring of gas near the two X-ray cold fronts identified in previous analyses and measure a velocity of this ring of $810 \pm 330 {\rm km s^{-1}}$ larger than the cluster mean velocity. Our analysis suggests the presence of another ring surrounding the core, whose velocity is $660 \pm 300 {\rm km s^{-1}}$ larger than the cluster velocity. These X-ray features are not associated to any optical substructures, and support the core-sloshing scenario suggested in previous work.

We develop the Blooming Tree Algorithm, a new technique that uses spectroscopic redshift data alone to identify the substructures and the surrounding groups of galaxy clusters, along with their member galaxies. Based on the estimated binding energy of galaxy pairs, the algorithm builds a binary tree that hierarchically arranges all the galaxies in the field of view. The algorithm searches for buds, corresponding to gravitational potential minima on the binary tree branches; for each bud, the algorithm combines the number of galaxies, their velocity dispersion and their average pairwise distance into a parameter that discriminates between the buds that do not correspond to any substructure or group, and thus eventually die, and the buds that correspond to substructures and groups, and thus bloom into the identified structures. We test our new algorithm with a sample of 300 mock redshift surveys of clusters in different dynamical states; the clusters are extracted from a large cosmological $N$-body simulation of a $\Lambda$CDM model. We limit our analysis to substructures and surrounding groups identified in the simulation with mass larger than $10^{13} h^{-1} M_{\odot}$. With mock redshift surveys with 200 galaxies within 6 $h^{-1}$~Mpc from the cluster center, the technique recovers $ 80$\% of the real substructures and $ 60$\% of the surrounding groups; in $57$\% of the identified structures, at least 60\% of the member galaxies of the substructures and groups belong to the same real structure. These results improve by roughly a factor of two the performance of the best substructure identification algorithm currently available, the $\sigma$ plateau algorithm, and suggest that our Blooming Tree Algorithm can be an invaluable tool for detecting substructures of galaxy clusters and investigating their complex dynamics., Comment: 17 pages, 20 figures, accepted by ApJ

We show how Conformal Gravity (CG) has to satisfy a fine-tuning condition to describe the rotation curves of disk galaxies without the aid of dark matter. Interpreting CG as a gauge natural theory yields conservation laws and their associated superpotentials without ambiguities. We consider the light deflection of a point-like lens and impose that the two Schwarzschild-like metrics with and without the lens are identical at infinite distances from the lens. The energy conservation law implies that the parameter $\gamma$ in the linear term of the metric has to vanish, otherwise the two metrics are physically inaccessible from each other. This linear term is responsible to mimic the role of dark matter in disk galaxies and gravitational lensing systems. Our analysis shows that removing the need of dark matter with CG thus relies on a fine-tuning condition on $\gamma$. We also illustrate why the results of previous investigations of gravitational lensing in CG largely disagree. These discrepancies derive from the erroneous use of the deflection angle definition adopted in General Relativity, where the vacuum solution is asymptotically flat, unlike CG. In addition, the lens mass is identified with various combinations of the metric parameters. However, these identifications are arbitrary, because the mass is not a conformally invariant quantity, unlike the conserved charge associated to the energy conservation law. Based on this conservation law and by removing the fine-tuning condition on $\gamma$, i.e. by setting $\gamma=0$, the energy difference between the metric with the point-like lens and the metric without it defines a conformally invariant quantity that can in principle be used for (1) a proper derivation of light deflection in CG, and (2) the identification of the lens mass with a function of the parameters $\beta$ and $k$ of the Schwarzschild-like metric., Comment: 16 pages, 1 figure. Revised version according to the referees comments. The results reported in the original version remain unchanged

We use the dense HectoMAP redshift survey to explore the properties of 104 redMaPPer cluster candidates. The redMaPPer systems in HectoMAP cover the full range of richness and redshift (0.08 $< z <$ 0.60). Fifteen systems included in the Subaru/Hyper Suprime-Cam public data release are bona fide clusters. The median number of spectroscopic members per cluster is $\sim20$. We include redshifts of 3547 member candidates listed in the redMaPPer catalog whether they are cluster members or not. We evaluate the redMaPPer membership probability spectroscopically. The scaled richness ({\lambda}rich/S) provided by redMaPPer correlates tightly with the spectroscopic richness regardless of the cluster redshift and appears to be a better mass proxy than the original richness, {\lambda}rich. The purity (number of real systems) in redMaPPer exceeds 90% even at the lowest richness; however, there is some incompleteness. Five massive galaxy clusters (M $\gtrsim 2 \times 10^{13}$ M$_{\odot}$) associated with X-ray emission in the HectoMAP region are missing from the catalog., Comment: submitted to ApJ, a revised version in response to the referee's comments, 15 pages, 14 figures, 3 tables; data will be available when the paper is accepted

We use dense redshift surveys to explore the properties of galaxy clusters selected from the redMaPPer catalog of overdensities of red galaxies. Our new survey, HeCS-red (Hectospec Cluster Survey of red-sequence selected clusters), includes 10,589 new or remeasured redshifts from MMT/Hectospec observations of redMaPPer clusters at redshifts $z$=0.08-0.25 with large estimated richnesses (richness estimate $\lambda >64$). Our spectra confirm that each of these candidate clusters corresponds to an overdensity in redshift space. The redMaPPer photometric redshifts have a slight bias towards higher redshifts. We measure the scaling relation between velocity dispersion $\sigma_p$ and redMaPPer richness estimates $\lambda$. The observed relation shows intrinsic scatter of 24\% in velocity dispersion at fixed richness, and a range of a factor of two in measured $\sigma_p$ at fixed richness. We extend our analysis to HeCS-red-ext, a sample that includes several clusters selected by X-ray flux or SZ signal. The heterogeneous sample of 121 clusters in HeCS-red-ext shows similar intrinsic scatter, but the range of $\sigma_p$ at fixed richness increases to a factor of three. We evaluate the membership probability estimates $P_{mem}$ for individual galaxies provided by redMaPPer. The spectroscopic membership fraction is larger than $P_{mem}$ for $0.05\leq P_{mem}\leq 0.7$; conversely, it is smaller than $P_{mem}$ at $P_{mem}\geq 0.8$. We compare spectroscopic richness estimates to redMaPPer richness estimates and find good agreement on average, but a range of a factor of two in spectroscopic richness at fixed redMaPPer richness. Overall, within the high-richness and low-redshift cut of our sample, spectroscopically estimated parameters such as velocity dispersion correlate well with photometric richness estimates, although the relations contain substantial scatter., Comment: 15 pages, 16 figures, 10,589 redshifts, submitted to ApJ, comments welcome

We apply a friends-of-friends algorithm to the HectoMAP redshift survey and cross-identify associated X-ray emission in the ROSAT All-Sky Survey data (RASS). The resulting flux limited catalog of X-ray cluster survey is complete to a limiting flux of $\sim3 \times10^{-13}$ erg s$^{-1}$ cm$^{-2}$ and includes 15 clusters (7 newly discovered) with redshift $z \leq 0.4$. HectoMAP is a dense survey ($\sim1200$ galaxies deg$^{-2}$) that provides $\sim50$ members (median) in each X-ray cluster. We provide redshifts for the 1036 cluster members. Subaru/Hyper Suprime-Cam imaging covers three of the X-ray systems and confirms that they are impressive clusters. The HectoMAP X-ray clusters have an $L_{X} - {\sigma}_{cl}$ scaling relation similar to that of known massive X-ray clusters. The HectoMAP X-ray cluster sample predicts $\sim 12000 \pm3000$ detectable X-ray clusters in the RASS to the limiting flux, comparable with previous estimates., Comment: submitted to ApJ, a revised version in response to the referee's comments, 18 pages, 12 figures, 4 tables, Table 3 will be available when the paper is accepted

Compact radio galaxies with a GHz-peaked spectrum (GPS) and/or compact-symmetric-object (CSO) morphology (GPS/CSOs) are increasingly detected in the X-ray domain. Their radio and X-ray emissions are affected by significant absorption. However, the locations of the X-ray and radio absorbers are still debated. We investigated the relationship between the column densities of the total ($N_{\mathrm{H}}$) and neutral ($N_{\mathrm{HI}}$) hydrogen to statistically constrain the picture. We compiled a sample of GPS/CSOs including both literature data and new radio data that we acquired with the Westerbork Synthesis Radio Telescope for sources whose X-ray emission was either established or under investigation. In this sample, we compared the X-ray and radio hydrogen column densities, and found that $N_{\mathrm{H}}$ and $N_{\mathrm{HI}}$ display a significant positive correlation, with $N_{\mathrm{HI}} \propto N_{\mathrm{H}}^b$, where $b=0.47$ and $b=0.35$, depending on the subsample. The $N_{\mathrm{H}}$ - $N_{\mathrm{HI}}$ correlation suggests that the X-ray and radio absorbers are either co-spatial or different components of a continuous structure. The correlation displays a large intrinsic spread that we suggest to originate from fluctuations, around a mean value, of the ratio between the spin temperature and the covering factor of the radio absorber, $T_{\rm s}/C_{\rm f}$., Comment: 18 pages, 5 figures, 6 tables; final version: a few typos corrected, minor style changes

In the context of the ESA M5 (medium mission) call we proposed a new satellite mission, Theia, based on relative astrometry and extreme precision to study the motion of very faint objects in the Universe. Theia is primarily designed to study the local dark matter properties, the existence of Earth-like exoplanets in our nearest star systems and the physics of compact objects. Furthermore, about 15 $\%$ of the mission time was dedicated to an open observatory for the wider community to propose complementary science cases. With its unique metrology system and "point and stare" strategy, Theia's precision would have reached the sub micro-arcsecond level. This is about 1000 times better than ESA/Gaia's accuracy for the brightest objects and represents a factor 10-30 improvement for the faintest stars (depending on the exact observational program). In the version submitted to ESA, we proposed an optical (350-1000nm) on-axis TMA telescope. Due to ESA Technology readiness level, the camera's focal plane would have been made of CCD detectors but we anticipated an upgrade with CMOS detectors. Photometric measurements would have been performed during slew time and stabilisation phases needed for reaching the required astrometric precision., Comment: http://theia.phyip3.dur.ac.uk

Galaxies in clusters are strongly affected by their environment. They evolve according to several physical mechanisms that are active in clusters. Their efficiency can strongly depend on the orbital configuration of the galaxies. Our aim is to analyse the orbits of the galaxies in the cluster Abell 85, based on the study of the galaxy velocity anisotropy parameter. We have solved the Jeans equation under the assumption that the galaxies in A85 are collisionless objects, within the spherically symmetric gravitational potential of the virialized cluster. The mass of the cluster was estimated with X-ray and caustic analyses. We find that the anisotropy profile of the full galaxy population in A85 is an increasing monotonic function of the distance from the cluster centre: on average, galaxies in the central region (r/r200 < 0.3) are on isotropic orbits, while galaxies in the outer regions are on radial orbits. We also find that the orbital properties of the galaxies strongly depend on their stellar colour. In particular, blue galaxies are on less radial orbits than red galaxies. The different families of cluster galaxies considered here have the pseudo phase-space density profiles Q(r) and Qr(r) consistent with the profiles expected in virialized dark matter halos in $N$-body simulations. This result suggests that the galaxies in A85 have reached dynamical equilibrium within the cluster potential. Our results indicate that the origin of the blue and red colour of the different galaxy populations is the different orbital shape rather than the accretion time., Comment: 15 pages, 15 figures. Accepted for publication at MNRAS

We carried out the deep spectroscopic observations of the nearby cluster A2151 with AF2/WYFFOS@WHT. The caustic technique enables us to identify 360 members brighter than $M_r = -16$ and within 1.3$R_{200}$. We separated the members into subsamples according to photometrical and dynamical properties such as colour, local environment and infall time. The completeness of the catalogue and our large sample allow us to analyse the velocity dispersion and the luminosity functions of the identified populations. We found evidence of a cluster still in its collapsing phase. The LF of the red population of A2151 shows a deficit of dwarf red galaxies. Moreover, the normalized LFs of the red and blue populations of A2151 are comparable to the red and blue LFs of the field, even if the blue galaxies start dominating one magnitude fainter and the red LF is well represented by a single Schechter function rather than a double Schechter function. We discuss how the evolution of cluster galaxies depends on their mass: bright and intermediate galaxies are mainly affected by dynamical friction and internal/mass quenching, while the evolution of dwarfs is driven by environmental processes which need time and a hostile cluster environment to remove the gas reservoirs and halt the star formation., Comment: Accepted for publication on MNARS, 15 pages,16 figures, 6 tables

Based on an extensive redshift survey for galaxy cluster Abell 2029 and Coma, we measure the luminosity functions (LFs), stellar mass functions (SMFs) for the entire cluster member galaxies. Most importantly, we measure the velocity dispersion functions (VDFs) for quiescent members. The MMT/Hectospec redshift survey for galaxies in A2029 identifies 982 spectroscopic members; for 838 members we derive the central velocity dispersion from the spectroscopy. Coma is the only other cluster surveyed as densely. The LFs, SMFs and VDFs for A2029 and Coma are essentially identical. The SMFs of the clusters are consistent with simulations. The A2029 and Coma VDFs for quiescent galaxies have a significantly steeper slope than those of field galaxies for velocity dispersion $\lesssim 100$ km s$^{-1}$. The cluster VDFs also exceed the field at velocity dispersion $\gtrsim 250$ km s$^{-1}$. The differences between cluster and field VDFs are potentially important tests of simulations and of the formation of structure in the universe., Comment: 16 pages, 18 figures, 4 tables, submitted to ApJ

We discuss the phenomenology of gravitational lensing in the purely metric $f\left(\chi\right)$ gravity, an $f(R)$ gravity where the action of the gravitational field depends on the source mass. We focus on the strong lensing regime in galaxy-galaxy lens systems and in clusters of galaxies. Using an approximate metric solution accurate to second order of the velocity field $v/c$, we show how, in the $f\left(\chi\right)=\chi^{3/2}$ gravity, the same light deflection can be produced by point-like lenses with masses smaller than in General Relativity; this mass difference increases with increasing impact parameter and decreasing lens mass. However, for sufficiently massive point-like lenses and small impact parameters, $f\left(\chi\right)=\chi^{3/2}$ and GR yield indistinguishable light deflection angles: this regime occurs both in observed galaxy-galaxy lens systems and in the central regions of galaxy clusters. In the former systems, the GR and $f\left(\chi\right)$ masses are compatible with the mass of standard stellar populations and little or no dark matter, whereas, on the scales of the core of galaxy clusters, the presence of substantial dark matter is required both in General Relativity, and in our approximate $f\left(\chi\right)=\chi^{3/2}$ point-like lens solution. We thus conclude that our approximate metric solution of $f\left(\chi\right)=\chi^{3/2}$ is unable to describe the observed phenomenology of the strong lensing regime without the aid of dark matter., Comment: 16 pages, 3 figures, prepared for submission to JCAP; comments are welcome

For the first time, we explore the dynamics of the central region of a galaxy cluster within $r_{500}\sim 600h^{-1}$~kpc from its center by combining optical and X-ray spectroscopy. We use (1) the caustic technique that identifies the cluster substructures and their galaxy members with optical spectroscopic data, and (2) the X-ray redshift fitting procedure that estimates the redshift distribution of the intracluster medium (ICM). We use the spatial and redshift distributions of the galaxies and of the X-ray emitting gas to associate the optical substructures to the X-ray regions. When we apply this approach to Abell 85 (A85), a complex dynamical structure of A85 emerges from our analysis: a galaxy group, with redshift $z=0.0509 \pm 0.0021$ is passing through the cluster center along the line of sight dragging part of the ICM present in the cluster core; two additional groups, at redshift $z=0.0547 \pm 0.0022$ and $z=0.0570 \pm 0.0020$, are going through the cluster in opposite directions, almost perpendicularly to the line of sight, and have substantially perturbed the dynamics of the ICM. An additional group in the outskirts of A85, at redshift $z=0.0561 \pm 0.0023$, is associated to a secondary peak of the X-ray emission, at redshift $z=0.0583^{+0.0039}_{-0.0047}$. Although our analysis and results on A85 need to be confirmed by high-resolution spectroscopy, they demonstrate how our new approach can be a powerful tool to constrain the formation history of galaxy clusters by unveiling their central and surrounding structures., Comment: 12 pages, 11 figures, accepted by ApJ

The Andromeda galaxy is observed to have a system of two large dwarf ellipticals and ~13 smaller satellite galaxies that are currently co-rotating in a thin plane, in addition to 2 counter-rotating satellite galaxies. We explored the consistency of those observations with a scenario where the majority of the co-rotating satellite galaxies originated from a subhalo group, where NGC 205 was the host and the satellite galaxies occupied dark matter sub-subhalos. We ran N-body simulations of a close encounter between NGC 205 and M31. In the simulations, NGC 205 was surrounded by massless particles to statistically sample the distribution of the sub-subhalos expected in a subhalo that has a mass similar to NGC 205. We made Monte Carlo samplings and found that, using a set of reference parameters, the probability of producing a thinner distribution of sub-subhalos than the observed NGC 205 + 15 smaller satellites (thus including the 2 counter-rotators, but excluding M32) increased from <1e-8 for the initial distribution to ~0.01 at pericentre. The probability of the simulated sub-subhalos occupying the locations of the observed co-rotating satellites in the line of sight velocity versus projected on-sky distance plane is at most 0.002 for 11 out of 13 satellites. Increasing the mass of M31 and the extent of the initial distribution of sub-subhalos gives a maximum probability of 0.004 for all 13 co-rotating satellites, but the probability of producing the thinness would drop to ~ 0.001., Comment: 19 pages, 15 figures, to be published in MNRAS