We study the dependence of satellite galaxy properties on the distance to the host galaxy and the orbital motion using the SDSS data. From SDSS DR7 we find 3515 isolated satellite systems of galaxies at z<0.03 that contain 8904 satellite galaxies. Using this sample we construct a catalog of 635 satellites associated with 215 host galaxies whose spin directions are determined by our inspection of the SDSS color images and/or by spectroscopic observations in the literature. We divide satellite galaxies into prograde and retrograde orbit subsamples depending on their orbital motion respect to the spin direction of the host. We find that the number of galaxies in prograde orbit is nearly equal to that of retrograde orbit galaxies: the fraction of satellites in prograde orbit is 50+/-2%. The velocity distribution of satellites with respect to their hosts is found almost symmetric: the median bulk rotation of satellites is -1+/- 8 km/s. It is found that the radial distribution of early-type satellites in prograde orbit is strongly concentrated toward the host while that of retrograde ones shows much less concentration. We also find the orbital speed of late-type satellites in prograde orbit increases as the projected distance to the host (R) decreases while the speed decreases for those in retrograde orbit. At R less than 0.1 times the host virial radius the orbital speed decreases in both prograde and retrograde orbit cases. Prograde satellites are on average fainter than retrograde satellites for both early and late morphological types. The u-r color becomes redder as R decreases for both prograde and retrograde orbit late-type satellites. The differences between prograde and retrograde orbit satellites may be attributed to their different origin or the different strength of physical processes that they have experienced through hydrodynamic interactions with their host galaxies.
We present distributions of orbital parameters of infalling satellites of $Λ$CDM haloes in the mass range $10^{12}-10^{14}$M$_\odot$, which represent the initial conditions for the subsequent evolution of substructures within the host halo. We use merger trees constructed in a high resolution cosmological N-body simulation to trace satellite haloes, and identify the time of infall. We find signficant trends in the distribution of orbital parameters with both the host halo mass and the ratio of satellite-to-host halo masses. For all host halo masses, satellites whose infall mass is a larger fra…
We select satellite galaxies from the galaxy group catalog constructed with the SDSS spectroscopic galaxies and measure the tangential shear around these galaxies with source catalog extracted from CFHT/MegaCam Stripe-82 Survey to constrain the mass of subhalos associated with them. The lensing signal is measured around satellites in groups with masses in the range [10^{13}, 5x10^{14}]h^{-1}M_{sun}, and is found to agree well with theoretical expectation. Fitting the data with a truncated NFW profile, we obtain an average subhalo mass of log M_{sub}= 11.68 \pm 0.67 for satellites whose project…
We compute the locations of satellite galaxies in the Two-Degree Field Galaxy Redshift Survey using two sets of selection criteria and three sources of photometric data. Using the SuperCOSMOS r_F photometry, we find that the satellites are located preferentially near the major axes of their hosts, and the anisotropy is detected at a highly-significant level (confidence levels of 99.6% to 99.9%). The locations of satellites that have high velocities relative to their hosts are statistically indistinguishable from the locations of satellites that have low velocities relative to their hosts. Addi…
We present a Bayesian hierarchical inference formalism (Basilisk) to constrain the galaxy-halo connection using satellite kinematics. Unlike traditional methods, Basilisk does not resort to stacking the kinematics of satellite galaxies in bins of central luminosity, and does not make use of summary statistics, such as satellite velocity dispersion. Rather, Basilisk leaves the data in its raw form and computes the corresponding likelihood. In addition, Basilisk can be applied to flux-limited, rather than volume-limited samples, greatly enhancing the quantity and dynamic range of the data. And f…
The Sloan Digital Sky Survey (SDSS) provides data on several hundred thousand galaxies. Precise location of these galaxies in the sky, along with information about their luminosities and line-of-sight (Doppler) velocities allows one to construct a three-dimensional map of their location and estimate their line-of-sight velocity dispersion. This information, in principle, allows one to test dynamical gravity models, specifically models of satellite galaxy velocity dispersions near massive hosts. A key difficulty is the separation of true satellites from interlopers. We sidestep this problem by …
We study the abundance of satellite galaxies as a function of primary stellar mass using the SDSS/DR7 spectroscopic catalogue. In contrast with previous studies, which focussed mainly on bright primaries, our central galaxies span a wide range of stellar mass, 10^7.5 < M_*^pri/M_sun < 10^11, from dwarfs to central cluster galaxies. Our analysis confirms that the average number of satellites around bright primaries, when expressed in terms of satellite-to-primary stellar mass ratio (m_*^sat/M_*^pri), is a strong function of M_*^pri. On the other hand, satellite abundance is largely independent …
We study the correlation of orbital poles of the 11 classical satellite galaxies of the Milky Way, comparing results from previous proper motions with the independent data by Gaia DR2. Previous results on the degree of correlation and its significance are confirmed by the new data. A majority of the satellites co-orbit along the Vast Polar Structure, the plane (or disk) of satellite galaxies defined by their positions. The orbital planes of eight satellites align to $<20^\circ$ with a common direction, seven even orbit in the same sense. Most also share similar specific angular momenta, though…
In this paper we study the tidal stripping process for satellite galaxies orbiting around a massive host galaxy, and focus on its dependence on the morphology of both satellite and host galaxy. For this purpose, we use three different morphologies for the satellites: pure disc, pure bulge and a mixture bulge+disc. Two morphologies are used for the host galaxies: bulge+disc and pure bulge. We find that while the spheroidal stellar component experiences a constant power-law like mass removal, the disc is exposed to an exponential mass loss when the tidal radius of the satellite is of the same or…
We present a wide field survey of satellite galaxies in M106 (NGC 4258) covering a $1.7\degr \times 2\degr$ field around M106 using Canada-France-Hawaii Telescope/MegaCam. We find 16 satellite galaxy candidates of M106. Eight of these galaxies are found to be dwarf galaxies that are much smaller and fainter than the remaining galaxies. Four of these galaxies are new findings. Surface brightness profiles of 15 out of 16 satellite galaxies can be represented well by an exponential disk profile with varying scale length. We derive the surface number density distribution of these satellite galaxie…
We present structural measurements for the galaxies in the 0.05<z<0.0585 groups of the Zurich Environmental Study, aimed at establishing how galaxy properties depend on four environmental parameters: group halo mass M_GROUP, group-centric distance R/R_200, ranking into central or satellite, and large-scale structure density delta_LSS. Global galaxy structure is quantified both parametrically and non-parametrically. We correct all these measurements for observational biases due to PSF blurring and surface brightness effects as a function of galaxy size, magnitude, steepness of light profile and…
The orbital properties of infalling satellite halos set the initial conditions which control the subsequent evolution of subhalos and the galaxies that they host, with implications for mass stripping, star formation quenching, and merging. Using a high-resolution, cosmological N-body simulation, I examine the orbital parameters of satellite halos as they merge with larger host halos, focusing primarily on orbital circularity and pericenter. I explore in detail how these orbital parameters depend on mass and redshift. Satellite orbits become more radial and plunge deeper into their host halo at…
We extend the phenomenological study of the evolving galaxy population of Peng et al (2010) to the central/satellite dichotomy in Yang et al. SDSS groups. We find that satellite galaxies are responsible for all the environmental effects in our earlier work. The fraction of centrals that are red does not depend on their environment but only on their stellar masses, whereas that of the satellites depends on both. We define a relative satellite quenching efficiency, which is the fraction of blue centrals that are quenched upon becoming the satellite of another galaxy. This is shown to be independ…
We study the properties of building blocks (BBs, i.e. accreted satellites) and surviving satellites of present-day galaxies using the SAG semi-analytic model of galaxy formation in the context of a concordance Lambda Cold Dark Matter (LCDM) cosmology. We consider large numbers of DM halo merger trees spanning a wide range of masses (~1x10^10 - 2.14x10^15 Msun). We find higher metallicities for BBs with respect to surviving satellites, an effect produced by the same processes behind the build-up of the mass-metallicity relation. We prove that these metallicity differences arise from the higher …
Minor merging has been postulated as the most likely evolutionary path to produce the increase in size and mass observed in the massive galaxies since z$\sim$2. In this Letter, we test directly this hypothesis comparing the population of satellites around massive galaxies in cosmological simulations versus the observations. We use state-of-the-art, publically available, Millennium I and II simulations and the associated semi-analytical galaxy catalogues to explore the time evolution of the fraction of massive galaxies that have satellites, the number of satellites per galaxy, the projected dis…
We infer the local stellar-to-halo/subhalo mass relations (MRs) for central and satellite galaxies separately. We constraint this relations by using several combinations of observational data, consisting of the total galaxy stellar mass function, its decomposition into centrals and satellites, and the projected two-point correlation functions measured in different stellar mass bins. The differences among the resulting MRs are within the model-fit uncertainties (which are very small, smaller than the intrinsic scatter between galaxy and halo mass), no matter what combination of data are used. W…
Several scenarios have been suggested to explain the phase-space distribution of the Milky Way (MW) satellite galaxies in a disc of satellites (DoS). To quantitatively compare these different possibilities, a new method analysing angular momentum directions in modelled data is presented. It determines how likely it is to find sets of angular momenta as concentrated and as close to a polar orientation as is observed for the MW satellite orbital poles. The method can be easily applied to orbital pole data from different models. The observed distribution of satellite orbital poles is compared to …
In hierarchical structure formation, dark matter halos that merge with larger halos can persist as subhalos. These subhalos are likely hosts of visible galaxies. While the dense halo environment rapidly strips subhalos of their dark mass, the compact luminous material can remain intact for some time, making the correspondence of galaxies with severely stripped subhalos unclear. Many galaxy evolution models assume that satellite galaxies eventually merge with their central galaxy, but this ignores the possibility of satellite tidal disruption. We use a high-resolution $N$-body simulation of cos…
The kinematics of satellite galaxies moving in a dark matter halo are a direct probe of the underlying gravitational potential. Thus, the phase-space distributions of satellites represent a powerful tool to determine the galaxy-halo connection from observations. By stacking the signal of a large number of satellite galaxies this potential can be unlocked even for haloes hosting a few satellites on average. In this work, we test the impact of various modelling assumptions on constraints derived from analysing satellite phase-space distributions in the non-linear, 1-halo regime. We discuss their…
We present an analysis of the dynamics of the M31 satellite system. Proper motion data exist for only two of the M31 satellites. We account for this incompleteness in velocity data by a statistical analysis using a combination of the timing argument and phase-space distribution functions. The bulk of the M31 satellites are well fit by these models and we offer a table of orbital properties, including period, eccentricity and semi-major axis. This enables us to search for evidence of group infall based on orbital similarity rather than propinquity on the sky. Our results favour an association b…
Satellites within simulated massive clusters are significantly spatially correlated with each other, even when those satellites are not gravitationally bound to each other. This correlation is produced by satellites that entered their hosts relatively recently, and is undetectable for satellites that have resided in their hosts for multiple dynamical timescales. Therefore, a measurement of clustering statistics of cluster satellites may be used to determine the typical accretion redshifts of those satellites into their observed hosts. We argue that such measurements may be used to determine th…
We study the spatial distribution of satellite galaxies around isolated primaries using the Sloan Digital Sky Survey (SDSS) spectroscopic and photometric galaxy catalogues. We select isolated primaries from the spectroscopic sample and search for potential satellites in the much deeper photometric sample. For specific luminosity primaries we obtain robust statistical results by stacking as many as ~50, 000 galaxy systems. We find no evidence for any anistropy in the satellite galaxy distribution relative to the major axes of the primaries. We derive accurate projected number density profiles o…
We report the detection of two dwarf galaxies in a projected distance of ~50 kpc from NGC 7331 and suspect the physical nature of dwarfs of this spiral galaxy.
It has been shown, both in simulations and observationally, that the tidal field of a large galaxy can torque its satellites such that the major axis of satellite galaxies points towards their hosts. This so-called `shape alignment' has been observed in isolated Milky Way-like galaxies but not in `Local Group'-like pairs. In this study, we investigate the shape alignment of satellite galaxies in galaxy pairs similar to the Local Group identified in the Sloan Digital Sky Survey Data Release 13 (SDSS DR13). By stacking tens of thousands of satellite galaxies around primary galaxy pairs, we find …
The satellite galaxies of the Milky Way (MW) define a vast polar structure (VPOS), a thin plane perpendicular to the MW disc. Proper motion (PM) measurements are now available for all of the 11 brightest, `classical' satellites and allow an updated analysis of the alignment of their orbital poles with this spatial structure. The coherent orbital alignment of 7 to 9 out of 11 satellites demonstrates that the VPOS is a rotationally stabilized structure and not only a pressure-supported, flattened ellipsoid. This allows us to empirically and model independently predict the PMs of almost all satel…
The high-resolution, SPH galaxies of the McMaster Unbiased Galaxy Survey (MUGS) are used to examine the satellite systems of sixteen model host galaxies. Each galaxy has a different mass, angular momentum and merger history that yield a rich set of satellite luminosity functions. With new observations of distant satellite systems, we can compare these luminosity functions to satellite systems beyond the Local Group. We find that the luminosity functions of our simulations compare well to observations when the luminosity functions are scaled according to host mass. We use the recently-found rel…
We present new results on the relationship between central galaxies and dark matter haloes inferred from observations of satellite kinematics in the Sloan Digital Sky Survey (SDSS) DR7. We employ an updated analysis framework that includes detailed mock catalogues to model observational effects in SDSS. Our results constrain the colour-dependent conditional luminosity function (CLF) of dark matter haloes, as well as the radial profile of satellite galaxies. Confirming previous results, we find that red central galaxies live in more massive haloes than blue galaxies at fixed luminosity. Additio…
Satellite galaxies in rich clusters are subject to numerous physical processes that can significantly influence their evolution. However, the typical L* satellite galaxy resides in much lower mass galaxy groups, where the processes capable of altering their evolution are generally weaker and have had less time to operate. To investigate the extent to which satellite and central galaxy evolution differs, we separately model the stellar mass - halo mass (M* -Mh) relation for these two populations over the redshift interval 0 < z < 1. This relation for central galaxies is constrained by the galax…
The flattened, possibly co-rotating plane of satellite galaxies around Centaurus A, if more than a fortuitous alignment, adds to the pre-existing tension between the well-studied Milky Way and M31 planes and the $Λ$CDM model of structure formation. It was recently reported that the Centaurus A satellite plane (CASP) may be rotationally supported, but a further understanding of the system's kinematics is elusive in the absence of full three-dimensional velocities. We constrain the transverse velocities of 27 satellites that would rotationally stabilise the Centaurus A plane, and classify the sa…
Half of the satellite galaxies of Andromeda form a narrow plane termed the Great Plane of Andromeda (GPoA), and their line-of-sight velocities display correlation reminiscent of a rotating structure. Recently reported first proper motion measurements for the on-plane satellites NGC 147 and NGC 185 indicate that they indeed co-orbit along the GPoA. This provides a novel opportunity to compare the M31 satellite system to $Λ$CDM expectations. We perform the first detailed comparison of the orbital alignment of two satellite galaxies beyond the Milky Way with several hydrodynamical and dark-matter…
Observations of the Galactic Center (GC) have accumulated a multitude of "forensic" evidence indicating that several million years ago the center of the Milky Way galaxy was teaming with starforming and accretion-powered activity -- this paints a rather different picture from the GC as we understand it today. We examine a possibility that this epoch of activity could have been triggered by the infall of a satellite galaxy into the Milky Way which began at the redshift of 10 and ended few million years ago with a merger of the Galactic supermassive black hole with an intermediate mass black hol…
The reflex motion and distortion of the Milky Way (MW) halo caused by the infall of a massive Large Magellanic Cloud (LMC) has been demonstrated to result in an excess of orbital poles of dark matter halo particles towards the LMC orbital pole. This was suggested to help explain the observed preference of MW satellite galaxies to co-orbit along the Vast Polar Structure (VPOS). We test this idea by correcting the positions and velocities of the MW satellites for the Galactocentric-distance-dependent shifts inferred from a LMC-infall simulation. While this should substantially reduce the observe…
Galaxies that are several virial radii beyond groups/clusters show preferentially quiescent star formation rates. Using a galaxy group/cluster catalog from the Sloan Digital Sky Survey, together with a cosmological N-body simulation, we examine the origin of this environmental quenching beyond the virial radius. Accounting for the clustering of groups/clusters, we show that central galaxies show enhanced SFR quenching out to 2.5 virial radii beyond groups/clusters, and we demonstrate that this extended environmental enhancement can be explained simply by 'ejected' satellite galaxies that orbit…
The spatial distribution of satellite galaxies around pairs of galaxies in the Sloan Digital Sky Survey (SDSS) have been found to bulge significantly towards the respective partner. Highly anisotropic, planar distributions of satellite galaxies are in conflict with expectations derived from cosmological simulations. Does the lopsided distribution of satellite systems around host galaxy pairs constitute a similar challenge to the standard model of cosmology? We investigate whether such satellite distributions are present around stacked pairs of hosts extracted from the $Λ$CDM simulations Millen…
The shapes of cluster central galaxies are not randomly oriented, but rather exhibit coherent alignments with the shapes of their parent clusters as well as with the surrounding large-scale structures. In this work, we aim to identify the galaxy and cluster quantities that most strongly predict the central galaxy alignment phenomenon among a large parameter space with a sample of 8237 clusters and 94817 members within 0.1<z<0.35, based on the redMaPPer cluster catalog constructed from the Sloan Digital Sky Survey. We first quantify the alignment between the projected central galaxy shapes and …
It is well known that satellite galaxies are not isotropically distributed among their host galaxies as suggested by most interpretations of the $Λ$CDM model. One type of anisotropy recently detected in the SDSS (and seen when examining the distribution of satellites in the Local Group and in the Centaurus group) is a tendency to be so-called "lopsided". Namely, in pairs of galaxies (like Andromeda and the Milky Way) the satellites are more likely to inhabit the region in between the pair, rather than on opposing sides. Although recent studies found a similar set up when comparing pairs of gal…
Dark matter self interactions can leave distinctive signatures on the properties of satellite galaxies around Milky Way--like hosts through their impact on tidal stripping, ram pressure, and gravothermal collapse. We delineate the regions of self-interacting dark matter parameter space -- specified by interaction cross section and a velocity scale -- where each of these effects dominates, and show how the relative mass loss depends on the satellite's initial mass, density profile and orbit. We obtain novel, conservative constraints in this parameter space using Milky Way satellite galaxies wit…
The hierarchical galaxy formation scenario in the Cold Dark Matter cosmogony with a non-vanishing cosmological constant and geometrically flat space has been very successful in explaining the large-scale distribution of galaxies. However, there have been claims that the scenario predicts too many satellite galaxies associated with massive galaxies compared to observations, called the missing satellite galaxy problem. Isolated groups of galaxies hosted by passively evolving massive early-type galaxies are ideal laboratories for finding the missing physics in the current theory. Here we report f…
We investigate the properties of satellite galaxies in cosmological N-body/SPH simulations of galaxy formation in Milky Way-sized haloes. Because of their shallow potential wells, satellite galaxies are very sensitive to heating processes which affect their gas content. Their properties can therefore be used to constrain the nature of feedback processes that regulate galaxy formation. In our simulations, we assume that all the energy produced by supernovae is used as kinetic energy to drive galactic winds. Several of our simulations produce bright, disc-dominated galaxies. We find that wind mo…
Satellite galaxies in groups and clusters are more likely to have low star formation rates (SFR) and lie on the red-sequence than central (field) galaxies. Using galaxy group/cluster catalogs from SDSS DR7, together with a cosmological N-body simulation to track satellite orbits, we examine the star formation histories and quenching timescales of satellites of M_star > 5 x 10^9 M_sun at z=0. We first explore satellite infall histories: group preprocessing and ejected orbits are critical aspects of satellite evolution, and properly accounting for these, satellite infall typically occurred at z~…
We study the kinematics of galaxies within massive clusters, as a probe of the physics of star-formation quenching within clusters. Using N-body simulations, we argue that satellite kinematics provide information about galaxy infall that is complementary to the (instantaneous) spatial distribution of satellites. Comparing the simulation results with measurements of real cluster galaxies, we find evidence that the kinematics of red (quiescent) satellite galaxies are consistent with earlier infall times than that of blue (star-forming) satellites.
Halo models and halo occupation distributions (HODs) are important tools to model the galaxy and matter distribution. We present and assess a new method for constraining the parameters of HODs using the gravitational lensing shear around galaxy pairs, galaxy-galaxy-galaxy-lensing (G3L). In contrast to galaxy-galaxy-lensing, G3L is sensitive to correlations between the per-halo numbers of galaxies from different populations. We use G3L to probe these correlations and test the default hypothesis that they are negligible. We derive a halo model for G3L and validate it with realistic mock data fro…
According to the hierarchical model of galaxy formation underlying our current understanding of cosmology, the Milky Way (MW) has continued to accrete smaller-sized dwarf galaxies since its formation. Remnants of this process surround the MW as debris streams and satellite galaxies, and provide information that is complementary to studies of the Galaxy itself. The satellite system thus has the potential to teach us about the formation and evolution of the MW. Can the existence of a narrow, co-rotating plane of satellite galaxies (the Vast Polar Structure, VPOS) put constraints on our Galaxy's …
Intrinsic galaxy alignments are a source of bias for weak lensing measurements as well as a tool for understanding galaxy formation and evolution. In this work, we measure the alignment of shapes of satellite galaxies, in galaxy groups, with respect to the brightest group galaxy (BGG), as well as alignments of the BGG shape with the satellite positions, using the highly complete Galaxy And Mass Assembly (GAMA) spectroscopic survey and deep imaging from the Kilo Degree Survey. We control systematic errors with dedicated image simulations and measure accurate shapes using the DEIMOS shape measur…
Satellites are not randomly distributed around their central galaxies but show polar and planar structures. In this paper, we investigate the axis-asymmetry or lopsidedness of satellite galaxy distributions around isolated galaxies in a hydrodynamic cosmological simulation. We find a statistically significant lopsided signal by studying the angular distribution of the satellite galaxies' projected positions around isolated central galaxies in a two-dimensional plane. The signal is dependent on galaxy mass, color and large-scale environment. Satellites that inhabit low-mass blue hosts, or locat…
We present a semi-analytic model of satellite galaxies, SatGen, which can generate large samples of satellite populations for a host halo of desired mass, redshift, and assembly history. The model combines dark-matter halo merger trees, empirical relations for the galaxy-halo connection, and analytic prescriptions for tidal effects, dynamical friction, and ram pressure stripping. SatGen emulates cosmological zoom-in hydro-simulations in certain aspects. Satellites can reside in cored or cuspy DM subhaloes, depending on the halo response to baryonic physics that can be formulated from hydro-sim…
The clustering amplitude of galaxies depends on their intrinsic luminosity. We compare the properties of publicly available galaxy formation models with clustering measurements from the two-degree field galaxy redshift survey. The model predictions show the same qualitative behaviour as the data but fail to match the observations at the level of accuracy at which current measurements can be made. We demonstrate that this is due to the model producing too many satellite galaxies in massive haloes. We implement simple models to describe two new processes, satellite-satellite mergers and the tida…
Both major galaxies in the Local Group host planar distributions of co-orbiting satellite galaxies, the Vast Polar Structure (VPOS) of the Milky Way and the Great Plane of Andromeda (GPoA). The $Λ$CDM cosmological model did not predict these features. However, according to three recent studies the properties of the GPoA and the flattening of the VPOS are common features among sub-halo based $Λ$CDM satellite systems, and the GPoA can be naturally explained by satellites being acquired along cold gas streams. We point out some methodological issues in these studies: either the selection of model…
Our 'home galaxy' - the Milky Way - is a fairly large spiral galaxy, prototype of the most common morphological class in the local Universe. Although being only a galaxy, it is the only one that can be studied in unique detail: for the MilkyWay and for a number of members of the Local Group, a wealth of observational data is available about the ages and chemical abundances of their stars. Much more information is expected to come in the next few years, from ongoing and planned spectroscopic and astrometric surveys, providing a unique benchmark for modern theories of galaxy formation. In this r…
We study the alignments of satellite galaxies, and their anisotropic distribution, with respect to location and orientation of their host central galaxy in MassiveBlack-II and IllustrisTNG simulations. We find that: the shape of the satellite system in halos of mass ($> 10^{13}h^{-1}M_{\odot}$) is well aligned with the shape of the central galaxy at $z=0.06$ with the mean alignment between the major axes being $\sim Δθ= 12^{\circ}$ when compared to a uniform random distribution; that satellite galaxies tend to be anisotropically distributed along the major axis of the central galaxy with a str…
Intracluster light as a dark matter tracer: how their spatial and kinematic relationship is shaped by satellite demographics
University of Nottingham（诺丁汉大学）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Universidad Autónoma de Madrid（马德里自治大学）；Royal Observatory, Edinburgh（爱丁堡皇家天文台）
We present a fit to observational data in an asymmetric self-interacting dark matter model using our recently calculated cross sections that incorporate both $t$-channel and $u$-channel exchanges in the scattering of identical particles. We find good fits to the data ranging from dwarf galaxies to galaxy clusters, and equivalent relative velocities from $\sim 20$ km/sec to $\gtrsim 10^3$ km/s. We compare our results with previous fits that used only $t$-channel exchange contributions to the scattering.
