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We measure the clustering of low-redshift SDSS galaxies as a function of stellar mass ($10.0<\log(M_*/M_\odot)<11.5$) and specific star formation rate (sSFR) and compare the results to models of the galaxy--halo connection. We find that the auto-correlation functions of central galaxies exhibit little dependence on sSFR, with the well-known stronger clustering of quiescent galaxies mainly attributable to satellites. Because halo assembly history is known to affect distinct halo clustering, this result implies that there is little net correlation between halo assembly history and central galaxy sSFR. However, cross-correlations with satellites are stronger for quiescent centrals than star-forming centrals, consistent with quiescent centrals having more satellites in their haloes at fixed $M_*$, as found in SDSS group catalogues. We model the galaxy--halo connection in an $N$-body simulation by assigning sSFRs to central galaxies in three different ways. Two of the models depend on halo assembly history (being based on halo accretion rate or concentration), while the third is independent of halo assembly history (being based on peak halo circular velocity, $V_\text{peak}$, a proxy for halo mass). All three models replicate the observed auto-correlations of central galaxies, while only the $V_\text{peak}$ model reproduces the observed cross-correlations with satellites. This further suggests that the effects of halo assembly history may not be easily seen in auto-correlations of centrals and implies that a more complete understanding of central galaxy clustering may require more than auto-correlations of centrals alone. Additionally, the good agreement with the $V_\text{peak}$ model supports the idea that quiescent galaxies reside in more massive haloes than star-forming galaxies at fixed $M_*$., Comment: MNRAS accepted, 26 pages

We investigate the formation of brightest cluster galaxies (BCGs) in the TNG300 cosmological simulation of the IllustrisTNG project. Our cluster sample consists of 700 haloes with $M_{200} \geq 5 \times 10^{13} \, \mathrm{M}_{\odot}$ at $z=0$, along with their progenitors at earlier epochs. This includes 280 systems with $M_{200} \geq 10^{14} \, \mathrm{M}_{\odot}$ at $z=0$, as well as three haloes with $M_{200} \geq 10^{15} \, \mathrm{M}_{\odot}$. We find that the stellar masses and star formation rates of our simulated BCGs are in good agreement with observations at $z \lesssim 0.4$, and that they have experienced, on average, $\sim$2 ($\sim$3) major mergers since $z=1$ ($z=2$). Separating the BCG from the intracluster light (ICL) by means of a fixed 30 kpc aperture, we find that the fraction of stellar mass contributed by ex situ (i.e. accreted) stars at $z=0$ is approximately 70, 80, and 90 per cent for the BCG, BCG+ICL, and ICL, respectively. Tracking our simulated BCGs back in time using the merger trees, we find that they became dominated by ex situ stars at $z \sim $1-2, and that half of the stars that are part of the BCG at $z=0$ formed early ($z \sim 3$) in other galaxies, but `assembled' onto the BCG until later times ($z \approx 0.8$ for the whole sample, $z \approx 0.5$ for BCGs in $M_{200} \geq 5 \times 10^{14} \, \mathrm{M}_{\odot}$ haloes). Finally, we show that the stellar mass profiles of BCGs are often dominated by ex situ stars at all radii, with stars from major mergers being found closer to the centre, while stars that were tidally stripped from other galaxies dominate the outer regions., Comment: 19 pages, 11 figures. Accepted for publication in MNRAS

The stochastic order redshift technique (SORT) is a simple, efficient, and robust method to improve cosmological redshift measurements. The method relies upon having a small ($\sim$10 per cent) reference sample of high-quality redshifts. Within pencil-beam-like sub-volumes surrounding each galaxy, we use the precise dN/d$z$ distribution of the reference sample to recover new redshifts and assign them one-to-one to galaxies such that the original rank order of redshifts is preserved. Preserving the rank order is motivated by the fact that random variables drawn from Gaussian probability density functions with different means but equal standard deviations satisfy stochastic ordering. The process is repeated for sub-volumes surrounding each galaxy in the survey. This results in every galaxy with an uncertain redshift being assigned multiple "recovered" redshifts from which a new redshift estimate can be determined. An earlier paper applied SORT to a mock Sloan Digital Sky Survey at $z \lesssim$ 0.2 and accurately recovered the two-point correlation function on scales $\gtrsim$4 $h^{-1}$Mpc. In this paper, we test the performance of SORT in surveys spanning the redshift range 0.75$

LCDM cosmological models with Early Dark Energy (EDE) have been proposed to resolve tensions between the Hubble constant H0 = 100h km/s/Mpc measured locally, giving h ~ 0.73, and H0 deduced from Planck cosmic microwave background (CMB) and other early universe measurements plus LCDM, giving h ~ 0.67. EDE models do this by adding a scalar field that temporarily adds dark energy equal to about 10% of the cosmological energy density at the end of the radiation-dominated era at redshift z ~ 3500. Here we compare linear and nonlinear predictions of a Planck-normalized LCDM model including EDE giving h = 0.728 with those of standard Planck-normalized LCDM with h = 0.678. We find that nonlinear evolution reduces the differences between power spectra of fluctuations at low redshifts. As a result, at z = 0 the halo mass functions on galactic scales are nearly the same, with differences only 1-2%. However, the differences dramatically increase at high redshifts. The EDE model predicts 50% more massive clusters at z = 1 and twice more galaxy-mass halos at z = 4. Even greater increases in abundances of galaxy-mass halos at higher redshifts may make it easier to reionize the universe with EDE. Predicted galaxy abundances and clustering will soon be tested by JWST observations. Positions of baryonic acoustic oscillations (BAOs) and correlation functions differ by about 2% between the models -- an effect that is not washed out by nonlinearities. Both standard LCDM and the EDE model studied here agree well with presently available acoustic-scale observations, but DESI and Euclid measurements will provide stringent new tests., Comment: 13 pages, 12 figures, submitted to MNRAS

Over the past decade, empirical constraints on the galaxy-dark matter halo connection have significantly advanced our understanding of galaxy evolution. Past techniques have focused on connections between halo properties and galaxy stellar mass and/or star formation rates. Empirical techniques in the next decade will link halo assembly histories with galaxies' circumgalactic media, supermassive black holes, morphologies, kinematics, sizes, colors, metallicities, and transient rates. Uncovering these links will resolve many critical uncertainties in galaxy formation and will enable much higher-fidelity mock catalogs essential for interpreting observations. Achieving these results will require broader and deeper spectroscopic coverage of galaxies and their circumgalactic media; survey teams will also need to meet several criteria (cross-comparisons, public access, and covariance matrices) to facilitate combining data across different surveys. Acting on these recommendations will continue enabling dramatic progress in both empirical modeling and galaxy evolution for the next decade., Comment: Science white paper submitted to the Astro2020 Decadal Survey

We investigate the dependence of the galaxy-halo connection and galaxy density field in modified gravity models using the $N-$body simulations for $f(R)$ and nDGP models at $z=0$. Because of the screening mechanisms employed by these models, chameleon and Vainshtein, halos are clustered differently in the non-linear regime of structure formation. We quantify their deviations in the galaxy density field from the standard $\Lambda$CDM model under different environments. We populate galaxies in halos via the (Sub)Halo Abundance Matching. Our main results are: 1) The galaxy-halo connection {\it strongly} depends on the gravity model; a maximum variation of $\sim40\%$ is observed between Halo Occupational Distribution (HOD) parameters; 2) $f(R)$ gravity models predict an excess of galaxies in low density environments of $\sim10\%$ but predict a deficit of $\sim10\%$ at high density environments for $|f_{R0}| = 10^{-4}$ and $10^{-6}$ while $|f_{R0}| = 10^{-5}$ predicts more high density structures; nDGP models are consistent with $\Lambda$CDM; 3) Different gravity models predict different dependences of the galaxy luminosity function (GLF) with the environment, especially in void-like regions we find differences around $\sim10\%$ for the $f(R)$ models while nDPG models remain closer to $\Lambda$CDM for low-luminosity galaxies but there is a deficit of $\sim11\%$ for high-luminosity galaxies in all environments. We conclude that the dependence of the GLF with environment might provide a test to distinguish between gravity models and their screening mechanisms from the $\Lambda$CDM. We provide HOD parameters for the gravity models analyzed in this paper., Comment: 22 pages, 14 figures, 4 tables

We study the effects of the local environmental density and the cosmic web environment (filaments, walls, and voids) on key properties of dark matter halos using the Bolshoi-Planck LCDM cosmological simulation. The z = 0 simulation is analysed into filaments, walls, and voids using the SpineWeb method and also the VIDE package of tools, both of which use the watershed transform. The key halo properties that we study are the specific mass accretion rate, spin parameter, concentration, prolateness, scale factor of the last major merger, and scale factor when the halo had half of its z = 0 mass. For all these properties, we find that there is no discernible difference between the halo properties in filaments, walls, or voids when compared at the same environmental density. As a result, we conclude that environmental density is the core attribute that affects these properties. This conclusion is in line with recent findings that properties of galaxies in redshift surveys are independent of their cosmic web environment at the same environmental density at z ~ 0. We also find that the local web environment of the Milky Way and the Andromeda galaxies near the centre of a cosmic wall does not appear to have any effect on the properties of these galaxies' dark matter halos except for their orientation, although we find that it is rather rare to have such massive halos near the centre of a relatively small cosmic wall., Comment: 23 pages

We study the global and radial stellar mass assembly of eight zoomed-in MW-sized galaxies produced in Hydrodynamics cosmological simulations. The disk-dominated galaxies (4) show a fast initial stellar mass growth in the innermost parts, driven mostly by in-situ SF, but since $z\sim2-1$ the SF enters in a long-term quenching phase. The outer regions follow this trend but more gentle as more external they are. As the result, the radial stellar mass growth is highly inside-out due to both the inside-out structural growth and inside-out SF quenching. The half-mass radius evolves fast; for instance, $R_{0.5}$($z=1$)$<0.5$$R_{0.5}$($z=0$). Two other runs resemble lenticular galaxies. One shows also a pronounced inside-out growth and the other one presents a nearly uniform radial mass assembly. The other two galaxies suffered late major mergers. Their normalized radial mass growth histories (MGHs) are nearly close among them but with periods of outside-in assembly during or after the mergers. For all the simulations, the archaeological radial MGHs calculated from the $z = 0$ stellar-particles age distribution are similar to the current MGHs, which evidences that the mass assembly by ex-situ stars and the radial mass transport do not change significantly their radial mass distributions. Our results agree qualitatively with observational inferences from the fossil record method applied to a survey of local galaxies and from look-back observations of progenitors of MW-sized galaxies. However, the inside-out growth mode is more pronounced and the $R_{0.5}$ growth is faster in simulations than in observational inferences., Comment: 23 pages, 15 figures. Accepted for publication in ApJ. Minor corrections and more references added. The discussion was extended in section 6.1

SubHalo Abundance Matching (SHAM) assumes that one (sub)halo property, such as mass Mvir or peak circular velocity Vpeak, determines properties of the galaxy hosted in each (sub)halo such as its luminosity or stellar mass. This assumption implies that the dependence of Galaxy Luminosity Functions (GLFs) and the Galaxy Stellar Mass Function (GSMF) on environmental density is determined by the corresponding halo density dependence. In this paper, we test this by determining from an SDSS sample the observed dependence with environmental density of the ugriz GLFs and GSMF for all galaxies, and for central and satellite galaxies separately. We then show that the SHAM predictions are in remarkable agreement with these observations, even when the galaxy population is divided between central and satellite galaxies. However, we show that SHAM fails to reproduce the correct dependence between environmental density and g-r color for all galaxies and central galaxies, although it better reproduces the color dependence on environmental density of satellite galaxies., Comment: 21 pages, 11 figures. Accepted for publication in MNRAS

We present a simple, efficient and robust approach to improve cosmological redshift measurements. The method is based on the presence of a reference sample for which a precise redshift number distribution (dN/dz) can be obtained for different pencil-beam-like sub-volumes within the original survey. For each sub-volume we then impose: (i) that the redshift number distribution of the uncertain redshift measurements matches the reference dN/dz corrected by their selection functions; and (ii) the rank order in redshift of the original ensemble of uncertain measurements is preserved. The latter step is motivated by the fact that random variables drawn from Gaussian probability density functions (PDFs) of different means and arbitrarily large standard deviations satisfy stochastic ordering. We then repeat this simple algorithm for multiple arbitrary pencil-beam-like overlapping sub-volumes; in this manner, each uncertain measurement has multiple (non-independent) "recovered" redshifts which can be used to estimate a new redshift PDF. We refer to this method as the Stochastic Order Redshift Technique (SORT). We have used a state-of-the-art N-body simulation to test the performance of SORT under simple assumptions and found that it can improve the quality of cosmological redshifts in an efficient and robust manner. Particularly, SORT redshifts are able to recover the distinctive features of the 'cosmic web' and can provide unbiased measurement of the two-point correlation function on scales > 4 Mpc/h. Given its simplicity, we envision that a method like SORT can be incorporated into more sophisticated algorithms aimed to exploit the full potential of large extragalactic photometric surveys., Comment: MNRAS accepted; 15 pages, 9 figures

We report and provide fitting functions for the abundance of dark matter halos and subhalos as a function of mass, circular velocity, and redshift from the new Bolshoi-Planck and MultiDark-Planck $\Lambda$CDM cosmological simulations, based on the Planck cosmological parameters. We also report the halo mass accretion rates, which may be connected with galaxy star formation rates. We show that the higher cosmological matter density of the Planck parameters compared with the WMAP parameters leads to higher abundance of massive halos at high redshifts. We find that the median halo spin parameter $\lambda_{\rm B} = J(2M_{\rm vir}R_{\rm vir}V_{\rm vir})^{-1}$ is nearly independent of redshift, leading to predicted evolution of galaxy sizes that is consistent with observations, while the significant decrease with redshift in median $\lambda_{\rm P} = J|E|^{-1/2}G^{-1}M^{-5/2}$ predicts more decrease in galaxy sizes than is observed. Using the Tully-Fisher and Faber-Jackson relations between galaxy velocity and mass, we show that a simple model of how galaxy velocity is related to halo maximum circular velocity leads to increasing overprediction of cosmic stellar mass density as redshift increases beyond redshifts $z\sim1$, implying that such velocity-mass relations must change at redshifts $z>1$. By making a realistic model of how observed galaxy velocities are related to halo circular velocity, we show that recent optical and radio observations of the abundance of galaxies are in good agreement with our $\Lambda$CDM simulations. Our halo demographics are based on updated versions of the \rockstar\ and \ctrees\ codes, and this paper includes appendices explaining all of their outputs. This paper is an introduction to a series of related papers presenting other analyses of the Bolshoi-Planck and MultiDark-Planck simulations., Comment: 27 pages, 26 figures. To match the published version at MNRAS. Rockstar and Consistent Trees outputs are available at http://hipacc.ucsc.edu/Bolshoi/MergerTrees.html

The galaxy stellar-to-halo mass relation (SHMR) is nearly time-independent for $z < 4$. We therefore construct a time-independent SHMR model for central galaxies, wherein the in-situ star formation rate (SFR) is determined by the halo mass accretion rate (MAR), which we call Stellar-Halo Accretion Rate Coevolution (SHARC). We show that the $\sim0.3$ dex dispersion of the halo MAR matches the observed dispersion of the SFR on the star-formation main sequence (MS). In the context of "bathtub"-type models of galaxy formation, SHARC leads to mass-dependent constraints on the relation between SFR and MAR. Despite its simplicity and the simplified treatment of mass growth from mergers, the SHARC model is likely to be a good approximation for central galaxies with $M_*=10^9- 10^{10.5}M_\odot$ that are on the MS, representing most of the star formation in the Universe. SHARC predictions agree with observed SFRs for galaxies on the MS at low redshifts, agree fairly well at $z\sim4$, but exceed observations at $z>4$. Assuming that the interstellar gas mass is constant for each galaxy (the "equilibrium condition" in bathtub models), the SHARC model allows calculation of net mass loading factors for inflowing and outflowing gas. With assumptions about preventive feedback based on simulations, SHARC allows calculation of galaxy metallicity evolution. If galaxy SFRs indeed track halo MARs, especially at low redshifts, that may help explain the success of models linking galaxy properties to halos (including age-matching) and the similarities between two-halo galaxy conformity and halo mass accretion conformity., Comment: Accepted for publication in MNRAS. No substantial changes. Abstract slightly modified in order to match the MNRAS Abstract length limit of 250 words. 18 pages, 12 figures

We perform an exhaustive comparison among central galaxies from SDSS catalogs in different local environments at 0.01<=z<=0.08. The central galaxies are separated into two categories: group centrals (host halos containing satellites) and field centrals (host halos without satellites). From the latter, we select other two subsamples: isolated centrals and bright field centrals, both with the same magnitude limit. The stellar mass (Ms) distributions of the field and group central galaxies are different, which explains why in general the field central galaxies are mainly located in the blue cloud/star forming regions, whereas the group central galaxies are strongly biased to the red sequence/passive regions. The isolated centrals occupy the same regions as the bright field centrals since both populations have similar Ms distributions. At parity of Ms, the color and specific star formation rate (sSFR) distributions of the samples are similar, specially between field and group centrals. Furthermore, we find that the stellar-to-halo mass (Ms-Mh) relation of isolated galaxies does not depend on the color, sSFR and morphological type. For systems without satellites, the Ms-Mh relation steepens at high halo masses compared to group centrals, which is a consequence of assuming a one-to-one relation between group total stellar mass and halo mass. Under the same assumption, the scatter around the Ms-Mh relation of centrals with satellites increases with halo mass. Our results suggest that the mass growth of central galaxies is mostly driven by the halo mass, with environment and mergers playing a secondary role., Comment: 17 pages, 11 figures after last Referee's report. Accepted for publication in ApJ

We present high-resolution N-body/hydrodynamics simulations of dwarf galaxies formed in isolated CDM halos with the same virial mass, Mv~2.5x10^10 Msun at z=0, in order to (1) study the mass assembly histories (MAHs) of the halo, stars, and gas components, and (2) explore the effects of the halo MAHs on the stellar/baryonic assembly of the simulated dwarfs and on their z~0 properties. Overall, the simulated dwarfs are roughly consistent with observations. Our main results are: a) The stellar-to-halo mass ratio is ~0.01 and remains roughly constant since z~1 (the stellar MAHs follow closely the halo MAHs), with a smaller value at higher z's for those halos that assemble their mass later. b) The evolution of the galaxy gas fraction, fg, is episodic and higher, most of the time, than the stellar fraction. When fg decreases (increases), the gas fraction in the halo typically increases (decreases), showing that the SN driven outflows play an important role in regulating the gas fractions -and hence the SFR- of the dwarfs. However, in most cases, an important fraction of the gas escapes the virial radius, Rv; at z=4 the total baryon fraction inside Rv is 1.5-2 times smaller than the universal one, while at z=0 is 2-6 times smaller, with the earlier assembled halos ejecting more gas. c) The SF histories are episodic with changes in the SFRs of factors 2-10 on average. d) Although the dwarfs formed in late assembled halos show more extended SF histories, their z~0 SFRs are still below the ones measured for local isolated dwarfs. e) The effects of baryons on Mv are such that at almost any time Mv is 10-20% smaller than the corresponding Mv obtained in pure N-body simulations. Our results suggest that rather than increasing the strength of the SN-driven outflows, processes that reduce the SF efficiency even more will help to solve the potential issues faced by the CDM-based simulations of dwarfs., Comment: 14 pages, 12 figures. ApJ, published. Minor changes after final Referee's report

We use a sample of ~6000 galaxies detected by the Arecibo Legacy Fast ALFA (ALFALFA) 21cm survey, to measure the clustering properties of HI-selected galaxies. We find no convincing evidence for a dependence of clustering on the galactic atomic hydrogen (HI) mass, over the range M_HI ~ 10^{8.5} - 10^{10.5} M_sun. We show that previously reported results of weaker clustering for low-HI mass galaxies are probably due to finite-volume effects. In addition, we compare the clustering of ALFALFA galaxies with optically selected samples drawn from the Sloan Digital Sky Survey (SDSS). We find that HI-selected galaxies cluster more weakly than even relatively optically faint galaxies, when no color selection is applied. Conversely, when SDSS galaxies are split based on their color, we find that the correlation function of blue optical galaxies is practically indistinguishable from that of HI-selected galaxies. At the same time, SDSS galaxies with red colors are found to cluster significantly more than HI-selected galaxies, a fact that is evident in both the projected as well as the full two-dimensional correlation function. A cross-correlation analysis further reveals that gas-rich galaxies "avoid" being located within ~3 Mpc of optical galaxies with red colors. Next, we consider the clustering properties of halo samples selected from the Bolshoi LambdaCDM simulation. A comparison with the clustering of ALFALFA galaxies suggests that galactic HI mass is not tightly related to host halo mass, and that a sizable fraction of subhalos do not host HI galaxies. Lastly, we find that we can recover fairly well the correlation function of HI galaxies by just excluding halos with low spin parameter. This finding lends support to the hypothesis that halo spin plays a key role in determining the gas content of galaxies., Comment: Accepted to ApJ. 27 figures, 1 table; 50 pages in aastex (equivalent to 19 pages of emulateapj)

Several occupational distributions for satellite galaxies more massive than ms~4E7 Msun around MW-sized hosts are presented and used to predict their internal dynamics. For this, a galaxy group mock catalog is constructed on the basis of (sub)halo-to-stellar mass relations constrained with the observed Galaxy Stellar Mass Function decomposed into centrals and satellites, and the 2-point correlation functions. For the MW-sized hosts we find that: 6.6% have 2 satellites in the SMC-LMC mass range; their probabilities to have 1, 2 or 3 satellites equal or larger than the LMC, the SMC or Sgr, respectively, are 0. 26, 0. 14, and 0. 14; those hosts with 3 satellites >= Sgr (as the MW) are among the most common cases, though the most and 2nd most massive satellites in these systems are SMALLER than the LMC and SMC by 0.7 and 0.8 dex, respectively. The cumulative satellite mass function is quite broad, the particular configuration of the MW being of low frequency but NOT an outlier (it is within the upper 1sig yet). For the MW satellite configuration, we constrain the halo mass to be Mh>1.4E12 Msun (1sig level). We find that the abundance of massive subhalos should agree with the abundance of massive satellites in all MW-sized hosts (there is not a massive satellite missing problem for LCDM). However, the vmax of the subhalos of satellites with ms<1E8 Msun is systematically larger than the vmax inferred from current observational studies of the MW bright dwarfs; at difference of previous works, this conclusion is based on an analysis of the overall population of MW-sized galaxies. Some pieces of evidence suggest that the issue could refer only to satellite dwarfs but not to central dwarfs; then, environmental processes associated to dwarfs inside host halos combined with SN-driven core expansion could be at the basis of the lowering of vmax.[Abridged], Comment: 10 pages, 6 figures. Accepted for publication in ApJ. arXiv abstract improved

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. We also constrain the values of the intrinsic scatter around the central-halo (CH) and satellite-subhalo (SS) MRs assuming them to be constant: sigma_c= 0.168+-0.051 dex and sigma_s = 0.172+-0.057 dex, respectively. The CH and SS MRs are actually different, in particular when we take the subhalo mass at the present-day epoch instead of at their accretion time. We calculate several population statistics. We find that the central galaxy is not on average within the mass distribution of the most-massive satellite, even for cluster-sized halos, i.e., centrals are not a mere realization of the high-end of the satellite mass function; however for > 3x10^13 msun halos, ~15% of centrals could be. We also find that the probabilities of MW-sized halos of having N Magellanic-Clouds (MCs)-sized satellites agree well with observational measures; for a halo mass of 2x10^12 msun, the probability to have 2 MCs is 5.4%, but if we exclude those systems with satellites larger than the MCs, then the probability decreases to <2.2%., Comment: 18 pages, 7 figures. Accepted for publication in ApJ. Some references were added

We extend the abundance matching technique (AMT) to infer the satellite-subhalo and central-halo mass relations (MRs) of galaxies, as well as the corresponding satellite conditional mass functions (CMFs). We use the observed galaxy stellar mass function (GSMF) decomposed into centrals and satellites and the LCDM halo/subhalo mass functions as inputs. We explore the effects of defining the subhalo mass at the time of accretion (m_acc) vs. at the time of observation (m_obs). We test the standard assumption that centrals and satellites follow the same MRs, showing that this assumption leads to predictions in disagreement with observations, specially for m_obs. Instead, when the satellite-subhalo MRs are constrained following our AMT, they are always different from the central-halo MR: the smaller the stellar mass (Ms), the less massive is the subhalo of satellites as compared to the halo of centrals of the same Ms. On average, for Ms<2x10^11Msol, the dark mass of satellites decreased by 60-65% with respect to their masses at accretion time. The resulting MRs for both definitions of subhalo mass yield satellite CMFs in agreement with observations. Also, when these MRs are used in a HOD model, the predicted correlation functions agree with observations. We show that the use of m_obs leads to less uncertain MRs than m_acc, and discuss implications of the obtained satellite-subhalo MR. For example, we show that the tension between abundance and dynamics of MW satellites in LCDM gives if the slope of the GSMF faint-end slope upturns to -1.6., Comment: 13, pages, 4 figures. Accepted for publication in ApJ. Minor changes to previous version