arXiv subjects

H. J. Mo

Publications and source records attributed to H. J. Mo.

At least 91 records · Page 5Linked to original sources

arXiv2009

Structural Properties of Central Galaxies in Groups and Clusters

Using a representative sample of 911 central galaxies (CENs) from the SDSS DR4 group catalogue, we study how the structure of the most massive members in groups and clusters depend on (1) galaxy stellar mass (Mstar), (2) dark matter halo mass of the host group (Mhalo), and (3) their halo-centric position. We establish and thoroughly test a GALFIT-based pipeline to fit 2D Sersic models to SDSS data. We find that the fitting results are most sensitive to the background sky level determination and strongly recommend using the SDSS global value. We find that uncertainties in the background translate into a strong covariance between the total magnitude, half-light size (r50), and Sersic index (n), especially for bright/massive galaxies. We find that n depends strongly on Mstar for CENs, but only weakly or not at all on Mhalo. Less (more) massive CENs tend to be disk (spheroid)-like over the full Mhalo range. Likewise, there is a clear r50-Mstar relation for CENs, with separate slopes for disks and spheroids. When comparing CENs with satellite galaxies (SATs), we find that low mass (<10e10.75 Msun/h^2) SATs have larger median n than CENs of similar Mstar. Low mass, late-type SATs have moderately smaller r50 than late-type CENs of the same Mstar. However, we find no size differences between spheroid-like CENs and SATs, and no structural differences between CENs and SATs matched in both mass and colour. The similarity of massive SATs and CENs shows that this distinction has no significant impact on the structure of spheroids. We conclude that Mstar is the most fundamental property determining the basic structure of a galaxy. The lack of a clear n-Mhalo relation rules out a distinct group mass for producing spheroids, and the responsible morphological transformation processes must occur at the centres of groups spanning a wide range of masses. (abridged)

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arXiv2008

Reconstructing the cosmic density field with the distribution of dark matter halos

We develop a new method to reconstruct the cosmic density field from the distribution of dark matter haloes above a certain mass threshold. Our motivation is that well-defined samples of galaxy groups/clusters, which can be used to represent the dark halo population, can now be selected from large redshift surveys of galaxies, and our ultimate goal is to use such data to reconstruct the cosmic density field in the local universe. Our reconstruction method starts with a sample of dark matter haloes above a given mass threshold. Each volume element in space is assigned to the domain of the nearest halo according to a distance measure that is scaled by the virial radius of the halo. The distribution of the mass in and around dark matter haloes of a given mass is modelled using the cross-correlation function between dark matter haloes and the mass distribution within their domains. We use N-body cosmological simulations to show that the density profiles required in our reconstruction scheme can be determined reliably from large cosmological simulations, and that our method can reconstruct the density field accurately using haloes with masses down to $\sim 10^{12}\msun$ (above which samples of galaxy groups can be constructed from current large redshift surveys of galaxies). Working in redshift space, we demonstrate that the redshift distortions due to the peculiar velocities of haloes can be corrected in an iterative way. We also describe some applications of our method.

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arXiv2008

The subhalo - satellite connection and the fate of disrupted satellite galaxies

In the standard paradigm, satellite galaxies are believed to be associated with the population of dark matter subhalos. In this paper, we use the conditional stellar mass functions of {\it satellite galaxies} obtained from a large galaxy group catalogue together with models of the subhalo mass functions to explore the fraction and fate of stripped stars from satellites in galaxy groups and clusters of different masses. The majority of the stripped stars in massive halos are predicted to end up as intra-cluster stars, and the predicted amounts of the intra-cluster component as a function of the velocity dispersion of galaxy system match well the observational results obtained by Gonzalez et al. (2007). The fraction of the mass in the stripped stars to that remain bound in the central and satellite galaxies is the highest ($\sim 40%$ of the total stellar mass) in halos with masses $M_h\sim 10^{14}\msunh$. If all these stars end up in the intra-cluster component (Max), or maximum of them are accreted into the central galaxy (Min), then we can predict that a maximum $\sim 19%$ and a minimum $\sim 5%$ of the total stars in the whole universe are in terms of the diffused intra-cluster component. In the former case, in massive halos with $M_h \sim 10^{15} \msunh$, the stellar mass of the intra-cluster component is roughly 6 times as large as that of the central galaxy. This factor decreases to $\sim 2$, 1 and 0.1 in halos with $M_h \sim 10^{14}$, $10^{13}$, and $10^{12} \msunh$, respectively. The total amount of stars stripped from satellite galaxies is insufficient to build up the central galaxies in halos with masses $\la 10^{12.5}\msunh$, and so the quenching of star formation must occur in halos with higher masses. Abridged.

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arXiv2008

Feedback from galactic stellar bulges and hot gaseous haloes of galaxies

We demonstrate that the feedback from stellar bulges can play an essential role in shaping the halo gas of galaxies with substantial bulge components by conducting 1-D hydrodynamical simulations. The feedback model we consider consists of two distinct phases: 1) an early starburst during the bulge formation and 2) a subsequent long-lasting mass and energy injection from stellar winds of low-mass stars and Type Ia SNe. An energetic outward blastwave is initiated by the starburst and is maintained and enhanced by the long-lasting stellar feedback. For a MW-like galactic bulge, this blastwave sweeps up the halo gas in the proto-galaxy and heats up the surrounding medium to a scale much beyond the virial radius of the halo, thus the accretion of the halo hot gas can be completely stopped. In addition, the long-lasting feedback in the later phase powers a galactic bulge wind that is reverse-shocked at a large radius in the presence of surrounding intergalactic medium and hence maintains a hot gaseous halo. As the mass and energy injection decreases with time, the feedback evolves to a subsonic and quasi-stable outflow, which is enough to prevent halo gas from cooling. The two phases of the feedback thus re-enforce each-other's impact on the gas dynamics. The simulation results demonstrate that the stellar bulge feedback may provide a plausible solution to the long-standing problems in understanding the MW type galaxies, such as the "missing stellar feedback" problem and the "over-cooling" problem. The simulations also show that the properties of the hot gas in the subsonic outflow state depend sensitively on the environment and the formation history of the bulge. This dependence and variance may explain the large dispersion in the X-ray to B-band luminosity ratio of the low $L_X/L_B$ Es.

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arXiv2008

Galaxy Groups in the SDSS DR4: I. The Catalogue and Basic Properties

We use a modified version of the halo-based group finder developed by Yang et al. to select galaxy groups from the Sloan Digital Sky Survey (SDSS DR4). In the first step, a combination of two methods is used to identify the centers of potential groups and to estimate their characteristic luminosity. Using an iterative approach, the adaptive group finder then uses the average mass-to-light ratios of groups, obtained from the previous iteration, to assign a tentative mass to each group. This mass is then used to estimate the size and velocity dispersion of the underlying halo that hosts the group, which in turn is used to determine group membership in redshift space. Finally, each individual group is assigned two different halo masses: one based on its characteristic luminosity, and the other based on its characteristic stellar mass. Applying the group finder to the SDSS DR4, we obtain 301237 groups in a broad dynamic range, including systems of isolated galaxies. We use detailed mock galaxy catalogues constructed for the SDSS DR4 to test the performance of our group finder in terms of completeness of true members, contamination by interlopers, and accuracy of the assigned masses. This paper is the first in a series and focuses on the selection procedure, tests of the reliability of the group finder, and the basic properties of the group catalogue (e.g. the mass-to-light ratios, the halo mass to stellar mass ratios, etc.). The group catalogues including the membership of the groups are available at http://gax.shao.ac.cn/data/Group.html and http://www.astro.umass.edu/~xhyang/Group.html

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arXiv2008

Galaxy Clustering & Galaxy-Galaxy Lensing: A Promising Union to Constrain Cosmological Parameters

Galaxy clustering and galaxy-galaxy lensing probe the connection between galaxies and their dark matter haloes in complementary ways. On one hand, the halo occupation statistics inferred from the observed clustering properties of galaxies are degenerate with the adopted cosmology. Consequently, different cosmologies imply different mass-to-light ratios for dark matter haloes. On the other hand, galaxy-galaxy lensing yields direct constraints on the actual mass-to-light ratios and it can be used to break this degeneracy, and thus to constrain cosmological parameters. In this paper we establish the link between galaxy luminosity and dark matter halo mass using the conditional luminosity function (CLF). We constrain the CLF parameters using the galaxy luminosity function and the luminosity dependence of the correlation lengths of galaxies. The resulting CLF models are used to predict the galaxy-galaxy lensing signal. For a cosmology with $(Ω_{\rm m},σ_8)=(0.238,0.734)$, the model accurately fits the galaxy-galaxy lensing data obtained from the SDSS. For a comparison cosmology with $(Ω_{\rm m},σ_8)=(0.3,0.9)$, however, we can accurately fit the luminosity function and clustering properties of the galaxy population, but the model predicts mass-to-light ratios that are too high, resulting in a strong overprediction of the galaxy-galaxy lensing signal. We conclude that the combination of galaxy clustering and galaxy-galaxy lensing is a powerful probe of the galaxy-dark matter connection, with the potential to yield tight constraints on cosmological parameters. Since this method mainly probes the mass distribution on non-linear scales, it is complementary to constraints obtained from the galaxy power-spectrum, which mainly probes the large-scale (linear) matter distribution.

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arXiv2008

The Rise and Fall of Galaxy Activity in Dark Matter Haloes

We use a SDSS galaxy group catalogue to study the dependence of galaxy activity on stellar mass, halo mass, and group hierarchy (centrals vs. satellites). We split our galaxy sample in star-forming galaxies, galaxies with optical AGN activity and radio sources. We find a smooth transition in halo mass as the activity of central galaxies changes from star formation to optical AGN activity to radio emission. Star-forming centrals preferentially reside in haloes with M<10^{12} Msun, central galaxies with optical-AGN activity typically inhabit haloes with M \sim 10^{13} Msun, and centrals emitting in the radio mainly reside in haloes more massive than 10^{14} Msun. Although this seems to suggest that the environment (halo mass) determines the type of activity of its central galaxy, we find a similar trend with stellar mass: central star formers typically have stellar masses below 10^{10} Msun, while optical-AGN hosts and central radio sources have characteristic stellar masses of 10^{10.8} Msun and 10^{11.6} Msun, respectively. Since more massive haloes typically host more massive centrals, it is unclear whether the activity of a central galaxy is causally connected to its stellar mass or to its halo mass. In general, satellite galaxies have their activity suppressed wrt central galaxies of the same stellar mass. At fixed stellar mass, we find that the activity of satellite galaxies depends only weakly on halo mass. In fact, for satellite galaxies the dependence of galaxy activity on halo mass is more than four times weaker than the dependence on stellar mass. As we discuss, all these results are consistent with a picture in which low mass haloes accrete cold gas, while massive haloes have coronae of hot gas that promote radio activity of their central galaxies. [Abridged]

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arXiv2008

The clustering of SDSS galaxy groups: mass and color dependence

We use a sample of galaxy groups selected from the SDSS DR 4 with an adaptive halo-based group finder to probe how the clustering strength of groups depends on their masses and colors. In particular, we determine the relative biases of groups of different masses, as well as that of groups with the same mass but with different colors. In agreement with previous studies, we find that more massive groups are more strongly clustered, and the inferred mass dependence of the halo bias is in good agreement with predictions for the $Λ$CDM cosmology. Regarding the color dependence, we find that groups with red centrals are more strongly clustered than groups of the same mass but with blue centrals. Similar results are obtained when the color of a group is defined to be the total color of its member galaxies. The color dependence is more prominent in less massive groups and becomes insignificant in groups with masses $\gta 10^{14}\msunh$. We construct a mock galaxy redshift survey constructed from the large Millenium simulation that is populated with galaxies according to the semi-analytical model of Croton et al. Applying our group finder to this mock survey, and analyzing the mock data in exactly the same way as the true data, we are able to accurately recover the intrinsic mass and color dependencies of the halo bias in the model. This suggests that our group finding algorithm and our method of assigning group masses do not induce spurious mass and/or color dependencies in the group-galaxy correlation function. The semi-analytical model reveals the same color dependence of the halo bias as we find in our group catalogue. In halos with $M\sim 10^{12}\msunh$, though, the strength of the color dependence is much stronger in the model than in the data.

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arXiv2008

Satellite Ecology: The Dearth of Environment Dependence

Using the Sloan Digital Sky Survey (SDSS) galaxy group catalogue of Yang et al. (2007), we study the average colour and average concentration of satellite galaxies as function of (i) their stellar mass, (ii) their group mass, and (iii) their group-centric radius. We find that the colours and concentrations of satellite galaxies are (almost) completely determined by their stellar mass. In particular, at fixed stellar mass, the average colours and concentrations of satellite galaxies are independent of either halo mass or halo-centric radius. We find clear evidence for mass segregation of satellite galaxies in haloes of all masses, and argue that this explains why satellites at smaller halo-centric radii are somewhat redder and somewhat more concentrated. In addition, the weak colour and concentration dependence of satellite galaxies on halo mass is simply a reflection of the fact that more massive haloes host, on average, more massive satellites. Combining these results with the fact that satellite galaxies are, on average, redder and somewhat more concentrated than central galaxies of the same stellar mass, the following picture emerges: galaxies become redder and somewhat more concentrated once they fall into a bigger halo (i.e., once they become a satellite galaxy). This is a clear manifestation of environment dependence. However, there is no indication that the magnitude of the transformation (or its timescale) depends on environment; a galaxy undergoes a transition when it becomes a satellite, but it does not matter whether it becomes a satellite of a small (Milky Way sized) halo, or of a massive cluster. We discuss the implication of this `dearth' of environment dependence for the physical processes responsible for transforming satellite galaxies.

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arXiv2008

On Halo Formation Times and Assembly Bias

In this paper we use the ``Millennium Simulation'' to re-examine the mass assembly history of dark matter halos and the age dependence of halo clustering. We use eight different definitions of halo formation times to characterize the different aspects of the assembly history of a dark matter halo. We find that these formation times have different dependence on halo mass. While some formation times characterize well the hierarchical nature of halo formation, in the sense that more massive halos have later formation, the trend is reversed for other definitions of the formation time. In particular, the formation times that are likely to be related to the formation of galaxies in dark halos show strong trends of ``down-sizing'', in that lower-mass halos form later. We also investigate how the correlation amplitude of dark matter halos depends on the different formation times. We find that this dependence is quite strong for some definitions of formation time but weak or absent for other definitions. In particular, the correlation amplitude of halos of a given mass is almost independent of their last major merger time. For the definitions that are expected to be more related to the formation of galaxies in dark halos, a significant assembly bias is found only for halos less massive than M_*. We discuss our results in connection to the hierarchical assembly of dark matter halos, the ``archaeological down-sizing'' observed in the galaxy population, and the observed color-dependence of the clustering strength of galaxy groups and clusters.

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arXiv2008

Probing the Intrinsic Shape and Alignment of Dark Matter Haloes using SDSS Galaxy Groups

We study the three-dimensional and projected shapes of galaxy groups in the Sloan Digital Sky Survey Data Release 4, and examine the alignment between the orientation of the central galaxy and the spatial distribution of satellite galaxies. The projected ellipticity of a group is measured using the moments of the discrete distribution of its member galaxies. We infer the three-dimensional and projected axis ratios of their dark matter haloes by comparing the measured ellipticity distributions with those obtained from Monte Carlo simulations of projected, triaxial dark matter haloes with different axis ratios. We find that the halo shape has a strong dependence on the halo mass. While the haloes of low-mass groups are nearly spherical, those of massive groups tend to be prolate. For groups containing at least four members, the statistical distribution of their measured ellipticities does not have a strong dependence on the colors of their central galaxies. Our analysis further shows that the average three-dimensional axis ratio for haloes with $12<{\rm log}[M/(h^{-1}M_{\odot})]\leq15$ is about $1:0.46:0.46$, resulting in a projected axis ratio of $\sim 0.77$. Our results for the alignment between the orientation of the central galaxy of a group and the distribution of their satellite galaxies are in broad agreement with those obtained by Yang et al. The distribution of satellite galaxies preferentially aligns with the major axis of the central galaxy, with a clear dependence on both halo mass and galaxy colors. (abridged)

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arXiv2007

Galaxy Groups in the SDSS DR4: II. halo occupation statistics

We investigate various halo occupation statistics using a large galaxy group catalogue constructed from the SDSS DR4 with an adaptive halo-based group finder. The conditional luminosity function (CLF) is measured separately for all, red and blue galaxies, as well as in terms of central and satellite galaxies. The CLFs for central and satellite galaxies can be well modelled with a log-normal distribution and a modified Schechter form, respectively. About 85% of the central galaxies and about 80% of the satellite galaxies in halos with masses $M_h\ga 10^{14}\msunh$ are red galaxies. These numbers decrease to 50% and 40%, respectively, in halos with $M_h \sim 10^{12}\msunh$. For halos of a given mass, the distribution of the luminosities of central galaxies, $L_c$, has a dispersion of about 0.15 dex. The mean luminosity (stellar mass) of the central galaxies scales with halo mass as $L_c\propto M_h^{0.17}$ ($M_{*,c}\propto M_h^{0.22}$) for halos with masses $M\gg 10^{12.5}\msunh$, and both relations are significantly steeper for less massive halos. We also measure the luminosity (stellar mass) gap between the first and second brightest (most massive) member galaxies, $\log L_1 - \log L_2$ ($\log M_{*,1}-\log M_{*,2}$). These gap statistics, especially in halos with $M_h \la 10^{14.0}\msunh$, indicate that the luminosities of central galaxies are clearly distinct from those of their satellites. The fraction of fossil groups, defined as those groups with $\log L_1 - \log L_2\ge 0.8$, ranges from $\sim 2.5%$ for groups with $M_h\sim 10^{14}\msunh$ to 18-60% for groups with $M_h\sim 10^{13}\msunh$. Finally, we measure the fraction of satellites, which changes from $\sim 5.0%$ for galaxies with $\rmag\sim -22.0$ to $\sim40%$ for galaxies with $\rmag\sim -17.0$. (abridged)

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arXiv2007

Spatial and kinematic alignments between central and satellite halos

Based on a cosmological N-body simulation we analyze spatial and kinematic alignments of satellite halos within six times the virial radius of group size host halos (Rvir). We measure three different types of spatial alignment: halo alignment between the orientation of the group central substructure (GCS) and the distribution of its satellites, radial alignment between the orientation of a satellite and the direction towards its GCS, and direct alignment between the orientation of the GCS and that of its satellites. In analogy we use the directions of satellite velocities and probe three further types of alignment: the radial velocity alignment between the satellite velocity and connecting line between satellite and GCS, the halo velocity alignment between the orientation of the GCS and satellite velocities and the auto velocity alignment between the satellites orientations and their velocities. We find that satellites are preferentially located along the major axis of the GCS within at least 6 Rvir (the range probed here). Furthermore, satellites preferentially point towards the GCS. The most pronounced signal is detected on small scales but a detectable signal extends out to 6 Rvir. The direct alignment signal is weaker, however a systematic trend is visible at distances < 2 Rvir. All velocity alignments are highly significant on small scales. Our results suggest that the halo alignment reflects the filamentary large scale structure which extends far beyond the virial radii of the groups. In contrast, the main contribution to the radial alignment arises from the adjustment of the satellite orientations in the group tidal field. The projected data reveal good agreement with recent results derived from large galaxy surveys. (abridged)

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arXiv2007

The Importance of Satellite Quenching for the Build-Up of the Red Sequence of Present Day Galaxies

In the current paradigm, red sequence galaxies are believed to have formed as blue disk galaxies that subsequently had their star formation quenched. Since red-sequence galaxies typically have an early-type morphology, the transition from the blue to the red sequence also involves a morphological transformation. In this paper we study the impact of transformation mechanisms that operate only on satellite galaxies, such as strangulation, ram-pressure stripping and galaxy harassment. Using a large galaxy group catalogue constructed from the SDSS, we compare the colors and concentrations of satellites galaxies to those of central galaxies of the same stellar mass, adopting the hypothesis that the latter are the progenitors of the former. On average, satellites are redder and more concentrated than central galaxies of the same stellar mass. Central-satellite pairs that are matched in both stellar mass and color, however, show no average concentration difference, indicating that the transformation mechanisms affect color more than morphology. The color and concentration differences of matched central-satellite pairs are completely independent of the halo mass of the satellite galaxy, indicating that satellite-specific transformation mechanisms are equally efficient in haloes of all masses. This strongly favors strangulation as the main quenching mechanism for satellite galaxies. Finally, we determine the relative importance of satellite quenching for the build-up of the red sequence. We find that roughly 70 percent of red sequence satellite galaxies with a stellar mass of 10^9 Msun had their star formation quenched as satellites. This drops rapidly to zero with increasing stellar mass, indicating that a significant fraction of red satellites were already quenched before they became a satellite.

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arXiv2007

Ongoing Assembly of Massive Galaxies by Major Merging in Large Groups and Clusters from the SDSS

We investigate the incidence of major mergers creating >10e11 Msun galaxies in present-day groups and clusters more massive than 2.5e13 Msun. We identify 38 pairs of massive galaxies with mutual tidal interaction signatures selected from >5000 galaxies with >5e10 Msun that reside in 845 such groups. We fit the images of each galaxy pair as the line-of-sight projection of symmetric models and identify mergers by the presence of residual asymmetries around each progenitor, such as off-center isophotes, broad tidal tails, and dynamical friction wakes. At the resolution and sensitivity of the SDSS, such mergers are found in 16% of high-mass, galaxy-galaxy pairs with magnitude differences of <1.5 and <30 kpc projected separations. We find that 90% of these mergers have nearly equal-mass progenitors with red-sequence colors and centrally-concentrated morphologies, the hallmarks of dissipationless merger simulations. Mergers at group centers are more common than between 2 satellites, but both are morphologically indistinguishable and we tentatively conclude that the latter are likely located at the dynamical centers of recently accreted subhalos. The frequency of central and satellite merging diminishes with group mass consistent with dynamical friction expectations. Based on reasonable assumptions, the centers of these massive halos are growing in stellar mass by 1-9% per Gyr, on average. Compared to all LRG-LRG mergers, we find a 2-9 times higher rate for their merging when restricted to these dense environments. Our results imply that the massive end of the galaxy population continues to evolve hierarchically at a measurable level, and that the centers of massive groups are the preferred environment for merger-driven galaxy assembly. (abridged)

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arXiv2007

Three Different Types of Galaxy Alignment within Dark Matter Halos

Using a large galaxy group catalogue based on the Sloan Digital Sky Survey Data Release 4 we measure three different types of intrinsic galaxy alignment within groups: halo alignment between the orientation of the brightest group galaxies (BGG) and the distribution of its satellite galaxies, radial alignment between the orientation of a satellite galaxy and the direction towards its BGG, and direct alignment between the orientation of the BGG and that of its satellites. In agreement with previous studies we find that satellite galaxies are preferentially located along the major axis. In addition, on scales r < 0.7 Rvir we find that red satellites are preferentially aligned radially with the direction to the BGG. The orientations of blue satellites, however, are perfectly consistent with being isotropic. Finally, on scales r < 0.1 \Rvir, we find a weak but significant indication for direct alignment between satellites and BGGs. We briefly discuss the implications for weak lensing measurements.

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arXiv2007

On The Assembly History of Dark Matter Haloes

(abridged) We study the mass assembly history (MAH) of dark matter haloes. We compare MAHs obtained using (i) merger trees constructed with the extended Press-Schechter (EPS) formalism, (ii) numerical simulations, and (iii) the Lagrangian perturbation code PINOCCHIO. We show that the PINOCCHIO MAHs are in excellent agreement with those obtained using numerical simulations. Using a suite of 55 PINOCCHIO simulations, with 256^3 particles each, we study the MAHs of 12,924 cold dark matter haloes in a \LambdaCDM concordance cosmology. We show that haloes less massive than the characteristic non-linear mass scale establish their potential wells much before they acquire most of their mass. The time when a halo reaches its maximum virial velocity roughly divides its mass assembly into two phases, a fast accretion phase which is dominated by major mergers, and a slow accretion phase dominated by minor mergers. Each halo experiences about 3 \pm 2 major mergers since its main progenitor had a mass equal to one percent of the final halo mass. This major merger statistic is found to be virtually independent of halo mass. However, the average redshift at which these major mergers occur, is strongly mass dependent, with more massive haloes experiencing their major mergers later.

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arXiv2007

The cross-correlation between galaxies of different luminosities and Colors

We study the cross-correlation between galaxies of different luminosities and colors, using a sample selected from the SDSS Dr 4. Galaxies are divided into 6 samples according to luminosity, and each of these samples is divided into red and blue subsamples. Projected auto-correlation and cross-correlation is estimated for these subsample. At projected separations r_p > 1\mpch, all correlation functions are roughly parallel, although the correlation amplitude depends systematically on luminosity and color. On r_p < 1\mpch, the auto- and cross-correlation functions of red galaxies are significantly enhanced relative to the corresponding power laws obtained on larger scales. Such enhancement is absent for blue galaxies and in the cross-correlation between red and blue galaxies. We esimate the relative bias factor on scales r > 1\mpch for each subsample using its auto-correlation function and cross-correlation functions. The relative bias factors obtained from different methods are similar. For blue galaxies the luminosity-dependence of the relative bias is strong over the luminosity range probed (-23.0<M_r < -18.0),but for red galaxies the dependence is weaker and becomes insignificant for luminosities below L^*. To examine whether a significant stochastic/nonlinear component exists in the bias relation, we study the ratio R_ij= W_{ii}W_{jj}/W_{ij}^2, where W_{ij} is the projected correlation between subsample i and j. We find that the values of R_ij are all consistent with 1 for all-all, red-red and blue-blue samples, however significantly larger than 1 for red-blue samples. For faint red - faint blue samples the values of R_{ij} are as high as ~ 2 on small scales r_p < 1 \mpch and decrease with increasing r_p.

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