Mass Function (mass + function)

Distribution by Scientific Domains

Kinds of Mass Function

  • cluster mass function
  • initial mass function
  • stellar initial mass function

  • Selected Abstracts

    Metallicity and kinematical clues to the formation of the Local Group

    R.F.G. Wyse
    Abstract The kinematics and elemental abundances of resolved stars in the nearby Universe can be used to infer conditions at high redshift, trace how galaxies evolve and constrain the nature of dark matter. This approach is complementary to direct study of systems at high redshift, but I will show that analysis of individual stars allows one to break degeneracies, such as between star formation rate and stellar Initial Mass Function, that complicate the analysis of unresolved, distant galaxies (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

    Abundances, masses and weak-lensing mass profiles of galaxy clusters as a function of richness and luminosity in ,CDM cosmologies

    Stefan Hilbert
    ABSTRACT We test the concordance , cold dark matter (,CDM) cosmology by comparing predictions for the mean properties of galaxy clusters to observations. We use high-resolution N -body simulations of cosmic structure formation and semi-analytic models of galaxy formation to compute the abundance, mean density profile and mass of galaxy clusters as a function of richness and luminosity, and we compare these predictions to observations of clusters in the Sloan Digital Sky Survey (SDSS) maxBCG catalogue. We discuss the scatter in the mass,richness relation, the reconstruction of the cluster mass function from the mass,richness relation and fits to the weak-lensing cluster mass profiles. The impact of cosmological parameters on the predictions is investigated by comparing results from galaxy models based on the Millennium Simulation (MS) and the WMAP1 simulation to those from the WMAP3 simulation. We find that the simulated weak-lensing mass profiles and the observed profiles of the SDSS maxBCG clusters agree well in shape and amplitude. The mass,richness relations in the simulations are close to the observed relation, with differences ,30 per cent. The MS and WMAP1 simulations yield cluster abundances similar to those observed, whereas abundances in the WMAP3 simulation are two to three times lower. The differences in cluster abundance, mass and density amplitude between the simulations and the observations can be attributed to differences in the underlying cosmological parameters, in particular the power spectrum normalization ,8. Better agreement between predictions and observations should be reached with a normalization 0.722 < ,8 < 0.9 (probably closer to the upper value), i.e. between the values underlying the two simulation sets. [source]

    The substructure hierarchy in dark matter haloes

    Carlo Giocoli
    ABSTRACT We present a new algorithm for identifying the substructure within simulated dark matter haloes. The method is an extension of that proposed by Tormen, Moscardini & Yoshida and Giocoli, Tormen & van den Bosch, which identifies a subhalo as a group of self-bound particles that prior to being accreted by the main progenitor of the host halo belonged to one and the same progenitor halo (hereafter ,satellite'). However, this definition does not account for the fact that these satellite haloes themselves may also have substructure, which thus gives rise to sub-subhaloes, etc. Our new algorithm identifies substructures at all levels of this hierarchy, and we use it to determine the mass function of all substructure (counting subhaloes, sub-subhaloes, etc.). On average, haloes which are formed more recently tend to have a larger mass fraction in substructure and to be less concentrated than average haloes of the same mass. We provide quantitative fits to these correlations. Even though our algorithm is very different from that of Gao et al., we also find that the subhalo mass function per unit mass at redshift z= 0 is universal. This universality extends to any redshift only if one accounts for the fact that host haloes of a given mass are less concentrated at higher redshifts, and concentration and substructure abundance are anticorrelated. This universality allows a simple parametrization of the subhalo mass function integrated over all host halo masses, at any given time. We provide analytic fits to this function which should be useful in halo model analyses which equate galaxies with halo substructure when interpreting clustering in large sky surveys. Finally, we discuss systematic differences in the subhalo mass function that arise from different definitions of (host) halo mass. [source]

    X-ray groups and clusters of galaxies in the Subaru,XMM Deep Field

    A. Finoguenov
    Abstract We present the results of a search for galaxy clusters in the Subaru,XMM Deep Field (SXDF). We reach a depth for a total cluster flux in the 0.5,2 keV band of 2 × 10,15 erg cm,2 s,1 over one of the widest XMM,Newton contiguous raster surveys, covering an area of 1.3 deg2. Cluster candidates are identified through a wavelet detection of extended X-ray emission. The red-sequence technique allows us to identify 57 cluster candidates. We report on the progress with the cluster spectroscopic follow-up and derive their properties based on the X-ray luminosity and cluster scaling relations. In addition, three sources are identified as X-ray counterparts of radio lobes, and in three further sources, an X-ray counterpart of the radio lobes provides a significant fraction of the total flux of the source. In the area covered by near-infrared data, our identification success rate achieves 86 per cent. We detect a number of radio galaxies within our groups, and for a luminosity-limited sample of radio galaxies we compute halo occupation statistics using a marked cluster mass function. We compare the cluster detection statistics in the SXDF with that in the literature and provide the modelling using the concordance cosmology combined with current knowledge of the X-ray cluster properties. The joint cluster log(N) , log(S) is overpredicted by the model, and an agreement can be achieved through a reduction of the concordance ,8 value by 5 per cent. Having considered the dn/dz and the X-ray luminosity function of clusters, we conclude that to pin down the origin of disagreement a much wider (50 deg2) survey is needed. [source]

    The star formation efficiency and its relation to variations in the initial mass function

    Paul C. Clark
    ABSTRACT We investigate how the dynamical state of a turbulently supported, 1000 M,, molecular cloud affects the properties of the cluster it forms, focusing our discussion on the star formation efficiency (SFE) and the initial mass function (IMF). A variety of initial energy states are examined in this paper, ranging from clouds with |Egrav| = 0.1 Ekin to clouds with |Egrav| = 10 Ekin, and for both isothermal and piece-wise polytropic equations of state (similar to that suggested by Larson). It is found that arbitrary SFEs are possible, with strongly unbound clouds yielding very low SFEs. We suggest that the low SFE in the Maddelena cloud may be a consequence of the relatively unbound state of its internal structure. It is also found that competitive accretion results in the observed IMF when the clouds have initial energy states of |Egrav| ,Ekin. We show that under such conditions the shape of the IMF is independent of time in the calculations. This demonstrates that the global accretion process can be terminated at any stage in the cluster's evolution, while still yielding a distribution of stellar masses that is consistent with the observed IMF. As the clouds become progressively more unbound, competitive accretion is less important and the protostellar mass function flattens. These results predict that molecular clouds should be permeated with a distributed population of stars that follow a flatter than Salpeter IMF. [source]

    The poorly constrained cluster disruption time-scale in the Large Magellanic Cloud

    Geneviève Parmentier
    ABSTRACT We use Monte Carlo simulations, combined with homogeneously determined age and mass distributions, based on multiwavelength photometry, to constrain the cluster formation history and the rate of bound cluster disruption in the Large Magellanic Cloud (LMC) star cluster system. We evolve synthetic star cluster systems formed with a power-law initial cluster mass function (ICMF) of spectral index ,=,2 assuming different cluster disruption time-scales. For each of these cluster disruption time-scales, we derive the corresponding cluster formation rate (CFR) required to reproduce the observed cluster age distribution. We then compare, in a ,Poissonian',2 sense, model mass distributions and model two-dimensional distributions in log(mass) versus log(age) space of the detected surviving clusters to the observations. Because of the bright detection limit (MlimV,,4.7 mag) above which the observed cluster sample is complete, one cannot constrain the characteristic cluster disruption time-scale for a 104 M, cluster, tdis4[where the disruption time-scale depends on cluster mass as tdis=tdis4(Mcl/104 M,),, with ,, 0.62], to better than a lower limit, tdis4, 1 Gyr. We conclude that the CFR has been increasing steadily from 0.3 clusters Myr,1 5 Gyr ago to a present rate of (20,30) clusters Myr,1 for clusters spanning a mass range of ,100,107 M,. For older ages, the derived CFR depends sensitively on our assumption of the underlying CMF shape. If we assume a universal Gaussian ICMF, then the CFR has increased steadily over a Hubble time from ,1 cluster Gyr,1 15 Gyr ago to its present value. On the other hand, if the ICMF has always been a power law with a slope close to ,=,2, the CFR exhibits a minimum some 5 Gyr ago, which we tentatively identify with the well-known age gap in the LMC's cluster age distribution. [source]

    Stellar contents and star formation in the young star cluster Be 59

    A. K. Pandey
    ABSTRACT We present UBV Ic CCD photometry of the young open cluster Be 59 with the aim to study the star formation scenario in the cluster. The radial extent of the cluster is found to be ,10 arcmin (2.9 pc). The interstellar extinction in the cluster region varies between E(B,V) , 1.4 to 1.8 mag. The ratio of total-to-selective extinction in the cluster region is estimated as 3.7 ± 0.3. The distance of the cluster is found to be 1.00 ± 0.05 kpc. Using near-infrared (NIR) colours and slitless spectroscopy, we have identified young stellar objects (YSOs) in the open cluster Be 59 region. The ages of these YSOs range between <1 and ,2 Myr, whereas the mean age of the massive stars in the cluster region is found to be ,2 Myr. There is evidence for second-generation star formation outside the boundary of the cluster, which may be triggered by massive stars in the cluster. The slope of the initial mass function, ,, in the mass range 2.5 < M/M,, 28 is found to be ,1.01 ± 0.11 which is shallower than the Salpeter value (,1.35), whereas in the mass range 1.5 < M/M,, 2.5 the slope is almost flat. The slope of the K -band luminosity function is estimated as 0.27 ± 0.02, which is smaller than the average value (,0.4) reported for young embedded clusters. Approximately 32 per cent of H, emission stars of Be 59 exhibit NIR excess indicating that inner discs of the T Tauri star (TTS) population have not dissipated. The Midcourse Space Experiment (MSX) and IRAS-HIRES images around the cluster region are also used to study the emission from unidentified infrared bands and to estimate the spatial distribution of optical depth of warm and cold interstellar dust. [source]

    The mass function of , Centauri down to 0.15 M,,

    A. Sollima
    ABSTRACT By means of deep FORS1/VLT and ACS/Hubble Space Telescope observations of a wide area in the stellar system , Cen we measured the luminosity function of main-sequence stars down to R= 22.6 and IF814W= 24.5. The luminosity functions obtained have been converted into mass functions and compared with analytical initial mass functions (IMFs) available in the literature. The mass function obtained, reaching M, 0.15 M,, can be well reproduced by a broken power law with indices ,=,2.3 for M > 0.5 M, and ,=,0.8 for M < 0.5 M,. Since the stellar populations of , Cen have been proved to be actually unaffected by dynamical evolution processes, the mass function measured in this stellar system should represent the best approximation of the IMF of a star cluster. The comparison with the MF measured in other Galactic globular clusters suggests that possible primordial differences in the slope of the low-mass end of their MF could exist. [source]

    The dust temperatures of the pre-stellar cores in the , Oph main cloud and in other star-forming regions: consequences for the core mass function

    Dimitris Stamatellos
    ABSTRACT We estimate the dust temperatures of the clumps in the , Oph main cloud taking into account the 3D geometry of the region, and external heating from the interstellar radiation field and from HD 147879, a nearby luminous B2V star, which is believed to dominate the radiation field in the region. We find that the regions where pre-stellar cores are observed (i.e. at optical visual extinctions >7 mag) are colder than ,10 ,11 K. These dust temperatures are smaller than those which previous studies of the same region have assumed. We use the new dust temperatures to estimate the masses of the pre-stellar cores in the , Oph main cloud from millimetre observations, and we find core masses that are larger than previous estimates by a factor of ,2 ,3. This affects the core mass function (CMF) of the region; we find that the mass at which the core mass spectrum steepens from a slope ,, 1.5 to a slope ,, 2.5 has moved from ,0.5 to ,1 M,. In contrast with the CMF in other star-forming regions (e.g. Orion), there is no indication for a turnover down to the completeness limit (,0.2 M,), but the CMF may flatten at around ,0.4 M,. We generalize our results to the pre-stellar cores in Taurus and in Orion. In Taurus, the ambient radiation field heating the pre-stellar cores is believed to be weaker than that in , Oph. Hence, the dust temperatures of the cores in Taurus are expected to be below ,10 ,11 K. In Orion, the radiation field is believed to be 103 times stronger than the standard interstellar radiation field. Based on this assumption, we estimate that the dust temperatures of the pre-stellar cores in Orion are around ,20 ,30 K. [source]

    The UKIRT Infrared Deep Sky Survey (UKIDSS)

    A. Lawrence
    ABSTRACT We describe the goals, design, implementation, and initial progress of the UKIRT Infrared Deep Sky Survey (UKIDSS), a seven-year sky survey which began in 2005 May. UKIDSS is being carried out using the UKIRT Wide Field Camera (WFCAM), which has the largest étendue of any infrared astronomical instrument to date. It is a portfolio of five survey components covering various combinations of the filter set ZYJHK and H2. The Large Area Survey, the Galactic Clusters Survey, and the Galactic Plane Survey cover approximately 7000 deg2 to a depth of K, 18; the Deep Extragalactic Survey covers 35 deg2 to K, 21, and the Ultra Deep Survey covers 0.77 deg2 to K, 23. Summed together UKIDSS is 12 times larger in effective volume than the 2MASS survey. The prime aim of UKIDSS is to provide a long-term astronomical legacy data base; the design is, however, driven by a series of specific goals , for example, to find the nearest and faintest substellar objects, to discover Population II brown dwarfs, if they exist, to determine the substellar mass function, to break the z= 7 quasar barrier; to determine the epoch of re-ionization, to measure the growth of structure from z= 3 to the present day, to determine the epoch of spheroid formation, and to map the Milky Way through the dust, to several kpc. The survey data are being uniformly processed. Images and catalogues are being made available through a fully queryable user interface , the WFCAM Science Archive ( The data are being released in stages. The data are immediately public to astronomers in all ESO member states, and available to the world after 18 months. Before the formal survey began, UKIRT and the UKIDSS consortia collaborated in obtaining and analysing a series of small science verification (SV) projects to complete the commissioning of the camera. We show some results from these SV projects in order to demonstrate the likely power of the eventual complete survey. Finally, using the data from the First Data Release, we assess how well UKIDSS is meeting its design targets so far. [source]

    The halo mass function from the dark ages through the present day

    Darren S. Reed
    ABSTRACT We use an array of high-resolution N -body simulations to determine the mass function of dark matter haloes at redshifts 10,30. We develop a new method for compensating for the effects of finite simulation volume that allows us to find an approximation to the true ,global' mass function. By simulating a wide range of volumes at different mass resolution, we calculate the abundance of haloes of mass 105,12 h,1 M,. This enables us to predict accurately the abundance of the haloes that host the sources that reionize the Universe. In particular, we focus on the small mass haloes (,105.5,6 h,1 M,) likely to harbour Population III stars where gas cools by molecular hydrogen emission, early galaxies in which baryons cool by atomic hydrogen emission at a virial temperature of ,104K (,107.5,8 h,1 M,), and massive galaxies that may be observable at redshift ,10. When we combine our data with simulations that include high-mass haloes at low redshift, we find that the best fit to the halo mass function depends not only on the linear overdensity, as is commonly assumed in analytic models, but also on the slope of the linear power spectrum at the scale of the halo mass. The Press,Schechter model gives a poor fit to the halo mass function in the simulations at all epochs; the Sheth-Tormen model gives a better match, but still overpredicts the abundance of rare objects at all times by up to 50 per cent. Finally, we consider the consequences of the recently released WMAP 3-yr cosmological parameters. These lead to much less structure at high redshift, reducing the number of z= 10,mini-haloes' by more than a factor of two and the number of z= 30 galaxy hosts by nearly four orders of magnitude. Code to generate our best-fitting halo mass function may be downloaded from [source]

    Transients from initial conditions in cosmological simulations

    Martín Crocce
    ABSTRACT We study the impact of setting initial conditions in numerical simulations using the standard procedure based on the Zel'dovich approximation (ZA). As it is well known from the perturbation theory, ZA initial conditions have incorrect second- and higher-order growth and therefore excite long-lived transients in the evolution of the statistical properties of density and velocity fields. We also study the improvement brought by using more accurate initial conditions based on second-order Lagrangian perturbation theory (2LPT). We show that 2LPT initial conditions reduce transients significantly and thus are much more appropriate for numerical simulations devoted to precision cosmology. Using controlled numerical experiments with ZA and 2LPT initial conditions, we show that simulations started at redshift zi= 49 using the ZA underestimate the power spectrum in the non-linear regime by about 2, 4 and 8 per cent at z= 0, 1, and 3, respectively, whereas the mass function of dark matter haloes is underestimated by 5 per cent at m= 1015 M, h,1 (z= 0) and 10 per cent at m= 2 × 1014 M, h,1 (z= 1). The clustering of haloes is also affected to the few per cent level at z= 0. These systematics effects are typically larger than statistical uncertainties in recent mass function and power spectrum fitting formulae extracted from numerical simulations. At large scales, the measured transients in higher-order correlations can be understood from first principle calculations based on perturbation theory. [source]

    Constraints on the initial mass function of the first stars

    Raffaella Schneider
    ABSTRACT Motivated by theoretical predictions that the first stars were predominantly very massive, we investigate the physics of the transition from an early epoch dominated by massive Pop III stars to a later epoch dominated by familiar low-mass Pop II/I stars by means of a numerically generated catalogue of dark matter haloes coupled with a self-consistent treatment of chemical and radiative feedback. Depending on the strength of the chemical feedback, Pop III stars can contribute a substantial fraction (several per cent) of the cosmic star formation activity even at moderate redshifts, z, 5. We find that the three z, 10 sources tentatively detected in Near Infrared Camera and Multi-Object Spectrometer (NICMOS) Ultra Deep Fields (UDFs) should be powered by Pop III stars, if these are massive; however, this scenario fails to reproduce the derived Wilkinson Microwave Anisotropy Probe (WMAP) electron scattering optical depth. Instead, both the UDFs and WMAP constraints can be fulfilled if stars at any time form with a more standard, slightly top-heavy, Larson initial mass function. [source]

    Clumpy shocks and the clump mass function

    Paul C. Clark
    ABSTRACT One possible mechanism for the formation of molecular clouds is large-scale colliding flows. In this paper, we examine whether clumpy, colliding, flows could be responsible for the clump mass functions that have been observed in several regions of embedded star formation, which have been shown to be described by a Salpeter-type slope. The flows presented here, which comprise a population of initially identical clumps, are modelled using smoothed particle hydrodynamics (SPH) and calculations are performed with and without the inclusion of self-gravity. When the shock region is at its densest, we find that the clump mass spectrum is always well modelled by a Salpeter-type slope. This is true regardless of whether the self-gravity is included in the simulations or not, and for our choice of filling factors for the clumpy flows (10, 20 and 40 per cent), and Mach number (5, 10 and 20). In the non-self-gravitating simulations, this slope is retained at lower Mach numbers as the simulations progress past the densest phase. In the simulations which include self-gravity, we find that low Mach number runs yield a flatter mass function after the densest phase. This is simply a result of increased coagulation due to gravitational collapse of the flows. In the high Mach number runs the Salpeter slope is always lost. The self-gravitating calculations also show that the subgroup of gravitationally bound clumps in which star formation occurs, always contain the most massive clumps in the population. Typically these clumps have a mass of order of the Jeans mass of the initial clumps. The mass function of these bound star-forming clumps is not at all similar to the Salpeter-type mass function observed for stars in the field. We conclude that the clump mass function may not only have nothing to do with gravity, but also nothing to do with the star formation process and the resulting mass distribution of stars. This raises doubt over the claims that the clump mass function is the origin of the stellar initial mass function (IMF), for regions such as , Oph, Serpens and the Orion B cloud. [source]

    The SAURON project , IV.

    The mass-to-light ratio, lenticular galaxies, the Fundamental Plane of elliptical, the virial mass estimator
    ABSTRACT We investigate the well-known correlations between the dynamical mass-to-light ratio (M/L) and other global observables of elliptical (E) and lenticular (S0) galaxies. We construct two-integral Jeans and three-integral Schwarzschild dynamical models for a sample of 25 E/S0 galaxies with SAURON integral-field stellar kinematics to about one effective (half-light) radius Re. They have well-calibrated I -band Hubble Space Telescope WFPC2 and large-field ground-based photometry, accurate surface brightness fluctuation distances, and their observed kinematics is consistent with an axisymmetric intrinsic shape. All these factors result in an unprecedented accuracy in the M/L measurements. We find a tight correlation of the form (M/L) = (3.80 ± 0.14) × (,e/200 km s,1)0.84±0.07 between the M/L (in the I band) measured from the dynamical models and the luminosity-weighted second moment ,e of the LOSVD within Re. The observed rms scatter in M/L for our sample is 18 per cent, while the inferred intrinsic scatter is ,13 per cent. The (M/L),,e relation can be included in the remarkable series of tight correlations between ,e and other galaxy global observables. The comparison of the observed correlations with the predictions of the Fundamental Plane (FP), and with simple virial estimates, shows that the ,tilt' of the FP of early-type galaxies, describing the deviation of the FP from the virial relation, is almost exclusively due to a real M/L variation, while structural and orbital non-homology have a negligible effect. When the photometric parameters are determined in the ,classic' way, using growth curves, and the ,e is measured in a large aperture, the virial mass appears to be a reliable estimator of the mass in the central regions of galaxies, and can be safely used where more ,expensive' models are not feasible (e.g. in high-redshift studies). In this case the best-fitting virial relation has the form (M/L)vir= (5.0 ± 0.1) ×Re,2e/(LG), in reasonable agreement with simple theoretical predictions. We find no difference between the M/L of the galaxies in clusters and in the field. The comparison of the dynamical M/L with the (M/L)pop inferred from the analysis of the stellar population, indicates a median dark matter fraction in early-type galaxies of ,30 per cent of the total mass inside one Re, in broad agreement with previous studies, and it also shows that the stellar initial mass function varies little among different galaxies. Our results suggest a variation in M/L at constant (M/L)pop, which seems to be linked to the galaxy dynamics. We speculate that fast-rotating galaxies have lower dark matter fractions than the slow-rotating and generally more-massive ones. If correct, this would suggest a connection between the galaxy assembly history and the dark matter halo structure. The tightness of our correlation provides some evidence against cuspy nuclear dark matter profiles in galaxies. [source]

    Weighing the young stellar discs around Sgr A*

    Sergei Nayakshin
    ABSTRACT It is believed that young massive stars orbiting Sgr A* in two stellar discs on scales of , 0.1,0.2 parsec were formed either farther out in the Galaxy and then quickly migrated inwards or in situ in a massive self-gravitating disc. Comparing N -body evolution of stellar orbits with observational constraints, we set upper limits on the masses of the two stellar systems. These masses turn out to be a few times lower than the expected total stellar mass estimated from the observed young high-mass stellar population and the standard galactic initial mass function (IMF). If these stars were formed in situ, in a massive self-gravitating disc, our results suggest that the formation of low-mass stars was suppressed by a factor of at least a few, requiring a top-heavy IMF for stars formed near Sgr A*. [source]

    The properties of Ly, emitting galaxies in hierarchical galaxy formation models

    M. Le Delliou
    ABSTRACT We present detailed predictions for the properties of Ly,-emitting galaxies in the framework of the , cold dark matter cosmology, calculated using the semi-analytical galaxy formation model galform. We explore a model that assumes a top-heavy initial mass function in starbursts and that has previously been shown to explain the sub-millimetre number counts and the luminosity function of Lyman-break galaxies at high redshift. We show that this model, with the simple assumption that a fixed fraction of Ly, photons escape from each galaxy, is remarkably successful at explaining the observed luminosity function of Ly, emitters (LAEs) over the redshift range 3 < z < 6.6. We also examine the distribution of Ly, equivalent widths and the broad-band continuum magnitudes of emitters, which are in good agreement with the available observations. We look more deeply into the nature of LAEs, presenting predictions for fundamental properties such as the stellar mass and radius of the emitting galaxy and the mass of the host dark matter halo. The model predicts that the clustering of LAEs at high redshifts should be strongly biased relative to the dark matter, in agreement with observational estimates. We also present predictions for the luminosity function of LAEs at z > 7, a redshift range that is starting to be be probed by near-infrared surveys and using new instruments such as the Dark Ages Z Lyman Explorer (DAzLE). [source]

    Halo model at its best: constraints on conditional luminosity functions from measured galaxy statistics

    Asantha Cooray
    ABSTRACT Using the conditional luminosity function (CLF; the luminosity distribution of galaxies in a dark matter halo) as the fundamental building block, we present an empirical model for the galaxy distribution. The model predictions are compared with the published luminosity function (LF) and clustering statistics from the Sloan Digital Sky Survey (SDSS) at low redshifts, galaxy correlation functions from the Classifying Objects by Medium-Band Observations 17 (COMBO-17) survey at a redshift of 0.6, the Deep Extragalactic Evolutionary Probe 2 (DEEP2) survey at a redshift of unity, the Great Observatories Deep Origins Survey (GOODS) at a redshift around 3 and the Subaru/XMM,Newton Deep Field data at a redshift of 4. The comparison with statistical measurements allows us to constrain certain parameters related to analytical descriptions on the relation between a dark matter halo and its central galaxy luminosity, its satellite galaxy luminosity, and the fraction of early- and late-type galaxies of that halo. With the SDSS r -band LF at Mr < ,17, the lognormal scatter in the central galaxy luminosity at a given halo mass in the central galaxy,halo mass, Lc(M), relation is constrained to be 0.17+0.02,0.01, with 1, errors here and below. For the same galaxy sample, we find no evidence for a low-mass cut-off in the appearance of a single central galaxy in dark matter haloes, with the 68 per cent confidence level upper limit on the minimum mass of dark matter haloes to host a central galaxy, with luminosity Mr < ,17, is 2 × 1010 h,1 M,. If the total luminosity of a dark matter halo varies with halo mass as Lc(M) (M/Msat),s when M > Msat, using SDSS data, we find that Msat= (1.2+2.9,1.1) × 1013 h,1 M, and power-law slope ,s= 0.56+0.19,0.17 for galaxies with Mr < ,17 at z < 0.1. At z, 0.6, the COMBO-17 data allows these parameters for MB < ,18 galaxies to be constrained as (3.3+4.9,3.0) × 1013 h,1 M, and (0.62+0.33,0.27), respectively. At z, 4, Subaru measurements constrain these parameters for MB < ,18.5 galaxies as (4.12+5.90,4.08) × 1012 h,1 M, and (0.55+0.32,0.35), respectively. The redshift evolution associated with these parameters can be described as a combination of the evolution associated with the halo mass function and the luminosity,halo mass relation. The single parameter well constrained by clustering measurements is the average of the total satellite galaxy luminosity corresponding to the dark matter halo distribution probed by the galaxy sample. For SDSS, ,Lsat,= (2.1+0.8,0.4) × 1010 h,2 L,, while for GOODS at z, 3, ,Lsat, < 2 × 1011 h,2 L,. For SDSS, the fraction of galaxies that appear as satellites is 0.13+0.03,0.03, 0.11+0.05,0.02, 0.11+0.12,0.03 and 0.12+0.33,0.05 for galaxies with luminosities in the r, band from ,22 to ,21, ,21 to ,20, ,20 to ,19 and ,19 to ,18, respectively. In addition to constraints on central and satellite CLFs, we also determine model parameters of the analytical relations that describe the fraction of early- and late-type galaxies in dark matter haloes. We use our CLFs to establish the probability distribution of halo mass in which galaxies of a given luminosity could be found either at halo centres or as satellites. Finally, to help establish further properties of the galaxy distribution, we propose the measurement of cross-clustering between galaxies divided into two distinctly different luminosity bins. Our analysis shows how CLFs provide a stronger foundation to built-up analytical models of the galaxy distribution when compared with models based on the halo occupation number alone. [source]

    Effects of dynamical evolution on the distribution of substructures

    Jorge Peñarrubia
    ABSTRACT We develop a semi-analytical model that determines the evolution of the mass and position of dark matter substructures orbiting in dark matter haloes. We apply this model to the case of the Milky Way. We focus in particular on the effects of mass loss, dynamical friction and substructure,substructure interactions, the last of which has previously been ignored in analytic models of substructure evolution. Our semi-analytical treatment reproduces both the spatial distribution of substructures and their mass function as obtained from the most recent N -body cosmological calculations of Gao et al. We find that, if mass loss is taken into account, the present distribution of substructures is practically insensitive to dynamical friction and scatterings from other substructures. Implementing these phenomena leads to a slight increase (,5 per cent) in the number of substructures at r < 0.25rvir, whereas their effects on the mass function are negligible. We find that mass-loss processes lead to the disruption of substructures before dynamical friction and gravitational scattering can significantly alter their orbits. Our results suggest that the present substructure distribution at r > 0.25rvir reflects the orbital properties at infall and is therefore purely determined by the dark matter environment around the host halo and has not been significantly altered by dynamical evolution. [source]

    The evolution of substructure in galaxy, group and cluster haloes , II.

    Global properties
    ABSTRACT In a previous paper, we described a new method for including detailed information about substructure in semi-analytic models of dark matter halo formation based on merger trees. In this paper, we present the basic predictions of our full model of halo formation. We first describe the overall properties of substructure in galaxy, group or cluster haloes at the present day. We then discuss the evolution of substructure, and the effect of the mass-accretion history of an individual halo on the mass function and orbital grouping of its subhalo population. We show, in particular, that the shape of the subhalo mass function is strongly correlated with the formation epoch of the halo. In a third paper in this series, we will compare the results of our semi-analytic method with the results of self-consistent numerical simulations of halo formation. [source]

    The origin of the initial mass function and its dependence on the mean Jeans mass in molecular clouds

    Matthew R. Bate
    ABSTRACT We investigate the dependence of stellar properties on the mean thermal Jeans mass in molecular clouds. We compare the results from the two largest hydrodynamical simulations of star formation to resolve the fragmentation process down to the opacity limit, the first of which was reported by Bate, Bonnell & Bromm. The initial conditions of the two calculations are identical except for the radii of the clouds, which are chosen so that the mean densities and mean thermal Jeans masses of the clouds differ by factors of 9 and 3, respectively. We find that the denser cloud, with the lower mean thermal Jeans mass, produces a higher proportion of brown dwarfs and has a lower characteristic (median) mass of the stars and brown dwarfs. This dependence of the initial mass function (IMF) on the density of the cloud may explain the observation that the Taurus star-forming region appears to be deficient in brown dwarfs when compared with the Orion Trapezium cluster. The new calculation also produces wide binaries (separations >20 au), one of which is a wide binary brown dwarf system. Based on the hydrodynamical calculations, we develop a simple accretion/ejection model for the origin of the IMF. In the model, all stars and brown dwarfs begin with the same mass (set by the opacity limit for fragmentation) and grow in mass until their accretion is terminated stochastically by their ejection from the cloud through dynamically interactions. The model predicts that the main variation of the IMF in different star-forming environments should be in the location of the peak (due to variations in the mean thermal Jeans mass of the cloud) and in the substellar regime. However, the slope of the IMF at high masses may depend on the dispersion in the accretion rates of protostars. [source]

    The 2dF QSO Redshift Survey , XIV.

    Structure, evolution from the two-point correlation function
    ABSTRACT In this paper we present a clustering analysis of quasi-stellar objects (QSOs) using over 20 000 objects from the final catalogue of the 2dF QSO Redshift Survey (2QZ), measuring the redshift-space two-point correlation function, ,(s). When averaged over the redshift range 0.3 < z < 2.2 we find that ,(s) is flat on small scales, steepening on scales above ,25 h,1 Mpc. In a WMAP/2dF cosmology (,m= 0.27, ,,= 0.73) we find a best-fitting power law with s0= 5.48+0.42,0.48 h,1 Mpc and ,= 1.20 ± 0.10 on scales s= 1 to 25 h,1 Mpc. We demonstrate that non-linear redshift-space distortions have a significant effect on the QSO ,(s) at scales less than ,10 h,1 Mpc. A cold dark matter model assuming WMAP/2dF cosmological parameters is a good description of the QSO ,(s) after accounting for non-linear clustering and redshift-space distortions, and allowing for a linear bias at the mean redshift of bQ(z= 1.35) = 2.02 ± 0.07. We subdivide the 2QZ into 10 redshift intervals with effective redshifts from z= 0.53 to 2.48. We find a significant increase in clustering amplitude at high redshift in the WMAP/2dF cosmology. The QSO clustering amplitude increases with redshift such that the integrated correlation function, , within 20 h,1 Mpc is and . We derive the QSO bias and find it to be a strong function of redshift with bQ(z= 0.53) = 1.13 ± 0.18 and bQ(z= 2.48) = 4.24 ± 0.53. We use these bias values to derive the mean dark matter halo (DMH) mass occupied by the QSOs. At all redshifts 2QZ QSOs inhabit approximately the same mass DMHs with MDH= (3.0 ± 1.6) × 1012 h,1 M,, which is close to the characteristic mass in the Press,Schechter mass function, M*, at z= 0. These results imply that L*Q QSOs at z, 0 should be largely unbiased. If the relation between black hole (BH) mass and MDH or host velocity dispersion does not evolve, then we find that the accretion efficiency (L/LEdd) for L*Q QSOs is approximately constant with redshift. Thus the fading of the QSO population from z, 2 to ,0 appears to be due to less massive BHs being active at low redshift. We apply different methods to estimate, tQ, the active lifetime of QSOs and constrain tQ to be in the range 4 × 106,6 × 108 yr at z, 2. We test for any luminosity dependence of QSO clustering by measuring ,(s) as a function of apparent magnitude (equivalent to luminosity relative to L*Q). However, we find no significant evidence of luminosity-dependent clustering from this data set. [source]

    The mass function of the stellar component of galaxies in the Sloan Digital Sky Survey

    Benjamin Panter
    ABSTRACT Using the moped algorithm, we determine non-parametrically the stellar mass function of 96 545 galaxies from the Sloan Digital Sky Survey Data Release One. By using the reconstructed spectrum due to starlight, we can eliminate contamination from either emission lines or active galactic nuclei components. Our results give excellent agreement with previous works, but extend their range by more than two decades in mass to 107.5,Ms/h,2 M,, 1012. We present both a standard Schechter fit and a fit modified to include an extra, high-mass contribution, possibly from cluster central dominant galaxies. The Schechter fit parameters are ,,= (7.8 ± 0.1) × 10,3 h3 Mpc,3, M,= (7.64 ± 0.09) × 1010 h,2 M, and ,=,1.159 ± 0.008. Our sample also yields an estimate for the contribution from baryons in stars to the critical density of ,b*h= (2.39 ± 0.08) × 10,3, in good agreement with other indicators. Error bars are statistical and a Salpeter initial mass function is assumed throughout. We find no evolution of the mass function in the redshift range 0.05 < z < 0.34, indicating that almost all stars were already formed at z, 0.34 with little or no star formation activity since then and that the evolution seen in the luminosity function must be largely due to stellar fading. [source]

    Mass segregation in young compact clusters in the Large Magellanic Cloud , III.

    Implications for the initial mass function
    ABSTRACT The distribution of core radii of rich clusters in the Large Magellanic Cloud (LMC) systematically increases in both upper limit and spread with increasing cluster age. Cluster-to-cluster variations in the stellar initial mass function (IMF) have been suggested as an explanation. We discuss the implications of the observed degree of mass segregation in our sample clusters for the shape of the initial mass function. Our results are based on Hubble Space Telescope/WFPC2 observations of six rich star clusters in the LMC, selected to include three pairs of clusters of similar age, metallicity and distance from the LMC centre, and exhibiting a large spread in core radii between the clusters in each pair. All clusters show clear evidence of mass segregation: (i) their luminosity function slopes steepen with increasing cluster radius, and (ii) the brighter stars are characterized by smaller core radii. For all sample clusters, both the slope of the luminosity function in the cluster centres and the degree of mass segregation are similar to each other, within observational errors of a few tenths of power-law slope fits to the data. This implies that their initial mass functions must have been very similar, down to ,0.8,1.0 M,. We therefore rule out variations in the IMF of the individual sample clusters as the main driver of the increasing spread of cluster core radii with cluster age. [source]

    Accretion in stellar clusters and the collisional formation of massive stars

    Ian A. Bonnell
    Abstract We present results from a numerical simulation of gas accretion in a cluster containing 1000 stars. The accretion forces the cluster to contract, leading to the development of a high-density core with a maximum density 105 times the mean stellar density. This density is sufficient for a significant number of stellar collisions to occur, resulting in the most massive stars being formed through a combination of gas accretion and stellar mergers. In the simulation, 19 mergers occur, generally where a binary is forced to merge owing to the interaction with another star in a small- N group. These small- N groups form owing to the self-gravity of the gas and constitute the highest-density regions in the cluster. Binary formation in these groups is common, occurring through dynamical three-body capture. The massive stars are thus generally in binary systems, which can be relatively wide. The self-gravity of the gas also forms significant structure in the vicinity of the cluster core, while continuing infall forms a circumbinary disc around the most massive star. This structure may be the source of collimation for the observed outflows from young massive stars. Finally, the resultant initial mass function from the combination of gas accretion and stellar mergers is indistinguishable from a Salpeter mass function. [source]

    An excursion set model of hierarchical clustering: ellipsoidal collapse and the moving barrier

    Ravi K. Sheth
    The excursion set approach allows one to estimate the abundance and spatial distribution of virialized dark matter haloes efficiently and accurately. The predictions of this approach depend on how the non-linear processes of collapse and virialization are modelled. We present simple analytic approximations that allow us to compare the excursion set predictions associated with spherical and ellipsoidal collapse. In particular, we present formulae for the universal unconditional mass function of bound objects and the conditional mass function which describes the mass function of the progenitors of haloes in a given mass range today. We show that the ellipsoidal collapse based moving barrier model provides a better description of what we measure in the numerical simulations than the spherical collapse based constant barrier model, although the agreement between model and simulations is better at large lookback times. Our results for the conditional mass function can be used to compute accurate approximations to the local-density mass function, which quantifies the tendency for massive haloes to populate denser regions than less massive haloes. This happens because low-density regions can be thought of as being collapsed haloes viewed at large lookback times, whereas high-density regions are collapsed haloes viewed at small lookback times. Although we have applied our analytic formulae only to two simple barrier shapes, we show that they are, in fact, accurate for a wide variety of moving barriers. We suggest how they can be used to study the case in which the initial dark matter distribution is not completely cold. [source]

    The build-up of haloes within Press,Schechter theory

    Will J. Percival
    Modelling the build-up of haloes is important for linking the formation of galaxies with cosmological models. A simple model of halo growth is provided by Press,Schechter (PS) theory, where the initial field of density fluctuations is smoothed using spherically symmetric filters centred on a given position to obtain information about the likelihood of later collapse on varying scales. In this paper the predicted halo mass growth is compared for three filter shapes: Gaussian, top-hat and sharp k -space. Preliminary work is also presented analysing the build-up of haloes within numerical simulations using a friends-of-friends group finder. The best-fit to the simulation mass function was obtained using PS theory with a top-hat filter. By comparing both the backwards conditional mass function, which gives the distribution of halo progenitors, and the distribution of halo mergers in time, the build-up of haloes in the simulations is shown to be better fitted by PS theory with a sharp k -space filter. This strengthens previous work, which also found the build-up of haloes in simulations to be well matched to PS theory with a sharp k -space filter by providing a direct comparison of different filters and by extending the statistical tools used to analyse halo mass growth. The usefulness of this work is illustrated by showing that the cosmological evolution in the proportion of haloes that have undergone recent merger is predicted to be independent of mass and power spectrum and to only depend upon cosmology. Recent results from observations of field galaxies are shown to match the evolution expected, but are not sufficiently accurate to distinguish usefully between cosmological parameters. [source]

    Stellar populations and surface brightness fluctuations: new observations and models

    John P. Blakeslee
    We investigate the use of surface brightness fluctuations (SBF) measurements in optical and near-IR bandpasses for both stellar population and distance studies. New V -band SBF data are reported for five galaxies in the Fornax cluster and combined with literature data to define a V -band SBF distance indicator, calibrated against Cepheid distances to the Leo group and the Virgo and Fornax clusters. The colour dependence of the V -band SBF indicator is only ,15 per cent steeper than that found for the I band, and the mean ,fluctuation colour' of the galaxies is We use new stellar population models, based on the latest Padua isochrones transformed empirically to the observational plane, to predict optical and near-IR SBF magnitudes and integrated colours for a wide range of population ages and metallicities. We examine the sensitivity of the predicted SBF,colour relations to changes in the isochrones, stellar transformations, and initial mass function. The new models reproduce fairly well the weak dependence of V and I SBF in globular clusters on metallicity, especially if the more metal-rich globulars are younger. Below solar metallicity, the near-IR SBF magnitudes depend mainly on age, while the integrated colours depend mainly on metallicity. This could prove a powerful new approach to the age,metallicity degeneracy problem; near-IR SBF observations of globular clusters would be an important test of the models. The models also help in understanding the and fluctuation colours of elliptical galaxies, with much less need for composite stellar populations than in previous models. However, in order to obtain theoretical calibrations of the SBF distance indicators, we combine the homogeneous population models into composite models and select out those ones with fluctuation colours consistent with observations. We are able to reproduce the observed range of elliptical galaxy colours, the slopes of the V and I SBF distance indicators against (fainter SBF in redder populations), and the flattening of the I -band relation for The models also match the observed slope of I -band SBF against the Mg2 absorption index and explain the steep colour dependence found by Ajhar et al. for the HST/WFPC2 F814W-band SBF measurements. In contrast to previous models, ours predict that the near-IR SBF magnitudes will also continue to grow fainter for redder populations. The theoretical V -band SBF zero-point predicted by these models agrees well with the Cepheid-calibrated V -band empirical zero-point. However, the model zero-point is 0.15,0.27 mag too faint in the I band and 0.24,0.36 mag too faint in K. The zero-points for the I band (empirically the best determined) would come into close agreement if the Cepheid distance scale were revised to agree with the recent dynamical distance measured to NGC 4258. We note that the theoretical SBF calibrations are sensitive to the uncertain details of stellar evolution, and conclude that the empirical calibrations remain more secure. However, the sensitivity of SBF to these finer details potentially makes it a powerful, relatively unexploited, constraint for stellar evolution and population synthesis. [source]

    An analytic model for the epoch of halo creation

    W. J. Percival
    In this paper we describe the Bayesian link between the cosmological mass function and the distribution of times at which isolated haloes of a given mass exist. By assuming that clumps of dark matter undergo monotonic growth on the time-scales of interest, this distribution of times is also the distribution of ,creation' times of the haloes. This monotonic growth is an inevitable aspect of gravitational instability. The spherical top-hat collapse model is used to estimate the rate at which clumps of dark matter collapse. This gives the prior for the creation time given no information about halo mass. Applying Bayes' theorem then allows any mass function to be converted into a distribution of times at which haloes of a given mass are created. This general result covers both Gaussian and non-Gaussian models. We also demonstrate how the mass function and the creation time distribution can be combined to give a joint density function, and discuss the relation between the time distribution of major merger events and the formula calculated. Finally, we determine the creation time of haloes within three N -body simulations, and compare the link between the mass function and creation rate with the analytic theory. [source]

    Evolution of the cluster abundance in non-Gaussian models

    J. Robinson
    We carry out N -body simulations of several non-Gaussian structure formation models, including Peebles' isocurvature cold dark matter model, cosmic string models, and a model with primordial voids. We compare the evolution of the cluster mass function in these simulations with that predicted by a modified version of the Press,Schechter formalism. We find that the Press,Schechter formula can accurately fit the cluster evolution over a wide range of redshifts for all of the models considered, with typical errors in the mass function of less than 25 per cent, considerably smaller than the amount by which predictions for different models may differ. This work demonstrates that the Press,Schechter formalism can be used to place strong model-independent constraints on non-Gaussianity in the Universe. [source]