Baryonic conversion tree: the global assembly of stars and dark matter in galaxies from the Sloan Digital Sky Survey

Using the spectroscopic sample of the Sloan Digital Sky Survey Data Release 1 (SDSS DR1), we measure how gas was transformed into stars as a function of time and stellar mass: the baryonic conversion tree (BCT). There is a clear correlation between early star formation activity and present-day stellar mass: the more massive galaxies have formed approximately 80 per cent of their stars at   z > 1  , while for the less massive ones the value is only approximately 20 per cent. By comparing the BCT with the dark matter merger tree, we find indications that star formation efficiency at   z > 1  had to be approximately a factor of two higher than today (∼10 per cent) in galaxies with present-day stellar mass larger than  2 × 10¹¹ M_⊙  , if this early star formation occurred in the main progenitor. Therefore, the λ cold dark matter (LCDM) paradigm can accommodate a large number of red objects. On the other hand, in galaxies with present-day stellar mass less than  10¹¹ M_⊙  , efficient star formation seems to have been triggered at   z ∼ 0.2  . We show that there is a characteristic mass  ( M _*∼ 10¹⁰ M_⊙)  for feedback efficiency (or lack of star formation). For galaxies with masses lower than this, feedback (or star formation suppression) is very efficient while for higher masses it is not. The BCT, determined here for the first time, should be an important observable with which to confront theoretical models of galaxy formation.     

Simulating the formation of a protocluster at z∼ 2

We present results from two high-resolution hydrodynamical simulations of protocluster regions at   z ≃ 2.1  . The simulations have been compared to observational results for the so-called Spiderweb galaxy system, the core of a putative protocluster region at   z = 2.16  , found around a radio galaxy. The simulated regions have been chosen so as to form a poor cluster with   M ₂₀₀≃ 10¹⁴  h ⁻¹ M_⊙  (C1) and a rich cluster with   M ₂₀₀≃ 2 × 10¹⁵  h ⁻¹ M_⊙  (C2) at   z = 0  . The simulated protoclusters show evidence of ongoing assembly of a dominating central galaxy. The stellar mass of the brightest cluster galaxy of the C2 system is in excess with respect to observational estimates for the Spiderweb galaxy, with a total star formation rate which is also larger than indicated by observations. We find that the projected velocities of galaxies in the C2 cluster are consistent with observations, while those measured for the poorer cluster C1 are too low compared with the observed velocities. We argue that the Spiderweb complex resembles the high-redshift progenitor of a rich galaxy cluster. Our results indicate that the included supernovae feedback is not enough to suppress star formation in these systems, supporting the need of introducing active galactic nuclei feedback. According to our simulations, a diffuse atmosphere of hot gas in hydrostatic equilibrium should already be present at this redshift, and enriched at a level comparable to that of nearby galaxy clusters. The presence of this gas should be detectable with future deep X-ray observations.     

The growth of central and satellite galaxies in cosmological smoothed particle hydrodynamics simulations

We examine the accretion and merger histories of central and satellite galaxies in a smoothed particle hydrodynamics (SPH) cosmological simulation that resolves galaxies down to  7 × 10⁹ M_⊙  . Most friends-of-friends haloes in the simulation have a distinct central galaxy, typically 2–5 times more massive than the most massive satellite. As expected, satellites have systematically higher assembly redshifts than central galaxies of the same baryonic mass, and satellites in more massive haloes form earlier. However, contrary to the simplest expectations, satellite galaxies continue to accrete gas and convert it to stars; the gas accretion declines steadily over a period of 0.5–1 Gyr after the satellite halo merges with a larger parent halo. Satellites in a cluster mass halo eventually begin to lose baryonic mass. Typically, satellites in our simulation are 0.1–0.2 mag bluer than in models that assume no gas accretion on to satellites after a halo merger. Since   z = 1  , 27 per cent of central galaxies (above  3 × 10¹⁰ M_⊙  ) and 22 per cent of present-day satellite galaxies have merged with a smaller system above a 1:4 mass ratio; about half of the satellite mergers occurred after the galaxy became a satellite and half before. In effect, satellite galaxies can remain 'central' objects of halo substructures, with continuing accretion and mergers, making the transition in assembly histories and physical properties a gradual one. Implementing such a gradual transformation in semi-analytic models would improve their agreement with observed colour distributions of satellite galaxies in groups and with the observed colour dependence of galaxy clustering.     

The local star formation rate and radio luminosity density

We present a new determination of the local volume-averaged star formation rate from the 1.4-GHz luminosity function of star forming galaxies. Our sample, taken from the   B ≤12  Revised Shapley–Ames catalogue (231 normal spiral galaxies over an effective area of 7.1 sr) has ≃100 per cent complete radio detections and is insensitive to dust obscuration and cirrus contamination. After removal of known active galaxies, the best-fitting Schechter function has a faint-end slope of  −1.27±0.07  in agreement with the local H α luminosity function, characteristic luminosity   L ∗=(2.6±0.7)×10²² W Hz⁻¹  and density   φ ∗=(4.8±1.1)×10⁻⁴ Mpc⁻³.  The inferred local radio luminosity density of  (1.73±0.37±0.03)×10¹⁹ W Hz⁻¹ Mpc⁻³  (Poisson noise, large-scale structure fluctuations) implies a volume-averaged star formation rate ∼2 times larger than the Gallego et al. H α estimate, i.e.   ρ _1.4 GHz=(2.10±0.45±0.04)×10⁻² M_⊙ yr⁻¹ Mpc⁻³  for a Salpeter initial mass function from  0.1–125 M_⊙  and Hubble constant of 50 km s⁻¹ Mpc⁻¹. We demonstrate that the Balmer decrement is a highly unreliable extinction estimator, and argue that optical–ultraviolet (UV) star formation rates (SFRs) are easily underestimated, particularly at high redshift.     

Two new large-separation gravitational lenses from SDSS

We present discovery images, together with follow-up imaging and spectroscopy, of two large-separation gravitational lenses found by our survey for wide arcs [the CAmbridge Sloan Survey Of Wide ARcs in the skY (CASSOWARY)]. The survey exploits the multicolour photometry of the Sloan Digital Sky Survey to find multiple blue components around red galaxies. CASSOWARY 2 (or 'the Cheshire Cat') is composed of two massive early-type galaxies at   z = 0.426  and 0.432, respectively, lensing two background sources, the first a star-forming galaxy at   z = 0.97  and the second a high -redshift galaxy  ( z > 1.4)  . There are at least three images of the former source and probably four or more of the latter, arranged in two giant arcs. The mass enclosed within the larger arc of radius ∼11 arcsec is  ∼33 × 10¹² M_⊙  . CASSOWARY 3 comprises an arc of three bright images of a   z = 0.725  source, lensed by a foreground elliptical at   z = 0.274  . The radius of the arc is ∼4 arcsec and the enclosed mass is  ∼2.5 × 10¹² M_⊙  . Together with earlier discoveries like the Cosmic Horseshoe and the 8 o'clock Arc, these new systems, with separations intermediate between the arcsecond-separation lenses of typical strong galaxy lensing and arcminute-separation cluster lenses, probe the very high end of the galaxy mass function.     

On the formation of massive galaxies: a simultaneous study of number density, size and intrinsic colour evolution in GOODS

The evolution of number density, size and intrinsic colour is determined for a volume-limited sample of visually classified early-type galaxies selected from the Hubble Space Telescope /Advanced Camera for Surveys images of the Great Observatories Origins Deep Survey (GOODS) North and South fields (version 2). The sample comprises 457 galaxies over 320 arcmin² with stellar masses above  3 × 10¹⁰ M_⊙  in the redshift range  0.4 < z < 1.2  . Our data allow a simultaneous study of number density, intrinsic colour distribution and size. We find that the most massive systems  (≳3 × 10¹¹ M_⊙)  do not show any appreciable change in comoving number density or size in our data. Furthermore, when including the results from 2dF galaxy redshift survey, we find that the number density of massive early-type galaxies is consistent with no evolution between   z = 1.2  and 0, i.e. over an epoch spanning more than half of the current age of the Universe. We find large discrepancies between the predictions of semi-analytic models. Massive galaxies show very homogeneous intrinsic colour distributions, with nearly flat radial colour gradients, but with a significant negative correlation between stellar mass and colour gradient, such that red cores appear predominantly in massive galaxies. The distribution of half-light radii – when compared to   z ∼ 0  and   z > 1  samples – is compatible with the predictions of semi-analytic models relating size evolution to the amount of dissipation during major mergers.     

The host galaxy of a narrow-line Seyfert 1 galaxy, RE J1034+396, with X-ray quasi-periodic oscillations

Using simple stellar population synthesis, we model the bulge stellar contribution in the optical spectrum of a narrow-line Seyfert 1 galaxy, RE J1034+396. We find that its bulge stellar velocity dispersion is  67.7 ± 8 km s⁻¹  . The supermassive black hole (SMBH) mass is about  (1–4) × 10⁶ M_⊙  if it follows the well-known   M _BH–σ_*  relation found in quiescent galaxies. We also derive the SMBH mass from the Hβ second moment, which is consistent with that from its bulge stellar velocity dispersion. The SMBH mass of (1–4)  × 10⁶ M_⊙  implies that the X-ray quasi-periodic oscillation (QPO) of RE J1034+396 can be scaled to a high-frequency QPO at 27–108 Hz found in Galactic black hole binaries with a  10-M_⊙  black hole. With the mass distribution in different age stellar populations, we find that the mean specific star formation rate (SSFR) over the past 0.1 Gyr is  0.0163 ± 0.0011  Gyr⁻¹, the stellar mass in the logarithm is  10.155 ± 0.06  in units of solar mass and the current star formation rate is  0.23 ± 0.016 M_⊙ yr⁻¹  . For RE J1034+396, there is no relation between the Eddington ratio and the SSFR as suggested by Chen et al., despite a larger scatter in their relation. We also suggest that about 7.0 per cent of the total Hα luminosity and 50 per cent of the total [O  ii ] luminosity come from the star formation process.     

The first galaxies: assembly, cooling and the onset of turbulence

We investigate the properties of the first galaxies at   z ≳ 10  with highly resolved numerical simulations, starting from cosmological initial conditions and taking into account all relevant primordial chemistry and cooling. A first galaxy is characterized by the onset of atomic hydrogen cooling, once the virial temperature exceeds  ≃10⁴ K  , and its ability to retain photoheated gas. We follow the complex accretion and star formation history of a  ≃5 × 10⁷ M_⊙  system by means of a detailed merger tree and derive an upper limit on the number of Population III (Pop III) stars formed prior to its assembly. We investigate the thermal and chemical evolution of infalling gas and find that partial ionization at temperatures  ≳10⁴ K  catalyses the formation of  H₂  and hydrogen deuteride, allowing the gas to cool to the temperature of the cosmic microwave background. Depending on the strength of radiative and chemical feedback, primordial star formation might be dominated by intermediate-mass Pop III stars formed during the assembly of the first galaxies. Accretion on to the nascent galaxy begins with hot accretion, where gas is accreted directly from the intergalactic medium and shock heated to the virial temperature, but is quickly accompanied by a phase of cold accretion, where the gas cools in filaments before flowing into the parent halo with high velocities. The latter drives supersonic turbulence at the centre of the galaxy and could lead to very efficient chemical mixing. The onset of turbulence in the first galaxies thus likely marks the transition to Pop II star formation.     

On the galaxy stellar mass function, the mass–metallicity relation and the implied baryonic mass function

A comparison between published field galaxy stellar mass functions (GSMFs) shows that the cosmic stellar mass density is in the range 4–8 per cent of the baryon density (assuming  Ω_b= 0.045  ). There remain significant sources of uncertainty for the dust correction and underlying stellar mass-to-light ratio even assuming a reasonable universal stellar initial mass function. We determine the   z < 0.05  GSMF using the New York University Value-Added Galaxy Catalog sample of 49 968 galaxies derived from the Sloan Digital Sky Survey and various estimates of stellar mass. The GSMF shows clear evidence for a low-mass upturn and is fitted with a double Schechter function that has  α₂≃−1.6  . At masses below  ∼10^8.5 M_⊙  , the GSMF may be significantly incomplete because of missing low-surface-brightness galaxies. One interpretation of the stellar mass–metallicity relation is that it is primarily caused by a lower fraction of available baryons converted to stars in low-mass galaxies. Using this principle, we determine a simple relationship between baryonic mass and stellar mass and present an 'implied baryonic mass function'. This function has a faint-end slope,  α₂≃−1.9  . Thus, we find evidence that the slope of the low-mass end of the galaxy mass function could plausibly be as steep as the halo mass function. We illustrate the relationship between halo baryonic mass function → galaxy baryonic mass function → GSMF. This demonstrates the requirement for peak galaxy formation efficiency at baryonic masses  ∼10¹¹ M_⊙  corresponding to a minimum in feedback effects. The baryonic-infall efficiency may have levelled off at lower masses.     

Galaxy groups at 0.3 ≤z≤ 0.55 – II. Evolution to z∼ 0

We compare deep Magellan spectroscopy of 26 groups at  0.3 ≤ z ≤ 0.55  , selected from the Canadian Network for Observational Cosmology 2 field survey, with a large sample of nearby groups from the 2PIGG catalogue. We find that the fraction of group galaxies with significant [O  ii ]λ3727 emission (≥5 Å) increases strongly with redshift, from ∼29 per cent in 2dFGRS to ∼58 per cent in CNOC2, for all galaxies brighter than  ∼ M _*+ 1.75  . This trend is parallel to the evolution of field galaxies, where the equivalent fraction of emission-line galaxies increases from ∼53 to ∼75 per cent. The fraction of emission-line galaxies in groups is lower than in the field, across the full redshift range, indicating that the history of star formation in groups is influenced by their environment. We show that the evolution required to explain the data is inconsistent with a quiescent model of galaxy evolution; instead, discrete events in which galaxies cease forming stars (truncation events) are required. We constrain the probability of truncation ( P _trunc) and find that a high value is required in a simple evolutionary scenario neglecting galaxy mergers  ( P _trunc≳ 0.3 Gyr⁻¹)  . However, without assuming significant density evolution, P _trunc is not required to be larger in groups than in the field, suggesting that the environmental dependence of star formation was embedded at redshifts   z ≳ 0.45  .     

Australia Telescope Compact Array H i observations of the NGC 6845 galaxy group

We present the results of Australia Telescope Compact Array (ATCA) H  i line and 20-cm radio continuum observations of the galaxy quartet NGC 6845. The H  i emission extends over all four galaxies but can only be associated clearly with the two spiral galaxies, NGC 6845A and B, which show signs of strong tidal interaction. We derive a total H  i mass of at least  1.8 × 10¹⁰ M_⊙  , most of which is associated with NGC 6845A, the largest galaxy of the group. We investigate the tidal interaction between NGC 6845A and B by studying the kinematics of distinct H  i components and their relation to the known H  ii regions. No H  i emission is detected from the two lenticular galaxies, NGC 6845C and D. A previously uncatalogued dwarf galaxy, ATCA  J2001−4659  , was detected 4.4 arcmin NE from NGC 6845B and has an H  i mass of  ∼5 × 10⁸ M_⊙  . No H  i bridge is visible between the group and its newly detected companion. Extended 20-cm radio continuum emission is detected in NGC 6845A and B as well as in the tidal bridge between the two galaxies. We derive star formation rates of  15–40 M_⊙ yr⁻¹  .     

X-ray active galactic nuclei in the core of the Perseus cluster

We present a study of the X-ray emission from the nuclei of galaxies observed in the core of the Perseus cluster in a deep exposure with Chandra . Point sources are found coincident with the nuclei of 13 early-type galaxies, as well as the central galaxy NGC 1275. This corresponds to all galaxies brighter than M _B > −18 in the Chandra field. All of these sources have a steep power-law spectral component and four have an additional thermal component. The unabsorbed power-law luminosities in the 0.5–7.0 keV band range from 8 × 10³⁸ to 5 × 10⁴⁰ erg s⁻¹. We find no simple correlations between the K -band luminosity, or the FUV and NUV AB magnitudes of these galaxies and their X-ray properties. We have estimated the black hole masses of the nuclei using the K -band   M _BH– L _{K bol}  relation and again find no correlation between black hole mass and the X-ray luminosity. Bondi accretion on to the black holes in the galaxies with minihaloes should make them much more luminous than observed.     

Predicting the peculiar velocities of nearby PSCz galaxies using the Least Action Principle

We use the Least Action Principle to predict the peculiar velocities of PSC z galaxies inside cz =2000 km s⁻¹. Linear theory is used to account for tidal effects to cz =15 000 km s⁻¹, and we iterate galaxy positions to account for redshift distortions. As the Least Action Principle is valid beyond linear theory, we can predict reliable peculiar velocities even for very nearby galaxies (i.e., cz ≤500 km s⁻¹). These predicted peculiar velocities are then compared with the observed velocities of 12 galaxies with Cepheid distances. The combination of the PSC z galaxy survey (with its large sky coverage and uniform selection) with the accurate Cepheid distances makes this comparison relatively free from systematic effects. We find that galaxies are good tracers of the mass, even at small (≤10  h ⁻¹ Mpc) scales; under the assumption of no biasing, 0.25≤ β ≤0.75 (at 90 per cent confidence). We use the reliable predicted peculiar velocities to estimate the Hubble constant H ₀ from the local volume without 'stepping up' the distance ladder, finding a confidence range of 65–75 km s⁻¹ Mpc⁻¹ (at 90 per cent confidence).     

A constant dark matter halo surface density in galaxies

We confirm and extend the recent finding that the central surface density  μ_0D≡ r ₀ρ₀  of galaxy dark matter haloes, where r ₀ and  ρ₀  are the halo core radius and central density, is nearly constant and independent of galaxy luminosity. Based on the co-added rotation curves (RCs) of ∼1000 spiral galaxies, the mass models of individual dwarf irregular and spiral galaxies of late and early types with high-quality RCs, and the galaxy–galaxy weak-lensing signals from a sample of spiral and elliptical galaxies, we find that  log μ_0D= 2.15 ± 0.2  in units of  log(M_⊙ pc⁻²)  . We also show that the observed kinematics of Local Group dwarf spheroidal galaxies are consistent with this value. Our results are obtained for galactic systems spanning over 14 mag, belonging to different Hubble types and whose mass profiles have been determined by several independent methods. In the same objects, the approximate constancy of  μ_0D  is in sharp contrast to the systematical variations, by several orders of magnitude, of galaxy properties, including  ρ₀  and central stellar surface density.     

Halo masses for optically selected and for radio-loud AGN from clustering and galaxy–galaxy lensing

We compute two-point correlation functions and measure the shear signal due to galaxy–galaxy lensing for 80 000 optically identified and 5700 radio-loud active galactic nuclei (AGN) from Data Release 4 of the Sloan Digital Sky Survey. Halo occupation models are used to estimate halo masses and satellite fractions for these two types of AGN. The large sample size allows us to separate AGN according to the stellar mass of their host galaxies. We study how the halo masses of optical and radio AGN differ from those of the parent population at fixed   M _*  . Halo masses deduced from clustering and from lensing agree satisfactorily. Radio AGN are found in more massive haloes than optical AGN: in our samples, their mean halo masses are  1.6 × 10¹³  and  8 × 10¹¹  h ⁻¹ M_⊙  , respectively. Optical AGN follow the same relation between stellar mass and halo mass as galaxies selected without regard to nuclear properties, but radio-loud AGN deviate significantly from this relation. The dark matter haloes of radio-loud AGN are about twice as massive as those of control galaxies of the same stellar mass. This boost is independent of radio luminosity, and persists even when our analysis is restricted to field galaxies. The large-scale gaseous environment of the galaxy clearly plays a crucial role in producing observable radio emission. The dark matter halo masses that we derive for the AGN in our two samples are in good agreement with recent models in which feedback from radio AGN becomes dominant in haloes where gas cools quasi-statically.     

Major dry mergers in early-type brightest cluster galaxies

We search for ongoing major dry mergers in a well-selected sample of local brightest cluster galaxies (BCGs) from the C4 cluster catalogue. 18 out of 515 early-type BCGs with redshift between 0.03 and 0.12 are found to be in major dry mergers, which are selected as pairs (or triples) with r -band magnitude difference  δ m _r < 1.5  and projected separation   r _p < 30 kpc  , and showing signatures of interaction in the form of significant asymmetry in residual images. We find that the fraction of BCGs in major dry mergers increases with the richness of the clusters, consistent with the fact that richer clusters usually have more massive (or luminous) BCGs. We estimate that present-day early-type BCGs may have experienced on average  ∼0.6 ( t _merge/0.3 Gyr)⁻¹  major dry mergers and through this process increases their luminosity (mass) by 15 per cent  ( t _merge/0.3 Gyr)⁻¹ ( f _mass/0.5)  on average since   z = 0.7  , where t _merge is the merging time-scale and f _mass is the mean mass fraction of companion galaxies added to the central ones. We also find that major dry mergers do not seem to elevate radio activities in BCGs. Our study shows that major dry mergers involving BCGs in clusters of galaxies are not rare in the local Universe, and they are an important channel for the formation and evolution of BCGs.     

The clustering of hot and cold IRAS galaxies: the redshift-space correlation function

We measure the autocorrelation function, ξ , of galaxies in the IRAS Point Source Catalogue galaxy redshift (PSC z ) survey and investigate its dependence on the far-infrared colour and absolute luminosity of the galaxies. We find that the PSC z survey correlation function can be modelled out to a scale of 10  h ⁻¹ Mpc as a power law of slope 1.30±0.04 and correlation length 4.77±0.20 . At a scale of 75  h ⁻¹ Mpc we find the value of J ₃ to be 1500±400 .
We also find that galaxies with higher 100 μm/60 μm flux ratio, corresponding to cooler dust temperatures, are more strongly clustered than warmer galaxies. Splitting the survey into three colour subsamples, we find that, between 1 and 10  h ⁻¹ Mpc, the ratio of ξ is a factor of 1.5 higher for the cooler galaxies compared with the hotter galaxies. This is consistent with the suggestion that hotter galaxies have higher star formation rates, and correspond to later-type galaxies which are less clustered than earlier types.
Using volume-limited subsamples, we find a weak variation of ξ as a function of absolute luminosity, in the sense that more luminous galaxies are less clustered than fainter galaxies. The trend is consistent with the colour dependence of ξ and the observed colour–luminosity correlation, but the large uncertainties mean that it has a low statistical significance.     

Galaxy bimodality versus stellar mass and environment

We analyse a   z < 0.1  galaxy sample from the Sloan Digital Sky Survey focusing on the variation in the galaxy colour bimodality with stellar mass     and projected neighbour density Σ, and on measurements of the galaxy stellar mass functions. The characteristic mass increases with environmental density from about  10^10.6  to     (Kroupa initial mass function,   H ₀= 70  ) for Σ in the range  0.1–10 Mpc⁻²  . The galaxy population naturally divides into a red and blue sequence with the locus of the sequences in colour–mass and colour–concentration indices not varying strongly with environment. The fraction of galaxies on the red sequence is determined in bins of 0.2 in  log Σ  and     bins). The red fraction   f _r   generally increases continuously in both Σ and     such that there is a unified relation:     . Two simple functions are proposed which provide good fits to the data. These data are compared with analogous quantities in semi-analytical models based on the Millennium N -body simulation: the Bower et al. and Croton et al. models that incorporate active galactic nucleus feedback. Both models predict a strong dependence of the red fraction on stellar mass and environment that is qualitatively similar to the observations. However, a quantitative comparison shows that the Bower et al. model is a significantly better match; this appears to be due to the different treatment of feedback in central galaxies.     

The effects of gas on morphological transformation in mergers: implications for bulge and disc demographics

Transformation of discs into spheroids via mergers is a well-accepted element of galaxy formation models. However, recent simulations have shown that the bulge formation is suppressed in increasingly gas-rich mergers. We investigate the global implications of these results in a cosmological framework, using independent approaches: empirical halo-occupation models (where galaxies are populated in haloes according to observations) and semi-analytic models. In both, ignoring the effects of gas in mergers leads to the overproduction of spheroids: low- and intermediate-mass galaxies are predicted to be bulge-dominated (   B / T ∼ 0.5  at  <10¹⁰ M_⊙  , with almost no 'bulgeless' systems), even if they have avoided major mergers. Including the different physical behaviour of gas in mergers immediately leads to a dramatic change: bulge formation is suppressed in low-mass galaxies, observed to be gas-rich (giving   B / T ∼ 0.1  at  <10¹⁰ M_⊙  , with a number of bulgeless galaxies in good agreement with observations). Simulations and analytic models which neglect the similarity-breaking behaviour of gas have difficulty reproducing the strong observed morphology–mass relation. However, the observed dependence of gas fractions on mass, combined with suppression of bulge formation in gas-rich mergers, naturally leads to the observed trends. Discrepancies between observations and models that ignore the role of gas increase with redshift; in models that treat gas properly, galaxies are predicted to be less bulge-dominated at high redshifts, in agreement with the observations. We discuss implications for the global bulge mass density and future observational tests.