[Show abstract][Hide abstract] ABSTRACT: We present a new framework for estimating a galaxy's gravitational potential,
Phi(x), from its stellar kinematics by adopting a fully non-parametric model
for the galaxy's unknown action-space distribution function, f(J). Having an
expression for the joint likelihood of Phi and f, the likelihood of Phi is
calculated by using a Dirichlet process mixture to represent the prior on f and
marginalising. We demonstrate that modelling machinery constructed using this
framework is successful at recovering the potentials of some simple systems
from perfect discrete kinematical data, a situation handled effortlessly by
traditional moment-based methods, such as the virial theorem, but in which
other, more modern, methods are less than satisfactory. We show how to
generalise the machinery to account for realistic observational errors and
selection functions. A practical implementation is likely to raise some
interesting algorithmic and computational challenges.
Monthly Notices of the Royal Astronomical Society 03/2013; · 5.23 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This work aims to study the distribution of the luminous and dark matter in Coma early-type galaxies. Dynamical masses obtained under the assumption that mass follows light do not match with the masses of strong gravitational lens systems of similar velocity dispersions. Instead, dynamical fits with dark matter haloes are in good agreement with lensing results. We derive mass-to-light ratios of the stellar populations from Lick absorption line indices, reproducing well the observed galaxy colours. Even in dynamical models with dark matter haloes the amount of mass that follows the light increases more rapidly with the galaxy velocity dispersion than expected for a constant stellar initial mass function (IMF). While galaxies around σeff≈ 200 km s−1 are consistent with a Kroupa IMF, the same IMF underpredicts luminous dynamical masses of galaxies with σeff≈ 300 km s−1 by a factor of 2 and more. A systematic variation in the stellar IMF with the galaxy velocity dispersion could explain this trend with a Salpeter IMF for the most massive galaxies. If the IMF is instead constant, then some of the dark matter in high-velocity-dispersion galaxies must follow a spatial distribution very similar to that of the light. A combination of both, a varying IMF and a component of dark matter that follows the light is possible as well. For a subsample of galaxies with old stellar populations, we show that the tilt in the Fundamental Plane can be explained by systematic variations of the total (stellar + dark) mass inside the effective radius. We tested commonly used mass estimator formulae, finding them accurate at the 20–30 per cent level.
Monthly Notices of the Royal Astronomical Society 07/2011; 415(1):545 - 562. · 5.52 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This work aims to study the distribution of luminous and dark matter in Coma
early-type galaxies. Dynamical masses obtained under the assumption that mass
follows light do not match with the masses of strong gravitational lens systems
of similar velocity dispersions. Instead, dynamical fits with dark matter halos
are in good agreement with lensing results. We derive mass-to-light ratios of
the stellar populations from Lick absorption line indices, reproducing well the
observed galaxy colours. Even in dynamical models with dark matter halos the
amount of mass that follows the light increases more rapidly with galaxy
velocity dispersion than expected for a constant stellar initial mass function
(IMF). While galaxies around sigma ~ 200 km/s are consistent with a Kroupa IMF,
the same IMF underpredicts luminous dynamical masses of galaxies with sigma ~
300 km/s by a factor of two and more. A systematic variation of the stellar IMF
with galaxy velocity dispersion could explain this trend with a Salpeter IMF
for the most massive galaxies. If the IMF is instead constant, then some of the
dark matter in high velocity dispersion galaxies must follow a spatial
distribution very similar to that of the light. A combination of both, a
varying IMF and a component of dark matter that follows the light is possible
as well. For a subsample of galaxies with old stellar populations we show that
the tilt in the fundamental plane can be explained by systematic variations of
the total (stellar + dark) mass inside the effective radius. We tested commonly
used mass estimator formulae, finding them accurate at the 20-30% level.
[Show abstract][Hide abstract] ABSTRACT: The photometric and spectroscopic data of the sample galaxies were obtained at the very large telescope (VLT) of the European Southern Observatory (ESO) at Paranal Observatory during three different runs between 2001 and 2003. The observations were carried out in service mode on May 05 - 2001 July 03 (run 1), April 13 - 2002 June 03 (run 2) and 2002 October 30 - 2003 February 04 (run 3). (5 data files). Associated Articles Source Paper Catalog Description Bibtex entry for this abstract Preferred format for this abstract (see Preferences) Find Similar Abstracts: Use: Authors Title Keywords (in text query field) Abstract Text Return: Query Results Return items starting with number Query Form Database: Astronomy Physics arXiv e-prints
[Show abstract][Hide abstract] ABSTRACT: We derive improved versions of the relations between supermassive black hole mass (M BH) and host-galaxy bulge velocity dispersion (σ) and luminosity (L; the M-σ and M-L relations), based on 49 M BH measurements and 19 upper limits. Particular attention is paid to recovery of the intrinsic scatter (0) in both relations. We find log(M BH/M ☉) = α + βlog(σ/200 km s–1) with (α, β, 0) = (8.12 ± 0.08, 4.24 ± 0.41, 0.44 ± 0.06) for all galaxies and (α, β, 0) = (8.23 ± 0.08, 3.96 ± 0.42, 0.31 ± 0.06) for ellipticals. The results for ellipticals are consistent with previous studies, but the intrinsic scatter recovered for spirals is significantly larger. The scatter inferred reinforces the need for its consideration when calculating local black hole mass function based on the M-σ relation, and further implies that there may be substantial selection bias in studies of the evolution of the M-σ relation. We estimate the M-L relationship as log(M BH/M ☉) = α + βlog(LV /1011 L ☉,V ) of (α, β, 0) = (8.95 ± 0.11, 1.11 ± 0.18, 0.38 ± 0.09); using only early-type galaxies. These results appear to be insensitive to a wide range of assumptions about the measurement errors and the distribution of intrinsic scatter. We show that culling the sample according to the resolution of the black hole's sphere of influence biases the relations to larger mean masses, larger slopes, and incorrect intrinsic residuals.
The Astrophysical Journal 05/2009; 698(1):198. · 6.28 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We use oblate axisymmetric dynamical models including dark haloes to determine the orbital structure of intermediate mass to massive early-type galaxies in the Coma galaxy cluster. We find a large variety of orbital compositions. Averaged over all sample galaxies the unordered stellar kinetic energy in the azimuthal and the radial direction are of the same order, but they can differ by up to 40 per cent in individual systems. In contrast, both for rotating and non-rotating galaxies the vertical kinetic energy is on average smaller than in the other two directions. This implies that even most of the rotating ellipticals are flattened by an anisotropy in the stellar velocity dispersions. Using three-integral axisymmetric toy models, we show that flattening by stellar anisotropy maximizes the entropy for a given density distribution. Collisionless disc merger remnants are radially anisotropic. The apparent lack of strong radial anisotropy in observed early-type galaxies implies that they may not have formed from mergers of discs unless the influence of dissipational processes was significant.
Monthly Notices of the Royal Astronomical Society 02/2009; 393(2):641 - 652. · 5.52 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Black hole (BH) masses that have been measured by reverberation mapping in active galaxies fall significantly below the correlation between bulge luminosity and BH mass determined from spatially resolved kinematics of nearby normal galaxies. This discrepancy has created concern that one or both techniques suffer from systematic errors. We show that BH masses from reverberation mapping are consistent with the recently discovered relationship between BH mass and galaxy velocity dispersion. Therefore, the bulge luminosities are the probable source of the disagreement, not problems with either method of mass measurement. This result underscores the utility of the BH mass-velocity dispersion relationship. Reverberation mapping can now be applied with increased confidence to galaxies whose active nuclei are too bright or whose distances are too large for BH searches based on spatially resolved kinematics.
The Astrophysical Journal 12/2008; 543(1):L5. · 6.28 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We analyze the nuclear stellar dynamics of the SB0 galaxy NGC 1023, utilizing observational data both from the Space Telescope Imaging Spectrograph aboard the Hubble Space Telescope and from the ground. The stellar kinematics measured from these long-slit spectra show rapid rotation (V ≈ 70 km s-1 at a distance of 01 = 4.9 pc from the nucleus) and increasing velocity dispersion toward the nucleus (where σ = 295 ± 30 km s-1). We model the observed stellar kinematics assuming an axisymmetric mass distribution with both two and three integrals of motion. Both modeling techniques point to the presence of a central dark compact mass (which presumably is a supermassive black hole) with confidence greater than 99%. The isotropic two-integral models yield a best-fitting black hole mass of (6.0 ± 1.4) × 107 M☉ and mass-to-light ratio (M/LV) of 5.38 ± 0.08, and the goodness of fit (χ2) is insensitive to reasonable values for the galaxy's inclination. The three-integral models, which nonparametrically fit the observed line-of-sight velocity distribution as a function of position in the galaxy, suggest a black hole mass of (3.9 ± 0.4) × 107 M☉ and M/LV of 5.56 ± 0.02 (internal errors), and the edge-on models are vastly superior fits over models at other inclinations. The internal dynamics in NGC 1023 as suggested by our best-fit three-integral model shows that the velocity distribution function at the nucleus is tangentially anisotropic, suggesting the presence of a nuclear stellar disk. The nuclear line-of-sight velocity distribution has enhanced wings at velocities ≥600 km s-1 from systemic, suggesting that perhaps we have detected a group of stars very close to the central dark mass.
The Astrophysical Journal 12/2008; 550(1):75. · 6.28 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We describe a correlation between the mass Mbh of a galaxy's central black hole and the luminosity-weighted line-of-sight velocity dispersion σe within the half-light radius. The result is based on a sample of 26 galaxies, including 13 galaxies with new determinations of black hole masses from Hubble Space Telescope measurements of stellar kinematics. The best-fit correlation is Mbh = 1.2(±0.2) × 108 M☉(σe/200 km s-1)3.75 (±0.3) over almost 3 orders of magnitude in Mbh; the scatter in Mbh at fixed σe is only 0.30 dex, and most of this is due to observational errors. The Mbh-σe relation is of interest not only for its strong predictive power but also because it implies that central black hole mass is constrained by and closely related to properties of the host galaxy's bulge.
The Astrophysical Journal 12/2008; 539(1):L13. · 6.28 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Observations of nearby galaxies reveal a strong correlation between the mass of the central dark object MBH and the velocity dispersion σ of the host galaxy, of the form log(MBH/M☉) = α + β log(σ/σ0); however, published estimates of the slope β span a wide range (3.75-5.3). Merritt & Ferrarese have argued that low slopes (4) arise because of neglect of random measurement errors in the dispersions and an incorrect choice for the dispersion of the Milky Way Galaxy. We show that these explanations and several others account for at most a small part of the slope range. Instead, the range of slopes arises mostly because of systematic differences in the velocity dispersions used by different groups for the same galaxies. The origin of these differences remains unclear, but we suggest that one significant component of the difference results from Ferrarese & Merritt's extrapolation of central velocity dispersions to re/8 (re is the effective radius) using an empirical formula. Another component may arise from dispersion-dependent systematic errors in the measurements. A new determination of the slope using 31 galaxies yields β = 4.02 ± 0.32, α = 8.13 ± 0.06 for σ0 = 200 km s-1. The MBH-σ relation has an intrinsic dispersion in log MBH that is no larger than 0.25-0.3 dex and may be smaller if observational errors have been underestimated. In an appendix, we present a simple kinematic model for the velocity-dispersion profile of the Galactic bulge.
The Astrophysical Journal 12/2008; 574(2):740. · 6.28 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present axisymmetric, orbit superposition models for 12 galaxies using data taken with the Hubble Space Telescope (HST) and ground-based observatories. In each galaxy, we detect a central black hole (BH) and measure its mass to accuracies ranging from 10% to 70%. We demonstrate that in most cases the BH detection requires both the HST and ground-based data. Using the ground-based data alone does provide an unbiased measure of the BH mass (provided that they are fitted with fully general models), but at a greatly reduced significance. The most significant correlation with host galaxy properties is the relation between the BH mass and the velocity dispersion of the host galaxy; we find no other equally strong correlation and no second parameter that improves the quality of the mass-dispersion relation. We are also able to measure the stellar orbital properties from these general models. The most massive galaxies are strongly biased to tangential orbits near the BH, consistent with binary BH models, while lower mass galaxies have a range of anisotropies, consistent with an adiabatic growth of the BH.
The Astrophysical Journal 12/2008; 583(1):92. · 6.28 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present stellar kinematics for a sample of 10 early-type galaxies observed using the Space Telescope Imaging Spectrograph (STIS) aboard the Hubble Space Telescope and the Modular Spectrograph on the MDM Observatory 2.4 m telescope. These observations are a part of an ongoing program to understand the coevolution of supermassive black holes and their host galaxies. Our spectral ranges include either the calcium triplet absorption lines at 8498, 8542, and 8662 Å or the Mg b absorption at 5175 Å. The lines are used to derive line-of-sight velocity distributions (LOSVDs) of the stars using a maximum penalized likelihood method. We use Gauss-Hermite polynomials to parameterize the LOSVDs and find predominantly negative h4 values (boxy distributions) in the central regions of our galaxies. One galaxy, NGC 4697, has significantly positive central h4 (high tail weight). The majority of galaxies have a central velocity dispersion excess in the STIS kinematics over ground-based velocity dispersions. The galaxies with the strongest rotational support, as quantified with vmax/σSTIS, have the smallest dispersion excess at STIS resolution. The best-fitting, general, axisymmetric dynamical models (described in a companion paper) require black holes in all cases, with masses ranging from 106.5 to 109.3 M☉. We replot these updated masses on the MBH-σ relation and show that the fit to only these 10 galaxies has a slope consistent with the fits to larger samples. The greatest outlier is NGC 2778, a dwarf elliptical with relatively poorly constrained black hole mass. The two best candidates for pseudobulges, NGC 3384 and NGC 7457, do not deviate significantly from the established relation between MBH and σ. Neither do the three galaxies that show the most evidence of a recent merger, NGC 3608, NGC 4473, and NGC 4697.
The Astrophysical Journal 12/2008; 596(2):903. · 6.28 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A sample of galaxies characterized by a low surface brightness disk has dynamically studied using, as tracer, the stellar component. The kinematical data, taken along the major and minor axis, extend well within the disk region. The stellar kinematics is more regular and symmetric than the ionized-gas kinematics. Moreover, when comparing the circular velocity derived by means of the dynamical mass model and the one measured from the ionized-gas we find that the later is characterized by a shallower velocity gradient in the central regions.
[Show abstract][Hide abstract] ABSTRACT: Axisymmetric, orbit-based dynamical models are used to derive dark matter
scaling relations for Coma early-type galaxies. From faint to bright galaxies
halo core-radii and asymptotic circular velocities increase. Compared to
spirals of the same brightness, the majority of Coma early-types -- those with
old stellar populations -- have similar halo core-radii but more than 2 times
larger asymptotic halo velocities. The average dark matter density inside 2
reff decreases with increasing luminosity and is 6.8 times larger than in disk
galaxies of the same B-band luminosity. Compared at the same stellar mass, dark
matter densities in ellipticals are 13.5 times higher than in spirals.
Different baryon concentrations in ellipticals and spirals cannot explain the
higher dark matter density in ellipticals. Instead, the assembly redshift (1+z)
of Coma early-type halos is likely about two times larger than of comparably
bright spirals. Assuming that local spirals typically assemble at a redshift of
one, the majority of bright Coma early-type galaxy halos must have formed
around z = 2-3. For about half of our Coma galaxies the assembly redshifts
match with constraints derived from stellar populations. We find dark matter
densities and estimated assembly redshifts of our observed Coma galaxies in
reasonable agreement with recent semi-analytic galaxy formation models.
The Astrophysical Journal 09/2008; 691(1). · 6.28 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present a general scheme for constructing Monte Carlo realizations of equilibrium, collisionless galaxy models with known distribution function (DF) f0. Our method uses importance sampling to find the sampling DF fs that minimizes the mean-square formal errors in a given set of projections of the DF f0. The result is a multimass N-body realization of the galaxy model in which ‘interesting’ regions of phase space are densely populated by lots of low-mass particles, increasing the effective N there, and less interesting regions by fewer, higher mass particles.As a simple application, we consider the case of minimizing the shot noise in estimates of the acceleration field for an N-body model of a spherical Hernquist model. Models constructed using our scheme easily yield a factor of ∼100 reduction in the variance at the central acceleration field when compared to a traditional equal-mass model with the same number of particles. When evolving both models with a real N-body code, the diffusion coefficients in our model are reduced by a similar factor. Therefore, for certain types of problems, our scheme is a practical method for reducing the two-body relaxation effects, thereby bringing the N-body simulations closer to the collisionless ideal.
Monthly Notices of the Royal Astronomical Society 07/2008; 387(4):1719 - 1726. · 5.52 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Photometry and long-slit spectroscopy are presented for a sample of six galaxies with a low surface-brightness stellar disc and a bulge. The characterizing parameters of the bulge and disc components were derived by means of a two-dimensional photometric decomposition of the images of the sample galaxies. Their surface-brightness distribution was assumed to be the sum of the contribution of a Sérsic bulge and an exponential disc, with each component being described by elliptical and concentric isophotes of constant ellipticity and position angle. The stellar and ionized-gas kinematics were measured along the major and minor axes in half of the sample galaxies, whereas the other half was observed only along two diagonal axes. Spectra along two diagonal axes were obtained also for one of the objects with major and minor axis spectra. The kinematic measurements extend in the disc region out to a surface-brightness level μR≈ 24 mag arcsec−2, reaching in all cases the flat part of the rotation curve. The stellar kinematics turns out to be more regular and symmetric than the ionized-gas kinematics, which often shows the presence of non-circular, off-plane and non-ordered motions. This raises the question about the reliability of the use of the ionized gas as the tracer of the circular velocity in the modelling of the mass distribution, in particular in the central regions of low surface-brightness galaxies.
Monthly Notices of the Royal Astronomical Society 06/2008; 387(3):1099 - 1116. · 5.52 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present observations of 77 early-type galaxies imaged with the PC1 CCD of the Hubble Space Telescope (HST) WFPC2. "Nuker-law" parametric fits to the surface brightness profiles are used to classify the central structure into "core" or "power-law" forms. Core galaxies are typically rounder than power-law galaxies. Nearly all power-law galaxies with central ellipticities ≥ 0.3 have stellar disks, implying that disks are present in power-law galaxies with < 0.3 but are not visible because of unfavorable geometry. A few low-luminosity flattened core galaxies also have disks; these may be transition forms from power-law galaxies to more luminous core galaxies, which lack disks. Several core galaxies have strong isophote twists interior to their break radii, although power-law galaxies have interior twists of similar physical significance when the photometric perturbations implied by the twists are evaluated. Central color gradients are typically consistent with the envelope gradients; core galaxies have somewhat weaker color gradients than power-law galaxies. Nuclei are found in 29% of the core galaxies and 60% of the power-law galaxies. Nuclei are typically bluer than the surrounding galaxy. While some nuclei are associated with active galactic nuclei (AGNs), just as many are not; conversely, not all galaxies known to have a low-level AGN exhibit detectable nuclei in the broadband filters. NGC 4073 and 4382 are found to have central minima in their intrinsic starlight distributions; NGC 4382 resembles the double nucleus of M31. In general, the peak brightness location is coincident with the photocenter of the core to a typical physical scale of <1 pc. Five galaxies, however, have centers significantly displaced from their surrounding cores; these may be unresolved asymmetric double nuclei. Finally, as noted by previous authors, central dust is visible in about half of the galaxies. The presence and strength of dust correlates with nuclear emission; thus, dust may outline gas that is falling into the central black hole. The prevalence of dust and its morphology suggest that dust clouds form, settle to the center, and disappear repeatedly on ~108 yr timescales. We discuss the hypothesis that cores are created by the decay of a massive black hole binary formed in a merger. Apart from their brightness profiles, there are no strong differences between core galaxies and power-law galaxies that demand this scenario; however, the rounder shapes of core, their lack of disks, and their reduced color gradients may be consistent with it.
The Astronomical Journal 12/2007; 129(5):2138. · 4.97 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We used Hubble Space Telescope WFPC2 images to identify six early-type galaxies with surface brightness profiles that decrease inward over a limited range of radii near their centers. The inferred luminosity density profiles of these galaxies have local minima interior to their core break radii. NGC 3706 harbors a high surface brightness ring of starlight with radius ≈20 pc. Its central structure may be related to that in the double-nucleus galaxies M31 and NGC 4486B. NGC 4406 and NGC 6876 have nearly flat cores that, on close inspection, are centrally depressed. Colors for both galaxies imply that this is not due to dust absorption. The surface brightness distributions of both galaxies are consistent with stellar tori that are more diffuse than the sharply defined system in NGC 3706. The remaining three galaxies are the brightest cluster galaxies in A260, A347, and A3574. Color information is not available for these objects, but they strongly resemble NGC 4406 and NGC 6876 in their cores. The thin ring in NGC 3706 may have formed dissipatively. The five other galaxies resemble the endpoints of some simulations of the merging of two gas-free stellar systems, each harboring a massive nuclear black hole. In one version of this scenario, diffuse stellar tori are produced when stars initially bound to one black hole are tidally stripped away by the second black hole. Alternatively, some inward-decreasing surface brightness profiles may reflect the ejection of stars from a core during the hardening of the binary black hole created during the merger.
The Astronomical Journal 12/2007; 124(4):1975. · 4.97 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We fit axisymmetric three-integral dynamical models to NGC 3379 using the line-of-sight velocity distribution obtained from Hubble Space Telescope FOS spectra of the galaxy center and ground-based long-slit spectroscopy along four position angles, with the light distribution constrained by WFPC2 and ground-based images. We have fitted models with inclinations from 29° (intrinsic galaxy type E5) to 90° (intrinsic E1) and black hole masses from 0 to 109 M. The best-fit black hole masses range from 6 × 107 to 2 × 108 M, depending on inclination. The preferred inclination is 90° (edge-on); however, the constraints on allowed inclination are not very strong, owing to our assumption of constant M/LV. The velocity ellipsoid of the best model is not consistent with either isotropy or a two-integral distribution function. Along the major axis, the velocity ellipsoid becomes tangential at the innermost bin, radial in the midrange radii, and tangential again at the outermost bins. The rotation rises quickly at small radii owing to the presence of the black hole. For the acceptable models, the radial-to-tangential [(σ + σ)/2] dispersion in the midrange radii ranges over 1.1 < σr/σt < 1.7, with the smaller black holes requiring larger radial anisotropy. Compared with these three-integral models, two-integral isotropic models overestimate the black hole mass since they cannot provide adequate radial motion. However, the models presented in this paper still contain restrictive assumptions—namely, assumptions of constant M/LV and spheroidal symmetry—requiring yet more models to study black hole properties in complete generality.
The Astronomical Journal 12/2007; 119(3):1157. · 4.97 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We construct dynamical models for a sample of 36 nearby galaxies with Hubble Space Telescope (HST) photometry and ground-based kinematics. The models assume that each galaxy is axisymmetric, with a two-integral distribution function, arbitrary inclination angle, a position-independent stellar mass-to-light ratio , and a central massive dark object (MDO) of arbitrary mass M•. They provide acceptable fits to 32 of the galaxies for some value of M• and ; the four galaxies that cannot be fitted have kinematically decoupled cores. The mass-to-light ratios inferred for the 32 well-fitted galaxies are consistent with the fundamental-plane correlation ∝ L0.2, where L is galaxy luminosity. In all but six galaxies the models require at the 95% confidence level an MDO of mass M• ~ 0.006Mbulge ≡ 0.006L. Five of the six galaxies consistent with M• = 0 are also consistent with this correlation. The other (NGC 7332) has a much stronger upper limit on M•. We predict the second-moment profiles that should be observed at HST resolution for the 32 galaxies that our models describe well. We consider various parameterizations for the probability distribution describing the correlation of the masses of these MDOs with other galaxy properties. One of the best models can be summarized thus: a fraction f 0.97 of early-type galaxies have MDOs, whose masses are well described by a Gaussian distribution in log (M•/Mbulge) of mean -2.28 and standard deviation ~0.51. There is also marginal evidence that M• is distributed differently for "core" and "power law" galaxies, with core galaxies having a somewhat steeper dependence on Mbulge.
The Astronomical Journal 12/2007; 115(6):2285. · 4.97 Impact Factor