Power-law Galaxies Research Articles

Orbits in elementary, power-law galaxy bars – 1. Occurrence and role of single loops

Orbits in galaxy bars are generally complex, but simple closed loop orbits play an important role in our conceptual understanding of bars. Such orbits are found in some well-studied potentials, provide a simple model of the bar in themselves, and may generate complex orbit families. The precessing, power ellipse (p-ellipse) orbit approximation provides accurate analytic orbit orbits in symmetric galaxy potentials. It remains useful for finding and fitting simple loop orbits in the frame of a rotating bar with bar-like and symmetric power-law potentials. Second order perturbation theory yields two or fewer simple loop solutions in these potentials. Numerical integrations in the parameter space neighborhood of perturbation solutions reveal zero or one ac- tual loops in a range of such potentials with rising rotation curves. These loops are embedded in a small parameter region of similar, but librating orbits, which have a subharmonic frequency superimposed on the basic loop. These loops and their librat- ing companions support annular bars. Solid bars can be produced in more complex potentials, as shown by an example with power-law indices varying with radius. The power-law potentials can be viewed as the elementary constituents of more complex potentials. Numerical integrations also reveal interesting classes of orbits with multiple loops. In two-dimensional, self-gravitating bars, with power-law potentials, single loop orbits are very rare. This result suggests that gas bars or oval distortions are unlikely to be long-lived, and that complex orbits or three-dimensional structure must support self-gravitating stellar bars.

Massive Elliptical Galaxies: BH Scouring or a Bottom-Heavy IMF?

AbstractWe present indirect constraints on the stellar initial-mass-function (IMF) in nine massive elliptical galaxies with σ ≈ 300 km/s, via a comparison of dynamical and stellar-population based stellar masses. We use adaptive-optics assisted, high resolution kinematical data from the SINFONI Search for Supermassive Black Holes that allow us to constrain the dynamical stellar mass-to-light ratio in the very centre of each galaxy. Hence we measure the IMF in a galaxy region where the stellar mass dominates over dark matter, minimising any potential degeneracy between the two mass components. In six of our galaxies – those which have depleted stellar cores – we find an IMF consistent with the one measured in the Milky-Way via direct star counts. The three remaining, power-law galaxies have instead stellar masses about a factor of two times larger than expected from a Milky-Way type IMF, indicating either a more bottom-heavy IMF (like, e.g., the Salpeter IMF) or a dark-matter distribution that is degenerate with the stellar mass down to the very centres of these galaxies. The bottom-light IMF in our core galaxies is surprising in view of previous studies that suggested a systematic IMF variation where early-type galaxies with σ ≈ 300 km/s have a Salpeter or even more dwarf-dominated IMF. Core galaxies are particularly important since their unique central orbital structure offers an independent crosscheck for the dynamical models. Our models with a bottom-light IMF are consistent with the distribution of orbits predicted by SMBH-binary core-formation models. This indicates that spatially well resolved central kinematical data are important for determining unbiased dynamical stellar mass-to-light ratios. Our results imply either that the IMF in massive galaxies varies over a wider range than previously anticipated, and is not the same in core and power-law ellipticals, or else that there are systematic variations in the distribution of dark matter among massive early-type galaxies.

The XMM deep survey in the CDF-S

Accretion onto SMBH is believed to occur mostly in obscured AGN. Such objects are proving rather elusive in surveys of distant galaxies, including those at X-ray energies. Our main goal is to determine whether the revised IRAC criteria of Donley et al. (2012) (objects with an IR power-law spectral shape), are effective at selecting X-ray type-2 AGN. We present the results from the X-ray spectral analysis of 147 AGN selected by cross-correlating the highest spectral quality ultra-deep XMM-Newton and the Spitzer/IRAC catalogues in the CDF-S. Consequently it is biased towards sources with high S/N X-ray spectra. In order to measure the amount of intrinsic absorption in these sources, we adopt a simple X-ray spectral model that includes a power-law modified by intrinsic absorption and a possible soft X-ray component. We find 21/147 sources to be heavily absorbed but the uncertainties in their obscuring column densities do not allow us to confirm their Compton-Thick nature without resorting to additional criteria. Although IR power-law galaxies are less numerous in our sample than IR non-power-law galaxies (60 versus 87 respectively), we find that the fraction of absorbed (N_{H} > 10^{22} cm^{-2}) AGN is significantly higher (at about 3 sigma level) for IR-power-law sources ($\sim$2/3) than for those sources that do not meet this IR selection criteria ($\sim$1/2). This behaviour is particularly notable at low luminosities, but it appears to be present, although with a marginal significance, at all luminosities. We therefore conclude that the IR power-law method is efficient in finding X-ray-absorbed sources. We would then expect that the long-sought dominant population of absorbed AGN is abundant among IR power-law spectral shape sources not detected in X-rays.

CORES AND THE KINEMATICS OF EARLY-TYPE GALAXIES

I have combined the Emsellem et al. ATLAS3D rotation measures of a large sample of early-type galaxies with HST-based classifications of their central structure to characterize the rotation velocities of galaxies with cores. "Core galaxies" rotate slowly, while "power-law galaxies" (galaxies that lack cores) rotate rapidly, confirming the analysis of Faber et al. Significantly, the amplitude of rotation sharply discriminates between the two types in the -19 > Mv > -22 domain over which the two types coexist. The slow rotation in the small set of core galaxies with Mv > -20, in particular, brings them into concordance with the more massive core galaxies. The ATLAS3D "fast-rotating" and "slow-rotating" early-type galaxies are essentially the same as power-law and core galaxies, respectively, or the Kormendy & Bender two families of elliptical galaxies based on rotation, isophote shape, and central structure. The ATLAS3D fast rotators do include roughly half of the core galaxies, but their rotation-amplitudes are always at the lower boundary of that subset. Essentially all core galaxies have ATLAS3D rotation-amplitudes lambda_(R_e/2) <= 0.25, while all galaxies with lambda_(R_e/2) > 0.25 and figure eccentricity > 0.2 lack cores. Both figure rotation and the central structure of early-type galaxies should be used together to separate systems that appear to have formed from "wet" versus "dry" mergers.

A physical model for z∼ 2 dust-obscured galaxies★

We present a physical model for the origin of z~2 Dust-Obscured Galaxies (DOGs), a class of high-redshift ULIRGs selected at 24 micron which are particularly optically faint (24/R>1000). By combining N-body/SPH simulations of high redshift galaxy evolution with 3D polychromatic dust radiative transfer models, we find that luminous DOGs (with F24 > 0.3 mJy at z~2 are well-modeled as extreme gas-rich mergers in massive (~5x10^12-10^13 Msun) halos, with elevated star formation rates (~500-1000 Msun/yr) and/or significant AGN growth (Mdot > 0.5 Msun/yr), whereas less luminous DOGs are more diverse in nature. At final coalescence, merger-driven DOGs transition from being starburst dominated to AGN dominated, evolving from a "bump" to a power-law shaped mid-IR (IRAC) spectral energy distribution (SED). After the DOG phase, the galaxy settles back to exhibiting a "bump" SED with bluer colors and lower star formation rates. While canonically power-law galaxies are associated with being AGN-dominated, we find that the power-law mid-IR SED can owe both to direct AGN contribution, as well as to a heavily dust obscured stellar bump at times that the galaxy is starburst dominated. Thus power-law galaxies can be either starburst or AGN dominated. Less luminous DOGs can be well-represented either by mergers, or by massive ($M_{\rm baryon} ~5x10^11 Msun) secularly evolving gas-rich disc galaxies (with SFR > 50 Msun/yr). By utilising similar models as those employed in the SMG formation study of Narayanan et al. (2010), we investigate the connection between DOGs and SMGs. We find that the most heavily star-forming merger driven DOGs can be selected as Submillimetre Galaxies (SMGs), while both merger-driven and secularly evolving DOGs typically satisfy the BzK selection criteria.

The host galaxy/AGN connection in nearby early-type galaxies

This is the third in a series of three papers exploring the connection between the multiwavelength properties of AGN in nearby early-type galaxies and the characteristics of their hosts. Starting from an initial sample of 332 galaxies, we selected 116 AGN candidates requiring the detection of a radio source with a flux limit of ~1 mJy, as measured from 5 GHz VLA observations. In Paper I we classified the objects with available archival HST images into “core” and “power-law” galaxies, discriminating on the basis of the nuclear slope of their brightness profiles. We used HST and Chandra data to isolate the nuclear emission of these galaxies in the optical and X-ray bands, thus enabling us (once combined with the radio data) to study the multiwavelength behaviour of their nuclei. The properties of the nuclei hosted by the 29 core galaxies were presented in Paper II Core galaxies invariably host a radio-loud nucleus, with a median radio-loudness of Log and an X-ray based radio-loudness parameter of Log . Here we discuss the properties of the nuclei of the 22 “power-law” galaxies. They show a substantial excess of optical and X-ray emission with respect to core galaxies at the same level of radio luminosity. Conversely, their radio-loudness parameters, Log and Log , are similar to those measured in Seyfert galaxies. Thus the radio-loudness of AGN hosted by early-type galaxies appears to be univocally related to the host's brightness profile: radio-loud AGN are only hosted by core galaxies, while radio-quiet AGN are found only in power-law galaxies. The brightness profile is determined by the galaxy's evolution, through its merger history; our results suggest that the same process sets the AGN flavour. In this scenario, the black holes hosted by the merging galaxies rapidly sink toward the centre of the newly formed object, setting its nuclear configuration, described by e.g. the total mass, spin, mass ratio, or separation of the SMBHs. These parameters are most likely at the origin of the different levels of the AGN radio-loudness. This connection might open a new path toward understanding the origin of the radio-loud/radio-quiet AGN dichotomy and provide us with a further tool for exploring the co-evolution of galaxies and supermassive black holes.

Infrared Power‐Law Galaxies in the Chandra Deep Field–South: Active Galactic Nuclei and Ultraluminous Infrared Galaxies

We investigate the nature of a sample of 92 Spitzer MIPS 24 � m–selected galaxies in the CDF-S, showing powerlaw–like emission in the Spitzer IRAC 3.6–8 � m bands. The main goal is to determine whether the galaxies not detectedinX-rays (47%ofthesample)arepartofthehypotheticalpopulationofobscuredAGNsnotdetectedevenin deep X-ray surveys. The majority of the IR power-law galaxies are ULIRGs at z > 1, and those with LIRG-like IR luminosities are usually detected in X-rays. The optical-to-IR SEDs of the X-ray–detected galaxies are almost equally divided between aBLAGN SED class (similar to anopticallyselected QSO) and an NLAGN SED (similar to the BLAGN SED but with an obscured UV/optical continuum). A small fraction of SEDs resemble warm ULIRGs (e.g., Mrk 231). Most galaxies not detected in X-rays have SEDs in the NLAGN+ULIRG class as they tend to be optically fainter and possibly more obscured. Moreover, the IR power-law galaxies have SEDs significantly different from those of high-z (zsp > 1) IR (24 � m) selected and optically bright (VVDS IAB � 24) star-forming galaxies whoseSEDsshow averyprominent stellar bumpat1.6 � m.ThegalaxiesdetectedinX-rays have2–8keVrest-frame luminosities typical ofAGNs. Thegalaxies notdetectedinX-rayshave global X-ray–to–mid-IR SED properties that make them good candidates to contain IR-bright X-ray–absorbed AGNs. If all these sources are actually obscured AGNs, we would observe a ratio of obscured to unobscured 24 � m–detected AGNs of 2:1, whereas models predict a ratio of up to 3:1. Additional studies using Spitzer to detect X-ray–quiet AGNs are likely to find more such obscured sources. Subject headings: galaxies: active — galaxies: high-redshift — infrared: galaxies — X-rays: galaxies Online material: color figures

The host galaxy/AGN connection in nearby early-type galaxies

This is the first of a series of three papers exploring the connection between the multiwavelength properties of AGNs in nearby early-type galaxies and the characteristics of their hosts. We selected two samples, both with high resolution 5 GHz VLA observations available and providing measurements down to 1 mJy level, reaching radio-luminosities as low as 1019 W Hz-1. We focus on the 116 radio-detected galaxies as to boost the fraction of AGN with respect to a purely optically selected sample. Here we present the analysis of the optical brightness profiles based on archival HST images, available for 65 objects. We separate early-type galaxies on the basis of the slope of their nuclear brightness profiles, into core and power-law galaxies following the Nuker's scheme, rather than on the traditional morphological classification (i.e. into E and S0 galaxies). Our sample of AGN candidates is indistinguishable, when their brightness profiles are concerned, from galaxies of similar optical luminosity but hosting weaker (or no) radio-sources. We confirm previous findings that relatively bright radio-sources ( W Hz-1) are uniquely associated to core galaxies. However, below this threshold in radio-luminosity core and power-law galaxies coexist and they do not show any apparent difference in their radio-properties. Not surprisingly, since our sample is deliberately biased to favour the inclusion of active galaxies, we found a higher fraction of optically nucleated galaxies. Addressing the multiwavelength properties of these nuclei will be the aim of the two forthcoming papers.

The Centers of Early-Type Galaxies withHubble Space Telescope. V. New WFPC2 Photometry

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.

Spherical models for early-type galaxies with cuspy mass densities

Spherical mass density models are used to fit the central surface brightness profiles of early-type galaxies which are generated from Nuker law parameters obtained from the literature. The mass density and the corresponding potential are in an analytical form. It is shown that only a few mass density components are necessary to obtain a good fit and that for all power-law galaxies and for the core galaxies that we consider, most or all of the mass density components must have cusps to provide good fits. The applied quadratic programming fitting allows for a method of deprojection, which is reliable and convenient. The results can be used directly for further dynamical modelling.

A General Formulation of the Source Confusion Statistics and Application to Infrared Galaxy Surveys

Source confusion has been a long-standing problem in the astronomical history. In the previous formulation of the confusion problem, sources are assumed to be distributed homogeneously on the sky. This fundamental assumption is, however, not realistic in many applications. In this work, by making use of the point field theory, we derive general analytic formulae for the confusion problems with arbitrary distribution and correlation functions. As a typical example, we apply these new formulae to the source confusion of infrared galaxies. We first calculate the confusion statistics for power-law galaxy number counts as a test case. When the slope of differential number counts, γ, is steep, the confusion limits become much brighter and the probability distribution function (PDF) of the fluctuation field is strongly distorted. Then we estimate the PDF and confusion limits based on the realistic number count model for infrared galaxies. The gradual flattening of the slope of the source counts makes the clustering effect rather mild. Clustering effects result in an increase of the limiting flux density with ~10%. In this case, the peak probability of the PDF decreases up to ~15% and its tail becomes heavier. Although the effects are relatively small, they will be strong enough to affect the estimation of galaxy evolution from number count or fluctuation statistics. We also comment on future submillimeter observations.

The Halo Occupation Distribution and the Physics of Galaxy Formation

The halo occupation distribution (HOD) describes the bias between galaxies and dark matter by specifying (a) the probability P(N|M) that a halo of virial mass M contains N galaxies of a particular class and (b) the relative distributions of galaxies and dark matter within halos. We calculate predicted HODs for a Lambda-CDM cosmological model using an SPH hydrodynamic simulation and a semi-analytic (SA) galaxy formation model. Although the two methods predict different galaxy mass functions, their HOD predictions agree remarkably well. For mass-selected samples, the mean occupation <N(M)> exhibits a sharp cutoff at low halo masses, a slowly rising plateau for <N>~1-2, and a more steeply rising high occupancy regime. At low <N>, the mean pair and triple counts are well below Poisson expectations, with important consequences for small scale behavior of 2- and 3-point correlation functions. The HOD depends strongly on galaxy age, with high mass halos populated mainly by old galaxies and low mass halos by young galaxies. The SPH simulation supports several simplifying assumptions about HOD bias: the most massive galaxy in a halo usually lies close to the center and moves near the halo's mean velocity; satellite galaxies have the same radial profile and velocity dispersion as the dark matter; and the mean occupation at fixed halo mass is independent of the halo's larger scale environment. By applying the SPH and SA HODs to a large volume N-body simulation, we show that both methods predict slight, observable departures from a power-law galaxy correlation function. The predicted HODs are closely tied to the underlying galaxy formation physics, they offer useful guidance to theoretical models of galaxy clustering, and they will be tested empirically by ongoing analyses of galaxy redshift surveys. (Shortened)

ITAL]Hubble Space Telescope[/ITAL] Imaging of Brightest Cluster Galaxies

We used the Hubble Space Telescope Wide Field Planetary Camera 2 to obtain I-band images of the centers of 81 brightest cluster galaxies (BCGs), drawn from a volume-limited sample of nearby BCGs. The images show a rich variety of morphological features, including multiple or double nuclei, dust, stellar disks, point-source nuclei, and central surface brightness depressions. High-resolution surface brightness profiles could be inferred for 60 galaxies. Of those, 88% have well-resolved cores. The relationship between core size and galaxy luminosity for BCGs is indistinguishable from that of Faber et al. (published in 1997, hereafter F97) for galaxies within the same luminosity range. However, the core sizes of the most luminous BCGs fall below the extrapolation of the F97 relationship rb ~ L. A shallower relationship, rb ~ L, fits both the BCGs and the core galaxies presented in F97. Twelve percent of the BCG sample lacks a well-resolved core; all but one of these BCGs have power law profiles. Some of these galaxies have higher luminosities than any power-law galaxy identified by F97 and have physical upper limits on rb well below the values observed for core galaxies of the same luminosity. These results support the idea that the central structure of early-type galaxies is bimodal in its physical properties but also suggest that there exist high-luminosity galaxies with power-law profiles (or unusually small cores). The BCGs in the latter category tend to fall at the low end of the BCG luminosity function and tend to have low values of the quantity α (the logarithmic slope of the metric luminosity as a function of radius, at 10 kpc). Since theoretical calculations have shown that the luminosities and α-values of BCGs grow with time as a result of accretion, this suggests a scenario in which elliptical galaxies evolve from power-law profiles to core profiles through accretion and merging. This is consistent with theoretical scenarios that invoke the formation of massive black hole binaries during merger events. More generally, the prevalence of large cores in the great majority of BCGs, which are likely to have experienced several generations of galaxy merging, underscores the role of a mechanism that creates and preserves cores in such merging events.

Lensing Properties of Scale‐free Galaxies

The multiple images of lensed quasars provide evidence on the mass distribution of the lensing galaxy. The lensing invariants are constructed from the positions of the images, their parities, and their fluxes. They depend only on the structure of the lensing potential. The simplest is the magnification invariant, which is the sum of the signed magnifications of the images. Higher order configuration invariants are the sums of products of the signed magnifications with positive or negative powers of the position coordinates of the images. We consider the case of the four- and five-image systems produced by elliptical power-law galaxies with ψ ∝ (x2 + y2q-2)β/2. This paper provides simple contour integrals for evaluating all their lensing invariants. For practical evaluation, this offers considerable advantages over the algebraic methods used previously. The magnification invariant is exactly B = 2/(2 - β) for the special cases β = 0, 1, and 4/3; for other values of β, this remains an approximation, but an excellent one at small source offset. Similarly, the sums of the first and second powers of the image positions (or their reciprocals), when weighted with the signed magnifications, are just proportional to the same powers of the source offset, with a constant of proportionality B. To illustrate the power of the contour integral method, we calculate full expansions in the source offset for all lensing invariants in the presence of arbitrary external shear. As an example, we use the elliptical power-law galaxies to fit to the data on the four images of the Einstein Cross (G2237+030). The lensing invariants play a role by reducing the dimensionality of the parameter space in which the χ2 minimization proceeds with consequent gains in accuracy and speed.

WFPC2 Images of the Central Regions of Early-Type Galaxies. I. The Data

We present high-resolution R-band images of the central regions of 67 early-type galaxies obtained with the Wide Field and Planetary Camera 2 (WFPC2) aboard the Hubble Space Telescope (HST). This homogeneously selected sample roughly doubles the number of early-type galaxies that have now been imaged at HST resolution and complements similar data on the central regions of radio galaxies and the bulges of spiral galaxies. Our sample strikingly confirms the complex morphologies of the central regions of early-type galaxies which have become apparent from previous studies with HST. In particular, we detect dust, either in the form of nuclear disks or with a filamentary distribution, in 43% of all galaxies, in good agreement with previous estimates. In addition, we find evidence for embedded stellar disks in a remarkably large fraction of 51%. In 14 of those galaxies the disklike structures are misaligned with the main galaxy, suggesting that they correspond to stellar bars in S0 galaxies. We analyze the luminosity profiles of the galaxies in our sample and classify galaxies according to their central cusp slope. To a large extent we confirm the results from previous HST surveys in that early-type galaxies reveal a clear dichotomy: the bright ellipticals (MB ≲ -20.5) are generally boxy and have luminosity profiles that break from steep outer power laws to shallow inner cusps (referred to as "core" galaxies). The fainter ellipticals, on the other hand, typically have disky isophotes and luminosity profiles that lack a clear break and have a steep central cusp (referred to as "power-law" galaxies). The advantages and shortcomings of classification schemes utilizing the extrapolated central cusp slope γ are discussed, and it is shown that γ might be an inadequate representation for galaxies whose luminosity profile slope changes smoothly with radius rather than resembling a broken power law. Thus, we introduce a new, alternative parameter and show how this affects the classification. In fact, we find evidence for an "intermediate" class of galaxies that cannot unambiguously be classified as either core or power-law galaxies and that have central cusp slopes and absolute magnitudes intermediate between those of core and power-law galaxies. It is unclear at present, however, whether these galaxies make up a physically distinct class or whether distance and/or resolution effects cause them to lose their distinct core or power-law characteristics.

A NICMOS Survey of Early‐Type Galaxy Centers: The Relation Between Core Properties, Gas and Dust Content, and Environment

We present a NICMOS 1.6 micron imaging isophotal study of 27 early-type galaxies. Our selected sample is not as biased against dusty galaxies as the visible WFPC samples observed with HST. Core galaxies have reduced ellipticity and boxiness near and within their core or break radius. This supports a core formation mechanism which mixes or scatters stars such as scattering caused by a binary black hole. We find no correlation between core properties and dust mass or X-ray luminosity, suggesting that processes determining the current gas content (e.g., such as minor mergers and cooling flows) are unrelated to processes occurring during core formation. Core galaxies exist in a variety of environments ranging from poor groups to large clusters. A combined sample suggests that galaxy groups may harbor more luminous power law galaxies than clusters such as Virgo and Fornax.

The Black Hole Mass Distribution in Early-Type Galaxies: Cusps in [ITAL]Hubble Space Telescope[/ITAL] Photometry Interpreted through Adiabatic Black Hole Growth

Hubble Space Telescope (HST) observations show that the surface brightness profiles of early-type galaxies have central cusps. I show that the observed characteristics of these cusps are consistent with the hypothesis that (1) all early-type galaxies have central black holes that grew adiabatically in homogeneous isothermal cores and (2) these progenitor cores followed scaling relations similar to those of the fundamental plane. The models studied here are the ones first proposed by P. Young. They predict I ∝ r-1/2 at asymptotically small radii, but I ∝ r-γ at the radii observable with HST. The slope γ can take on all observed values and increases monotonically with μ = M•/Mcore. Both profiles (which have a break at a resolved radius and a shallow slope inside that radius) and profiles (which have a steep slope down to the resolution limit and no clear break) can be reproduced. Observations show that, with few exceptions, galaxies with MV -20.5 have power-law profiles; both profile types occur in galaxies with -22 -21.2 have power-law profiles. This reproduces both the sense and the absolute magnitude of the observed transition. Intrinsic scatter in BH and galaxy properties can explain why both types of galaxies are observed around the transition magnitude. The observed bimodality in cusp slopes may be due to a bimodality in M•/L, with rapidly rotating disky galaxies having larger M•/L than slowly rotating boxy galaxies. I apply the models to 46 galaxies with published HST photometry. Both core and power-law galaxies are well fitted. The models suggest a roughly linear correlation between BH mass and V-band galaxy luminosity, log M• ≈ -1.83 + log L in solar units (rms scatter 0.33 dex). This agrees with the average relation for nearby galaxies with kinematically determined BH masses. Photometrically and kinematically determined BH masses agree to within ~0.25 dex rms for galaxies that have both. These results provide additional support to the hypothesis that every galaxy (spheroid) has a central BH. The BH mass distribution inferred here is consistent with quasar statistics for a BH accretion efficiency of 4%. The proposed scenario is not a unique way to interpret the observed surface brightness cusps of galaxies, but it explains observational correlations that are otherwise unexplained, and it yields BH masses that agree with those determined kinematically.

The Centers of Early-Type Galaxies with HST. IV. Central Parameter Relations.

We analyze Hubble Space Telescope surface-brightness profiles of 61 elliptical galaxies and spiral bulges (hot galaxies). Luminous hot galaxies have cuspy cores with steep outer power-law profiles that break at r ~ r_b to shallow inner profiles with logslope less than 0.3. Faint hot galaxies show steep, largely featureless power-law profiles at all radii and lack cores. The centers of power-law galaxies are up to 1000 times denser in mass and luminosity than the cores of large galaxies at a limiting radius of 10 pc. At intermediate magnitudes (-22.0 < M_V < -20.5), core and power-law galaxies coexist, and there is a range in r_b at a given luminosity of at least two orders of magnitude. Central properties correlate with global rotation and shape: core galaxies tend to be boxy and slowly rotating, whereas power-law galaxies tend to be disky and rapidly rotating. The dense power-law centers of disky, rotating galaxies are consistent with their formation in gas-rich mergers. The parallel proposition that cores are simply the by-products of gas-free stellar mergers is less compelling. For example, core galaxies accrete small, dense, gas-free galaxies at a rate sufficient to fill in low-density cores if the satellites survived and sank to the center. An alternative model for core formation involves the orbital decay of massive black holes (BHs): the BH may heat and eject stars from the center, eroding a power law if any exists and scouring out a core. An average BH mass per spheroid of 0.002 times the stellar mass yields reasonably good agreement with the masses and radii of observed cores and in addition is consistent with the energetics of AGNs and kinematic detections of BHs in nearby galaxies.

Triaxial Galaxies with Cusps

We have constructed fully self-consistent models of triaxial galaxies with central density cusps. The triaxial generalizations of Dehnen's spherical models are presented, which have densities that vary as 1/r^gamma near the center and 1/r^4 at large radii. We computed libraries of about 7000 orbits in each of two triaxial models with gamma=1 (weak cusp) and gamma=2 (strong cusp); these two models have density profiles similar to those of the core and power-law galaxies observed by HST. Both mass models have short-to-long axis ratios of 1:2 and are maximally triaxial. A large fraction of the orbits in both model potentials are stochastic, as evidenced by their non-zero Liapunov exponents. We show that most of the stochastic orbits in the strong- cusp potential diffuse relatively quickly through their allowed phase-space volumes, on time scales of 100 - 1000 dynamical times. Stochastic orbits in the weak-cusp potential diffuse more slowly, often retaining their box-like shapes for 1000 dynamical times or longer. Attempts to construct self- consistent solutions using just the regular orbits failed for both mass models. Quasi-equilibrium solutions that include the stochastic orbits exist for both models; however, real galaxies constructed in this way would evolve near the center due to the continued mixing of the stochastic orbits. We attempted to construct more nearly stationary models in which stochastic phase space was uniformly populated at low energies. These ``fully mixed'' solutions were found to exist only for the weak-cusp potential. No significant fraction of the mass could be placed on fully-mixed stochastic orbits in the strong-cusp model, demonstrating that strong triaxiality can be inconsistent with a high central density.