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Most galaxies follow well-defined scaling relations of metallicity (O/H), star formation rate (SFR), and stellar mass. However, low-metallicity starbursts, rare in the Local Universe but more common at high redshift, deviate significantly from these scaling relations. On the "main sequence" of star formation, these galaxies have high SFR for a given M*; and on the mass-metallicity relation, they have excess M* for their low metallicity. In this paper, we characterize O/H, M*, and SFR for these deviant "low-metallicity starbursts", selected from a sample of ~1100 galaxies, spanning almost two orders of magnitude in metal abundance, a factor of ~10^6 in SFR, and of ~10^5 in stellar mass. Our sample includes quiescent star-forming galaxies and blue compact dwarfs at redshift 0, luminous compact galaxies at redshift 0.3, and Lyman Break galaxies at redshifts 1-3.4. Applying a Principal Component Analysis (PCA) to the galaxies in our sample with M*

We determine the near-infrared Fundamental Plane (FP) for $\sim10^4$ early-type galaxies in the 6dF Galaxy Survey (6dFGS). We fit the distribution of central velocity dispersion, near-infrared surface brightness and half-light radius with a three-dimensional Gaussian model using a maximum likelihood method. For the 6dFGS $J$ band sample we find a FP with $R_{e}$\,$\propto$\,$\sigma_0^{1.52\pm0.03}I_{e}^{-0.89\pm0.01}$, similar to previous near-IR determinations and consistent with the $H$ and $K$ band Fundamental Planes once allowance is made for differences in mean colour. The overall scatter in $R_e$ about the FP is $\sigma_r$,=,29%, and is the quadrature sum of an 18% scatter due to observational errors and a 23% intrinsic scatter. Because of the distribution of galaxies in FP space, $\sigma_r$ is not the distance error, which we find to be $\sigma_d$,=,23%. Using group richness and local density as measures of environment, and morphologies based on visual classifications, we find that the FP slopes do not vary with environment or morphology. However, for fixed velocity dispersion and surface brightness, field galaxies are on average 5% larger than galaxies in higher-density environments, and the bulges of early-type spirals are on average 10% larger than ellipticals and lenticulars. The residuals about the FP show significant trends with environment, morphology and stellar population. The strongest trend is with age, and we speculate that age is the most important systematic source of offsets from the FP, and may drive the other trends through its correlations with environment, morphology and metallicity.

As a demonstration of the capabilities of the new Oxford SWIFT integral field spectrograph, we present first observations for a set of 14 early-type galaxies in the core of the Coma cluster. Our data consist of I- and z-band spatially resolved spectroscopy obtained with the Oxford SWIFT spectrograph, combined with r-band photometry from the SDSS archive for 14 early- type galaxies. We derive spatially resolved kinematics for all objects from observations of the calcium triplet absorption features at \sim 8500 {AA} . Using this kinematic information we classify galaxies as either Fast Rotators or Slow Rotators. We compare the fraction of fast and slow rotators in our sample, representing the densest environment in the nearby Universe, to results from the ATLAS3D survey, finding the slow rotator fraction is \sim 50 per cent larger in the core of the Coma cluster than in the Virgo cluster or field, a 1.2 {\sigma} increase given our selection criteria. Comparing our sample to the Virgo cluster core only (which is 24 times less dense than the Coma core) we find no evidence of an increase in the slow rotator fraction. Combining measurements of the effective velocity dispersion {\sigma_e} with the photometric data we determine the Fundamental Plane for our sample of galaxies. We find the use of the average velocity dispersion within 1 effective radius, {\sigma_e}, reduces the residuals by 13 per cent with respect to comparable studies using central velocity dispersions, consistent with other recent integral field Fundamental Plane determinations.

We investigate where brightest cluster galaxies (BCGs) sit on the fundamental plane of black hole (BH) activity, an established relation between the X-ray luminosity, the radio luminosity and the mass of a BH. Our sample mostly consists of BCGs that lie at the centres of massive, strong cooling flow clusters, therefore requiring extreme mechanical feedback from their central active galactic nucleus (AGN) to offset cooling of the intracluster plasma (L_mech>10^44-45 erg/s). Based on the BH masses derived from the M_BH-sigma and M_BH-M_K correlations, we find that all of our objects are offset from the plane such that they appear to be less massive than predicted from their X-ray and radio luminosities (to more than a 99 per cent confidence level). For these objects to be consistent with the fundamental plane, the M_BH-sigma and M_BH-M_K correlations therefore seem to underestimate the BH masses of BCGs, on average by a factor of 10. Our results suggest that the standard relationships between BH mass and host galaxy properties no longer hold for these extreme galaxies. Furthermore, our results imply that if these BHs follow the fundamental plane, then many of those that lie in massive, strong cool core clusters must be ultramassive with M_BH>10^10M_sun. This rivals the largest BH masses known and has important ramifications for our understanding of the formation and evolution of BHs.

We study moderate gravitational lensing where a background galaxy is magnified substantially, but not multiply imaged, by an intervening galaxy. We focus on the case where both the lens and source are elliptical galaxies. The signatures of moderate lensing include isophotal distortions and systematic shifts in the fundamental plane and Kormendy relation, which can potentially be used to statistically determine the galaxy mass profiles. These effects are illustrated using Monte Carlo simulations of galaxy pairs where the foreground galaxy is modelled as a singular isothermal sphere model and observational parameters appropriate for the Large Synoptic Survey Telescope (LSST). The range in radius probed by moderate lensing will be larger than that by strong lensing, and is in the interesting regime where the density slope may be changing.

The coefficients a and b of the Fundamental Plane relation R ~ Sigma^a I^b depend on whether one minimizes the scatter in the R direction or orthogonal to the Plane. We provide explicit expressions for a and b (and confidence limits) in terms of the covariances between logR, logSigma and logI. Our analysis is more generally applicable to any other correlations between three variables: e.g., the color-magnitude-Sigma relation, the L-Sigma-Mbh relation, or the relation between the X-ray luminosity, Sunyaev-Zeldovich decrement and optical richness of a cluster, so we provide IDL code which implements these ideas, and we show how our analysis generalizes further to correlations between more than three variables. We show how to account for correlated errors and selection effects, and quantify the difference between the direct, inverse and orthogonal fit coefficients. We show that the three vectors associated with the Fundamental Plane can all be written as simple combinations of a and b because the distribution of I is much broader than that of Sigma, and Sigma and I are only weakly correlated. Why this should be so for galaxies is a fundamental open question about the physics of early-type galaxy formation. If luminosity evolution is differential, and Rs and Sigmas do not evolve, then this is just an accident: Sigma and I must have been correlated in the past. On the other hand, if the (lack of) correlation is similar to that at the present time, then differential luminosity evolution must have been accompanied by structural evolution. A model in which the luminosities of low-L galaxies evolve more rapidly than do those of higher-L galaxies is able to produce the observed decrease in a (by a factor of 2 at z~1) while having b decrease by only about 20 percent. In such a model, the Mdyn/L ratio is a steeper function of Mdyn at higher z.

Residual-gas expulsion after cluster formation has recently been shown to leave an imprint in the low-mass present-day stellar mass function (PDMF) which allowed the estimation of birth conditions of some Galactic globular clusters (GCs) such as mass, radius and star formation efficiency. We show that in order to explain their characteristics (masses, radii, metallicity, PDMF) their stellar initial mass function (IMF) must have been top-heavy. It is found that the IMF is required to become more top-heavy the lower the cluster metallicity and the larger the pre-GC cloud-core density are. The deduced trends are in qualitative agreement with theoretical expectation. The results are consistent with estimates of the shape of the high-mass end of the IMF in the Arches cluster, Westerlund 1, R136 and NGC 3603, as well as with the IMF independently constrained for ultra-compact dwarf galaxies (UCDs). The latter suggests that GCs and UCDs might have formed along the same channel or that UCDs formed via mergers of GCs. A fundamental plane is found which describes the variation of the IMF with density and metallicity of the pre-GC cloud-cores simultaneously. The implications for the evolution of galaxies and chemical enrichment over cosmological times are expected to be major.

We determine an absolute calibration of stellar mass-to-light ratios for the densest ≃3 per cent of early-type galaxies in the local Universe (redshift z≃ 0.08) from Sloan Digital Sky Survey (SDSS) Data Release 7. This sample of ∼4000 galaxies has, assuming a Chabrier initial mass function (IMF), effective stellar surface densities Σe > 2500 M⊙ pc−2, stellar population synthesis (SPS) stellar masses log10(MSPS/M⊙) < 10.8 and aperture velocity dispersions of (68 per cent range). In contrast to typical early-type galaxies, we show that these dense early-type galaxies follow the virial Fundamental Plane, which suggests that mass follows light. With the additional assumption that any dark matter does not follow the light, the dynamical masses of dense galaxies provide a direct measurement of stellar masses. Our dynamical masses (Mdyn), obtained from the spherical Jeans equations, are only weakly sensitive to the choice of anisotropy (β) due to the relatively large aperture of the SDSS fibre for these galaxies: Rap≃ 1.5Re. Assuming isotropic orbits (β= 0), we find a median log10(Mdyn/MSPS) = 0.233 ± 0.003, consistent with a Salpeter IMF, while more bottom-heavy IMFs and standard Milky Way IMFs are strongly disfavoured. Our results are consistent with, but do not require, a dependence of the IMF on dynamical mass or velocity dispersion. We find evidence for a colour dependence to the IMF such that redder galaxies have heavier IMFs with Mdyn/MSPS∝ (g−r)1.13 ± 0.09. This may reflect a more fundamental dependence of the IMF on the age or metallicity of a stellar population, or the density at which the stars formed.

We present a study of the fundamental plane, FP, for a sample of 71 dwarf galaxies in the core of Coma cluster in magnitude range $-21 < M_I

We present results from an analysis of stellar population parameters for 7132 galaxies in the 6dFGS Fundamental Plane (FP) sample. We bin the galaxies along the axes, $v_1$, $v_2$, and $v_3$, of the tri-variate Gaussian to which we have fit the galaxy distribution in effective radius, surface brightness, and central velocity dispersion (FP space), and compute median values of stellar age, [Fe/H], [Z/H], and [$\alpha$/Fe]. We determine the directions of the vectors in FP space along which each of the binned stellar population parameters vary most strongly. In contrast to previous work, we find stellar population trends not just with velocity dispersion and FP residual, but with radius and surface brightness as well. The most remarkable finding is that the stellar population parameters vary through the plane ($v_1$ direction) and across the plane ($v_3$ direction), but show no variation at all along the plane ($v_2$ direction). The $v_2$ direction in FP space roughly corresponds to `luminosity density'. We interpret a galaxy's position along this vector as being closely tied to its merger history, such that early-type galaxies with lower luminosity density are more likely to have undergone major mergers. This conclusion is reinforced by an examination of the simulations of Kobayashi (2005), which show clear trends of merger history with $v_2$.

We report the results of study of the A1569 cluster (12h36m.3, +16°35′) and the neighboring A1589 cluster (12h41m.3, +18°34′), making up a pair (a supercluster) with a projected size of about 10Mpc. This study is done within the framework of our program for investigating the galaxy clusters with bimodal velocity distributions (i.e., clusters where the velocities of subsystems differ by more than Δcz ∼ 3000 km/s). In the A1569 cluster we have identified two subsystems: A1569A (cz = 20613 km/s) and A1569B (cz = 23783 km/s). These subsystems have the line-of-sight velocity dispersions of 484 km/s and 493 km/s, and dynamic masses within the R200 radius equal to 1.8 × 1014 and 2.0 × 1014M⊙, respectively. We directly estimate the distances to these subsystems using three methods applied to earlytype galaxies: the Kormendy relation, photometric plane, and fundamental plane. To this end, we use the results of our observations made with the 1-m telescope of the SAO RAS and the data adopted from the SDSS DR7 catalog. We found that A1569 consists of two independent clusters. The A1569B cluster is located at the Hubble distance corresponding to its radial velocity. The A1569A cluster has a peculiar velocity of −1290 ± 630 km/s, which can be explained by the effect of the more massive A1589 cluster (with a mass of 7.9 × 1014M⊙) and of the supercluster where it resides. In all the four bimodal clusters that we studied within the framework of our program, A1035, A1775, A1831, and A1569, the subsystems are independent clusters lying close to the Hubble relation between redshift and distance.

We use a large sample of upper limits and accurate estimates of supermassive black holes masses coupled with libraries of host galaxy velocity dispersions, rotational velocities and photometric parameters extracted from Sloan Digital Sky Survey i-band images to establish correlations between the SMBH and host galaxy parameters. We test whether the mass of the black hole, MBH, is fundamentally driven by either local or global galaxy properties. We explore correlations between MBH and stellar velocity dispersion sigma, bulge luminosity, bulge mass Sersic index, bulge mean effective surface brightness, luminosity of the galaxy, galaxy stellar mass, maximum circular velocity Vc, galaxy dynamical and effective masses. We verify the tightness of the MBH-sigma relation and find that correlations with other galaxy parameters do not yield tighter trends. We do not find differences in the MBH-sigma relation of barred and unbarred galaxies. The MBH-sigma relation of pseudo-bulges is also coarser and has a different slope than that involving classical bulges. The MBH-bulge mass is not as tight as the MBH-sigma relation, despite the bulge mass proving to be a better proxy of MBH than bulge luminosity. We find a rather poor correlation between MBH and Sersic index suggesting that MBH is not related to the bulge light concentration. The correlations between MBH and galaxy luminosity or mass are not a marked improvement over the MBH sigma relation. If Vc is a proxy for the dark matter halo mass, the large scatter of the MBH-Vc relation then suggests that MBH is more coupled to the baryonic rather than the dark matter. We have tested the need for a third parameter in the MBH scaling relations, through various linear correlations with bulge and galaxy parameters, only to confirm that the fundamental plane of the SMBH is mainly driven by sigma, with a small tilt due to the effective radius. (Abridged)

The fundamental plane of black hole activity is a relation between X-ray luminosity, radio luminosity, and black hole mass for hard state Galactic black holes and their supermassive analogs. The fundamental plane suggests that, at low-accretion rates, the physical processes regulating the conversion of an accretion flow into radiative energy could be universal across the entire black hole mass scale. However, there is still a need to further refine the fundamental plane in order to better discern the radiative processes and their geometry very close to the black hole, in particular the source of hard X-rays. Further refinement is necessary because error bars on the best-fit slopes of the fundamental plane are generally large, and also the inferred coefficients can be sensitive to the adopted sample of black holes. In this work, we regress the fundamental plane with a Bayesian technique. Our approach shows that sub-Eddington black holes emit X-ray emission that is predominantly optically thin synchrotron radiation from the jet, provided that their radio spectra are flat or inverted. X-ray emission dominated by very radiatively inefficient accretion flows are excluded at the >3\sigma\ level. We also show that it is difficult to place FR I galaxies onto the fundamental plane because their X-ray jet emission is highly affected by synchrotron cooling. On the other hand, BL Lac objects fit onto the fundamental plane. Including a uniform subset of high-energy peaked BL Lac objects from the SDSS, we find sub-Eddington black holes with flat/inverted radio spectra follow log L_x=(1.45\pm0.04)log L_R-(0.88\pm0.06)\logM_{BH}-6.07\pm1.10, with \sigma_{int}=0.07\pm0.05 dex. Finally, we discuss how the effects of synchrotron cooling of jet emission from the highest black hole masses can bias fundamental plane regressions, perhaps leading to incorrect inferences on X-ray radiation mechanisms.

[Abridged] We present ground-based MDM V-band and Spitzer/IRAC 3.6um-band photometric observations of the 72 representative galaxies of the SAURON Survey. In combination with the SAURON stellar velocity dispersion measured within an effective radius (se), this allows us to explore the location of our galaxies in the main scaling relations. We investigate the dependence of these relations on our recent kinematical classification of early-type galaxies (i.e. Slow/Fast Rotators) and the stellar populations. Slow Rotator and Fast Rotator E/S0 galaxies do not populate distinct locations in the scaling relations, although Slow Rotators display a smaller intrinsic scatter. Surprisingly, extremely young objects do not display the bluest (V-[3.6]) colours in our sample, as is usually the case in optical colours. This can be understood in the context of the large contribution of TP-AGB stars to the infrared, even for young populations, resulting in a very tight (V-[3.6]) - se relation that in turn allows us to define a strong correlation between metallicity and velocity dispersion. Many Sa galaxies appear to follow the Fundamental Plane defined by E/S0 galaxies. Galaxies that appear offset from the relations correspond mostly to objects with extremely young populations, with signs of on-going, extended star formation. We correct for this effect in the Fundamental Plane, by replacing luminosity with stellar mass using an estimate of the stellar mass-to-light ratio, so that all galaxies are part of a tight, single relation. The new estimated coefficients are consistent in both photometric bands and suggest that differences in stellar populations account for about half of the observed tilt with respect to the virial prediction. After these corrections, the Slow Rotator family shows almost no intrinsic scatter around the best-fit Fundamental Plane.

The R1/n law for the radial surface brightness of elliptical galaxies and the "Best Accretion Model" together with the "Concentration Model" have been combined in order to determine the mass and dynamical structure of largely-populated star systems. Families of models depending on four parameters have been used to fit the observed surface radial profiles of some spectro-photometric indices of a sample of eleven galaxies. We present the best agreements of the spectral index Mg2 with observations for three selected galaxies representative of the full sample. For them we have also computed the spatial distributions of the metal abundances, which are essential to achieve a population synthesis.

Early-type galaxies are characterized by many scaling relations. One of them, the so-called fundamental plane is a relatively tight correlation between three variables, and has resisted a clear physical understanding despite many years of intensive research. Here, we show that the correlation between the three variables of the fundamental plane can be the artifact of the effect of another parameter influencing all, so that the fundamental plane may be understood as a confounding correlation. Indeed, the complexity of the physics of galaxies and of their evolution suggests that the main confounding parameter must be related to the level of diversification reached by the galaxies. Consequently, many scaling relations for galaxies are probably evolutionary correlations.

There are strong correlations between the three structural properties of elliptical galaxies -- stellar mass, velocity dispersion and size -- in the form of a tight "fundamental plane" and a "scaling relation" between each pair. Major mergers of disk galaxies are assumed to be a mechanism for producing ellipticals, but semi-analytic galaxy formation models (SAM) have encountered apparent difficulties in reproducing the observed slope and scatter of the size-mass relation. We study the scaling relations of merger remnants using progenitor properties from two SAMs. We apply a simple merger model that includes gas dissipation and star formation based on theoretical considerations and simulations. Combining the SAMs and the merger model allows calculation of the structural properties of the remnants of major mergers that enter the population of elliptical galaxies at a given redshift. Without tuning the merger model parameters for each SAM, the results roughly match the slope and scatter in the observed scaling relations and their evolution in the redshift range $z=0-3$. Within this model, the observed scaling relations, including the tilt of the fundamental plane relative to the virial plane, result primarily from the decrease of gas fraction with increasing progenitor mass. The scatter in the size-mass relation of the remnants is reduced from that of the progenitors because of a correlation between progenitor size and gas fraction at a given mass.

We present the results of the analysis of a sample of 17 low-luminosity (LX . 10 42 erg/s), radio loud AGNs in massive galaxies. The sample is extracted from the SDSS database and it spans uniformly a wide range in optical [OIII] emission line and radio luminosity, but within a narrow redshift range (0.05 < z < 0.11) and a narrow super massive black hole mass range (� 10 8 M⊙). For these sources we measured core X-ray emission with the Chandra X-ray telescope and radio emission with the VLA. Our main goal is to establish which emission component, if any, can be regarded as the most reliable accretion/jet-power estimator at these regimes. In order to do so, we studied the correlation between emission line properties, radio luminosity, radio spectral slopes and X-ray luminosity, as well as more complex multi-variate relations involving black hole mass, such as the fundamental plane of black hole activity. We find that 15 out of 17 sources of our sample can be classified as Low-Excitation Galaxies (LEG) and their observed properties suggest X-ray and radio emission to originate from the jet basis. We also find that X-ray emission does not appear to be affected by nuclear obscuration and can be used as a reliable jet-power estimator. More generally, X-ray, radio and optical emission appear to be related, although no tight correlation is found. In accordance with a number of recent studies of this class of objects these findings may be explained by a lack of cold (molecular) gaseous structures in the innermost region of these massive galaxies.

Estimating black hole masses of blazars is still a big challenge. Because of the contamination of jets, using the previously suggested size -- continuum luminosity relation can overestimate the broad line region (BLR) size and black hole mass for radio-loud AGNs, including blazars. We propose a new relation between the BLR size and $H_{\beta}$ emission line luminosity and present evidences for using it to get more accurate black hole masses of radio-loud AGNs. For extremely radio-loud AGNs such as blazars with weak/absent emission lines, we suggest to use the fundamental plane relation of their elliptical host galaxies to estimate the central velocity dispersions and black hole masses, if their velocity dispersions are not known but the host galaxies can be mapped. The black hole masses of some well-known blazars, such as OJ 287, AO 0235+164 and 3C 66B, are obtained using these two methods and the M - $\sigma$ relation. The implications of their black hole masses on other related studies are also discussed., Comment: 7 pages, invited talk presented in the workshop on Multiwavelength Variability of Blazars (Guangzhou, China, Sept. 22-24, 2010). To be published in the Journal of Astrophysics and Astronomy

Dynamically hot stellar systems, whether star clusters or early-type galaxies, follow well-defined scaling relations over many orders of magnitudes in mass. These fundamental plane relations have been subject of several studies, which have been mostly confined to certain types of galaxies and/or star clusters so far. Here, we present a complete picture of hot stellar systems ranging from faint galaxies and star clusters of only a few hundred solar masses up to giant ellipticals (gEs) with 10 12 M � , in particular including – for the first time – large samples of compact ellipticals (cEs), ultra-compact dwarf galaxies (UCDs), dwarf ellipticals (dEs) of nearby galaxy clusters and Local Group ultra-faint dwarf spheroidals (dSphs). For all those stellar systems we show the effective radius–luminosity, effective radius–stellar mass, and effective mass surface density–stellar mass plane. Two clear families of hot stellar systems can be differentiated: the ’galaxian’ family, ranging from gEs over Es and dEs to dSphs, and the ’star cluster’ family, comprising globular clusters (GCs), UCDs and nuclear star clusters (NCs). Interestingly, massive ellipticals have a similar size–mass relation as cEs, UCDs and NCs, with a clear common boundary towards minimum sizes, which can be approximated by Reff > 2:24 �10 6 �M 4=5

We study the radial motion of an object in the gravitational field produced by an isotropic mass density that is singular at the origin. This problem applies to elliptical galaxies and can be used to illustrate motion in a central field appropriate for an intermediate-level mechanics course.

We explore the growth of ≤10 7 Mblack holes that reside at the centres of spiral and field dwarf galaxies in a Local Group type of environment. We use merger trees from a cosmological N-body simulation known as Via Lactea 2 (VL-2) as a framework to test two merger-driven semi-analytic recipes for black hole growth that include dynamical friction, tidal stripping and gravitational wave recoil in over 20 000 merger tree realizations. First, we apply a Fundamental Plane limited (FPL) model to the growth of Sgr A*, which drives the central black hole to a maximum mass limited by the black hole Fundamental Plane after every merger. Next, we present a new model that allows for low-level prolonged gas accretion (PGA) during the merger. We find that both models can generate an Sgr A* mass black hole. We predict a population of massive black holes in local field dwarf galaxies - if the VL-2 simulation is representative of the growth of the Local Group, we predict up to 35 massive black holes (≤10 6 M� ) in Local Group field dwarfs. We also predict that hundreds of ≤10 5 Mblack holes fail to merge, and instead populate the Milky Way halo, with the most massive of them at roughly the virial radius. In addition, we find that there may be hundreds of massive black holes ejected from their hosts into the nearby intergalactic medium due to gravitational wave recoil. We discuss how the black hole population in the Local Group field dwarfs may help to constrain the growth mechanism for Sgr A*.

Modified Newtonian Dynamics (MOND) has been shown to be able to fit spiral galaxy rotation curves as well as giving a theoretical foundation for empirically determined scaling relations, such as the Tully - Fisher law, without the need for a dark matter halo. As a complementary analysis, one should investigate whether MOND can also reproduce the dynamics of early - type galaxies (ETGs) without dark matter. As a first step, we here show that MOND can indeed fit the observed central velocity dispersion $\sigma_0$ of a large sample of ETGs assuming a simple MOND interpolating functions and constant anisotropy. We also show that, under some assumptions on the luminosity dependence of the Sersic n parameter and the stellar M/L ratio, MOND predicts a fundamental plane for ETGs : a log - linear relation among the effective radius $R_{eff}$, $\sigma_0$ and the mean effective intensity $\langle I_e \rangle$. However, we predict a tilt between the observed and the MOND fundamental planes.

We present an analysis of the fundamental plane of black hole accretion, an empirical correlation of the mass of a black hole ($M$), its 5 GHz radio continuum luminosity ($\nu L_{\nu}$), and its 2-10 keV X-ray power-law continuum luminosity ($L_X$). We compile a sample of black holes with primary, direct black hole-mass measurements that also have sensitive, high-spatial-resolution radio and X-ray data. Taking into account a number of systematic sources of uncertainty and their correlations with the measurements, we use Markov chain Monte Carlo methods to fit a mass-predictor function of the form $\log(M/10^{8}\,M_{\scriptscriptstyle \odot}) = \mu_0 + \xi_{\mu R} \log(L_R / 10^{38}\,\mathrm{erg\,s^{-1}}) + \xi_{\mu X} \log(L_X / 10^{40}\,\mathrm{erg\,s^{-1}})$. Our best-fit results are $\mu_0 = 0.55 \pm 0.22$, $\xi_{\mu R} = 1.09 \pm 0.10$, and $\xi_{\mu X} = -0.59^{+0.16}_{-0.15}$ with the natural logarithm of the Gaussian intrinsic scatter in the log-mass direction $\ln\epsilon_\mu = -0.04^{+0.14}_{-0.13}$. This result is a significant improvement over our earlier mass scaling result because of the increase in active galactic nuclei sample size (from 18 to 30), improvement in our X-ray binary sample selection, better identification of Seyferts, and improvements in our analysis that takes into account systematic uncertainties and correlated uncertainties. Because of these significant improvements, we are able to consider potential influences on our sample by including all sources with compact radio and X-ray emission but ultimately conclude that the fundamental plane can empirically describe all such sources. We end with advice for how to use this as a tool for estimating black hole masses., Comment: ApJ Accepted. Online interactive version of Figure 7 available at http://kayhan.astro.lsa.umich.edu/supplementary_material/fp/

We explore X-ray spectral evolution and radio–X-ray correlation simultaneously for four X-ray binaries (XRBs). We find that hard X-ray photon indices, Γ, are anti- and positively correlated to X-ray fluxes when the X-ray flux, F3–9keV, is below and above a critical flux, FX,crit, which may be regulated by ADAF and disk-corona respectively. We find that the data points with anti-correlation of Γ-F3–9keV follow the universal radio–X-ray correlation of FR ∝ FXb (b ~ 0.5-0.7), while the data points with positive X-ray spectral evolution follow a steeper radio–X-ray correlation (b ~ 1.4, the so-called ‘outliers track’). The bright active galactic nuclei (AGNs) share similar X-ray spectral evolution and radio–X-ray correlation as XRBs in ‘outliers’ track, and we present a new fundamental plane of log LR=1.59+0.28−0.22 log LX−0.22+0.19−0.20 log MBH−28.97+0.45−0.45 for these radiatively efficient BH sources.

The global properties of elliptical galaxies are connected through the so-called fundamental plane of ellipticals, which is an empirical relation between their parameters: effective radius, central velocity dispersion and mean surface brightness within the effective radius. We investigated the relation between the parameters of the fundamental plane equation and the parameters of modified gravity potential $f(R)$. With that aim, we compared theoretical predictions for circular velocity in $f(R)$ gravity with the corresponding values from a large sample of observed elliptical galaxies. Besides, we consistently reproduced the values of coefficients of the fundamental plane equation as deduced from observations, showing that the photometric quantities like mean surface brightness are related to gravitational parameters. We show that this type of modified gravity, especially its power-law version - $R^n$, is able to reproduce the stellar dynamics in elliptical galaxies. Also, it is shown that $R^n$ gravity fits the observations very well, without need for a dark matter., Comment: 9 pages, 2 figures. Accepted for publication in Atoms

We present the results of a ~ 3 year campaign to monitor the low luminosity active galactic nucleus (LLAGN) NGC 7213 in the radio (4.8 and 8.4 GHz) and X-ray bands (2-10 keV). With a reported X-ray Eddington ratio of 7 x 10^-4 L_Edd, NGC 7213 can be considered to be comparable to a hard state black hole X-ray binary. We show that a weak correlation exists between the X-ray and radio light curves. We use the cross-correlation function to calculate a global time lag between events in the X-ray and radio bands to be 24 +/- 12 days lag (8.4 GHz radio lagging X-ray), and 40 +/- 13 days lag (4.8 GHz radio lagging X-ray). The radio-radio light curves are extremely well correlated with a lag of 20.5 +/- 12.9 days (4.8 GHz lagging 8.4 GHz). We explore the previously established scaling relationship between core radio and X-ray luminosities and black hole mass L_{R} \propto M^{0.6-0.8} L_{X}^{0.6}, known as the `fundamental plane of black hole activity', and show that NGC 7213 lies very close to the best-fit `global' correlation for the plane as one of the most luminous LLAGN. With a large number of quasi-simultaneous radio and X-ray observations, we explore for the first time the variations of a single AGN with respect to the fundamental plane. Although the average radio and X-ray luminosities for NGC 7213 are in good agreement with the plane, we show that there is intrinsic scatter with respect to the plane for the individual data points.

We use stellar masses, photometry, lensing, and velocity dispersions to investigate empirical correlations for the final sample of 73 early-type lens galaxies (ETGs) from the SLACS survey. The traditional correlations (Fundamental Plane [FP] and its projections) are consistent with those found for non-lens galaxies, supporting the thesis that SLACS lens galaxies are representative of massive ETGs. The addition of strong lensing estimates of the total mass allows us to gain further insights into their internal structure: i) the mean slope of the total mass density profile is = 2.078+/-0.027 with an intrinsic scatter of 0.16+/-0.02; ii) gamma' correlates with effective radius and central mass density, in the sense that denser galaxies have steeper profiles; iii) the dark matter fraction within reff/2 is a monotonically increasing function of galaxy mass and size; iv) the dimensional mass M_dim is proportional to the total mass, and both increase more rapidly than stellar mass M*; v) the Mass Plane (MP), obtained by replacing surface brightness with surface mass density in the FP, is found to be tighter and closer to the virial relation than the FP and the M*P, indicating that the scatter of those relations is dominated by stellar population effects; vi) we construct the Fundamental Hyper-Plane by adding stellar masses to the MP and find the M* coefficient to be consistent with zero and no residual intrinsic scatter. Our results demonstrate that the dynamical structure of ETGs is not scale invariant and that it is fully specified by the total mass, r_eff, and sigma. Although the basic trends can be explained qualitatively in terms of varying star formation efficiency as a function of halo mass and as the result of dry and wet mergers, reproducing quantitatively the observed correlations and their tightness may be a significant challenge for galaxy formation models., Comment: 16 pages, 9 figures; submitted to ApJ after responding to the referee comments

In the pursuit of a general formulation for a modified gravitational theory at the non-relativistic level and as an alternative to the dark matter hypothesis, we construct a model valid over a wide variety of astrophysical scales. Through the inclusion of Milgrom's acceleration constant into a gravitational theory, we show that very general formulas can be constructed for the acceleration felt by a particle. Dimensional analysis shows that this inclusion naturally leads to the appearance of a mass-length scale in gravity, breaking its scale invariance. A particular form of the modified gravitational force is constructed and tested for consistency with observations over a wide range of astrophysical environments, from solar system to extragalactic scales. We show that over any limited range of physical parameters, which define a specific class of astrophysical objects, the dispersion velocity of a system must be a power law of its mass and size. These powers appear linked together through a natural constraint relation of the theory. This yields a generalised gravitational equilibrium relation valid for all astrophysical systems. A general scheme for treating spherical symmetrical density distributions is presented, which in particular shows that the fundamental plane of elliptical galaxies, the Newtonian virial equilibrium, the Tully-Fisher and the Faber-Jackson relations, as well as the scalings observed in local dwarf spheroidal galaxies, are nothing but particular cases of that relation when applied to the appropriate mass-length scales. We discuss the implications of this approach for a modified theory of gravity and emphasise the advantages of working with the force, instead of altering Newton's second law of motion, in the formulation of a gravitational theory.

We present deep spectroscopic data for a 24-object subsample of our full 41-object z~0.5 radio galaxy sample in order to investigate the evolution of the Fundamental Plane of radio galaxies. We find that the low-luminosity, FRI-type, radio galaxies in our sample are consistent with the local Fundamental Plane of radio galaxies defined by Bettoni et al. when corrected for simple passive evolution of their stellar populations. However, we find that the higher luminosity, FRII-type radio galaxies are inconsistent with the local Fundamental Plane if only passive evolution is considered, and find evidence for a rotation in the Fundamental Plane at z~0.5 when compared with the local relation. We show that neither passive evolution, nor a mass-dependent evolution in the mass-to-light ratio, nor an evolution in the size of the host galaxies can, by themselves, plausibly explain the observed tilt. However, we suggest that some combination of all three effects, with size evolution as the dominant factor, may be sufficient to explain the difference between the planes. We also find evidence for a correlation between host galaxy velocity dispersion and radio luminosity at the 97% significance level within our sub-sample, although further observations are required in order to determine whether this is different for the FRI and FRII radio sources. Assuming that the M_BH - sigma relation still holds at z~0.5, this implies that radio luminosity scales with black hole mass, in agreement with previous studies.

We analyze the equivalent widths of HI Ly-$\alpha$ ($W_{Ly\alpha}$) absorption from the inner (R < 160 kpc) circumgalactic medium (CGM) of 85 galaxies at $z \sim 0$ with stellar masses $M*$ ranging $\rm{8 \leq log M* / M_{\odot} \leq 11.6}$. Across three orders of magnitude in stellar mass, the CGM of present-day galaxies exhibits a very high covering fraction of cool hydrogen gas ($f_C = 87\pm 4$\%) indicating that the CGM is ubiquitous in modern, isolated galaxies. When HI Ly-$\alpha$ is detected, its equivalent width declines with increasing radius regardless of the galaxy mass, but the scatter in this trend correlates closely with $M*$. Using the radial and stellar mass correlations, we construct a planar surface describing the cool CGM of modern galaxies: $\log W^{\rm{s}}_{HI 1215} \; = \; (0.34 \pm 0.02) -( 0.0026 \pm 0.0005)\times (R) + (0.286 \pm 0.002) \times \log (M*/M_{\odot})$. The RMS scatter around this bivariate relation is $\sim$0.2 dex. We interpret the explicit correlation between $W_{Ly\alpha}$ and $M*$ to arise from the underlying dark matter halo mass ($M_{halo}$), thereby suggesting a CGM fundamental plane between $W_{Ly\alpha}$, $R$ and $M_{halo}$. This correlation can be used to estimate the underlying dark matter halo mass from observations of saturated HI Ly-$\alpha$ in the CGM of a modern galaxy., Comment: 8 pages, 4 figures, Accepted for publication in ApJ

We analyse the Fundamental Plane (FP) relation of 39 993 early-type galaxies (ETGs) in the optical (griz) and 5080 ETGs in the near-infrared (NIR; YJHK) wavebands, forming an optical+NIR sample of 4589 galaxies. We focus on the analysis of the FP as a function of the environment where galaxies reside. We characterize the environment using the largest group catalogue, based on 3D data, generated from the Sloan Digital Sky Survey at low redshift (z < 0.1). We find that the intercept 'c' of the FP decreases smoothly from high- to low-density regions, implying that galaxies at low density have on average lower mass-to-light ratios than their high-density counterparts. The 'c' also decreases as a function of the mean characteristic mass of the parent galaxy group. However, this trend is weak and completely accounted for by the variation of 'c' with local density. The variation of the FP offset is the same in all wavebands, implying that ETGs at low density have younger luminosity-weighted ages than cluster galaxies, consistent with the expectations of semi-analytical models of galaxy formation. We measure an age variation of ~0.048 dex (~11 per cent) per decade of local galaxy density. This implies an age difference of about 32 per cent (~3 Gyr) between galaxies in the regions of highest density and the field. We find the metallicity decreasing, at ~2σ, from low to high density. We also find 2.5σ evidence that the variation in age per decade of local density augments, up to a factor of 2, for galaxies residing in massive relative to poor groups. The velocity dispersion slope of the FP, a, tends to decrease with local galaxy density, with galaxies in groups having smaller a than those in the field, independent of the waveband used to measure the structural parameters. Environmental effects (such as tidal stripping) may elucidate this result, producing a steeper variation of dark-matter fraction and/or non-homology along the ETG's sequence at higher density. In the optical, the surface brightness slope, b, of the FP increases with local galaxy density, being larger for group relative to field galaxies. The difference vanishes in the NIR, as field galaxies show a small (~2.5 per cent) but significant increase of b from g through K, while group galaxies (particularly those in rich clusters) do not. The trend of b with the environment results from galaxies residing in more massive clusters, since for groups no variation of b with local density is detected. A possible explanation for these findings is that the variation of stellar population properties with mass in ETGs is shallower for galaxies at high density, resulting from tidal stripping and quenching of star formation in galaxies falling into the group's potential well. We do not detect any dependence of the FP coefficients on the presence of substructures in parent galaxy groups.

The origins of the bulge and disc components of galaxies are of primary importance to understanding galaxy formation. Here bulge-disc decomposition is performed simultaneously in B- and R-bands for 922 bright galaxies in 8 nearby (z < 0.06) clusters with deep redshift coverage using photometry from the NOAO Fundamental Plane Survey. The total galaxy colours follow a universal colour-magnitude relation (CMR). The discs of L_* galaxies are 0.24 magnitudes bluer in $B-R$ than bulges. Bulges have a significant CMR slope while the CMR slope of discs is flat. Thus the slope of the CMR of the total light is driven primarily (60%) by the bulge-CMR, and to a lesser extent (40%) by the change in the bulge-to-total ratio as a function of magnitude. The colours of the bulge and disc components do not depend on the bulge-to-total ratio, for galaxies with bulge-to-total ratios greater than 0.2. While the colours of the bulge components do not depend significantly on environment, the median colours of discs vary significantly, with discs in the cluster centre redder by 0.10 magnitudes than those at the virial radius. Thus while star formation in bulges appears to be regulated primarily by mass-dependent, and hence presumably internal, processes, that of discs is affected by the cluster environment.

Abtsrcat Regression planes using three variables have been derived including observed measuremental errors in all the variables. It is found that in most situations the variances of the regression coefficients are reduced by inclusion of measuremental errors. To get rid of the confusion of dependent and independent variables a symmetric regression plane is also suggested as a representative one, though the choice is never unique in case of three variables. The model is tested in case of fundamental planes (FP) for some early type galaxies.

Context. We continue to study star formation in dwarf galaxies located in nearby clusters. Aims. Known physical and chemical relations outlining the formation and evolution of dwarfs is compared in different environments, including the Local Volume (LV) and some nearby clusters studied previously. Methods. We used the TNG telescope for four nights in 2010 to acquire deep near-infrared imaging in K′ of 45 star forming dwarf galaxies located in the Abell 779, Abell 1367, Abell 1656 (Coma), and Abell 2151 (Hercules) clusters. Results. Surface photometry was approached based on past experience by using the sech law to account for the outer old stellar contribution plus a Gaussian component to model the inner starburst, proving the blue compact dwarf (BCD) classification of most targets. Sech central surface brightness, semimajor axis, sech, and total apparent magnitude were measured, allowing to estimate size, absolute luminosity and mass for all targets. Conclusions. The physical correlations between size, central brightness, and NIR luminosity appear to hold, but previously known linear fits break above MSK = − ​19 for Abell 779, Abell 1367 and especially for Hercules, while the dwarf fundamental plane (FP) is probed by only half cluster members, suggesting harassment by the denser cluster environments. Nevertheless, the chemical relations between the oxygen abundance, luminosity, gas mass, baryonic mass, and gas fraction in a closed box model are probed by most members of the four studied clusters, and the starburst grows linearly with the K′ luminosity.

In the three-dimensional parameter space defined by velocity dispersion, effective radius (R_e), and effective surface brightness (I_e), early-type galaxies are observed to populate a two-dimensional fundamental plane (FP) with finite thickness. In Paper III of this series, we showed that the thickness of the FP is predominantly due to variations in the stellar mass surface density (Sigma_*) inside the effective radius R_e. These variations represent differences in the dark matter fraction inside R_e (or possibly differences in the initial mass function) from galaxy to galaxy. This means that galaxies do not wind up below the FP at lower surface brightness due to the passive fading of their stellar populations; they are structurally different. Here, we show that these variations in Sigma_* at fixed dynamical mass (M_dyn) are linked to differences in the galaxy stellar populations, and therefore to differences in their star formation histories. We demonstrate that the ensemble of stellar population and Sigma_* variations through the FP thickness can be explained by a model in which early-type galaxies at fixed M_dyn have their star formation truncated at different times. The thickness of the FP can therefore be interpreted as a sequence of truncation times. Galaxies below the FP have earlier truncation times for a given M_dyn, resulting in lower Sigma_*, older ages, lower metallicities in both [Fe/H] and [Mg/H], and higher [Mg/Fe]. We show that this model is quantitatively consistent with simple expectations for chemical enrichment in galaxies. We also present fitting functions for luminosity-weighted age, [Fe/H], [Mg/H], and [Mg/Fe] as functions of the FP parameters velocity dispersion, R_e, and I_e. These provide a new tool for estimating the stellar population properties of quiescent early-type galaxies for which high-quality spectra are not available., 21 pages, 9 figures. Accepted to ApJ

Using high-quality optical images from the Carnegie-Irvine Galaxy Survey, we perform multi-component decompositions of S0 galaxies to derive accurate structural parameters to constrain their physical origin. Many S0s do not host prominent bulges. S0 galaxies have a broad distribution of bulge-to-total ratios ($B/T$) and S\'ersic indices ($n$), with average values of $B/T=0.34\pm0.15$ and $n=2.62\pm1.02$, qualitatively consistent with the notion that S0s define a parallel sequence with and may have evolved from spiral galaxies. This is further reinforced by the incidence of bars and lenses in S0s, which when compared with the statistics in spirals, supports the idea that lenses are demised bars. However, despite their wide range of prominence, the bulges of S0s form a surprisingly uniform sequence on both the Kormendy and fundamental plane relations. There is no evidence for population dichotomy or other indications of differentiation into classical and pseudo bulges. Most of the S0s reside in the field and in groups; cluster environment is not a necessary condition for S0 production. The properties of S0 bulges show little correlation with environmental indicators, after the dependence of galaxy stellar mass on environment is taken into account. As the bulges of late-type spirals and S0s are intrinsically different, and environmental effects that may account for such evolution appear to be minimal, we conclude that late-type spirals are not plausible progenitors of S0s. The bulges of S0s likely formed at an early epoch, after which secular processes contributed little to their subsequent evolution., Comment: ApJ in press; 18 pages, 6 figures

The rotational effect of the cosmic vacuum is investigated. The induced rotation of elliptical galaxies due to the anti-gravity of the vacuum is found to be 10−21 s−1 for real elliptical galaxies. The effect of the vacuum rotation of the entire Universe is discussed, and can be described by the invariant ω ν = ω 0 ∼ $$ \sqrt {G\rho v} $$ . The corresponding numerical angular velocity of the Universe is 10−19 s−1, in good agreement with modern data on the temperature fluctuations of the cosmic background radiation.

The fundamental plane of early-type galaxies is a rather tight three-parameter correlation discovered more than twenty years ago. It has resisted a both global and precise physical interpretation despite a consequent number of works, observational, theoretical or using numerical simulations. It appears that its precise properties depend on the population of galaxies in study. Instead of selecting a priori these populations, we propose to objectively construct homologous populations from multivariate analyses. We have undertaken multivariate cluster and cladistic analyses of a sample of 56 low-redshift galaxy clusters containing 699 early-type galaxies, using four parameters: effective radius, velocity dispersion, surface brightness averaged over effective radius, and Mg2 index. All our analyses are consistent with seven groups that define separate regions on the global fundamental plane, not across its thickness. In fact, each group shows its own fundamental plane, which is more loosely defined for less diversified groups. We conclude that the global fundamental plane is not a bent surface, but made of a collection of several groups characterizing several fundamental planes with different thicknesses and orientations in the parameter space. Our diversification scenario probably indicates that the level of diversity is linked to the number and the nature of transforming events and that the fundamental plane is the result of several transforming events. We also show that our classification, not the fundamental planes, is universal within our redshift range (0.007 - 0.053). We find that the three groups with the thinnest fundamental planes presumably formed through dissipative (wet) mergers. In one of them, this(ese) merger(s) must have been quite ancient because of the relatively low metallicity of its galaxies, Two of these groups have subsequently undergone dry mergers to increase their masses. In the k-space, the third one clearly occupies the region where bulges (of lenticular or spiral galaxies) lie and might also have formed through minor mergers and accretions. The two least diversified groups probably did not form by major mergers and must have been strongly affected by interactions, some of the gas in the objects of one of these groups having possibly been swept out. The interpretation, based on specific assembly histories of galaxies of our seven groups, shows that they are truly homologous. They were obtained directly from several observables, thus independently of any a priori classification. The diversification scenario relating these groups does not depend on models or numerical simulations, but is objectively provided by the cladistic analysis. Consequently, our classification is more easily compared to models and numerical simulations, and our work can be readily repeated with additional observables.

We study the A1831 cluster within the framework of our program of the investigation of galaxy clusters with bimodal velocity distributions (i.e., clusters where the velocities of subsystems differ by more than Δ cz ∼ 3000 km/s).We identify two subsystems in this cluster: A1831A (cz = 18970 km/s) and A1831B (cz = 22629 km/s) and directly estimate the distances to these subsystems using three methods applied to early-type galaxies: the Kormendy relation, the photometric plane, and the fundamental plane. To this end, we use the results of our observations made with the 1-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences and the data adopted from the SDSS DR6 catalog. We confirmed at a 99% confidence level that (1) the two subsystems are located at different distances, which are close to their Hubble distances, and (2) the two subsystems are located behind one another along the line of sight and are not gravitationally bound to each other. Both clusters have a complex internal structure, which makes it difficult to determine their dynamical parameters. Our estimates for the velocity dispersions and masses of the two clusters: 480 km/s and 1.9 × 1014 M ⊙ for A1831A, 952 km/s and 1.4 × 1015 M ⊙ for A1831B should be views as upper limits. At least three spatially and kinematically distinct groups of galaxies can be identified in the foreground cluster A1831A, and this fact is indicative of its incomplete dynamical relaxation. Neither can we rule out the possibility of a random projection. The estimate of the mass of the main cluster A1831B based on the dispersion of the line-of-sight velocities of galaxies is two-to-three times greater than the independent mass estimates based on the total K-band luminosity, temperature, and luminosity of the X-ray gas of the cluster. This fact, combined with the peculiarities of its kinematical structure, leads us to conclude that the cluster is in a dynamically active state: galaxies and groups of galaxies with large line-of-sight velocities relative to the center of the cluster accrete onto the virialized nucleus of the cluster (possibly, along the filament directed close to the line of sight).

It is widely known that in active galactic nuclei (AGNs) and black hole X-ray binaries (BHXBs), there is a tight correlation among their radio luminosity ($L_R$), X-ray luminosity ($L_X$) and BH mass ($\mbh$), the so-called `fundamental plane' (FP) of BH activity. Yet the supporting data are very limited in the $\mbh$ regime between stellar mass (i.e., BHXBs) and 10$^{6.5}$\,\msun\ (namely, the lower bound of supermassive BHs in common AGNs). In this work, we developed a new method to measure the 1.4 GHz flux directly from the images of the VLA FIRST survey, and apply it to the type-1 low-mass AGNs in the \cite{2012ApJ...755..167D} sample. As a result, we obtained 19 new low-mass AGNs for FP research with both \mbh\ estimates ($\mbh \approx 10^{5.5-6.5}$\,\msun), reliable X-ray measurements, and (candidate) radio detections, tripling the number of such candidate sources in the literature.Most (if not all) of the low-mass AGNs follow the standard radio/X-ray correlation and the universal FP relation fitted with the combined dataset of BHXBs and supermassive AGNs by \citet{2009ApJ...706..404G}; the consistency in the radio/X-ray correlation slope among those accretion systems supports the picture that the accretion and ejection (jet) processes are quite similar in all accretion systems of different \mbh. In view of the FP relation, we speculate that the radio loudness $\mathcal{R}$ (i.e., the luminosity ratio of the jet to the accretion disk) of AGNs depends not only on Eddington ratio, but probably also on \mbh., ApJ accepted

Understanding the formation and evolution of early-type, spheroid-dominated galaxies is an open question within the context of the hierarchical clustering scenario, particularly, in low-density environments. Our goal is to study the main structural, dynamical, and stellar population properties and assembly histories of field spheroid-dominated galaxies formed in a LCDM scenario to assess to what extend they are consistent with observations. We selected spheroid-dominated systems from a LCDM simulation that includes star formation, chemical evolution and Supernova feedback. A sample of 18 field systems with Mstar, Comment: 22 pages, 15 figures, accepted for publication in A&A, revised version, minor changes

In the context of modified Newtonian dynamics, the fundamental plane, as the observational signature of the Newtonian virial theorem, is defined by high surface brightness objects that deviate from being purely isothermal: the line-of-sight velocity dispersion should slowly decline with radius as observed in luminous elliptical galaxies. All high surface brightness objects (e.g. globular clusters, ultra-compact dwarfs) will lie, more or less, on the fundamental plane defined by elliptical galaxies, but low surface brightness objects (dwarf spheroidals) would be expected to deviate from this relation. This is borne out by observations. With MOND, the Faber-Jackson relation (the power-law relation between luminosity and velocity dispersion), ranging from globular clusters to clusters of galaxies and including both high and low surface brightness objects, is the more fundamental and universal scaling relation in spite of its larger scatter. Faber-Jackson reflects the presence of an additional dimensional constant (the MOND acceleration) in the structure equation.

The Fundamental Plane has finite thickness and is tilted from the virial relation, indicating that dynamical mass-to-light ratios (Mdyn/L) vary among early type galaxies. We use a sample of 16,000 quiescent galaxies from the Sloan Digital Sky Survey to map out variations in Mdyn/L through the 3D Fundamental Plane space defined by velocity dispersion (sigma), effective radius (R_e), and effective surface brightness. We consider contributions to Mdyn/L variation due to stellar population effects, IMF variations, and variations in the dark matter fraction within one R_e. Along the FP, we find that the stellar population contribution scales as M*/L ~ f(sigma), while the dark matter and/or IMF contribution scales as Mdyn/M* ~ g(Mdyn). The two contributions to the tilt of the FP rotate the plane around different axes in the 3D space, with dark matter/IMF variations likely dominating. Through the thickness of the FP, we find that Mdyn/L variations must be dominated either by IMF variations or by real differences in dark matter fraction with R_e. Thus the finite thickness of the FP is due to variations in the stellar mass surface density within R_e, not the fading of passive stellar populations. These structural variations are correlated with galaxy star formation histories such that galaxies with higher Mdyn/M* at a given sigma have higher [Mg/Fe], lower metallicities, and older mean stellar ages. It is difficult to explain the observed correlations by allowing the IMF to vary, suggesting difference in dark matter fraction dominate. These can be produced by variations in the "conversion efficiency" of baryons into stars or by the redistribution of stars and dark matter through dissipational merging. A model in which some galaxies experience low conversion efficiencies due to premature truncation of star formation provides a natural explanation for the observed trends.

In cold dark matter (CDM) cosmology, objects in the Universe have grown under the effect of gravity of dark matter. The intracluster gas in a galaxy cluster was heated when the dark-matter halo formed through gravitational collapse. The potential energy of the gas was converted to thermal energy through this process. However, this process and the thermodynamic history of the gas have not been clearly characterized in connection with with the formation and evolution of the internal structure of dark-matter halos. Here, we show that observational CLASH data of high-mass galaxy clusters lie on a plane in the three-dimensional logarithmic space of their characteristic radius $r_s$, mass $M_s$, and X-ray temperature $T_X$ with a very small orthogonal scatter. The tight correlation indicates that the gas temperature was determined at a specific cluster formation time, which is encoded in $r_s$ and $M_s$. The plane is tilted with respect to $T_X \propto M_s/r_s$, which is the plane expected in case of simplified virial equilibrium. We show that this tilt can be explained by a similarity solution, which indicates that clusters are not isolated but continuously growing through matter accretion from their outer environments. Numerical simulations reproduce the observed plane and its angle. This result holds independently of the gas physics implemented in the code, revealing the fundamental origin of this plane., Comment: Replaced with a revised version to match the ApJ accepted version

The relationship of high surface brightness Arakelian galaxies (ArG) to their environment is studied. This is done using the groups identified by the authors on the basis of the CfA2 red shift survey. Of the 15577 galaxies in the sample, 172 (1.104%) have a high surface brightness. The corresponding percentage for the galaxies with 13.0 < m ≤ 15.0 is 2.05. The following results are obtained: (a) On going from single to poor groups and on to more populated groups, the frequency of occurrence of ArG does not vary. (b) Groups of galaxies containing ArG do not differ on the average from groups which do not contain such galaxies in terms of their dynamic characteristics, such as the dispersion in radial velocity, size, and total luminosity, or their morphological content. (c) ArG do not follow the regular pattern according to which elliptical and lenticular galaxies are more often encountered in groups of galaxies than among single galaxies, i.e., it seems that the frequency of occurrence of elliptical and lenticular ArG in groups is the same as in single galaxies. (d) The surface brightnesses, diameters, and luminosities of ArG in groups of galaxies are greater than those of single ArG. This shows up especially strongly in spiral ArG.

We have investigated the radial g-r color gradients of early-type galaxies in the Sloan Digital Sky Survey (SDSS) DR6 in the redshift range 0.00

Mergers in the local universe present a unique opportunity for studying the transformations of galaxies in detail. Presented here are recent results, based on multi-wavelength, high-resolution imaging and medium resolution spectroscopy, which demonstrate how star-formation and the presence of Red Supergiants and/or Asymptotic Giant Branch stars has lead to a serious underestimation of the dynamical masses of infrared-bright galaxies. The dominance of a nuclear disk of young stars in the near-infrared bands, where dust obscuration does not block their signatures, can severely bias the global properties measured in a galaxy, including mass. This explains why past studies of gas-rich Luminous & Ultraluminous Infrared Galaxies, which have measured dynamical masses using the 1.62 or 2.29 micron CO band-heads, have found that these galaxies are forming m m* ellipticals. Moreover, merger remnants, including LIRGs, are placed on the I-band Fundamental Plane for the first time and appear to be virtually indistinguishable from elliptical galaxies.

We investigate the most plausible stellar Initial Mass Function (IMF) and the main origin of the tilt of the Fundamental Plane (FP) for old, massive early-type galaxies. We consider a sample of 13 bright galaxies of the Coma cluster and combine our results with those obtained from a sample of 57 lens galaxies in the same luminous mass range. We estimate the luminous mass and stellar mass-to-light ratio values of the sample galaxies by fitting their SDSS multi-band photometry with composite stellar population models computed with different dust-free, solar-metallicity templates and IMFs. We compare these measurements and those derived from two-component orbit-based dynamical modelling. The photometric and dynamical luminous mass estimates of the galaxies in our sample are consistent, within the errors, if a Salpeter IMF is adopted. On the contrary, with a Kroupa or Chabrier IMF the two luminous mass diagnostics differ at a more than 4 \sigma level. For the massive Coma galaxies, their stellar mass-to-light ratio scales with luminous mass as the corresponding effective quantities are observed to scale on the FP. This indicates that the tilt of the FP is primarily caused by stellar population properties. We conclude that old, massive lens and non-lens early-type galaxies obey the same luminous and dynamical scaling relations, favour a Salpeter IMF, and suggest a stellar population origin for the tilt of the FP. The validity of these results for samples of early-type galaxies with different age and mass properties still remains to be tested.

We explore the effects of dark matter and dark energy on the dynamical scaling properties of galaxy clusters. We investigate the cluster Faber-Jackson (FJ), Kormendy and Fundamental Plane (FP) relations between the mass, radius and velocity dispersion of cluster size halos in cosmological $N$-body simulations. The simulations span a wide range of cosmological parameters, representing open, flat and closed Universes. Independently of the cosmology, we find that the simulated clusters are close to a perfect virial state and do indeed define a Fundamental Plane. The fitted parameters of the FJ, Kormendy and FP relationships do not show any significant dependence on $\Omega_m$ and/or $\Omega_{\Lambda}$. The one outstanding effect is the influence of $\Omega_{m}$ on the thickness of the Fundamental Plane. Following the time evolution of our models, we find slight changes of FJ and Kormendy parameters in high $\Omega_m$ universe, along with a slight decrease of FP fitting parameters. We also see an initial increase of the FP thickness followed by a convergence to a nearly constant value. The epoch of convergence is later for higher values of $\Omega_m$ while the thickness remains constant in the low $\Omega_m$ $\Lambda$-models. We also find a continuous increase of the FP thickness in the Standard CDM (SCDM) cosmology. There is no evidence that these differences are due to the different power spectrum slope at cluster scales. From the point of view of the FP, there is little difference between clusters that quietly accreted their mass and those that underwent massive mergers. The principal effect of strong mergers is to change significantly the ratio of the half-mass radius $r_{half}$ to the harmonic mean radius $r_h$., Comment: 24 pages, 17 figures, submitted to MNRAS