Virial Velocity Research Articles

VLT/ISAAC spectra of the Hβregion in intermediate-redshift quasars

We derive black hole masses for a sample of about 300 AGNs in the redshift range . We use the same virial velocity measure (FWHM H) for all sources which represents a significant improvement over previous studies. We review methods and caveats for determining AGN black hole masses via the virial assumption for motions in the gas producing low ionization broad emission lines. We derive a corrected FWHM(H) measure for the broad component of Hβ that better estimates the virialized line emitting component by comparing our FWHM measures with a sample of reverberated sources with Hβ radial velocity dispersion measures. We also consider the FWHM of the Feiiλ 4570 blend as a potential alternative velocity estimator. We find a range of black hole mass between MBH ~ 6.0–10.0, where MBH is in solar masses. Estimates using corrected FWHM(Hβ), as well as FWHM(Feii) measures, reduce the number of sources with MBH > 9.5 and suggest that extremely large MBH values ( MBH 10) may not be realistic. Derived values show no evidence for a significant population of super-Eddington radiators especially after correction is made for sources with extreme orientation to our line of sight. Sources with FWHM(H) 4000 km s-1 show systematically higher and lower MBH values than broader lined AGNs (including almost all radio-loud sources).

Star formation through gravitational collapse and competitive accretion

Competitive accretion, a process to explain the origin of the IMF, occurs when stars in a common gravitational potential accrete from a distributed gaseous component. We show that concerns recently raised on the efficiency of competitive accretion are incorrect as they use globally averaged properties which are inappropriate for the detailed physics of a forming stellar cluster. A full treatment requires a realistic treatment of the cluster potential, the distribution of turbulent velocities and gas densities. Accreting gas does not travel at the global virial velocity of the system due to the velocity-sizescale relation inherent in turbulent gas and due to the lower velocity dispersion of small-N clusters in which much of the accretion occurs. Stars located in the gas-rich centres of such systems initially accrete from low relative velocity gas attaining larger masses before needing to accrete the higher velocity gas. Stars not in the centres of such potentials, or that enter the cluster later when the velocity dispersion is higher, do not accrete significantly and thus retain their low-masses. In competitive accretion, most stars do not continue to accrete significantly such that their masses are set from the fragmentation process. It is the few stars which continue to accrete that become higher-mass stars. Competitive accretion is therefore likely to be responsible for the formation of higher-mass stars and can explain the mass distribution, mass segregation and binary frequency of these stars. Global kinematics of competitive accretion models include large-scale mass infall, with mean inflow velocities of order 0.5 km/s at scales of 0.5 pc, but infall signatures are likely to be confused by the large tangential velocities and the velocity dispersion present.

Redshift Space 21 cm Power Spectra from Reionization

We construct a simple but self-consistent analytic ionization model for rapid exploration of 21 cm power spectrum observables in redshift space. It is fully described by the average ionization fraction xe(z) and H II patch size R(z) and has the flexibility to accommodate various reionization scenarios. The model associates ionization regions with dark matter halos of the number density required to recover xe and treats redshift space distortions self-consistently with the virial velocity of such halos. Based on this model, we study the line-of-sight structures in the brightness fluctuations, since they are the most immune to foreground contamination. We explore the degeneracy between the H II patch size and nonlinear redshift space distortion in the one-dimensional power spectrum. We also discuss the limitations experimental frequency and angular resolutions place on their distinguishability. Angular resolution dilutes even the radial signal and will be a serious limitation for resolving small bubbles before the end of reionization. Nonlinear redshift space distortions suggest that a resolution of the order of 1''-10'' and a frequency resolution of 10 kHz will ultimately be desirable to extract the full information in the radial field at z ~ 10. First-generation instruments such as LOFAR and MWA could potentially measure radial H II patches of a few comoving megaparsecs and larger at the end of reionization and are unlikely to be affected by nonlinear redshift space distortions.

Erratum: The many lives of active galactic nuclei: cooling flows, black holes and the luminosities and colours of galaxies

In Figure 6 we inadvertently labeled the proxy circular velocity as the virial velocity of the dark matter halo instead of what is actually plotted, the maximum circular velocity of the dark matter halo. The maximum halo circular velocity is a much better estimate of the disk V_c than is V_vir. This confusion influenced the discussion of the Tully-Fisher relation in our paper. In fact, Figure 6 demonstrates that it is possible to simultaneously reproduce both the local Tully-Fisher relation and luminosity function using semi-analytic techniques applied to the standard LCDM cosmology, thus contradicting previous studies of this issue and our own discussion in Section 3.6.

Local virial relation and velocity anisotropy in self-gravitating system

We investigate the merging process in N-body self-gravitating system from the viewpoints of the local virial relation which is the relation between the local kinetic energy and the local potential. We compare both the density profile and the phase space density profile in cosmological simulations with the critical solutions of collisionless static state satisfying the local virial (LV) relation. We got the results that the critical solution can explain the characteristic density profile with the appropriate value of anisotropy parameter β ∼ 0.5. It can also explain the power law of the phase space density profile in the outer part of a bound state. However, it fails in explaining the central low temperature part which is connected to the scale invariant phase space density. It can be well fitted to the critical solution with the higher value of β ∼ 0.75. These results indicate that the LV relation is not compatible with the scale invariant phase space density in cosmological simulation.

Internal kinematics of isolated modelled disc galaxies

We present a systematic investigation of rotation curves (RCs) of fully hydrodynamically simulated galaxies, including cooling, star formation with associated feedback, and galactic winds. Applying two commonly used fitting formulae to characterize the RCs, we investigated systematic effects on the shape of RCs by both the observational constraints and internal properties of the galaxies. We mainly focused on effects that occur in measurements of intermediate and high redshift galaxies. We found that RC parameters are affected by the observational setup, like slit misalignment or the spatial resolution and that they also depend on the evolution of a galaxy. Therefore, a direct comparison of quantities derived from measured RCs with predictions of semi-analytic models is difficult. The virial velocity V c , which is usually calculated and used by semi-analytic models, can differ significantly from fit parameters like V max or V opt inferred from RCs. We found that V c is usually lower than typical characteristic velocities derived from RCs. V max alone is in general not a robust estimator of the virial mass.

Velocity moments of dark matter haloes

Using cosmological N-body simulations we study the line-of-sight velocity distribution of dark matter haloes focusing on the lowest-order even moments, dispersion and kurtosis, and their application to estimate the mass profiles of cosmological structures. For each of the ten massive haloes selected from the simulation box we determine the virial mass, concentration and the anisotropy parameter. In order to emulate observations from each halo we choose randomly 300 particles and project their velocities and positions along the line of sight and on the surface of the sky, respectively. After removing interlopers we calculate the profiles of the line-of-sight velocity moments and fit them with the solutions of the Jeans equations. The estimates of virial mass, concentration parameter and velocity anisotropy obtained in this way are in good agreement with the values found from the full 3D analysis.

Local Virial Relation and Velocity Anisotropy for Collisionless Self-Gravitating Systems

The collisionless quasi-equilibrium state realized after the cold collapse of self-gravitating systems has two remarkable characters. One of them is the linear temperature-mass (TM) relation, which yields a characteristic non-Gaussian velocity distribution. The other is the local virial (LV) relation, the virial relation which holds even locally in collisionless systems through phase mixing such as cold-collapse. A family of polytropes is examined from a view point of these two characters. The LV relation imposes a strong constraint on these models: only polytropes with index n ∼ 5 with a flat boundary condition at the center are compatible with the numerical results, except for the outer region. Using the analytic solutions based on the static and spherical Jeans equation, we show that this incompatibility in the outer region implies the important effect of anisotropy of velocity dispersion. Furthermore, the velocity anisotropy is essential in explaining various numerical results under the condition of the local virial relation.

Dynamical and Photometric Imprints of Feedback Processes on the Formation and Evolution of E/S0 Galaxies

We show that the observed velocity dispersion function of E/S0 galaxies matches strikingly well the distribution function of virial velocities of massive halos virializing at z ? 1.5, as predicted by the standard hierarchical clustering scenario in a ?CDM cosmology, for a constant ratio ?/Vvir 0.55 ? 0.05, which is close to the value expected at virialization if it typically occurred at z 3. This strongly suggests that dissipative processes and later merging events had little impact on the matter density profile. Adopting the above ?/Vvir ratio, the observed relationships between photometric and dynamical properties that define the fundamental plane of elliptical galaxies, such as the luminosity-? (Faber-Jackson) and the luminosity-effective radius relations, as well as the MBH-? relation, are nicely reproduced. Their shapes turn out to be determined by the mutual feedback of star formation (and supernova explosions) and nuclear activity, along the lines discussed by Granato and coworkers. To our knowledge, this is the first semianalytic model for which simultaneous fits of the fundamental plane relations and of the epoch-dependent luminosity function of spheroidal galaxies have been presented.

Merger Dynamics of the Pair of Galaxy Clusters – A399 and A401

Convincing evidence of a past interaction between two rich clusters A399 and A401 was recently found by the X-ray imaging observations. In this paper we examine the structure and dynamics of this pair of galaxy clusters. A mixture-modeling algorithm has been applied to obtain a robust partition into two clusters, which allows us to discuss the virial mass and velocity distribution for each cluster. Assuming that these two clusters follow a linear orbit and they have once experienced a close encounter, we model the binary cluster as a two-body system. As a result, four gravitationally bound solutions are obtained. The recent X-ray observations seem to favor a scenario in which the two clusters with a true separation of $5.4h^{-1}$ Mpc are currently expanding at 583 km/s along the direction with a projection angle of 67.5 degree, and they will reach a maximum extent of $5.65h^{-1}$ Mpc in about $1.0h^{-1}$ Gyr.

Mass Modeling of Disk Galaxies: Degeneracies, Constraints, and Adiabatic Contraction

This paper addresses available constraints on mass models fitted to rotation curves. Mass models of disk galaxies have well-known degeneracies that prevent a unique mass decomposition. The most notable is due to the unknown value of the stellar mass-to-light ratio (the disk-halo degeneracy); even with this known, degeneracies between the halo parameters themselves may prevent an unambiguous determination of the shape of the dark halo profile, which includes the inner density slope of the dark matter halo. The latter is often referred to as the We explore constraints on the disk and halo parameters and apply these to four mock and six observed disk galaxies with high resolution and extended rotation curves. Our full set of constraints consists of mass-to-light (M/L) ratios from stellar population synthesis models based on B - R colors, constraints on halo parameters from N-body simulations, and constraining the halo virial velocity to be less than the maximum observed velocity. These constraints are only partially successful in lifting the cusp-core degeneracy. The effect of adiabatic contraction of the halo by the disk is to steepen cores into cusps and reduce the best-fit halo concentration and M/L values (often significantly). We also discuss the effect of disk thickness, halo flattening, distance errors, and rotation curve error values on mass modeling. Increasing the imposed minimum rotation curve error from typically low, underestimated values to more realistic estimates decreases the χ2 substantially and makes distinguishing between a cuspy or cored halo profile even more difficult. In spite of the degeneracies and uncertainties present, our constrained mass modeling favors submaximal disks (i.e., a dominant halo) at 2.2 disk scale lengths, with Vdisk/Vtot 0.6. This result holds for both the unbarred and weakly barred galaxies in our sample.

The baryonic mass-velocity relation: clues to feedback processes during structure formation and the cosmic baryon inventory

We show that a global relation between baryonic mass and virial velocity can be constructed from the scale of dwarf galaxies up to that of rich galaxy clusters. The slope of this relation is close to that expected if dark matter halos form in the standard hierarchical cosmogony and capture a universal baryon fraction, once the details of halo structure and the adiabatic contraction of halos due to cooling gas are taken into account. The scatter and deficiency of baryons within low mass halos ($V_{vir} < 50$ km/s) is consistent with the expected suppression of gas accretion by photo-evaporation due to the cosmic UV background at high redshift. The data are not consistent with significant gas removal from strong supernovae winds unless the velocities of galaxies measured from their gas kinematics are significantly lower than the true halo velocities for objects with $V_{vir} < 100$ km/s. Thus models such as $\Lambda$CDM with a steep mass function of halos may find it difficult to reproduce both the baryonic mass-velocity relation presented here whilst at the same time reproducing the flat luminosity/HI function of galaxies. Galaxies hold about 10% of the baryons in the Universe, which is close to the collapsed mass fraction expected within hierarchical models on these scales, suggesting a high efficiency for galaxy formation. Most of the baryons are expected to be evenly distributed between diffuse intergalactic gas in low density environments and the intra-galactic medium within galaxy groups.

Bulgeless Galaxies and Their Angular Momentum Problem

The specific angular momentum of cold dark matter (CDM) halos in a ΛCDM universe is investigated. Their dimensionless specific angular momentum λ' = j/(VvirRvir) with Vvir and Rvir the virial velocity and virial radius, respectively, depends strongly on their merging histories. We investigate a set of ΛCDM simulations and explore the specific angular momentum content of halos formed through various merging histories. Halos with a quiet merging history, dominated by minor mergers and accretion until the present epoch, acquire by tidal torques on average only 2%-3% of the angular momentum required for their rotational support (λ' = 0.02). This is in conflict with observational data for a sample of late-type bulgeless galaxies that indicates that those galaxies reside in dark halos with exceptionally high values of λ' ≈ 0.06-0.07. Minor mergers and accretion preserve or slowly increase the specific angular momentum of dark halos with time. This mechanism, however, is not efficient enough in order to explain the observed spin values for late-type dwarf galaxies. Energetic feedback processes have been invoked to solve the problem that gas loses a large fraction of its specific angular momentum during infall. Under the assumption that dark halos hosting bulgeless galaxies acquire their mass via quiescent accretion, our results indicate yet another serious problem: the specific angular momentum gained during the formation of these objects is not large enough to explain their observed rotational properties, even if no angular momentum would be lost during gas infall.

The reliability of the kinematical evidence for dark matter: the effects of non-sphericity, substructure and streaming motions

Using cosmological N-body simulations of dark matter haloes, we study the effects of non-sphericity, substructure and streaming motions in reproducing the structure and internal kinematics of clusters of galaxies from kinematical measurements. Fitting a Navarro, Frenk & White (NFW) model to the 3D density profile, we determine the virial mass, concentration parameter and velocity anisotropy of the haloes, and then calculate the profiles of projected velocity moments, as they would be measured by a distant observer. Using these mock data, we apply a Jeans analysis for spherical objects to reproduce the line-of-sight velocity dispersion and kurtosis profiles and fit the three parameters. We find that the line-of-sight velocity dispersion and kurtosis profiles of a given halo can vary considerably with the angle of view of the observer. We show that the virial mass, concentration parameter and velocity anisotropy of the haloes can be reproduced satisfactorily independently of the halo shape, although the virial mass tends to be underestimated, the concentration parameter overestimated, and the recovered anisotropy is typically more tangential than the true one. The mass, concentration and velocity anisotropy of haloes are recovered with better precision when their mean velocity profiles are near zero.

High-redshift quasars and the supermassive black hole mass budget: constraints on quasar formation models

We investigate the constraints on models of supermassive black hole (SMBH) and quasar formation obtainable from two recent observational developments: the discovery of luminous quasars at z~6, and estimates of the local mass density of SMBHs. If ~90 per cent of this mass was accreted at redshifts z<3, as suggested by the observed quasar luminosity functions, these joint constraints pose a challenge for models, which must account for the observed luminous quasar population at z~6 within a very limited `mass budget'. We investigate a class of models based within the hierarchical structure formation scenario, in which major mergers lead to black hole formation and fuelling, and the resulting quasars shine at their Eddington-limited rate until their fuel is exhausted. We show that the simplest such model, in which a constant fraction of the gas within the halo is accreted in each major merger, cannot satisfy both constraints simultaneously. When this model is normalized to reproduce the number density of luminous quasars at z~6, the mass budget is grossly exceeded due to an overabundance of lower mass SMBHs. We explore a range of modifications to the simple model designed to overcome this problem. We show that both constraints can be satisfied if the gas accretion fraction scales as a function of the halo virial velocity. Similar scalings have been proposed in order to reproduce the local M-sigma relation. Successful models can also be constructed by restricting the formation of seed black holes to redshifts above z~11.5 or to haloes above a velocity threshold ~55 km/s, or assuming that only a fraction of major mergers result in formation of a seed SMBH. (abridged)

Feedback and the fundamental line of low-luminosity low-surface-brightness/dwarf galaxies

We study in simple terms the role of feedback in establishing the scaling relations of low-surface-brightness (LSB) and dwarf galaxies with stellar masses in the range 6 × 10 5 ≤ M * ≤ 3 x 10 1 0 M O . . These galaxies - as measured, for example, from the Sloan Digital Sky Survey (SDSS) and in the Local Group - show tight correlations of internal velocity, metallicity and surface brightness (or radius) with M * . They define a fundamental line which distinguishes them from the brighter galaxies of high surface brightness and metallicity. The idealized model assumes spherical collapse of cold dark matter (CDM) haloes to virial equilibrium and angular momentum conservation. The relations for bright galaxies are reproduced by assuming that M * is a constant fraction of the halo mass M. The upper bound to the low-luminosity LSBs coincides with the virial velocity of haloes in which supernova feedback could significantly suppress star formation, V 30 km s - 1 , retain gas-rich discs with feedback-regulated star formation.

Damped Lyman alpha systems and galaxy formation models - II. High ions and Lyman-limit systems

We investigate a model for the high-ionization state gas associated with observed damped Lyman-alpha systems, based on a semi-analytic model of galaxy formation set within the paradigm of hierarchical structure formation. In our model, the hot gas in halos and sub-halos gives rise to CIV absorption, while the low-ionization state gas is associated with the cold gas in galaxies. The model matches the distribution of CIV column densities and leads naturally to kinematic properties that are in good agreement with the data. We examine the contribution of both hot and cold gas to sub-damped systems and suggest that the properties of these systems can be used as an important test of the model. We expect that sub-DLA systems will generally be composed of a single gas disk and thus predict that they should have markedly different kinematics than the damped systems. Finally, we find that hot halo gas produces less than one third of Lyman limit systems at redshift three. We model the contribution of mini-halos (halos with virial velocities < 35 km/s) to Lyman limit systems and find that they may contain as much gas as is observed in these systems. However, if we adopt realistic models of the gas density distribution we find that these systems are not a significant source of Lyman limit absorption. Instead we suggest that uncollapsed gas outside of virialized halos is responsible for most of the Lyman limit systems at high redshift.

ERRATUM: 'LONG-TERM X-RAY VARIABILITIES OF SEYFERT GALAXY MCG-2-58-22: GRADUAL DECREAES AND FLARES' (JKAS, 35, 1, [2002

Proof correction to the equation in the third paragraph of the DISCUSSION AND CONCLUSION has not been carried faithfully to the published version of the paper. The corrected equation should read , where Ms is the mass of the SMBH in units of , is the virial velocity of the stars, is the tidal radius of the SMBH. This estimates the frequency that a star would pass within a sphere with the radius r from the SMBH, rather than the frequency of the tidal disruption event. Therefore, it increases with the mass of the SMBH. However, the loss cone effect should also be taken into account, which reduces the actual event rate. Here, we adopted a factor of one hundred to consider the deficiency from the isotrophic rate. The authors sincerely regret this error.

Constraints on the Baryonic Compression and Implications for the Fraction of Dark Halo Lenses

We predict the fraction of dark halo lenses, that is, the fraction of lens systems produced by the gravitational potential of dark halos, on the basis of a simple parametric model of baryonic compression. The fraction of dark halo lenses primarily contains information on the effect of baryonic compression and the density profile of dark halos and is expected to be insensitive to cosmological parameters and source population. The model that we adopt comprises the galaxy formation probability pg(M), which describes the global efficiency of baryonic compression, and the ratio of circular velocities of galaxies to virial velocities of dark halos, ?v = vc/vvir, which describes how the inner structure of dark halos is modified because of baryonic compression. The model parameters are constrained from the velocity function of galaxies and the distribution of image separations in gravitational lensing, although the degeneracy between model parameters still remains. We show that the fraction of dark halo lenses depends strongly on ?v and the density profile of dark halos, such as inner slope ?. This means that the observation of the fraction of dark halos can break the degeneracy between model parameters if the density profile of dark halo lenses is fully settled. On the other hand, by restricting ?v to a physically plausible range, we can predict the lower limit of the fraction of dark halo lenses on the basis of our model. Our result indicates that steeper inner cusps of dark halos (? 1.5) or too centrally concentrated dark halos are inconsistent with the lack of dark halo lenses in observations.

1.65 Micron (HBand) Surface Photometry of Galaxies. X. Structural and Dynamical Properties of Elliptical Galaxies

We analyze the structural and dynamical properties of a sample of 324 nearby elliptical and dwarf elliptical galaxies observed during an extensive near-IR survey in the H band (1.65 μm). The fundamental plane is determined and a significant tilt is assessed. The origins of such a tilt are investigated by means of a spherically symmetric, isotropic, pressure-supported dynamical model relying on the observed surface brightness profiles. The systematic variation of the shape coefficient converting the measured central velocity dispersion σ0 into the virial rms velocity σrms is found to be the main cause of the tilt, due to aperture effects. Moreover, the ratio between the dynamical mass Mdyn and the total H-band luminosity LH turns out to be roughly constant along the luminosity sequence of ellipticals: H-band luminosity is therefore a reliable and cheap estimator of the dynamical mass of the E galaxies.