The M - sigma project
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There is an intimate link between supermassive black hole (SMBH) mass (M) and the stellar velocity dispersion (sigma) of the host bulge. This has a fundamental impact on our understanding of galaxy and SMBH formation and evolution. However, the scatter, slope and zero-point of the relation is a subject of some debate. For any progress to be made on this relation, the established values of M and sigma must be robust. Over 50% of current M estimates have been made using the technique of stellar dynamics. However, there is serious concern over this method that prompts their re-evaluation. In addition, it is not clear how best to define sigma. The aim of the M-Sigma Project is to use STIS long-slit spectroscopy, integral field spectroscopy and the latest stellar models, to best estimate the values of M and sigma in as many cases as possible. The project will determine the most appropriate properties of the M-Sigma relation itself.Keywords:
Sigma
Velocity dispersion
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The scaling relation for early type galaxies in the 6dF galaxy survey does not have the velocity dispersion dependence expected from standard stellar population models. As noted in recent work with SDSS, there seems to be an additional dependence of mass to light ratio with velocity dispersion, possibly due to a bottom heavy initial mass function. Here we offer a new understanding of the 6dF galaxy survey 3D gaussian Fundamental Plane in terms of a parameterized Jeans equation, but leave mass dependence of M/L and mass dependence of structure still degenerate with just the present constraints. Hybrid models have been proposed recently. Our new analysis brings into focus promising lines of enquiry which could be pursued to lift this degeneracy, including stellar atmospheres computation, kinematic probes of ellipticals at large radius, and a large sample of one micron spectra.
Velocity dispersion
Degeneracy (biology)
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In the local universe, the masses of Super-Massive Black-Holes (SMBH) appear to correlate with the physical properties of their hosts, including the mass of the dark-matter halo. Using these clues as a starting point many studies have produced models that can explain phenomena like the quasar luminosity function. The shortcoming of this approach is that working models are not unique, and as a result it is not always clear what input physics is being constrained. Here we take a different approach. We identify critical parameters that describe the evolution of SMBHs at high redshift, and constrain their parameter space based on observations of high redshift quasars from the Sloan Digital Sky Survey. We find that the luminosity function taken in isolation is somewhat limited in its ability to constrain SMBH evolution due to some strong degeneracies. This explains the presence in the literature of a range of equally successful models based on different physical hypotheses. Including the constraint of the local SMBH to halo mass ratio breaks some of the degeneracies, and our results suggest halo masses at z~4.8 of 10^{12.5+/-0.3}M_solar (with 90% confidence), with a SMBH to halo mass ratio that decreases with time (>99%). We also find a quasar luminosity to halo mass ratio that increases with halo mass (>99%). These features need to be incorporated in all successful models of SMBH evolution. On the other hand current observations do not permit any conclusions regarding the evolution of quasar lifetime, or the SMBH occupation fraction in dark matter halos.
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We develop a semi-analytic model to explore different prescriptions of supermassive black hole (SMBH) fuelling. This model utilises a merger-triggered burst mode in concert with two possible implementations of a long-lived steady mode for assembling the mass of the black hole in a galactic nucleus. We improve modelling of the galaxy-halo connection in order to more realistically determine the evolution of a halo's velocity dispersion. We use four model variants to explore a suite of observables: the M-sigma relation, mass functions of both the overall and broad-line quasar population, and luminosity functions as a function of redshift. We find that "downsizing" is a natural consequence of our improved velocity dispersion mappings, and that high-mass SMBHs assemble earlier than low-mass SMBHs. The burst mode of fuelling is sufficient to explain the assembly of SMBHs to z=2, but an additional steady mode is required to both assemble low-mass SMBHs and reproduce the low-redshift luminosity function. We discuss in detail the trade-offs in matching various observables and the interconnected modelling components that govern them. As a result, we demonstrate the utility as well as the limitations of these semi-analytic techniques.
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It is now well established that many galaxies have nuclear star clusters (NCs) whose total masses correlate with the velocity dispersion (sigma) of the galaxy spheroid in a very similar way to the well--known supermassive black hole (SMBH) M - sigma relation. Previous theoretical work suggested that both correlations can be explained by a momentum feedback argument. Observations further show that most known NCs have masses < 10^8 Msun, while SMBHs frequently have masses > 10^8 Msun, which remained unexplained in previous work. We suggest here that this changeover reflects a competition between the SMBH and nuclear clusters in the feedback they produce. When one of the massive objects reaches its limiting M-sigma value, it drives the gas away and hence cuts off its own mass and also the mass of the ``competitor''. The latter is then underweight with respect to the expected M-sigma mass (abridged).
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Thanks to the angular resolution of modern telescopes and kinematic models, the existence of supermassive black holes (SMBHs) in the inner part of galaxies has been established on quite solid grounds. A possible correlation between the mass of SMBHs and the evolutionary state of their host galaxies is expected. Based on the recent 2D decomposition of mid-infrared Spiter/IRAC images of local galaxies with M_bh measurements, we investigated various scaling laws, studying what the best predictor of the mass of the central SMBHs is. We focused on the M_bh-M_G sigma^2 law, the relation between the mass of SMBHs and the kinetic energy of random motions of the corresponding host galaxies. In order to find the best fit for each of the scaling laws examined, we performed a least-squares regression of M_bh on x for the considered sample of galaxies, x being a whatever known parameter of the galaxy bulge. Our analysis shows that M_bh-M_G sigma^2 law fits the examined experimental data successfully as much as the other known scaling laws and shows a value of chi^2 better than the others, a result which is consistent with previous determinations. This means that a combination of sigma and M_G could be necessary to drive the correlations between M_bh and other bulge properties. This issue has been investigated by a careful analysis of the residuals of the various relations. In order to avoid rushed conclusions on galaxy activity and evolution, the indirect inferring of M_bh from the kinetic energy of random motions should be considered, especially when applied to higher redshift galaxies. This statement is suggested by a reanalysis of the SDSS data used to study the SMBH growth in the nearby Universe. Adopting the M_bh-M_G sigma^2 relation instead of the M_bh-sigma, a radio-quiet/radio-loud dichotomy appears in the SMBH mass distribution of the corresponding SDSS early-type AGN galaxies.
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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 ΛCDM cosmology, for a constant ratio σ/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 σ/Vvir ratio, the observed relationships between photometric and dynamical properties that define the fundamental plane of elliptical galaxies, such as the luminosity-σ (Faber-Jackson) and the luminosity-effective radius relations, as well as the MBH-σ 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.
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After the discovery that supermassive black holes (SMBHs) are ubiquitous at the center of stellar spheroids and that their mass Mbh, in the range 10^6-10^9 Msun, is tightly related to global properties of the host stellar system, the idea of the co-evolution of elliptical galaxies and of their SMBHs has become a central topic of modern astrophysics. Here, I summarize some consequences that can be derived from the galaxy Scaling Laws (SLs) and present a coherent scenario for the formation and evolution of elliptical galaxies and their central SMBHs, focusing in particular on the establishment and maintenance of their SLs. In particular, after a first observationally based part, the discussion focuses on the physical interpretation of the Fundamental Plane. Then, two important processes in principle able to destroy the galaxy and SMBH SLs, namely galaxy merging and cooling flows, are analyzed. Arguments supporting the necessity to clearly distinguish between the origin and maintenance of the different SLs, and the unavoidable occurrence of SMBH feedback on the galaxy ISM in the late stages of galaxy evolution (when elliptical galaxies are sometimes considered as ``dead, red objects''), are then presented. At the end of the paper I will discuss some implications of the recent discovery of super-dense ellipticals in the distant Universe. In particular, I will argue that, if confirmed, these new observations would lead to the conclusion that at early epochs a relation between the stellar mass of the galaxy and the mass of the central SMBH should hold, consistent with the present day Magorrian relation, while the proportionality coefficient between Mbh and the scale of velocity dispersion of the hosting spheroids should be significantly smaller than that at the present epoch.
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Galaxy scaling relations, which describe a connection between ostensibly unrelated physical characteristics of galaxies, testify to an underlying order in galaxy formation that requires understanding. I review the development of a scaling relation that 1) unites the well-known Fundamental Plane (FP) relation of giant elliptical galaxies and Tully-Fisher (TF) relation of disk galaxies, 2) fits low mass spheroidal galaxies, including the ultra-faint satellites of our Galaxy, 3) explains the apparent shift of lenticular (S0) galaxies relative to both FP or TF, 3) describes all stellar dynamical systems, including systems with no dark matter (stellar clusters), 4) associates explicitly the numerical coefficients that account for the apparent tilt of the FP away from the direct expectation drawn from the virial theorem with systematic variations in the total mass-to-light ratio of galaxies within the half-light radius, 5) connects with independent results that demonstrate the robustness of mass estimators when applied at the half-light radius, and 6) results in smaller scatter for disk galaxies than the TF relation. The relation develops naturally from the virial theorem, but implies the existence of additional galaxy formation physics that must now be a focus of galaxy formation studies. More pragmatically, the relation provides a lynchpin that can be used to measure distances and galaxy masses. I review two applications: 1) the cross-calibration of distance measurement methods, and 2) the determination of mass-to-light ratios of simple stellar populations as a function of age, and implications of the latter for the stellar initial mass function.
Surface brightness fluctuation
Peculiar galaxy
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In this thesis we focused on the determination of the mass (MBH) of supermassive black hole (SMBHs) and on the interpretation of their demography. We studied their scaling relations with the aim of understanding the role of SMBHs in the evolution of galaxies.
This was done by increasing the demography of MBH and studying whether MBH results more closely linked to the bulge or to the global galaxy properties, including the dark matter halo.
In the first part of the thesis we focused on the presentation of a spectral and imaging atlas of a large and various sample of galaxies we studied to obtain upper limits on their MBH. The data were retrieved from Hubble Space Telescope (HST) archive (Chapter 2). This atlas comprises of 177 nearby galaxies (D < 100 Mpc) with nuclear spectra obtained with the Space Telescope Imaging Spectrograph (STIS) in the region of Halpha line and the [NII] and [SII] emission-line doublets. Structural parameters of bulge and disk derived from the two-dimensional bulge-to-disk decompositions of K-band 2MASS and UKIDSS images for 65 sample galaxies are presented, too.
We derived stringent upper bounds on the mass of the central SMBH for a sub-sample of 105 galaxies spanning a wide range of Hubble types (E-Sc) and values of the central stellar velocity dispersion, sigma (58-419 km/s).
These MBH upper limits were derived by modeling the widths of the observed emission lines in terms of gas motions in a thin disk of unknown orientation but known spatial extent.
The upper limits that we derived are consistent with both the MBH-sigma relation of Ferrarese & Ford (2005, Sp. Sci. Rev., 116, 523) and Lauer et al. (2007, ApJ, 670, 249) and with secure MBH determinations. Most important, independent of the galaxy distance, morphological type or bar presence, our MBH upper limits run parallel and above the previous two version of MBH-sigma relations.
This suggests that, although strictly speaking we cannot rule out the role of non-gravitational forces, our line-width measurements actually trace well the nuclear regions dominated by the central SMBH, which in practice allows us to estimate MBH (Chapter 3).
Yet, at small sigma some MBH upper limits systematically exceed the expected MBH, as the line-width measurements for such low-sigma outliers are most likely affected by the stellar contribution to the gravitational potential either due to the presence of conspicuous nuclear clusters or because of a greater distance compared to the other galaxies at the low-sigma end of the MBH-sigma relation.
Conversely, the MBH upper bounds appear to lie closer to the expected MBH in the most massive elliptical galaxies with values sigma>220 km/s. Such a flattening of the MBH-sigma relation at its high-sigma end would appear consistent with a coevolution of SMBHs and galaxies driven by dry mergers, although better and more consistent measurements for sigma and K-band luminosity are needed for these kinds of objects before systematic effects can be ruled out.
Following these results we focused on the interpretation of the demography of SMBHs, specifically in trying to understand whether the MBH relates more closely to the bulge or to the total mass of a galaxy (Chapter 4).
The large sample of upper limits on MBH and the latest compilation of secure MBH, coupled with libraries of host galaxy velocity dispersions, rotational velocities and photometric parameters extracted from SDSS i-band images were used to establish correlations between MBH and the properties of the bulge and of the host galaxy.
We tested the correlations between MBH and stellar velocity dispersion, i-band bulge luminosity, bulge virial mass, bulge Sersic index, total i-band luminosity of the galaxy, galaxy stellar mass, maximum circular velocity, and galaxy dynamical and virial masses.
The tightness of the MBH-sigma relation was derived, and it resulted that correlations with other galaxy parameters do not yield tighter trends. MBH is fundamentally driven by sigma for all Hubble types.
The fundamental plane of the SMBHs is mainly driven by sigma too, with a small fraction of the tilt being due to the effective radius.
We explored the high-mass end of the SMBH mass function to understand the link between the evolution of SMBHs and the hierarchical build-up of galaxies, by measuring MBH in the massive elliptical galaxy NGC1265 with adaptive-optics stellar observations (Chapter 5) and in three brightest cluster galaxies from the gaseous kinematics derived from HST data (Chapter 6). These works are important to understand the MBH distribution at high sigma, where different works found either a flattening or a steepening of the MBH-sigma relation.
We presented the K-band adaptive-optics assisted spectroscopic observations of the central region of the archetype head-tail radio galaxy NGC 1265/3C 83.1B with the aim of constraining the mass of its SMBH (Chapter 5). The near-infrared data taken with the Altair/NIRI on the Gemini North have a spatial resolution of FWHM = 0''.11 (39 pc).
To account for the stellar contribution, we performed a multi-Gaussian expansion by using a combination of our NIRI high-resolution K-band image and a TNG K'-band image to cover the outer parts of the galaxy.
We extracted the stellar kinematics by using the penalized pixel fitting method from the CO absorption bands at 2.29 microns. Jeans anisotropic models were adopted to fit the stellar kinematics and surface distribution to determine the best fitting value for anisotropy and MBH.
The limited quality of our kinematical data did not allow us to measure very extended kinematics. Hence, we resorted to assuming fixed values for both the (M/L)_K and the anisotropy, beta. The derived upper limit on MBH ranges between 1x 10e9 Msun and 3.45 x 10e9 Msun depending on the assumed values of beta and (M/L)_K, respectively.
This range of masses is consistent with the MBH-Lk relation of Marconi & Hunt (2003, ApJ, 589, L21).
We derived MBH in three brightest cluster galaxies (BCGs), Abell 1836-BCG, Abell 2052-BCG, and Abell 3565-BCG, by using observations with STIS, Wide Field and Planetary Camera 2 (WFPC2), and Advanced Camera for Surveys (ACS) on HST (Chapter 6).
The data provided detailed information on the structure and mass profile of the stellar component, dust optical depth, and spatial distribution and kinematics of the ionized gas within the innermost region of each galaxy. Dynamical models, which account for the observed stellar mass profile and include the contribution of a central SMBH were constructed to reproduce the kinematics derived from the [NII] emission line.
Secure SMBH detection with MBH = 3.61 (+0.41,-0.50) x 10e9 Msun and 1.34 (+021,-0.19) x 10e9 Msun, respectively, were obtained for Abell 1836-BCG and Abell 3565-BCG, which show regular rotation curves and strong central velocity gradients.
In the case of Abell 2052-BCG, the lack of an orderly rotational motion prevented a secure determination, although an upper limit of MBH < 4.60 x 10e9 Msun could be placed on the mass of the central black hole. These measurements are an important step forward in characterizing the high-mass end of the SMBH mass function.
In fact, the results suggest a steepening of the trend of the MBH-sigma relation in the high-sigma range, that suggest either a higher scatter or the necessity of a different law, which predicts a faster grow of the SMBH with respect to the sigma.
Finally, we estimated the mass of the SMBH of NGC 4278 by using the virial theorem and measuring the broad components of the emission lines observed in the STIS spectrum, assuming that the gas is uniformly distributed in a sphere of radius R. The MBH is found to be in the range between 7 x 10e7 and 2 x 10e9 Msun depending on the radius we obtained from simple estimation of the dimension of the broad line region (Chapter 7). This is in agreement with previous findings based on different assumptions about the gas distribution.
The nucleus of NGC 4278 hosts a barely resolved but strongly variable UV source. Its UV luminosity increased by a factor of 1.6 in a period of 6 months. The amplitude and scale time of this UV flare are remarkably similar to those of the brightest UV nuclear transients which were earlier found in other low-luminosity AGNs.
This ultraviolet variability represents the typical signatures of the low-luminosity active galactic nuclei.
The main conclusions of this thesis can be summarized as follows.
1) We could map the MBH-sigma relation from the lower to the upper end of the local SMBH population by using simple estimates of MBH but for the largest and most various sample of host galaxies.
These MBH estimates are consistent with the known MBH-sigma relation, with no dependence on galaxy distance, morphological type or bar presence. They can be adopted to study the trend and scatter of the other MBH scaling relations.
2) Following the results of this work we focused on the interpretation of the demography of SMBHs, specifically in trying to understand whether the MBH relates more closely to the mass of the bulge or to the total mass of the host galaxy, included dark matter. We confirmed that MBH is fundamentally driven by sigma for all Hubble types. The same is true for the fundamental plane of SMBHs.
3) We explored the high-mass end of the SMBH mass function to understand the link between the evolution of SMBHs and the hierarchical build-up of galaxies, by analyzing adaptive-optics stellar observations of the central regions of massive elliptical galaxies such us NGC 1265 and estimating MBH in three brightest cluster galaxies by measuring the gaseous kinematics with HST. The first results indicates a steepening of the trend of the MBH-sigma relation in the high-sigma range, that suggests either a higher scatter or the necessity of a different law, which predicts a faster grow of the SMBH with respect to sigma.
Dynamics
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Recent studies have found a dramatic difference between the observed number density evolution of low-mass galaxies and that predicted by semi-analytic models. Whilst models accurately reproduce the z = 0 number density, they require that the evolution occurs rapidly at early times, which is incompatible with the strong late evolution found in observational results. We report here the same discrepancy in two state-of-the-art cosmological hydrodynamical simulations, which is evidence that the problem is fundamental. We search for the underlying cause of this problem using two complementary methods. First, we consider a narrow range in stellar mass of log (Mstar/(h−2 M⊙)) = 9–9.5 and look for evidence of a different history of today's low-mass galaxies in models and observations. We find that the exclusion of satellite galaxies from the analysis brings the median ages and star formation rates of galaxies into reasonable agreement. However, the models yield too few young, strongly star-forming galaxies. Secondly, we construct a toy model to link the observed evolution of specific star formation rates with the evolution of the galaxy stellar mass function. We infer from this model that a key problem in both semi-analytic and hydrodynamical models is the presence of a positive instead of a negative correlation between specific star formation rate and stellar mass. A similar positive correlation is found between the specific dark matter halo accretion rate and the halo mass, indicating that model galaxies are growing in a way that follows the growth of their host haloes too closely. It therefore appears necessary to find a mechanism that decouples the growth of low-mass galaxies, which occurs primarily at late times, from the growth of their host haloes, which occurs primarily at early times. We argue that the current form of star formation-driven feedback implemented in most galaxy formation models is unlikely to achieve this goal, owing to its fundamental dependence on host halo mass and time.
Stellar mass
Halo mass function
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