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A. Beifiori

Publications and source records attributed to A. Beifiori.

At least 19 recordsLinked to original sources

The KMOS$^{\rm 3D}$ Survey: Investigating the Origin of the Elevated Electron Densities in Star-Forming Galaxies at $1\lesssim{z}\lesssim{3}$

We investigate what drives the redshift evolution of the typical electron density ($n_e$) in star-forming galaxies, using a sample of 140 galaxies drawn primarily from KMOS$^{\rm 3D}$ ($0.6\lesssim{z}\lesssim{2.6}$) and 471 galaxies from SAMI ($z<0.113$). We select galaxies that do not show evidence of AGN activity or outflows, to constrain the average conditions within H II regions. Measurements of the [SII]$λ$6716/[SII]$λ$6731 ratio in four redshift bins indicate that the local $n_e$ in the line-emitting material decreases from 187$^{+140}_{-132}$ cm$^{-3}$ at $z\sim$ 2.2 to 32$^{+4}_{-9}$ cm$^{-3}$ at $z\sim$ 0; consistent with previous results. We use the H$α$ luminosity to estimate the root-mean-square (rms) $n_e$ averaged over the volumes of star-forming disks at each redshift. The local and volume-averaged $n_e$ evolve at similar rates, hinting that the volume filling factor of the line-emitting gas may be approximately constant across $0\lesssim{z}\lesssim{2.6}$. The KMOS$^{\rm 3D}$ and SAMI galaxies follow a roughly monotonic trend between $n_e$ and star formation rate, but the KMOS$^{\rm 3D}$ galaxies have systematically higher $n_e$ than the SAMI galaxies at fixed offset from the star-forming main sequence, suggesting a link between the $n_e$ evolution and the evolving main sequence normalization. We quantitatively test potential drivers of the density evolution and find that $n_e$(rms) $\simeq{n_{H_2}}$, suggesting that the elevated $n_e$ in high-$z$ H II regions could plausibly be the direct result of higher densities in the parent molecular clouds. There is also tentative evidence that $n_e$ could be influenced by the balance between stellar feedback, which drives the expansion of H II regions, and the ambient pressure, which resists their expansion.

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The regulation of galaxy growth along the size-mass relation by star-formation, as traced by H$α$ in KMOS$^{3D}$ galaxies at 0.7 < z < 2.7

We present half-light sizes measured from H$α$ emission tracing star-formation in 281 star-forming galaxies from the KMOS3D survey at 0.7 < z < 2.7. Sizes are derived by fitting 2D exponential disk models, with bootstrap errors averaging 20%. H$α$ sizes are a median (mean) of 1.19 (1.26) times larger than those of the stellar continuum, which due to radial dust gradients places an upper limit on the growth in stellar size via star formation, with just 43% intrinsic scatter. At fixed continuum size the H$α$ size shows no residual trend with stellar mass, star formation rate, redshift or morphology. The only significant residual trend is with the excess obscuration of H$α$ by dust, at fixed continuum obscuration. The scatter in continuum size at fixed stellar mass is likely driven by the scatter in halo spin parameters. The stability of the ratio of H$α$ size to continuum size demonstrates a high degree of stability in halo spin and in the transfer of angular momentum to the disk over a wide range of physical conditions and cosmic time. This may require local regulation by feedback processes. The implication of our results, as we demonstrate using a toy model, is that our upper limit on star-formation driven growth is sufficient only to evolve star-forming galaxies approximately along the observed size-mass relation, consistent with the size growth of galaxies at constant cumulative co-moving number density. To explain the observed evolution of the size-mass relation of star-forming disk galaxies other processes, such as the preferential quenching of compact galaxies or galaxy mergers, may be required.

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The KMOS^3D Survey: data release and final survey paper

We present the completed KMOS$^\mathrm{3D}$ survey $-$ an integral field spectroscopic survey of 739, $\log(M_{\star}/M_{\odot})>9$, galaxies at $0.6 10.5$). We confirm our first year results of a high rotation dominated fraction (monotonic velocity gradient and $v_\mathrm{rot}$/$σ_0 > \sqrt{3.36}$) of 77% for the full KMOS$^\mathrm{3D}$ H$α$sample. The rotation-dominated fraction is a function of both stellar mass and redshift with the strongest evolution measured over the redshift range of the survey for galaxies with $\log(M_{\star}/M_{\odot})<10.5$. With this paper we include a final data release of all 739 observed objects.

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The KMOS^3D Survey: Demographics and Properties of Galactic Outflows at z = 0.6 - 2.7

We present a census of ionized gas outflows in 599 normal galaxies at redshift 0.6 11.2 galaxies. The incidence, strength, and velocity of AGN-driven winds strongly correlates with stellar mass and central concentration. Their outflowing ionized gas appears denser (n_e~1000 cm^-3), and possibly compressed and shock-excited. These winds have comparable mass loading factors as the SF-driven winds but carry ~10 (~50) times more momentum (energy). The results confirm our previous findings of high duty cycle, energy-driven outflows powered by AGN above the Schechter mass, which may contribute to star formation quenching.

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The KMOS$^\mathrm{3D}$ Survey: rotating compact star forming galaxies and the decomposition of integrated line widths

Using integral field spectroscopy we investigate the kinematic properties of 35 massive centrally-dense and compact star-forming galaxies (${\log{\overline{M}_*}}=11.1$, $\log{(Σ_\mathrm{1kpc})}>9.5$, $\log{(M_\ast/r_e^{1.5})}>10.3$) at $z\sim0.7-3.7$ within the KMOS$^\mathrm{3D}$survey. We spatially resolve 23 compact star-forming galaxies (SFGs) and find that the majority are dominated by rotational motions with velocities ranging from {$95-500$ km s$^{-1}$}. The range of rotation velocities is reflected in a similar range of integrated H$α$ linewidths, $75-400$ km s$^{-1}$, consistent with the kinematic properties of mass-matched extended galaxies from the full KMOS$^\mathrm{3D}$ sample. The fraction of compact SFGs that are classified as `rotation-dominated' or `disk-like' also mirrors the fractions of the full KMOS$^\mathrm{3D}$ sample. We show that integrated line-of-sight gas velocity dispersions from KMOS$^\mathrm{3D}$ are best approximated by a linear combination of their rotation and turbulent velocities with a lesser but still significant contribution from galactic scale winds. The H$α$ exponential disk sizes of compact SFGs are on average $2.5\pm0.2$ kpc, $1-2\times$ the continuum sizes, in agreement with previous work. The compact SFGs have a $1.4\times$ higher AGN incidence than the full KMOS$^\mathrm{3D}$ sample at fixed stellar mass with average AGN fraction of 76\%. Given their high and centrally concentrated stellar masses as well as stellar to dynamical mass ratios close to unity, the compact SFGs are likely to have low molecular gas fractions and to quench on a short time scale unless replenished with inflowing gas. The rotation in these compact systems suggests that their direct descendants are rotating passive galaxies.

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Stringent limits on the masses of the supermassive black holes in seven nearby galaxies

We present new stringent limits on the mass $M_{bh}$ of the central supermassive black hole for a sample of 7 nearby galaxies. Our $M_{bh}$ estimates are based on the dynamical modeling of the central width of the nebular emission lines measured over subarcsecond apertures with the Hubble Space Telescope. The central stellar velocity dispersion $σ_c$ of the sample galaxies is derived from new long-slit spectra from ground-based observations and the bulge effective radius is obtained from a two-dimensional photometric decomposition of the i-band images from the Sloan Digital Sky Survey. The derived stringent $M_{bh}$ limits run parallel and above the $M_{bh}-σ_c$ relation with no systematic trend depending on the galaxy distance or morphology. This gives further support to previous findings suggesting that the nuclear gravitational potential is remarkably well traced by the width of the nebular lines when the gas is centrally peaked. With our investigation, the number of galaxies with stringent $M_{bh}$ limits obtained from nebular-line width increases to 114 and can be used for studying the scaling relations between $M_{bh}$ and properties of their host galaxies.

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The evolution of the Tully-Fisher relation between z~2.3 and z~0.9 with KMOS^3D

We investigate the stellar mass and baryonic mass Tully-Fisher relations (TFRs) of massive star-forming disk galaxies at redshift z~2.3 and z~0.9 as part of the KMOS^3D integral field spectroscopy survey. Our spatially resolved data allow reliable modelling of individual galaxies, including the effect of pressure support on the inferred gravitational potential. At fixed circular velocity, we find higher baryonic masses and similar stellar masses at z~2.3 as compared to z~0.9. Together with the decreasing gas-to-stellar mass ratios with decreasing redshift, this implies that the contribution of dark matter to the dynamical mass at the galaxy scale increases towards lower redshift. A comparison to local relations reveals a negative evolution of the stellar and baryonic TFR zero-points from z=0 to z~0.9, no evolution of the stellar TFR zero-point from z~0.9 to z~2.3, and a positive evolution of the baryonic TFR zero-point from z~0.9 to z~2.3. We discuss a toy model of disk galaxy evolution to explain the observed, non-monotonic TFR evolution, taking into account the empirically motivated redshift dependencies of galactic gas fractions, and of the relative amount of baryons to dark matter on galaxy and halo scales.

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Falling outer rotation curves of star-forming galaxies at 0.6 < z < 2.6 probed with KMOS^3D and SINS/ZC-SINF

We exploit the deep resolved Halpha kinematic data from the KMOS^3D and SINS/zC-SINF surveys to examine the largely unexplored outer disk kinematics of star-forming galaxies (SFGs) out to the peak of cosmic star formation. Our sample contains 101 SFGs representative of the more massive (9.3 < log(M*/Msun) < 11.5) main sequence population at 0.6 ~0.05) in combination with a sizeable level of pressure support in the outer disk. These findings are in agreement with recent studies demonstrating that star-forming disks at high redshift are strongly baryon dominated within the disk scale, and furthermore suggest that pressure gradients caused by large turbulent gas motions are present even in their outer disks. We demonstrate that these results are largely independent of our model assumptions such as the presence of a central stellar bulge, the effect of adiabatic contraction at fixed m_d, and variations in the concentration parameter.

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Strongly baryon-dominated disk galaxies at the peak of galaxy formation ten billion years ago

In cold dark matter cosmology, the baryonic components of galaxies are thought to be mixed with and embedded in non-baryonic and non-relativistic dark matter, which dominates the total mass of the galaxy and its dark matter halo. In the local Universe, the mass of dark matter within a galactic disk increases with disk radius, becoming appreciable and then dominant in the outer, baryonic regions of the disks of star-forming galaxies. This results in rotation velocities of the visible matter within the disk that are constant or increasing with disk radius. Comparison between the dynamical mass and the sum of stellar and cold gas mass at the peak epoch of galaxy formation, inferred from ancillary data, suggest high baryon factions in the inner, star-forming regions of the disks. Although this implied baryon fraction may be larger than in the local Universe, the systematic uncertainties (stellar initial mass function, calibration of gas masses) render such comparisons inconclusive in terms of the mass of dark matter. Here we report rotation curves for the outer disks of six massive star-forming galaxies, and find that the rotation velocities are not constant, but decrease with radius. We propose that this trend arises because of two main factors: first, a large fraction of the massive, high-redshift galaxy population was strongly baryon dominated, with dark matter playing a smaller part than in the local Universe; and second, the large velocity dispersion in high-redshift disks introduces a substantial pressure term that leads to a decrease in rotation velocity with increasing radius. The effect of both factors appears to increase with redshift. Qualitatively, the observations suggest that baryons in the early Universe efficiently condensed at the centres of dark matter halos when gas fractions were high, and dark matter was less concentrated. [Abridged]

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Galaxy environment in the 3D-HST fields. Witnessing the onset of satellite quenching at z ~ 1-2

We make publicly available a catalog of calibrated environmental measures for galaxies in the five 3D-HST/CANDELS deep fields. Leveraging the spectroscopic and grism redshifts from the 3D-HST survey, multi wavelength photometry from CANDELS, and wider field public data for edge corrections, we derive densities in fixed apertures to characterize the environment of galaxies brighter than $JH_{140} < 24$ mag in the redshift range $0.5<z<3.0$. By linking observed galaxies to a mock sample, selected to reproduce the 3D-HST sample selection and redshift accuracy, each 3D-HST galaxy is assigned a probability density function of the host halo mass, and a probability that is a central or a satellite galaxy. The same procedure is applied to a $z=0$ sample selected from SDSS. We compute the fraction of passive central and satellite galaxies as a function of stellar and halo mass, and redshift, and then derive the fraction of galaxies that were quenched by environment specific processes. Using the mock sample, we estimate that the timescale for satellite quenching is $t_{\rm quench} \sim 2-5$ Gyr; longer at lower stellar mass or lower redshift, but remarkably independent of halo mass. This indicates that, in the range of environments commonly found within the 3D-HST sample, satellites are quenched by exhaustion of their gas reservoir in absence of cosmological accretion. We find that the quenching times can be separated into a delay phase during which satellite galaxies behave similarly to centrals at fixed stellar mass, and a phase where the star formation rate drops rapidly ($\sim 0.4-0.6$ Gyr), as shown previously at $z=0$. We conclude that this scenario requires satellite galaxies to retain a large reservoir of multi-phase gas upon accretion, even at high redshift, and that this gas sustains star formation for the long quenching times observed.

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KMOS^3D: Dynamical constraints on the mass budget in early star-forming disks

We exploit deep integral-field spectroscopic observations with KMOS/VLT of 240 star-forming disks at 0.6 < z < 2.6 to dynamically constrain their mass budget. Our sample consists of massive ($\gtrsim 10^{9.8} M_\odot$) galaxies with sizes $R_e \gtrsim 2$ kpc. By contrasting the observed velocity and dispersion profiles to dynamical models, we find that on average the stellar content contributes $32^{+8}_{-7}\%$ of the total dynamical mass, with a significant spread among galaxies (68th percentile range f_star ~ 18 - 62%). Including molecular gas as inferred from CO- and dust-based scaling relations, the estimated baryonic mass adds up to $56^{+17}_{-12}\%$ of total for the typical galaxy in our sample, reaching ~ 90% at z > 2. We conclude that baryons make up most of the mass within the disk regions of high-redshift star-forming disk galaxies, with typical disks at z > 2 being strongly baryon-dominated within $R_e$. Substantial object-to-object variations in both stellar and baryonic mass fractions are observed among the galaxies in our sample, larger than what can be accounted for by the formal uncertainties in their respective measurements. In both cases, the mass fractions correlate most strongly with measures of surface density. High $Σ_{star}$ galaxies feature stellar mass fractions closer to unity, and systems with high inferred gas or baryonic surface densities leave less room for additional mass components other than stars and molecular gas. Our findings can be interpreted as more extended disks probing further (and more compact disks probing less far) into the dark matter halos that host them.

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The angular momentum distribution and baryon content of star forming galaxies at z~1-3

We analyze the angular momenta of massive star forming galaxies (SFGs) at the peak of the cosmic star formation epoch (z~0.8-2.6). Our sample of ~360 log(M*/Msun) ~ 9.3-11.8 SFGs is mainly based on the KMOS3D and SINS/zC-SINF surveys of H$α$ kinematics, and collectively provides a representative subset of the massive star forming population. The inferred halo scale angular momentum distribution is broadly consistent with that theoretically predicted for their dark matter halos, in terms of mean spin parameter <$λ$> ~ 0.037 and its dispersion ($σ_{log(λ)}$~0.2). Spin parameters correlate with the disk radial scale, and with their stellar surface density, but do not depend significantly on halo mass, stellar mass, or redshift. Our data thus support the long-standing assumption that on average, even at high redshifts, the specific angular momentum of disk galaxies reflects that of their dark matter halos (j_d = j_DM). The lack of correlation between $λ$ x (j_d/j_DM) and the nuclear stellar density $Σ_{*}$(1kpc) favors a scenario where disk-internal angular momentum redistribution leads to "compaction" inside massive high-redshift disks. For our sample, the inferred average stellar-to-dark matter mass ratio is ~2%, consistent with abundance matching results. Including the molecular gas, the total baryonic disk-to-dark matter mass ratio is ~5% for halos near $10^{12}$ Msun, which corresponds to 31% of the cosmologically available baryons, implying that high-redshift disks are strongly baryon dominated.

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The SINFONI Black Hole Survey: The Black Hole Fundamental Plane revisited and the paths of (co-) evolution of supermassive black holes and bulges

We investigate the correlations between the black hole mass $M_{BH}$, the velocity dispersion $σ$, the bulge mass $M_{Bu}$, the bulge average spherical density $ρ_h$ and its spherical half mass radius $r_h$, constructing a database of 97 galaxies (31 core ellipticals, 17 power-law ellipticals, 30 classical bulges, 19 pseudo bulges) by joining 72 galaxies from the literature to 25 galaxies observed during our recent SINFONI black hole survey. For the first time we discuss the full error covariance matrix. We analyse the well known $M_{BH}-σ$ and $M_{BH}-M_{Bu}$ relations and establish the existence of statistically significant correlations between $M_{Bu}$ and $r_h$ and anti-correlations between $M_{Bu}$ and $ρ_h$. We establish five significant bivariate correlations ($M_{BH}-σ-ρ_h$, $M_{BH}-σ-r_h$, $M_{BH}-M_{Bu}-σ$, $M_{BH}-M_{Bu}-ρ_h$, $M_{BH}-M_{Bu}-r_h$) that predict $M_{BH}$ of 77 core and power-law ellipticals and classical bulges with measured and intrinsic scatter as small as $\approx 0.36$ dex and $\approx 0.33$ dex respectively, or 0.26 dex when the subsample of 45 galaxies defined by Kormendy and Ho (2013) is considered. In contrast, pseudo bulges have systematically lower $M_{BH}$, but approach the predictions of all the above relations at spherical densities $ρ_h\ge 10^{10} M_\odot/kpc^3$ or scale lengths $r_h\le 1$ kpc. These findings fit in a scenario of co-evolution of BH and classical-bulge masses, where core ellipticals are the product of dry mergers of power-law bulges and power-law Es and bulges the result of (early) gas-rich mergers and of disk galaxies. In contrast, the (secular) growth of BHs is decoupled from the growth of their pseudo bulge hosts, except when (gas) densities are high enough to trigger the feedback mechanism responsible for the existence of the correlations between $M_{BH}$ and galaxy structural parameters.

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The KMOS^3D Survey: design, first results, and the evolution of galaxy kinematics from 0.7<z<2.7

We present the KMOS^3D survey, a new integral field survey of over 600 galaxies at 0.7 1$, implying that the star-forming 'main sequence' (MS) is primarily composed of rotating galaxies at both redshift regimes. When considering additional stricter criteria, the Halpha kinematic maps indicate at least ~70% of the resolved galaxies are disk-like systems. Our high-quality KMOS data confirm the elevated velocity dispersions reported in previous IFS studies at z>0.7. For rotation-dominated disks, the average intrinsic velocity dispersion decreases by a factor of two from 50 km/s at z~2.3 to 25 km/s at z~0.9 while the rotational velocities at the two redshifts are comparable. Combined with existing results spanning z~0-3, disk velocity dispersions follow an approximate (1+z) evolution that is consistent with the dependence of velocity dispersion on gas fractions predicted by marginally-stable disk theory.

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Evidence for Wide-Spread AGN Driven Outflows in the Most Massive z~1-2 Star Forming Galaxies

In this paper we follow up on our previous detection of nuclear ionized outflows in the most massive (log(M*/Msun) >= 10.9) z~1-3 star-forming galaxies (Forster Schreiber et al.), by increasing the sample size by a factor of six (to 44 galaxies above log(M*/Msun) >= 10.9) from a combination of the SINS/zC-SINF, LUCI, GNIRS, and KMOS^3D spectroscopic surveys. We find a fairly sharp onset of the incidence of broad nuclear emission (FWHM in the Ha, [NII], and [SII] lines ~ 450-5300 km/s), with large [NII]/Ha ratios, above log(M*/Msun) ~ 10.9, with about two thirds of the galaxies in this mass range exhibiting this component. Broad nuclear components near and above the Schechter mass are similarly prevalent above and below the main sequence of star-forming galaxies, and at z~1 and ~2. The line ratios of the nuclear component are fit by excitation from active galactic nuclei (AGN), or by a combination of shocks and photoionization. The incidence of the most massive galaxies with broad nuclear components is at least as large as that of AGNs identified by X-ray, optical, infrared or radio indicators. The mass loading of the nuclear outflows is near unity. Our findings provide compelling evidence for powerful, high-duty cycle, AGN-driven outflows near the Schechter mass, and acting across the peak of cosmic galaxy formation.

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Stellar velocity dispersions and emission line properties of SDSS-III/BOSS galaxies

We perform a spectroscopic analysis of 492,450 galaxy spectra from the first two years of observations of the Sloan Digital Sky Survey-III/Baryonic Oscillation Spectroscopic Survey (BOSS) collaboration. This data set has been released in the ninth SDSS data release, the first public data release of BOSS spectra. We show that the typical signal-to-noise ratio of BOSS spectra is sufficient to measure stellar velocity dispersion and emission line fluxes for individual objects. The typical velocity dispersion of a BOSS galaxy is 240 km/s, with an accuracy of better than 30 per cent for 93 per cent of BOSS galaxies. The distribution in velocity dispersion is redshift independent between redshifts 0.15 and 0.7, which reflects the survey design targeting massive galaxies with an approximately uniform mass distribution in this redshift interval. The majority of BOSS galaxies lack detectable emission lines. We analyse the emission line properties and present diagnostic diagrams using the emission lines [OII], Hbeta, [OIII], Halpha, and [NII] (detected in about 4 per cent of the galaxies). We show that the emission line properties are strongly redshift dependent and that there is a clear correlation between observed frame colours and emission line properties. Within in the low-z sample around 0.15<z<0.3, half of the emission-line galaxies have LINER-like emission line ratios, followed by Seyfert-AGN dominated spectra, and only a small fraction of a few per cent are purely star forming galaxies. AGN and LINER-like objects, instead, are less prevalent in the high-z sample around 0.4<z<0.7, where more than half of the emission line objects are star forming. This is a pure selection effect caused by the non-detection of weak Hbeta emission lines in the BOSS spectra. Finally, we show that star forming, AGN and emission line free galaxies are well separated in the g-r vs r-i target selection diagram.

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Polar bulges and polar nuclear discs: the case of NGC 4698

The early-type spiral NGC 4698 is known to host a nuclear disc of gas and stars which is rotating perpendicularly with respect to the galaxy main disc. In addition, the bulge and main disc are characterised by a remarkable geometrical decoupling. Indeed they appear elongated orthogonally to each other. In this work the complex structure of the galaxy is investigated by a detailed photometric decomposition of optical and near-infrared images. The intrinsic shape of the bulge was constrained from its apparent ellipticity, its twist angle with respect to the major axis of the main disc, and the inclination of the main disc. The bulge is actually elongated perpendicular to the main disc and it is equally likely to be triaxial or axisymmetric. The central surface brightness, scalelength, inclination, and position angle of the nuclear disc were derived by assuming it is infinitesimally thin and exponential. Its size, orientation, and location do not depend on the observed passband. These findings support a scenario in which the nuclear disc is the end result of the acquisition of external gas by the pre-existing triaxial bulge on the principal plane perpendicular to its shortest axis and perpendicular to the galaxy main disc. The subsequent star formation either occurred homogeneously all over the extension of the nuclear disc or through an inside-out process that ended more than 5 Gyr ago.

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On the Correlations between Galaxy Properties and Supermassive Black Hole Mass

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)

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