BH-sigma Relation Research Articles

THE INFLUENCE OF DARK MATTER HALOS ON DYNAMICAL ESTIMATES OF BLACK HOLE MASS: 10 NEW MEASUREMENTS FOR HIGH-σ EARLY-TYPE GALAXIES

Adaptive-Optics assisted SINFONI observations of the central regions of ten early-type galaxies are presented. Based primarily on the SINFONI kinematics, ten black hole masses occupying the high-mass regime of the M_BH-sigma relation are derived using three-integral Schwarzschild models. The effect of dark matter inclusion on the black hole mass is explored. The omission of a dark matter halo in the model results in a higher stellar mass-to-light ratio, especially when extensive kinematic data are used in the model. However, when the diameter of the sphere of influence -- computed using the black hole mass derived without a dark halo -- is at least 10 times the PSF FWHM during the observations, it is safe to exclude a dark matter component in the dynamical modeling, i.e. the change in black hole mass is negligible. When the spatial resolution is marginal, restricting the mass-to-light ratio to the right value returns the correct M_BH although dark halo is not present in the model. Compared to the M_BH-sigma and M_BH-L relations of McConnell et al. (2011), the ten black holes are all more massive than expected from the luminosities and seven black hole masses are higher than expected from the stellar velocity dispersions of the host bulges. Using new fitted relations which include the ten galaxies, we find that the space density of the most massive black holes (M_BH >~ 10^9 Msun) estimated from the M_BH-L relation is higher than the estimate based on the M_BH-sigma relation and the latter is higher than model predictions based on quasar counts, each by about an order of magnitude.

STELLAR VELOCITY DISPERSION MEASUREMENTS IN HIGH-LUMINOSITY QUASAR HOSTS AND IMPLICATIONS FOR THE AGN BLACK HOLE MASS SCALE

We present new stellar velocity dispersion measurements for four luminous quasars with the NIFS instrument and the ALTAIR laser guide star adaptive optics system on the Gemini North 8-m telescope. Stellar velocity dispersion measurements and measurements of the supermassive black hole masses in luminous quasars are necessary to investigate the coevolution of black holes and galaxies, trace the details of accretion, and probe the nature of feedback. We find that higher-luminosity quasars with higher-mass black holes are not offset with respect to the MBH-sigma relation exhibited by lower-luminosity AGNs with lower-mass black holes, nor do we see correlations with galaxy morphology. As part of this analysis, we have recalculated the virial products for the entire sample of reverberation-mapped AGNs and used these data to redetermine the mean virial factor hfi that places the reverberation data on the quiescent M_BH-sigma relation. With our updated measurements and new additions to the AGN sample, we obtain <f> = 4.31 +/- 1.05, which is slightly lower than, but consistent with, most previous determinations.

Black hole wind speeds and the M − σ relation

We derive an M_bh-sigma relation between supermassive black hole mass and stellar velocity dispersion in galaxy bulges, that results from self-regulated, energy-conserving feedback. The relation is of the form M_bh v_w \propto sigma^5, where v_w is the velocity of the wind driven by the black hole. We take a sample of quiescent early-type galaxies and bulges with measured black hole masses and velocity dispersions and use our model to infer the wind speeds they would have had during an active phase. This approach, in effect, translates the scatter in the observed M_bh-sigma relation into a distribution of v_w. There are some remarkable similarities between the distribution of black hole wind speeds that we obtain and the distributions of outflow speeds observed in local AGN, including a comparable median of v_w = 0.035 c.

MASSIVE BLACK HOLES IN CENTRAL CLUSTER GALAXIES

We explore how the co-evolution of massive black holes (MBHs) and galaxies is affected by environmental effects, addressing in particular MBHs hosted in the central galaxies of clusters (we will refer to these galaxies in general as 'CGs'). Recently the sample of MBHs in CGs with dynamically measured masses has increased, and it has been suggested that these MBH masses (M_BH) deviate from the expected correlations with velocity dispersion (sigma) and mass of the bulge (M_bulge) of the host galaxy: MBHs in CGs appear to be `over-massive'. This discrepancy is more pronounced when considering the M_BH-sigma relation than the M_BH-M_bulge one. We show that this behavior stems from a combination of two natural factors, (i) that CGs experience more mergers involving spheroidal galaxies and their MBHs, and (ii) that such mergers are preferentially gas-poor. We use a combination of analytical and semi-analytical models to investigate the MBH-galaxy co-evolution in different environments and find that the combination of these two factors explains the trends observed in current data-sets.

DISK ASSEMBLY AND THEMBH-σeRELATION OF SUPERMASSIVE BLACK HOLES

Recent Hubble Space Telescope (HST) observations have revealed that a majority of active galactic nuclei (AGN) at z ~ 1-3 are resident in isolated disk galaxies, contrary to the usual expectation that AGN are triggered by mergers. Here we develop a new test of the cosmic evolution of supermassive black holes (SMBHs) in disk galaxies by considering the local population of SMBHs. We show that substantial SMBH growth in spiral galaxies is required as disks assemble. SMBHs exhibit a tight relation between their mass and the velocity dispersion of the spheroid within which they reside, the M_BH-sigma relation. In disk galaxies the bulge is the spheroid of interest. We explore the evolution of the M_BH-sigma relation when bulges form together with SMBHs on the M_BH-sigma relation and then slowly reform a disk around them. The formation of the disk compresses the bulge raising its sigma. We present evidence for such compression in the form of larger velocity dispersion of classical bulges compared with elliptical galaxies at the same mass. This compression leads to an offset in the M_BH-sigma relation if it is not accompanied by an increased M_BH. We quantify the expected offset based on photometric data and show that, on average, SMBHs must grow by ~ 50-65% just to remain on the M_BH-sigma relation. We find no significant offset in the M_BH-sigma relations of classical bulges and of ellipticals, implying that SMBHs have been growing along with disks. Our simulations demonstrate that SMBH growth is necessary for the local population of disk galaxies to have remained on the M_BH-sigma relation.

FORCE-FEEDING BLACK HOLES

We propose that the growth of supermassive black holes is associated mainly with brief episodes of highly super-Eddington infall of gas ("hyperaccretion"). This gas is not swallowed in real time, but forms an envelope of matter around the black hole that can be swallowed gradually, over a much longer timescale. However, only a small fraction of the black hole mass can be stored in the envelope at any one time. We argue that any infalling matter above a few per cent of the hole's mass is ejected as a result of the plunge in opacity at temperatures below a few thousand degrees K, corresponding to the Hayashi track. The speed of ejection of this matter, compared to the velocity dispersion (sigma) of the host galaxy's core, determines whether the ejected matter is lost forever or returns eventually to rejoin the envelope, from which it can be ultimately accreted. The threshold between matter recycling and permanent loss defines a relationship between the maximum black hole mass and sigma that resembles the empirical M_BH-sigma relation.

BREAKING THE LAW: THEMbh-MspheroidRELATIONS FOR CORE-SÉRSIC AND SÉRSIC GALAXIES

The popular log-linear relation between supermassive black hole mass, M_bh, and the dynamical mass of the host spheroid, M_sph, is shown to require a significant correction. Core galaxies, typically with M_bh > 2x10^8 M_Sun and thought to be formed in dry merger events, are shown to be well described by a linear relation for which the median black hole mass is 0.36% - roughly double the old value of constancy. Of greater significance is that M_bh ~ (M_sph)^2 among the (non-pseudobulge) lower-mass systems: specifically, log[M_bh/M_Sun] = (1.92+/-0.38)log[M_sph/7x10^{10}M_Sun] + (8.38+/-0.17). `Classical' spheroids hosting a 10^6 M_Sun black hole will have M_bh/M_sph ~ 0.025%. These new relations (i) bring consistency to the relation M_bh ~ sigma^5 and the fact that L ~ sigma^x with exponent x equal to 5 and 2 for bright (M_B < -20.5 mag) and faint spheroids, respectively, (ii) mimic the non-(log-linear) behavior in the M_bh-(Sersic n) diagram, (iii) necessitate the existence of a previously over-looked M_bh ~ L^{2.5} relation for Sersic (i.e.\ not core-Sersic) galaxies, and (iv) resolve past conflicts (in mass prediction) with the M_bh-sigma relation at the low-mass end. Furthermore, the bent nature of the M_bh-M_sph relation for `classical' spheroids will have a host of important implications that relate to (i) galaxy/black hole formation theories, (ii) searches for the fundamental black hole scaling relation, (iii) black hole mass predictions in other galaxies, (iv) alleged pseudobulge detections, (v) estimates of the black hole mass function and mass density based on luminosity functions, (vi) predictions for space-based gravitational wave detections, (vii) connections with nuclear star cluster scaling relations, (viii) evolutionary studies over different cosmic epochs, (ix) comparisons and calibrations matching inactive black hole masses with low-mass AGN data, and more.

MERGERS IN DOUBLE-PEAKED [O III] ACTIVE GALACTIC NUCLEI

As a natural consequence of galaxy mergers, binary active galactic nuclei (AGNs) should be commonplace. Nevertheless, observational confirmations are rare, especially for binaries with separations less than ten kpc. Such a system may show two sets of narrow emission lines in a single spectrum owing to the orbital motion of the binary. We have obtained high-resolution near-infrared images of 50 double-peaked [O III] 5007 AGNs with the Keck II laser guide star adaptive optics system. The Sloan Digital Sky Survey sample is compiled from the literature and consists of 17 type-1 AGNs between 0.18 < z < 0.56 and 33 type-2 AGNs between 0.03 < z < 0.24. The new images reveal eight type-1 and eight type-2 sources that are apparently undergoing mergers. These are strong candidates of kpc-scale binary AGNs, because they show multiple components separated between 0.6 and 12 kpc and often disturbed morphologies. Because most of the type-1s are at higher redshifts than the type-2s, the higher merger fraction of type-1s (47+/-20%) compared to that of type-2s (24+/-10%) can be attributed to the general evolution of galaxy merger fraction with redshift. Furthermore, we show that AGN mergers are outliers of the M_BH-sigma relation because of over-estimated stellar velocity dispersions, illustrating the importance of removing mergers from the samples defining the M_BH-sigma relations. Finally, we find that the emission-line properties are indistinguishable for spatially resolved and unresolved sources, emphasizing that scenarios involving a single AGN can produce the same double-peaked line profiles and they account for at least 70% of the double-peaked [O III] AGNs.

An expanded Mbh-σ diagram, and a new calibration of active galactic nuclei masses

[Abridged] We present an updated and improved M_bh-sigma diagram containing 64 galaxies for which M_bh measurements (not just upper limits) are available. Due to new and increased black hole masses at the high-mass end, and a better representation of barred galaxies at the low-mass end, the "classical" (all morphological type) M_bh-sigma relation for predicting black hole masses is log(M_bh/M_Sun) = (5.13+/-0.34)log[sigma/200] + (8.13+/-0.05), with an rms scatter of 0.43 dex. Modifying the regression analysis to correct for a hitherto over-looked sample bias in which black holes with masses <10^6 M_Sun are not (yet) detectable, the relation steepens further to give log(M_bh/M_Sun) = (5.95+/-0.44)log[sigma/200] + (8.15+/-0.06). We have also updated the "barless" and "elliptical-only" M_bh-sigma relations introduced by Graham and Hu in 2008 due to the offset nature of barred/disc galaxies. These relations have a total scatter as low as 0.34 dex and currently define the upper envelope of points in the M_bh-sigma diagram. These relations also have a slope consistent with the value 5, in agreement with the prediction by Silk & Rees based on feedback from massive black holes in bulges built by monolithic-collapse. Using updated virial products and velocity dispersions from 28 active galactic nuclei, we determine that the optimal scaling factor f - which brings their virial products in line with the 64 directly measured black hole masses - is 2.8^{+0.7}_{-0.5}. This is roughly half the value reported by Onken et al. and Woo et al., and consequently halves the mass estimates of most high-redshift quasars. We have explored the results after separating the samples into barred and non-barred galaxies, and we have also developed a preliminary corrective term to the velocity dispersion based on bar dynamics.

The growth of massive black holes in galaxy merger simulations with feedback by radiation pressure

We study the growth of massive black holes (BH) in galaxies using smoothed particle hydrodynamic simulations of major galaxy mergers with new implementations of BH accretion and feedback. The effect of BH accretion on gas in its host galaxy is modeled by depositing momentum at a rate ~ tau L/c into the ambient gas, where L is the luminosity produced by accretion onto the BH and tau is the wavelength-averaged optical depth of the galactic nucleus to the AGN's radiation (a free parameter of our model). The accretion rate onto the BH is relatively independent of our subgrid accretion model and is instead determined by the BH's dynamical impact on its host galaxy: BH accretion is thus self-regulated rather than `supply limited.' We show that the final BH mass and total stellar mass formed during a merger are more robust predictions of the simulations than the time dependence of the star formation rate or BH accretion rate. In particular, the latter depend on the assumed interstellar medium physics, which determines when and where the gas fragments to form star clusters; this in turn affects the fuel available for further star formation and BH growth. Simulations over a factor of ~ 30 in galaxy mass are consistent with the observed M_BH-sigma relation for a mean optical depth of tau ~ 25. This requires that most BH growth occur when the galactic nucleus is optically thick to far-infrared radiation, consistent with the hypothesized connection between ultra-luminous infrared galaxies and quasars. We find tentative evidence for a shallower M_BH-sigma relation in the lowest mass galaxies, sigma < 100 km/s. Our results demonstrate that feedback-regulated BH growth and consistency with the observed M_BH-sigma relation do not require that BH feedback terminate star formation in massive galaxies or unbind large quantities of cold gas.

The central black hole mass of the high-σ but low-bulge-luminosity lenticular galaxy NGC 1332★

The masses of the most massive supermassive black holes (SMBHs) predicted by the M_BH-sigma and M_BH-luminosity relations appear to be in conflict. Which of the two relations is the more fundamental one remains an open question. NGC 1332 is an excellent example that represents the regime of conflict. It is a massive lenticular galaxy which has a bulge with a high velocity dispersion sigma of ~320 km/s; bulge--disc decomposition suggests that only 44% of the total light comes from the bulge. The M_BH-sigma and the M_BH-luminosity predictions for the central black hole mass of NGC 1332 differ by almost an order of magnitude. We present a stellar dynamical measurement of the SMBH mass using an axisymmetric orbit superposition method. Our SINFONI integral-field unit (IFU) observations of NGC 1332 resolve the SMBH's sphere of influence which has a diameter of ~0.76 arcsec. The sigma inside 0.2 arcsec reaches ~400 km/s. The IFU data allow us to increase the statistical significance of our results by modelling each of the four quadrants separately. We measure a SMBH mass of (1.45 \pm 0.20) x 10^9 M_sun with a bulge mass-to-light ratio of 7.08 \pm 0.39 in the R-band. With this mass, the SMBH of NGC 1332 is offset from the M_BH-luminosity relation by a full order of magnitude but is consistent with the M_BH-sigma relation.

A CORRELATION BETWEEN CENTRAL SUPERMASSIVE BLACK HOLES AND THE GLOBULAR CLUSTER SYSTEMS OF EARLY-TYPE GALAXIES

Elliptical, lenticular, and early-type spiral galaxies show a remarkably tight power-law correlation between the mass M_BH of their central supermassive black hole (SMBH) and the number N_GC of globular clusters: M_BH=m*N_GC^(1.08+/-0.04) with m=1.7*10^5 solar masses. Thus, to a good approximation the SMBH mass is the same as the total mass of the globular clusters. Based on a limited sample of 13 galaxies, this relation appears to be a better predictor of SMBH mass (rms scatter 0.2 dex) than the M_BH-sigma relation between SMBH mass and velocity dispersion sigma. The small scatter reflects the fact that galaxies with high globular cluster specific frequency S_N tend to harbor SMBHs that are more massive than expected from the M_BH-sigma relation.

Do black hole masses scale with classical bulge luminosities only? The case of the two composite pseudo-bulge galaxies NGC 3368 and NGC 3489★

It is now well established that all galaxies with a massive bulge component harbour a central supermassive black hole (SMBH). The mass of the SMBH correlates with bulge properties such as the bulge mass and the velocity dispersion, which implies that the bulge and the SMBH of a galaxy have grown together during the formation process. The spiral galaxy NGC3368 and the S0 galaxy NGC3489 both host a pseudobulge and a much smaller classical bulge component at the centre. We present high resolution, near-infrared IFU data of these two galaxies, taken with SINFONI at the VLT, and use axisymmetric orbit models to determine the masses of the SMBHs. The SMBH mass of NGC3368 is M_BH=7.5x10^6 M_sun with an error of 1.5x10^6 M_sun, which mostly comes from the non-axisymmetry in the data. For NGC3489, a solution without black hole cannot be excluded when modelling the SINFONI data alone, but can be clearly ruled out when modelling a combination of SINFONI, OASIS and SAURON data, for which we obtain M_BH=6.00^{+0.56}_{-0.54} (stat) +/- 0.64 (sys) x 10^6 M_sun. Although both galaxies seem to be consistent with the M_BH-sigma relation, at face value they do not agree with the relation between bulge magnitude and black hole mass when the total bulge magnitude (i.e., including both classical bulge and pseudobulge) is considered; the agreement is better when only the small classical bulge components are considered. However, taking into account the ageing of the stellar population could change this conclusion.

Near-infrared imaging and spectroscopy of the nuclear region of the disturbed Virgo cluster spiral NGC 4438â˜

We present near-infrared VLT ISAAC imaging and spectroscopy of the peculiar Virgo galaxy NGC 4438, whose nucleus has been classified as a LINER. The data are supplemented by mid-infrared imaging, and compared to previous WFPC2 HST broadband images. Images and position-velocity maps of the [Fe II] and H2 line emissions are presented and compared with the distribution of the optical narrow-line region and radio features. Our results show that shocks (possibly driven by a radio jet) contribute to an important fraction of the excitation of [Fe II], while X-ray heating from a central AGN may be responsible for the H2 excitation. We address the question whether the outflow has an AGN or a starburst origin by providing new estimates of the central star formation rate and the kinetic energy associated with the gas. By fitting a Sersic bulge, an exponential disc and a compact nuclear source to the light distribution, we decomposed NGC 4438's light distribution and found an unresolved nuclear source at 0.8 arcsec resolution with M_K = -18.7 and J-H = 0.69. Our measured bulge velocity dispersion, 142 km/s, together with the standard M_bh-sigma relation, suggests a central black hole mass of log(M_bh/Msun) ~ 7.0. The stellar kinematics measured from the near-infrared CO lines shows a strong peak in the velocity dispersion of 178 km/s in the central 0.5 arcsec, which is possible kinematic evidence of a central black hole. We calculated a general expression for the integrated Sersic profile flux density in elliptical geometry, including the case of 'disky' isophotes.

The growth of supermassive black holes in pseudo-bulges, classical bulges and elliptical galaxies

Using results from structural analysis of a sample of nearly 1000 local galaxies from the Sloan Digital Sky Survey, we estimate how the mass in central black holes is distributed amongst elliptical galaxies, classical bulges and pseudo-bulges, and investigate the relation between their stellar masses and central stellar velocity dispersion sigma. Assuming a single relation between elliptical galaxy/bulge mass, M_Bulge, and central black hole mass, M_BH, we find that 55^{+8}_{-4} per cent of the mass in black holes in the local universe is in the centres of elliptical galaxies, 41^{+4}_{-2} per cent in classical bulges and 4^{+0.9}_{-0.4} per cent in pseudo-bulges. We find that ellipticals, classical bulges and pseudo-bulges follow different relations between their stellar masses and sigma, and the most significant offset occurs for pseudo-bulges in barred galaxies. This structural dissimilarity leads to discrepant black hole masses if single M_BH-M_Bulge and M_BH-sigma relations are used. Adopting relations from the literature, we find that the M_BH-sigma relation yields an estimate of the total mass density in black holes that is roughly 55 per cent larger than if the M_BH-M_Bulge relation is used.

THEMbh-σ DIAGRAM AND THE OFFSET NATURE OF BARRED ACTIVE GALAXIES

From a sample of 50 predominantly inactive galaxies with direct supermassive black hole mass measurements, it has recently been established that barred galaxies tend to reside rightward of the M_bh-sigma relation defined by non-barred galaxies. Either black holes in barred galaxies tend to be anaemic or the central velocity dispersions in these galaxies have a tendency to be elevated by the presence of the bar. The latter option is in accord with studies connecting larger velocity dispersions in galaxies with old bars, while the former scenario is at odds with the observation that barred galaxies do not deviate from the M_bh-luminosity relation. Using a sample of 88 galaxies with active galactic nuclei, whose supermassive black hole masses have been estimated from their associated emission lines, we reveal for the first time that they also display this same general behavior in the M_bh-sigma diagram depending on the presence of a bar or not. A new symmetrical and non-symmetrical "barless" M_bh-sigma relation is derived using 82 non-barred galaxies. The barred galaxies are shown to reside on or up to ~1 dex below this relation. This may explain why narrow-line Seyfert 1 galaxies appear offset from the "barless" M_bh-sigma relation, and has far reaching implications given that over half of the disk galaxy population are barred.

THE EVOLUTION OF THEMBH-σ RELATION INFERRED FROM THE AGE DISTRIBUTION OF LOCAL EARLY-TYPE GALAXIES AND ACTIVE GALACTIC NUCLEI EVOLUTION

We utilize the local velocity dispersion function (VDF) of spheroids, together with their inferred age--distributions, to predict the VDF at higher redshifts (0<z<6), under the assumption that (i) most of the stars in each nearby spheroid formed in a single episode, and (ii) the velocity dispersion sigma remained nearly constant afterward. We assume further that a supermassive black hole (BH) forms concurrently with the stars, and within ~1 Gyr of the formation of the potential well of the spheroid, and that the relation between the mass of the BH and host velocity dispersion maintains the form M_BH ~ sigma^{beta} with beta~4, but with the normalization allowed to evolve with redshift as ~(1+z)^{alpha}. We compute the BH mass function associated with the VDF at each redshift, and compare the accumulated total BH mass density with that inferred from the integrated quasar luminosity function (LF; the so--called Soltan argument). This comparison is insensitive to the assumed duty cycle or Eddington ratio of quasar activity, and we find that the match between the two BH mass densities favors a relatively mild redshift evolution, with alpha ~ 0.26, with a positive evolution as strong as alpha>1.3 excluded at the 99% confidence level. A direct match between the characteristic BH mass in the VDF--based and quasar LF--based BH mass functions also yields a mean Eddington ratio of lambda ~ 0.5-1 that is roughly constant within 0<z<3. A strong positive evolution in the M_BH-sigma relation is still allowed by the data if galaxies increase, on average, their velocity dispersions since the moment of formation, due to dissipative processes. If we assume that the mean velocity dispersion of the host galaxies evolves as sigma(z)=sigma(0)*(1+z)^{-gamma}, we find a lower limit of gamma>0.23 for alpha>1.5. abridged

A CHARACTERISTIC DIVISION BETWEEN THE FUELING OF QUASARS AND SEYFERTS: FIVE SIMPLE TESTS

Given the existence of the M_BH-sigma relation, models of self-regulated black hole (BH) growth require both a fuel supply and growth of the host bulge to deepen the potential, or else the system will either starve or self-regulate without sustained activity. This suggests that bright quasars must be triggered in major mergers: a large fraction of the galaxy must be converted to new bulge mass in a dynamical time or less. Low-luminosity AGN, in contrast, require little bulge growth and small gas supplies, and could be triggered in more common non-merger events. This predicts a transition to merger-induced fueling around the traditional quasar-Seyfert luminosity divide (growth of BH masses above/below 10^7 M_sun). We compile observations to test several predictions of such a division, including: (1) A transition to bulge-dominated hosts. (2) A transition between 'pseudobulges' and 'classical' bulges hosting the remnant BHs: pseudobulges are formed in secular processes and minor mergers, whereas classical bulges are relics of major mergers. (3) An increase in the amplitude of small-scale clustering where mergers are more efficient. (4) Different redshift evolution, with gas-rich merger rates rising to redshifts z>2 while secular processes are relatively constant in time. (5) An increasing prominence of post-starburst features in more luminous systems. Our compilation of observations provides tentative evidence for the predicted division around the Seyfert-quasar threshold. We discuss how future observations can improve these constraints and break degeneracies between different fueling models.

Measuring Distance and Properties of the Milky Way’s Central Supermassive Black Hole with Stellar Orbits

We report new precision measurements of the properties of our Galaxy's supermassive black hole. Based on astrometric (1995-2007) and radial velocity (2000-2007) measurements from the W. M. Keck 10-meter telescopes, a fully unconstrained Keplerian orbit for the short period star S0-2 provides values for Ro of 8.0+-0.6 kpc, M_bh of 4.1+-0.6x10^6 Mo, and the black hole's radial velocity, which is consistent with zero with 30 km/s uncertainty. If the black hole is assumed to be at rest with respect to the Galaxy, we can further constrain the fit and obtain Ro = 8.4+-0.4 kpc and M_bh = 4.5+-0.4x10^6 Mo. More complex models constrain the extended dark mass distribution to be less than 3-4x10^5 Mo within 0.01 pc, ~100x higher than predictions from stellar and stellar remnant models. For all models, we identify transient astrometric shifts from source confusion and the assumptions regarding the black hole's radial motion as previously unrecognized limitations on orbital accuracy and the usefulness of fainter stars. Future astrometric and RV observations will remedy these effects. Our estimates of Ro and the Galaxy's local rotation speed, which it is derived from combining Ro with the apparent proper motion of Sgr A*, (theta0 = 229+-18 km/s), are compatible with measurements made using other methods. The increased black hole mass found in this study, compared to that determined using projected mass estimators, implies a longer period for the innermost stable orbit, longer resonant relaxation timescales for stars in the vicinity of the black hole and a better agreement with the M_bh-sigma relation.

The Central Parsecs of Centaurus A: High‐excitation Gas, a Molecular Disk, and the Mass of the Black Hole

We present two-dimensional gas-kinematic maps of the central region in Centaurus A. The adaptive optics (AO) assisted SINFONI data from the VLT have a resolution of 0.12 in K-band. The ionized gas species (Br_gamma, [FeII], [SiVI]) show a rotational pattern that is increasingly overlaid by non-rotational motion for higher excitation lines in direction of Cen A's radio jet. The emission lines of molecular hydrogen (H_2) show regular rotation and no distortion due to the jet. The molecular gas seems to be well settled in the gravitational potential of the stars and the central supermassive black hole and we thus use it as a tracer to model the mass in the central +/-1.5. These are the first AO integral-field observations on the nucleus of Cen A, enabling us to study the regularity of the rotation around the black hole, well inside the radius of influence, and to determine the inclination angle of the gas disk in a robust way. The gas kinematics are best modeled through a tilted-ring model that describes the warped gas disk; its mean inclination angle is ~34deg and the mean position angle of the major axis is ~155deg. The best-fit black hole mass is M_BH~4.5x10^7 Msolar, based on a kinematically hot disk model where the velocity dispersion is included through the Jeans equation. This black hole mass estimate is somewhat lower than, but consistent with the mass values previously derived from ionized gas kinematics. It is also consistent with the stellar dynamical measurement from the same AO observations, which we present in a separate paper. It brings Cen A in agreement with the M_BH-sigma relation.