The MASSIVE Survey - VIII. Stellar Velocity Dispersion Profiles and Environmental Dependence of Early-Type Galaxies

We measure the radial profiles of the stellar velocity dispersions, $\sigma(R)$, for 90 early-type galaxies (ETGs) in the MASSIVE survey, a volume-limited integral-field spectroscopic (IFS) galaxy survey targeting all northern-sky ETGs with absolute $K$-band magnitude $M_K < -25.3$ mag, or stellar mass $M_* > 4 \times 10^{11} M_\odot$, within 108 Mpc. Our wide-field 107" $\times$ 107" IFS data cover radii as large as 40 kpc, for which we quantify separately the inner (2 kpc) and outer (20 kpc) logarithmic slopes $\gamma_{\rm inner}$ and $\gamma_{\rm outer}$ of $\sigma(R)$. While $\gamma_{\rm inner}$ is mostly negative, of the 56 galaxies with sufficient radial coverage to determine $\gamma_{\rm outer}$ we find 36% to have rising outer dispersion profiles, 30% to be flat within the uncertainties, and 34% to be falling. The fraction of galaxies with rising outer profiles increases with $M_*$ and in denser galaxy environment, with 10 of the 11 most massive galaxies in our sample having flat or rising dispersion profiles. The strongest environmental correlations are with local density and halo mass, but a weaker correlation with large-scale density also exists. The average $\gamma_{\rm outer}$ is similar for brightest group galaxies, satellites, and isolated galaxies in our sample. We find a clear positive correlation between the gradients of the outer dispersion profile and the gradients of the velocity kurtosis $h_4$. Altogether, our kinematic results suggest that the increasing fraction of rising dispersion profiles in the most massive ETGs are caused (at least in part) by variations in the total mass profiles rather than in the velocity anisotropy alone.Comment: Accepted/in press, MNRA

On the quasi-regularity of non-sectorial Dirichlet forms by processes having the same polar sets

We obtain a criterion for the quasi-regularity of generalized (non-sectorial) Dirichlet forms, which extends the result of P.J. Fitzsimmons on the quasi-regularity of (sectorial) semi-Dirichlet forms. Given the right (Markov) process associated to a semi-Dirichlet form, we present sufficient conditions for a second right process to be a standard one, having the same state space. The above mentioned quasi-regularity criterion is then an application. The conditions are expressed in terms of the associated capacities, nests of compacts, polar sets, and quasi-continuity. A second application is on the quasi-regularity of the generalized Dirichlet forms obtained by perturbing a semi-Dirichlet form with kernels .Comment: Correction of typos and other minor change

The MASSIVE Survey - VII. The Relationship of Angular Momentum, Stellar Mass and Environment of Early-Type Galaxies

We analyse the environmental properties of 370 local early-type galaxies (ETGs) in the MASSIVE and ATLAS3D surveys, two complementary volume-limited integral-field spectroscopic (IFS) galaxy surveys spanning absolute $K$-band magnitude $-21.5 > M_K > -26.6$, or stellar mass $8 \times 10^{9} < M_* < 2 \times 10^{12} M_\odot$. We find these galaxies to reside in a diverse range of environments measured by four methods: group membership (whether a galaxy is a brightest group/cluster galaxy, satellite, or isolated), halo mass, large-scale mass density (measured over a few Mpc), and local mass density (measured within the $N$th neighbour). The spatially resolved IFS stellar kinematics provide robust measurements of the spin parameter $\lambda_e$ and enable us to examine the relationship among $\lambda_e$, $M_*$, and galaxy environment. We find a strong correlation between $\lambda_e$ and $M_*$, where the average $\lambda_e$ decreases from $\sim 0.4$ to below 0.1 with increasing mass, and the fraction of slow rotators $f_{\rm slow}$ increases from $\sim 10$% to 90%. We show for the first time that at fixed $M_*$, there are almost no trends between galaxy spin and environment; the apparent kinematic morphology-density relation for ETGs is therefore primarily driven by $M_*$ and is accounted for by the joint correlations between $M_*$ and spin, and between $M_*$ and environment. A possible exception is that the increased $f_{\rm slow}$ at high local density is slightly more than expected based only on these joint correlations. Our results suggest that the physical processes responsible for building up the present-day stellar masses of massive galaxies are also very efficient at reducing their spin, in any environment.Comment: Accepted to MNRA

The nature of the methanol maser ring G23.657-00.127

Methanol masers are associated with young high-mass stars and are an important tool for investigating the process of massive star formation. The recently discovered methanol maser ring in G23.657-00.127 provides an excellent ``laboratory'' for a detailed study of the nature and physical origin of methanol maser emission, as well as parallax and proper motion measurements. Multi-epoch observations of the 12.2 GHz methanol maser line from the ring were conducted using the Very Long Baseline Array. Interferometric observations with milliarcsecond resolution enabled us to track single maser spots in great detail over a period of 2 years. We have determined the trigonometric parallax of G23.657-00.127 to be 0.313+/-0.039 mas, giving a distance of 3.19{+0.46}{-0.35} kpc. The proper motion of the source indicates that it is moving with the same circular velocity as the LSR, but it shows a large peculiar motion of about 35 km/s toward the Galactic center.Comment: 6 pages, 3 figures, accepted for publication in A&

The MASSIVE Survey XIII -- Spatially Resolved Stellar Kinematics in the Central 1 kpc of 20 Massive Elliptical Galaxies with the GMOS-North Integral-Field Spectrograph

We use observations from the GEMINI-N/GMOS integral-field spectrograph (IFS) to obtain spatially resolved stellar kinematics of the central $\sim 1$ kpc of 20 early-type galaxies (ETGs) with stellar masses greater than $10^{11.7} M_\odot$ in the MASSIVE survey. Together with observations from the wide-field Mitchell IFS at McDonald Observatory in our earlier work, we obtain unprecedentedly detailed kinematic maps of local massive ETGs, covering a scale of $\sim 0.1-30$ kpc. The high ($\sim 120$) signal-to-noise of the GMOS spectra enable us to obtain two-dimensional maps of the line-of-sight velocity, velocity dispersion $\sigma$, as well as the skewness $h_3$ and kurtosis $h_4$ of the stellar velocity distributions. All but one galaxy in the sample have $\sigma(R)$ profiles that increase towards the center, whereas the slope of $\sigma(R)$ at one effective radius ($R_e$) can be of either sign. The $h_4$ is generally positive, with 14 of the 20 galaxies having positive $h_4$ within the GMOS aperture and 18 having positive $h_4$ within $1 R_e$. The positive $h_4$ and rising $\sigma(R)$ towards small radii are indicative of a central black hole and velocity anisotropy. We demonstrate the constraining power of the data on the mass distributions in ETGs by applying Jeans anisotropic modeling (JAM) to NGC~1453, the most regular fast rotator in the sample. Despite the limitations of JAM, we obtain a clear $\chi^2$ minimum in black hole mass, stellar mass-to-light ratio, velocity anisotropy parameters, and the circular velocity of the dark matter halo.Comment: Accepted to Ap

Keck Integral-Field Spectroscopy of M87 Reveals an Intrinsically Triaxial Galaxy and a Revised Black Hole Mass

The three-dimensional intrinsic shape of a galaxy and the mass of the central supermassive black hole provide key insight into the galaxy's growth history over cosmic time. Standard assumptions of a spherical or axisymmetric shape can be simplistic and can bias the black hole mass inferred from the motions of stars within a galaxy. Here we present spatially-resolved stellar kinematics of M87 over a two-dimensional 250\mbox{^{\prime\prime}} \times 300\mbox{^{\prime\prime}} contiguous field covering a radial range of 50 pc to 12 kpc from integral-field spectroscopic observations at the Keck II Telescope. From about 5 kpc and outward, we detect a prominent 25 $\mathrm{km~s}^{-1}$ rotational pattern, in which the kinematic axis (connecting the maximal receding and approaching velocities) is $40^\circ$ misaligned with the photometric major axis of M87. The rotational amplitude and misalignment angle both decrease in the inner 5 kpc. Such misaligned and twisted velocity fields are a hallmark of triaxiality, indicating that M87 is not an axisymmetrically shaped galaxy. Triaxial Schwarzschild orbit modeling with more than 4000 observational constraints enabled us to determine simultaneously the shape and mass parameters. The models incorporate a radially declining profile for the stellar mass-to-light ratio suggested by stellar population studies. We find that M87 is strongly triaxial, with ratios of $p=0.845$ for the middle-to-long principal axes and $q=0.722$ for the short-to-long principal axes, and determine the black hole mass to be $(5.37^{+0.37}_{-0.25}\pm 0.22)\times 10^9 M_\odot$, where the second error indicates the systematic uncertainty associated with the distance to M87.Comment: Accepted for publication in ApJL. 15 pages, 8 figure

The MASSIVE Survey - X. Misalignment between Kinematic and Photometric Axes and Intrinsic Shapes of Massive Early-Type Galaxies

We use spatially resolved two-dimensional stellar velocity maps over a $107"\times 107"$ field of view to investigate the kinematic features of 90 early-type galaxies above stellar mass $10^{11.5}M_\odot$ in the MASSIVE survey. We measure the misalignment angle $\Psi$ between the kinematic and photometric axes and identify local features such as velocity twists and kinematically distinct components. We find 46% of the sample to be well aligned ($\Psi < 15^{\circ}$), 33% misaligned, and 21% without detectable rotation (non-rotators). Only 24% of the sample are fast rotators, the majority of which (91%) are aligned, whereas 57% of the slow rotators are misaligned with a nearly flat distribution of $\Psi$ from $15^{\circ}$ to $90^{\circ}$. 11 galaxies have $\Psi \gtrsim 60^{\circ}$ and thus exhibit minor-axis ("prolate") rotation in which the rotation is preferentially around the photometric major axis. Kinematic misalignments occur more frequently for lower galaxy spin or denser galaxy environments. Using the observed misalignment and ellipticity distributions, we infer the intrinsic shape distribution of our sample and find that MASSIVE slow rotators are consistent with being mildly triaxial, with mean axis ratios of $b/a=0.88$ and $c/a=0.65$. In terms of local kinematic features, 51% of the sample exhibit kinematic twists of larger than $20^{\circ}$, and 2 galaxies have kinematically distinct components. The frequency of misalignment and the broad distribution of $\Psi$ reported here suggest that the most massive early-type galaxies are mildly triaxial, and that formation processes resulting in kinematically misaligned slow rotators such as gas-poor mergers occur frequently in this mass range.Comment: Accepted to MNRA