Stellar orbits in triaxial clusters around black holes in galactic nuclei

We investigate the orbital structure of a model triaxial star cluster, centered around a supermassive black hole (BH), appropriate to galactic nuclei. Sridhar and Touma (1999) proved that the presence of the BH enforces some regularity in the dynamics within the radius of influence of the BH. We employ their averaging method to reduce the degrees of freedom from three to two. Numerical orbit integrations, together with Poincar\'e surfaces of section allow us to draw a global portrait of the orbital structure; in our calculations we employ a model cluster potential that is triaxial and harmonic. The averaged dynamics of the axisymmetric case is integrable, and we present a detailed comparison of orbits in oblate and prolate axisymmetric potentials. Both cases support resonant orbits with fixed values of eccentricity, inclination, and periapse, whose lines of nodes rotates steadily. We then systematically explore significantly triaxial potentials, possessing small oblateness, or prolateness. Resonant orbits and their families are studied both numerically, and through secular perturbation theory. Chaos appears to be suppressed for all the cases we studied, and we obtain effective third integrals. Some of the orbits appear to reinforce the shape of the potential; we provide phase space, as well as real space portraits of these orbits. A particularly promising resonant orbit exists in highly prolate, triaxial potentials

Dynamical Modeling of the Stellar Nucleus of M31

We present stellar dynamical models of the lopsided, double-peaked nucleus of M31, derived from Hubble Space Telescope (HST) photometry. A Schwarzscild-type method, in conjunction with Richardson-Lucy deconvolution, was employed to construct steadily rotating, hot, stellar disks. The stars orbit a massive dark object, on prograde and retrograde quasi-periodic loop orbits. Our results support Tremaine's eccentric disk model, extended to include a more massive disk, non zero pattern speed ($\Omega$), and different viewing angle. Most of the disk mass populated prograde orbits, with $\simeq 3.4$ on retrograde orbits. The best fits to photometric and kinematic maps were disks with \Omega\approx 16\kmspc . We speculate on the origins of the lopsidedness, invoking recent work on the linear overstability of nearly Keplerian disks, that possess even a small amount of a counter-rotating component. Accretion of material-no more massive than a globular cluster-onto a preexisting stellar disk, will account for the mass in our retrograde orbits, and could have stimulated the lopsidedness seen in the nucleus of M31.Comment: 6 pages, 5 figures, revised. To appear in Astronomy and Astrophysic

Constraining the internal dynamics of stellar systems using the NMAGIC particle code

NMAGIC is a parallel implementation of our made-to-measure (χ2M2M) algorithm for constructing N-particle models of stellar systems from observational data, which extends earlier ideas by Syer & Tremaine (1996). The χ2M2M algorithm properly accounts for observational errors, is flexible, and can be applied to various systems and geometries. We show its ability to reproduce the internal dynamics of an oblate isotropic rotator model and report on the modeling of the dark matter (DM) halo of NGC 3379 combining SAURON and PN.S kinematic data. The χ2M2M algorithm is practical, reliable and can be applied to various dynamical systems without symmetry restrictions. We conclude that χ2M2M holds great promise for unraveling the internal dynamics of bulge

The Planetary Nebula Luminosity Function at the Dawn of Gaia

The [O III] 5007 Planetary Nebula Luminosity Function (PNLF) is an excellent extragalactic standard candle. In theory, the PNLF method should not work at all, since the luminosities of the brightest planetary nebulae (PNe) should be highly sensitive to the age of their host stellar population. Yet the method appears robust, as it consistently produces < 10% distances to galaxies of all Hubble types, from the earliest ellipticals to the latest-type spirals and irregulars. It is therefore uniquely suited for cross-checking the results of other techniques and finding small offsets between the Population I and Population II distance ladders. We review the calibration of the method and show that the zero points provided by Cepheids and the Tip of the Red Giant Branch are in excellent agreement. We then compare the results of the PNLF with those from Surface Brightness Fluctuation measurements, and show that, although both techniques agree in a relative sense, the latter method yields distances that are ~15% larger than those from the PNLF. We trace this discrepancy back to the calibration galaxies and argue that, due to a small systematic error associated with internal reddening, the true distance scale likely falls between the extremes of the two methods. We also demonstrate how PNLF measurements in the early-type galaxies that have hosted Type Ia supernovae can help calibrate the SN Ia maximum magnitude-rate of decline relation. Finally, we discuss how the results from space missions such as Kepler and Gaia can help our understanding of the PNLF phenomenon and improve our knowledge of the physics of local planetary nebulae.Comment: 12 pages, invited review at the conference "The Fundamental Cosmic Distance Scale: State of the Art and Gaia Perspective", to appear in Astrophysics and Space Scienc

Kinematic properties of early-type galaxy haloes using planetary nebulae

We present new planetary nebulae (PNe) positions, radial velocities, and magnitudes for 6 early-type galaxies obtained with the Planetary Nebulae Spectrograph, their two-dimensional velocity and velocity dispersion fields. We extend this study to include an additional 10 early-type galaxies with PNe radial velocity measurements available from the literature, to obtain a broader description of the outer-halo kinematics in early-type galaxies. These data extend the information derived from stellar kinematics to typically up to ~8 Re. The combination of photometry, stellar and PNe kinematics shows: i) good agreement between the PNe number density and the stellar surface brightness in the region where the two data sets overlap; ii) good agreement between PNe and stellar kinematics; iii) that the mean rms velocity profiles fall into two groups: with of the galaxies characterized by slowly decreasing profiles and the remainder having steeply falling profiles; iv) a larger variety of velocity dispersion profiles; v) that twists and misalignments in the velocity fields are more frequent at large radii, including some fast rotators; vi) that outer haloes are characterised by more complex radial profiles of the specific angular momentum-related lambda_R parameter than observed within 1Re; vii) that many objects are more rotationally dominated at large radii than in their central parts; and viii) that the halo kinematics are correlated with other galaxy properties, such as total luminosity, isophotal shape, total stellar mass, V/sigma, and alpha parameter, with a clear separation between fast and slow rotators.Comment: 36 pages, 21 figures, revised version for MNRA

The PN.S Elliptical Galaxy Survey: the dark matter in NGC 4494

We present new Planetary Nebula Spectrograph observations of the ordinary elliptical galaxy NGC 4494, resulting in positions and velocities of 255 PNe out to 7 effective radii (25 kpc). We also present new wide-field surface photometry from MMT/Megacam, and long-slit stellar kinematics from VLT/FORS2. The spatial and kinematical distributions of the PNe agree with the field stars in the region of overlap. The mean rotation is relatively low, with a possible kinematic axis twist outside 1 Re. The velocity dispersion profile declines with radius, though not very steeply, down to ~70 km/s at the last data point. We have constructed spherical dynamical models of the system, including Jeans analyses with multi-component LCDM-motivated galaxies as well as logarithmic potentials. These models include special attention to orbital anisotropy, which we constrain using fourth-order velocity moments. Given several different sets of modelling methods and assumptions, we find consistent results for the mass profile within the radial range constrained by the data. Some dark matter (DM) is required by the data; our best-fit solution has a radially anisotropic stellar halo, a plausible stellar mass-to-light ratio, and a DM halo with an unexpectedly low central density. We find that this result does not substantially change with a flattened axisymmetric model. Taken together with other results for galaxy halo masses, we find suggestions for a puzzling pattern wherein most intermediate-luminosity galaxies have very low concentration halos, while some high-mass ellipticals have very high concentrations. We discuss some possible implications of these results for DM and galaxy formation.Comment: 29 pages, 17 figures. MNRAS, accepte

A deep kinematic survey of planetary nebulae in the Andromeda Galaxy using the Planetary Nebula Spectrograph

We present a catalogue of positions, magnitudes and velocities for 3300 emission-line objects found by the Planetary Nebula Spectrograph in a survey of the Andromeda Galaxy, M31. Of these objects, 2615 are found likely to be planetary nebulae (PNe) associated with M31. Initial results from this survey include: the likely non-existence of Andromeda VIII; a universal PN luminosity function, with the exception of a small amount of obscuration, and a small offset in normalization between bulge and disk components; very faint kinematically-selected photometry implying no cut-off in the disk to beyond 4 scalelengths and no halo population in excess of the bulge out to 10 effective bulge radii; disk kinematics that show significant dispersion and asymmetric drift out to large radii, consistent with a warm flaring disk; and no sign of any variation in kinematics with PN luminosity, suggesting that PNe arise from a fairly uniform population of old stars.Comment: Accepted by MNRAS. 23 pages, 37 figures. A full resolution version is available at http://www.astro.rug.nl/~pns/pns_pub.htm

The expansion field: The value of H_0

Any calibration of the present value of the Hubble constant requires recession velocities and distances of galaxies. While the conversion of observed velocities into true recession velocities has only a small effect on the result, the derivation of unbiased distances which rest on a solid zero point and cover a useful range of about 4-30 Mpc is crucial. A list of 279 such galaxy distances within v<2000 km/s is given which are derived from the tip of the red-giant branch (TRGB), from Cepheids, and from supernovae of type Ia (SNe Ia). Their random errors are not more than 0.15 mag as shown by intercomparison. They trace a linear expansion field within narrow margins from v=250 to at least 2000 km/s. Additional 62 distant SNe Ia confirm the linearity to at least 20,000 km/s. The dispersion about the Hubble line is dominated by random peculiar velocities, amounting locally to <100 km/s but increasing outwards. Due to the linearity of the expansion field the Hubble constant H_0 can be found at any distance >4.5 Mpc. RR Lyr star-calibrated TRGB distances of 78 galaxies above this limit give H_0=63.0+/-1.6 at an effective distance of 6 Mpc. They compensate the effect of peculiar motions by their large number. Support for this result comes from 28 independently calibrated Cepheids that give H_0=63.4+/-1.7 at 15 Mpc. This agrees also with the large-scale value of H_0=61.2+/-0.5 from the distant, Cepheid-calibrated SNe Ia. A mean value of H_0=62.3+/-1.3 is adopted. Because the value depends on two independent zero points of the distance scale its systematic error is estimated to be 6%. Typical errors of H_0 come from the use of a universal, yet unjustified P-L relation of Cepheids, the neglect of selection bias in magnitude-limited samples, or they are inherent to the adopted models.Comment: 44 pages, 4 figures, 6 tables, accepted for publication in the Astronony and Astrophysics Review 15