E. K. Verolme

The sauron project. I. the panoramic integral-field spectrograph

A new integral-field spectrograph, SAURON, is described. It is based on the TIGER principle, and uses a lenslet array. SAURON has a large field of view and high throughput, and allows simultaneous sky subtraction. Its design is optimized for studies of the stellar kinematics, gas kinematics, and line-strength distributions of nearby early-type galaxies. The instrument design and specifications are described, as well as the extensive analysis software which was developed to obtain fully calibrated spectra, and the associated kinematic and line-strength measurements. A companion paper will report on the first results obtained with SAURON on the William Herschel Telescope.

The SAURON project – II. Sample and early results

Early results are reported from the SAURON survey of the kinematics and stellar populations of a representative sample of nearby E, S0 and Sa galaxies. The survey is aimed at determining the intrinsic shape of the galaxies, their orbital structure, the mass-to-light ratio as a function of radius, the age and metallicity of the stellar populations, and the frequency of kinematically decoupled cores and nuclear black holes. The construction of the representative sample is described, and its properties are illustrated. A comparison with long-slit spectroscopic data establishes that the SAURON measurements are comparable to, or better than, the highest-quality determinations. Comparisons are presented for NGC 3384 and 4365, where stellar velocities and velocity dispersions are determined to a precision of 6 km s - 1 , and the h 3 and h 4 parameters of the line-of-sight velocity distribution to a precision of better than 0.02. Extraction of accurate gas emission-line intensities, velocities and linewidths from the data cubes is illustrated for NGC 5813. Comparisons with published line strengths for NGC 3384 and 5813 reveal uncertainties of 0.1 A on the measurements of the Hβ, Mg b and Fe5270 indices. Integral-field mapping uniquely connects measurements of the kinematics and stellar populations to the galaxy morphology. The maps presented here illustrate the rich stellar kinematics, gaseous kinematics, and line-strength distributions of early-type galaxies. The results include the discovery of a thin, edge-on, disc in NGC 3623, confirm the axisymmetric shape of the central region of M32, illustrate the LINER nucleus and surrounding counter-rotating star-forming ring in NGC 7742, and suggest a uniform stellar population in the decoupled core galaxy NGC 5813.

The dynamical distance and intrinsic structure of the globular cluster ω Centauri

We determine the dynamical distance D, inclination i, mass-to-light ratio M/L and the intrinsic orbital structure of the globular cluster ω Cen, by fitting axisymmetric dynamical models to the ground-based proper motions of van Leeuwen et al. and line-of-sight velocities from four independent data-sets. We bring the kinematic measurements onto a common coordinate system, and select on cluster membership and on measurement error. This provides a homogeneous data-set of 2295 stars with proper motions accurate to 0.20 mas yr -1 and 2163 stars with line-of-sight velocities accurate to 2 km s -1 , covering a radial range out to about half the tidal radius. We correct the observed velocities for perspective rotation caused by the space motion of the cluster, and show that the residual solid-body rotation component in the proper motions (caused by relative rotation of the photographic plates from which they were derived) can be taken out without any modelling other than assuming axisymmetry. This also provides a tight constraint on I) tan i. The corrected mean velocity fields are consistent with regular rotation, and the velocity dispersion fields display significant deviations from isotropy. We model ω Cen with an axisymmetric implementation of Schwarzschilds orbit superposition method, which accurately fits the surface brightness distribution, makes no assumptions about the degree of velocity anisotropy in the cluster, and allows for radial variations in M/L. We bin the individual measurements on the plane of the sky to search efficiently through the parameter space of the models. Tests on an analytic model demonstrate that this approach is capable of measuring the cluster distance to an accuracy of about 6 per cent. Application to w Cen reveals no dynamical evidence for a significant radial dependence of M/L, in harmony with the relatively long relaxation time of the cluster. The best-fit dynamical model has a stellar V-band mass-to-light ratio M/L V = 2.5 ±0.1 M ○. /L ○. and an inclination i = 50° ± 4°, which corresponds to an average intrinsic axial ratio of 0.78 ± 0.03. The best-fit dynamical distance D = 4.8 ± 0.3 kpc (distance modulus 13.75 ± 0.13 mag) is significantly larger than obtained by means of simple spherical or constant-anisotropy axisymmetric dynamical models, and is consistent with the canonical value 5.0 ± 0.2 kpc obtained by photometric methods. The total mass of the cluster is (2.5 ± 0.3) x 10 6 M ○. . The best-fit model is close to isotropic inside a radius of about 10 arcmin and becomes increasingly tangentially anisotropic in the outer region, which displays significant mean rotation. This phase-space structure may well be caused by the effects of the tidal field of the Milky Way. The cluster contains a separate disk-like component in the radial range between 1 and 3 arcmin, contributing about 4% to the total mass.

The Counterrotating Core and the Black Hole Mass of IC 1459

The E3 giant elliptical galaxy IC 1459 is the prototypical galaxy with a fast counterrotating stellar core. We obtained one Hubble Space Telescope (HST) Space Telescope Imaging Spectrograph (STIS) long-slit spectrum along the major axis of this galaxy and Cerro Tololo Inter-American Observatory (CTIO) spectra along five position angles. The signal-to-noise ratio (S/N) of the ground-based data is such that also the higher order Gauss-Hermite moments (h3-h6) can be extracted reliably. We present self-consistent three-integral axisymmetric models of the stellar kinematics, obtained with Schwarzschilds numerical orbit superposition method. The available data allow us to study the dynamics of the kinematically decoupled core (KDC) in IC 1459, and we find that it consists of stars that are well separated from the rest of the galaxy in phase space. In particular, our study indicates that the stars in the KDC counterrotate in a disk on orbits that are close to circular. We estimate that the KDC mass is ≈0.5% of the total galaxy mass or ≈3 × 109 M☉. We estimate the central black hole (BH) mass MBH of IC 1459 independently from both its stellar and its gaseous kinematics. Although both tracers rule out models without a central BH, neither yields a particularly accurate determination of the BH mass. The main problem for the stellar dynamical modeling is the fact that the modest S/N of the STIS spectrum and the presence of strong gas emission lines preclude measuring the full line-of-sight velocity distribution (LOSVD) at HST resolution. The main problem for the gasdynamical modeling is that there is evidence that the gas motions are disturbed, possibly as a result of nongravitational forces acting on the gas. These complications probably explain why we find rather discrepant BH masses with the different methods. The stellar kinematics suggest that MBH = (2.6 ± 1.1) × 109 M☉ (3 σ error). The gas kinematics suggests that MBH ≈ 3.5 × 108 M☉ if the gas is assumed to rotate at the circular velocity in a thin disk. If the observed velocity dispersion of the gas is assumed to be gravitational, then MBH could be as high as ~1.0 × 109 M☉. These different estimates bracket the value MBH = (1.1 ± 0.3) × 109 M☉ predicted by the MBH-σ relation. It will be an important goal for future studies to attempt comparisons of BH mass determinations from stellar and gaseous kinematics for other galaxies. This will assess the reliability of BH mass determinations with either technique. This is essential if one wants to interpret the correlation between the BH mass and other global galaxy parameters (e.g., velocity dispersion) and in particular the scatter in these correlations (believed to be only ~0.3 dex).

A SAURON study of M32: measuring the intrinsic flattening and the central black hole mass

We present dynamical models of the nearby compact elliptical galaxy M32, using high-quality kinematic measurements, obtained with the integral-field spectrograph SAURON mounted on the William Herschel Telescope on La Palma. We also include STIS data obtained previously by Joseph et al. We find a best-fitting black hole mass of M• = (2.5 ± 0.5) × 10 6 Mand a stellar I-band mass-to-light ratio of (1.85 ± 0.15) M � /L � . For the first time, we are also able to constrain the inclination along which M32 is observed to 70 ◦ ± 5 ◦ . Assuming that M32 is indeed axisymmetric, the averaged observed flattening of 0.73 then corresponds to an intrinsic flattening of 0.68 ± 0.03. These tight constraints are mainly caused by the use of integral-field data. We show this quantitatively by comparing with models that are constrained by multiple slits only. We show the phase-space distribution and intrinsic velocity structure of the best-fitting model and in- vestigate the effect of regularization on the orbit distribution.

Galaxy Mapping with the SAURON Integral-Field Spectrograph: The Star Formation History of NGC 4365

We report the first wide-field mapping of the kinematics and stellar populations in the E3 galaxy NGC 4365. The velocity maps extend previous long-slit work. They show two independent kinematic subsystems: the central 300 pc ? 700 pc rotates about the projected minor axis, and the main body of the galaxy, 3 kpc ? 4 kpc, rotates almost at right angles to this. The line strength maps show that the metallicity of the stellar population decreases from a central value greater than solar to one-half solar at a radius of 2 kpc. The decoupled core and main body of the galaxy have the same luminosity-weighted age, ?14 Gyr, and the same elevated magnesium-to-iron ratio. The two kinematically distinct components have thus shared a common star formation history. We infer that the galaxy underwent a sequence of mergers associated with dissipative star formation that ended 12 Gyr ago. The misalignment between the photometric and kinematic axes of the main body is unambiguous evidence of triaxiality. The similarity of the stellar populations in the two components suggests that the observed kinematic structure has not changed substantially in 12 Gyr.

Two-integral Schwarzschild models

We describe a practical method for constructing axisymmetric two-integral galaxy models [with distribution functions of the form f(E, L z ), in which E is the orbital energy, and L z is the vertical component of the angular momentum], based on Schwarzschilds orbit-superposition method. Other f(E, L z )-methods are mostly based on solving the Jeans equations or on finding the distribution function directly from the density, which often places restrictions on the shape of the galaxy. Here, no assumptions are made and any axisymmetric density distribution is possible. The observables are calculated (semi-)analytically, so that our method is faster than most previous, fully numerical implementations. Various aspects are tested extensively, the results of which apply directly to three-integral Schwarzschild methods. We show that a given distribution function can be reproduced with high accuracy and investigate the behaviour of the parameter that is used to measure the goodness-of-fit. Furthermore, we show that the method correctly identifies the range of cusp slopes for which axisymmetric two-integral models with a central black hole do not exist.

General solution of the Jeans equations for triaxial galaxies with separable potentials

The Jeans equations relate the second-order velocity moments to the density and potential of a stellar system. For general three-dimensional stellar systems, there are three equations and six independent moments. By assuming that the potential is triaxial and of separable Stackel form, the mixed moments vanish in confocal ellipsoidal coordinates. Consequently, the three Jeans equations and three remaining non-vanishing moments form a closed system of three highly symmetric coupled first-order partial differential equations in three variables. These equations were first derived by Lynden-Bell, over 40 years ago, but have resisted solution by standard methods. We present the general solution here. We consider the two-dimensional limiting cases first. We solve their Jeans equations by a new method which superposes singular solutions. The singular solutions, which are new, are standard Riemann–Green functions. The resulting solutions of the Jeans equations give the second moments throughout the system in terms of prescribed boundary values of certain second moments. The two-dimensional solutions are applied to non-axisymmetric discs, oblate and prolate spheroids, and also to the scale-free triaxial limit. There are restrictions on the boundary conditions that we discuss in detail. We then extend the method of singular solutions to the triaxial case, and obtain a full solution, again in terms of prescribed boundary values of second moments. There are restrictions on these boundary values as well, but the boundary conditions can all be specified in a single plane. The general solution can be expressed in terms of complete (hyper)elliptic integrals, which can be evaluated in a straightforward way, and provides the full set of second moments that can support a triaxial density distribution in a separable triaxial potential.

SAURON: integral-field spectroscopy of galaxies

Abstract We present the first results from a new and unique integral-field spectrograph, SAURON, for the 4.2-m William Herschel Telescope on La Palma. Based upon the TIGER concept, SAURON uses a lens array to obtain two-dimensional spectroscopy with complete spatial coverage over a field of 33″×41″ in low-resolution mode (0.94″ lenslets) and of 9″×11″ in high-resolution mode (0.26″ lenslets). The spectra cover 4800 A to 5400 A with a resolution of 3 A (σ=75 km s−1). SAURON achieved first light during commissioning on the WHT on 1 February 1999. The instrument performed well and we are commencing a systematic survey of the velocity dispersions, velocity fields, and line-strength distributions in nearby ellipticals and spiral bulges. The wide field of SAURON will be crucial for unravelling complicated velocity structures. In combination with available long-slit spectroscopy of the outer regions of the galaxies, HST spectra of the nuclei, and HST imaging, we will constrain the intrinsic shapes, mass-to-light ratios, and stellar populations in spheroids. In this presentation we will give a status report and preliminary results from our first science run in February 1999.

Orbital structure of triaxial galaxies

We have developed a method to construct realistic triaxial dynamical models for elliptical galaxies, allowing us to derive best-fitting parameters, such as the mass-to-light ratio and the black hole mass, and to study the orbital structure. We use triaxial theoretical Abel models to investigate the robustness of the method. 1. Triaxial dynamical models Many elliptical galaxies show significant signatures of triaxiality (e.g. de Zeeuw et al. 2002). Therefore, we have extended Schwarzschild’s orbit superposition method to construct realistic triaxial dynamical models, which fit the observed surface brightness, as well as (two-dimensional) kinematical measurements of elliptical galaxies (Verolme et al. 2003). This fully numerical method is, however, too computationally expensive to do a full search over the model parameters, such as mass-to-light ratio, black hole mass, viewing direction and intrinsic shape. Approximating the potential by one of Stackel form, we can construct velocity and velocity dispersion fields using the analytical solution of the continuity equation and the three Jeans equations (Statler 1994, van de Ven et al. 2003), and compare them with observations to constrain the large parameter range. Within this reduced parameter space, we can then apply the extended Schwarzschild method using the true potential, to find the true best-fitting triaxial model. Schwarzschild’s method not only provides the best-fitting parameters, but also results in an orbital weight distribution, which after appropriate smoothing allows us to study the orbital structure of the observed galaxy. 2. Triaxial Abel models To investigate the robustness of the derived internal structure, we are applying our method to theoretical models with known distribution function (DF). We use Abel models (Dejonghe & Laurent 1991; Mathieu & Dejonghe 1999), for which the potential is assumed to be of Stackel form and the DF to be a function of a single parameter F (E, I2, I3) = F (S), with S = E + wI2 + uI3 a linear combination of the explicitly known integrals of motion. The density and higher velocity moments can be calculated efficiently. Besides this analytical simplicity, the Abel models have, with the choice of a three-integral DF, enough freedom to incorporate many of the observed triaxial features (Figure 1).