The fundamental plane of elliptical galaxies with modified Newtonian dynamics

The modified Newtonian dynamics (MOND), suggested by Milgrom as an alternative to dark matter, implies that isothermal spheres with a fixed anisotropy parameter should exhibit a near-perfect relation between the mass and velocity dispersion of the form M ∝ σ  ⁴. This is consistent with the observed Faber–Jackson relation for elliptical galaxies: a luminosity–velocity dispersion relation with large scatter. However, the observable global properties of elliptical galaxies comprise a three-parameter family; they lie on a 'fundamental plane' in a logarithmic space consisting of central velocity dispersion, effective radius ( r _e) and luminosity. The scatter perpendicular to this plane is significantly less than that about the Faber–Jackson relation. I show here that, in order to match the observed properties of elliptical galaxies with MOND, models must deviate from being strictly isothermal and isotropic; such objects can be approximated by high-order polytropic spheres with a radial orbit anisotropy in the outer regions. MOND imposes boundary conditions on the inner Newtonian regions which restrict these models to a dynamical fundamental plane of the form where the exponents may differ from the Newtonian expectations ( α =2, γ =1). Scatter about this plane is relatively insensitive to the necessary deviations from homology.     

The Tully–Fisher relation for S0 galaxies

We present a study of the local B - and K _s-band Tully–Fisher relation (TFR) between absolute magnitude and maximum circular speed in S0 galaxies. To make this study, we have combined kinematic data, including a new high-quality spectral data set from the Fornax cluster, with homogeneous photometry from the Third Reference Catalogue of Bright Galaxies and Two Micron All Sky Survey catalogues, to construct the largest sample of S0 galaxies ever used in a study of the TFR. Independent of environment, S0 galaxies are found to lie systematically below the TFR for nearby spirals in both optical and infrared bands. This offset can be crudely interpreted as arising from the luminosity evolution of spiral galaxies that have faded since ceasing star formation.
However, we also find a large scatter in the TFR. We show that most of this scatter is intrinsic, not due to the observational uncertainties. The presence of such a large scatter means that the population of S0 galaxies cannot have formed exclusively by the above simple fading mechanism after all transforming at a single epoch. To better understand the complexity of the transformation mechanism, we have searched for correlations between the offset from the TFR and other properties of the galaxies such as their structural properties, central velocity dispersions and ages (as estimated from line indices). For the Fornax cluster data, the offset from the TFR correlates with the estimated age of the stars in the individual galaxies, in the sense and of the magnitude expected if S0 galaxies had passively faded since being converted from spirals. This correlation implies that a significant part of the scatter in the TFR arises from the different times at which galaxies began their transformation.     

Line-of-sight velocity distributions of low-luminosity elliptical galaxies

The shape of the line-of-sight velocity distribution (LOSVD) is measured for a sample of 14 elliptical galaxies, predominantly low-luminosity ellipticals. The sample is dominated by galaxies in the Virgo cluster but also contains ellipticals in nearby groups and low-density environments. The parametrization of the LOSVD given by Gerhard and van der Marel & Franx is adopted, which measures the asymmetrical and symmetrical deviations of the LOSVD from a Gaussian by the amplitudes h ₃ and h ₄ of the Gauss–Hermite series. Rotation, velocity dispersion, h ₃ and h ₄ are determined as a function of radius for both major and minor axes. Non-Gaussian LOSVDs are found for all galaxies along the major axes. Deviations from a Gaussian LOSVD along the minor axis are of much lower amplitude if present at all. Central decreases in velocity dispersion are found for three galaxies. Two galaxies have kinematically decoupled cores: NGC 4458 and the well-known case of NGC 3608.     

The dynamics of S0 galaxies and their Tully–Fisher relation

This paper investigates the detailed dynamical properties of a relatively homogeneous sample of disc-dominated S0 galaxies, with a view to understanding their formation, evolution and structure. By using high signal-to-noise ratio long-slit spectra of edge-on systems, we have been able to reconstruct the complete line-of-sight velocity distributions of stars along the major axes of the galaxies. From these data, we have derived both model distribution functions (the phase density of their stars) and the approximate form of their gravitational potentials.
The derived distribution functions are all consistent with these galaxies being simple disc systems, with no evidence for a complex formation history. Essentially no correlation is found between the characteristic mass scalelengths and the photometric scalelengths in these galaxies, suggesting that they are dark-matter dominated even in their inner parts. Similarly, no correlation is found between the mass scalelengths and asymptotic rotation speed, implying a wide range of dark matter halo properties.
By comparing their asymptotic rotation speeds with their absolute magnitudes, we find that these S0 galaxies are systematically offset from the Tully–Fisher relation for later-type galaxies. The offset in luminosity is what one would expect if star formation had been suddenly switched off a few Gyr ago, consistent with a simple picture in which these S0s were created from ordinary later-type spirals which were stripped of their star-forming interstellar medium when they encountered a dense cluster environment.     

Radial orbital anisotropy and the Fundamental Plane of elliptical galaxies

The existence of the Fundamental Plane imposes strong constraints on the structure and dynamics of elliptical galaxies, and thus contains important information on the processes of their formation and evolution. Here we focus on the relations between the Fundamental Plane thinness and tilt and the amount of radial orbital anisotropy: in fact, the problem of the compatibility between the observed thinness of the Fundamental Plane and the wide spread of orbital anisotropy admitted by galaxy models has often been raised. By using N -body simulations of galaxy models characterized by observationally motivated density profiles, and also allowing for the presence of live, massive dark matter haloes, we explore the impact of radial orbital anisotropy and instability on the Fundamental Plane properties. The numerical results confirm a previous semi-analytical finding (based on a different class of one-component galaxy models): the requirement of stability matches almost exactly the thinness of the Fundamental Plane. In other words, galaxy models that are radially anisotropic enough to be found outside the observed Fundamental Plane (with their isotropic parent models lying on the Fundamental Plane) are unstable, and their end-products fall back on the Fundamental Plane itself. We also find that a systematic increase of radial orbit anisotropy with galaxy luminosity cannot explain by itself the whole tilt of the Fundamental Plane, the galaxy models becoming unstable at moderately high luminosities: at variance with the previous case, their end-products are found well outside the Fundamental Plane itself. Some physical implications of these findings are discussed in detail.     

Specific angular momentum of disc merger remnants and the λR-parameter

We use two-dimensional kinematic maps of simulated binary disc mergers to investigate the  λ_R  -parameter, which is a luminosity-weighted measure of projected angular momentum per unit mass. This parameter was introduced to subdivide the SAURON sample of early-type galaxies in so-called fast  λ_R > 0.1  and slow rotators  λ_R < 0.1  . Tests on merger remnants reveal that  λ_R  is a robust indicator of the true angular momentum content in elliptical galaxies. We find the same range of  λ_R  values in our merger remnants as in the SAURON galaxies. The merger mass ratio is decisive in transforming fast rotators into slow rotators in a single binary merger, the latter being created mostly in an equal-mass merger. Slow rotators have a  λ_R  which does not vary with projection. The confusion rate with face-on fast rotators is very small. Mergers with a gas component form slow rotators with smaller ellipticities than collisionless merger remnants have, and are in much better agreement with the SAURON slow rotators. Remergers of merger remnants are slow rotators, but tend to have too high ellipticities. Fast rotators maintain the angular momentum content from the progenitor disc galaxy if merger mass ratio is high. Some SAURON galaxies have values of  λ _R   as high as our progenitor disc galaxies.     

S0 galaxies in Fornax: data and kinematics

We have obtained long-slit spectroscopy for a sample of nine S0 galaxies in the Fornax Cluster using the FORS2 spectrograph at the 8.2-m European Southern Observatory (ESO) Very Large Telescope (VLT). From these data, we have extracted the kinematic parameters, comprising the mean velocity, velocity dispersion and higher moment h ₃ and h ₄ coefficients, as a function of position along the major axes of these galaxies. Comparison with published kinematics indicates that earlier data are often limited by their lower signal-to-noise ratio and relatively poor spectral resolution. The greater depth and higher dispersion of the new data mean that we reach well beyond the bulges of these systems, probing their disc kinematics in some detail for the first time. Qualitative inspection of the results for individual galaxies shows that they are not entirely simple systems, perhaps indicating a turbulent past. None the less, we are able to derive reliable circular velocities for most of these systems, which points the way towards a study of their Tully–Fisher relation. This study, along with an analysis of the stellar populations of these systems out to large galactocentric distances, will form the bases of future papers exploiting these new high-quality data, hopefully shedding new light on the evolutionary history of these systems.     

Evidence of fast rotation in dwarf elliptical galaxies

In this letter we investigate the kinematical properties of early-type dwarfs by significantly enlarging the scarce observational sample so far available. We present rotation curves and mean velocity dispersions for four bright dwarf ellipticals and two dwarf lenticular galaxies in the Virgo cluster. Most of these galaxies exhibit conspicuous rotation curves. In particular, five out of the six new galaxies are found to be close to the predictions for oblate spheroids flattened by rotation. Therefore, and contrary to the previous observational hints, the present data suggest that an important fraction of dwarf early-type galaxies may be rotationally supported.     

The properties of field elliptical galaxies at intermediate redshift – II. Photometry and spectroscopy of an HST-selected sample

A sample of field early-type galaxies (E/S0) at intermediate redshift ( z ∼0.1–0.6) is selected, based on morphology and colours from HST -WFPC2 parallel images. Photometric structural parameters (effective radius R _e and effective surface brightness SB _e) are derived through the F606W and F814W filters, using luminosity profile fitting and two-dimensional fitting techniques. The combined parameter that enters the Fundamental Plane (log  R _e− βSB _e , with β ≈0.32) is shown to suffer from significantly smaller uncertainties (rms 0.03) than the individual structural parameters (e.g. ∼15 per cent rms on the effective radius).
High signal-to-noise ratio, intermediate-resolution spectra, taken at the ESO 3.6-m telescope, yield redshifts for 35 galaxies and central velocity dispersions for 22 galaxies. Central velocity dispersions are derived using a library of stellar templates covering a wide range of spectral types, in order to study the effects of template mismatches. The average random error on the central velocity dispersion is found to be 8 per cent, and the average systematic error caused by template mismatch is found to be 5 per cent. The errors in the velocity dispersion measurement and the effects of template mismatches are studied by means of extensive Monte Carlo simulations. In addition, we investigate whether the determination of the velocity dispersion is sensitive to the spectral range used, finding that the value of velocity dispersion is unchanged when the spectral regions that include the absorption features Ca H and K and NaD are masked out during the fit.