Range Of Velocity Dispersions Research Articles

MaNGA DynPop – V. The dark-matter fraction versus stellar velocity dispersion relation and stellar initial mass function variations in galaxies: dynamical models and full spectrum fitting of integral-field spectroscopy

ABSTRACT Using the final Mapping Nearby Galaxies at Apache Point Observatory sample of 10K galaxies, we investigate the dark matter (DM) fraction fDM within one half-light radius Re for about 6K galaxies with good kinematics spanning a wide range of morphologies and stellar velocity dispersion. We employ two techniques to estimate fDM: (i) Jeans anisotropic modelling (JAM), which performs DM decomposition based on stellar kinematics and (ii) comparing the total dynamical mass-to-light ratios (M/L)JAM and (M*/L)SPS from stellar population synthesis (SPS). We find that both methods consistently show a significant trend of increasing fDM with decreasing σe and low fDM at larger σe. For 235 early-type galaxies with the best models, we explore the variation of stellar initial mass function (IMF) by comparing the stellar mass-to-light ratios from JAM and SPS. We confirm that the stellar mass excess factor αIMF increases with σe, consistent with previous studies that reported a transition from Chabrier-like to Salpeter IMF among galaxies. We show that the αIMF trend cannot be driven by M*/L or IMF gradients as it persists when allowing for radial gradients in our model. We find no evidence for the total M/L increasing toward the centre. We detect weak positive correlations between αIMF and age, but no correlations with metallicity. We stack galaxy spectra according to their αIMF to search for differences in IMF-sensitive spectral features (e.g. the $\rm Na_{\rm I}$ doublet). We only find marginal evidence for such differences, which casts doubt on the validity of one or both methods to measure the IMF.

Necessary conditions for the formation of filaments and star clusters in the cold neutral medium

ABSTRACT Star formation takes place in filamentary molecular clouds which arise by physical processes that take place in the cold neutral medium (CNM). We address the necessary conditions for this diffuse (n ≈ 30 cm−3), cold (T ≈ 60 K), magnetized gas undergoing shock waves, and supersonic turbulence, to produce filamentary structures capable of fragmenting into cluster forming regions. Using ramses and a magnetized CNM environment as our initial conditions, we simulate a 0.5 kpc turbulent box to model a uniform gas with magnetic field strength of 7 μG, varying the 3D velocity dispersion via decaying turbulence. We use a surface density of 320 M⊙ pc−2, representative of the inner 4.0 kpc central molecular zone of the Milky Way and typical luminous galaxies. Filamentary molecular clouds are formed dynamically via shocks within a narrow range of velocity dispersions in the CNM of 5–10 km s−1 with a preferred value at 8 km s−1. Cluster sink particles appear in filaments which exceed their critical line mass, occurring optimally for velocity dispersions of 8 km s−1. Tracking the evolution of magnetic fields, we find that they lead to double the dense star-forming gas than in purely hydro runs. Perpendicular orientations between magnetic field and filaments can increase the accretion rates onto filaments and hence their line masses. Because magnetic fields help support gas, magnetohydrodynamic runs result in average temperatures an order of magnitude higher than unmagnetized counterparts. Finally, we find magnetic fields delay the onset of cluster formation by ∝ 0.4 Myr.

Initial mass function variability from the integrated light of diverse stellar systems

ABSTRACT We present a uniform analysis of the stellar initial mass function (IMF) from integrated light spectroscopy of 15 compact stellar systems (11 globular clusters in M31 and 4 ultra compact dwarfs in the Virgo cluster, UCDs) and two brightest Coma cluster galaxies (BCGs), covering a wide range of metallicities (−1.7 < [Fe/H] < 0.01) and velocity dispersions (7.4 km s−1 <σ < 275 km s−1). The S/N ∼100 Å−1 Keck LRIS spectra are fitted over the range 4000 < λ/Å < 10 000 with flexible full-spectrum stellar population synthesis models. We use the models to fit simultaneously for ages, metallicities, and individual elemental abundances of the population, allowing us to decouple abundance variations from variations in IMF slope. We show that compact stellar systems do not follow the same trends with physical parameters that have been found for early-type galaxies. Most globular clusters in our sample have an IMF consistent with that of the Milky Way, over a wide range of [Fe/H] and [Mg/Fe]. There is more diversity among the UCDs, with some showing evidence for a bottom-heavy IMF, but with no clear correlation with metallicity, abundance, or velocity dispersion. The two Coma BCGs have similar velocity dispersion and metallicity, but we find the IMF of NGC 4874 is consistent with that of the Milky Way while NGC 4889 presents evidence for a significantly bottom-heavy IMF. For this sample, the IMF appears to vary between objects in a way that is not explained by a single metallicity-dependent prescription.

Generation of high-energy near-infrared femtosecond laser pulses by optical parametric amplification in YCOB crystals

"The energy of near-infrared femtosecond laser pulses generated by optical parametric amplification (OPA) in β-barium borate (BBO) crystals pumped by femtosecond Ti:sapphire lasers is restricted to few-mJ due to the 20 mm limited diam- eter of available crystals. In a type I collinear OPA with an yttrium calcium oxoborate (YCOB) crystal, pumped with femtosecond Ti:sapphire lasers at 800 nm wavelength, the 1300 nm signal wavelength and 2080 nm idler wavelength are located in the normal and anomalous group velocity dispersion range, respectively. Due to the small group velocity mismatch (GVM) between signal and idler pulses, as broad as 27 THz gain bandwidth can be obtained in a 3-mm YCOB crystal at 100 GW/cm2 pump intensity. A high parametric gain is the result of the increased parametric interaction length due to the different signs of GVM between pump-signal and pump-idler pulses. More than 10-mJ energy femtosecond laser pulses at 1300 nm wavelength can be generated by OPA in YCOB crystals with larger than 50 mm clear aperture."

What drives the variance of galaxy spectra?

ABSTRACT We present a study aimed at understanding the physical phenomena underlying the formation and evolution of galaxies following a data-driven analysis of spectroscopic data based on the variance in a carefully selected sample. We apply principal component analysis (PCA) independently to three subsets of continuum-subtracted optical spectra, segregated into their nebular emission activity as quiescent, star-forming, and active galactic nuclei (AGNs). We emphasize that the variance of the input data in this work only relates to the absorption lines in the photospheres of the stellar populations. The sample is taken from the Sloan Digital Sky Survey (SDSS) in the stellar velocity dispersion range 100–150 km s−1, to minimize the ‘blurring’ effect of the stellar motion. We restrict the analysis to the first three principal components (PCs) and find that PCA segregates the three types with the highest variance mapping SSP-equivalent age, along with an inextricable degeneracy with metallicity, even when all three PCs are included. Spectral fitting shows that stellar age dominates PC1, whereas PC2 and PC3 have a mixed dependence of age and metallicity. The trends support – independently of any model fitting – the hypothesis of an evolutionary sequence from star formation to AGN to quiescence. As a further test of the consistency of the analysis, we apply the same methodology in different spectral windows, finding similar trends, but the variance is maximal in the blue wavelength range, roughly around the 4000 Å break.

WISDOM Project – XVII. Beam-by-beam properties of the molecular gas in early-type galaxies

ABSTRACT We present a study of the molecular gas of seven early-type galaxies with high angular resolution data obtained as part of the mm-Wave Interferometric Survey of Dark Object Masses (WISDOM) project with the Atacama Large Millimeter/submillimeter Array. Using a fixed spatial-scale approach, we study the mass surface density (Σ) and velocity dispersion (σ) of the molecular gas on spatial scales ranging from 60 to 120 pc. Given the spatial resolution of our data (20–70 pc), we characterize these properties across many thousands of individual sightlines (≈50 000 at our highest physical resolution). The molecular gas along these sightlines has a large range (≈2 dex) of mass surface densities and velocity dispersions $\approx 40~{{\ \rm per\ cent}}$ higher than those of star-forming spiral galaxies. It has virial parameters αvir that depend weakly on the physical scale observed, likely due to beam smearing of the bulk galactic rotation, and is generally supervirial. Comparing the internal turbulent pressure (Pturb) to the pressure required for dynamic equilibrium (PDE), the ratio Pturb/PDE is significantly less than unity in all galaxies, indicating that the gas is not in dynamic equilibrium and is strongly compressed, in apparent contradiction to the virial parameters. This may be due to our neglect of shear and tidal forces, and/or the combination of three-dimensional and vertical diagnostics. Both αvir and Pturb anticorrelate with the global star-formation rate of our galaxies. We therefore conclude that the molecular gas in early-type galaxies is likely unbound, and that large-scale dynamics likely plays a critical role in its regulation. This contrasts to the giant molecular clouds in the discs of late-type galaxies, that are much closer to dynamical equilibrium.

Study on the effect of seafloor sound speed dispersion on sound propagation

As one of the boundaries of ocean waveguide, the acoustic properties of seafloor sediments have been a hot research problem in ocean acoustic propagation and acoustic field modeling. The existing research has shown that the sound velocity in seafloor sediment is frequency dependent. In order to solve the problem that the sedimentary sound speed dispersing often be ignored in actual applications, this article uses the parabolic Newton to iterate to solve the dispersion equation to obtain the characteristic value of the normal mode. And the impact of frequency dispersion of sediment sound speed through simulation are studied. The results show that the sound wave in the time domain will appear more obvious broadening phenomenon, and the propagation loss will be reduced after considering the sound velocity dispersion of the sediment. Also, with the increase of frequency, the more obvious the effect of sound velocity dispersion on the sound propagation in the frequency range of sound velocity dispersion.

Individual element sensitivity for stellar evolutionary isochrones

ABSTRACT Stellar evolution calculations with variable abundance ratios were used to gauge the effects on temperatures, luminosities, and lifetimes in various phases. The individual elements C, N, O, Mg, Si, and Fe were included. Most of the effect relevant to integrated light models is contained in the temperature variable, as opposed to the time-scale or luminosity. We derive a recipe for including abundance-sensitive temperature effects that is applicable to existing isochrone grids. The resultant enhanced isochrones are incorporated into composite stellar population models and compared with galaxy data from the Sloan Digital Sky Survey. A severe oxygen–age degeneracy is apparent, 2–3 Gyr per 0.1 dex in [O/R], where R represents a heavy element such as Fe. Over the range of early-type galaxy velocity dispersion, the spans of all abundance ratios are reduced but the age range increases and becomes systematically older. Allowing Fe-peak elements the freedom to vary accentuates this increase of age span. Overall, these results sharpen the age–mass correlation known as downsizing but decrease the steepness of abundance ratio gradients. Both of these observations, in turn, imply a more robust contribution from gas-free mergers in the histories of typical elliptical galaxies.

The Circumnuclear Disk Revealed by ALMA. I. Dense Clouds and Tides in the Galactic Center

Abstract Utilizing the Atacama Large Millimeter/submillimeter Array, we present CS line maps in five rotational lines (J u = 7, 5, 4, 3, 2) toward the circumnuclear disk (CND) and streamers of the Galactic center. Our primary goal is to resolve the compact structures within the CND and the streamers, in order to understand the stability conditions of molecular cores in the vicinity of the supermassive black hole (SMBH) Sgr A*. Our data provide the first homogeneous high-resolution (1.″3 = 0.05 pc) observations aiming at resolving density and temperature structures. The CS clouds have sizes of 0.05–0.2 pc with a broad range of velocity dispersion (σ FWHM = 5–40 km s−1). The CS clouds are a mixture of warm (T k ≥ 50–500 K, n H 2 = 103–105 cm−3) and cold gas (T k ≤ 50 K, n H 2 = 106–108 cm−3). A stability analysis based on the unmagnetized virial theorem including tidal force shows that 84 − 37 + 16 % of the total gas mass is tidally stable, which accounts for the majority of gas mass. Turbulence dominates the internal energy and thereby sets the threshold densities 10–100 times higher than the tidal limit at distance ≥1.5 pc to Sgr A*, and therefore it inhibits the clouds from collapsing to form stars near the SMBH. However, within the central 1 pc, the tidal force overrides turbulence and the threshold densities for a gravitational collapse quickly grow to ≥ 108 cm−3.

Detection of metallicity correlations in 100 nearby galaxies

ABSTRACT In this paper, we analyse the statistics of the 2D gas-phase oxygen abundance distributions of 100 nearby galaxies drawn from the Calar Alto Legacy Integral Field spectroscopy Area survey. After removing the large-scale radial metallicity gradient, we compute the two-point correlation functions of the resulting metallicity fluctuation maps. We detect correlations in the majority of our targets, which we show are significantly in excess of what is expected due to beam-smearing, and are robust against the choice of metallicity diagnostic. We show that the correlation functions are generally well-fit by the predictions of a simple model for stochastic metal injection coupled with diffusion, and from the model we show that, after accounting for the effects of both beam smearing and noise, the galaxies in our sample have characteristic correlation lengths of ∼1 kpc. Correlation lengths increase with both stellar mass and star formation rate, but show no significant variation with Hubble type, barredness, or merging state. We also find no evidence for a theoretically predicted relationship between gas velocity dispersion and correlation length, though this may be due to the small dynamic range in gas velocity dispersion across our sample. Our results suggest that measurements of 2D metallicity correlation functions can be a powerful tool for studying galaxy evolution.

Molecular Gas Properties on Cloud Scales across the Local Star-forming Galaxy Population

Abstract Using the PHANGS–ALMA CO(2–1) survey, we characterize molecular gas properties on ∼100 pc scales across 102,778 independent sightlines in 70 nearby galaxies. This yields the best synthetic view of molecular gas properties on cloud scales across the local star-forming galaxy population obtained to date. Consistent with previous studies, we observe a wide range of molecular gas surface densities (3.4 dex), velocity dispersions (1.7 dex), and turbulent pressures (6.5 dex) across the galaxies in our sample. Under simplifying assumptions about subresolution gas structure, the inferred virial parameters suggest that the kinetic energy of the molecular gas typically exceeds its self-gravitational binding energy at ∼100 pc scales by a modest factor (1.3 on average). We find that the cloud-scale surface density, velocity dispersion, and turbulent pressure (1) increase toward the inner parts of galaxies, (2) are exceptionally high in the centers of barred galaxies (where the gas also appears less gravitationally bound), and (3) are moderately higher in spiral arms than in inter-arm regions. The galaxy-wide averages of these gas properties also correlate with the integrated stellar mass, star formation rate, and offset from the star-forming main sequence of the host galaxies. These correlations persist even when we exclude regions with extraordinary gas properties in galaxy centers, which contribute significantly to the inter-galaxy variations. Our results provide key empirical constraints on the physical link between molecular cloud populations and their galactic environment.

Comparing IMF-sensitive indices of intermediate-mass quiescent galaxies in various environments

ABSTRACT Using samples drawn from the Sloan Digital Sky Survey, we study for the first time the relation between large-scale environments (clusters, groups, and voids) and the stellar initial mass function (IMF). We perform an observational approach based on the comparison of IMF-sensitive indices of quiescent galaxies with similar mass in varying environments. These galaxies are selected within a narrow redshift interval (0.020 < z < 0.055) and spanning a range in velocity dispersion from 100 to 200 km s−1. The results of this paper are based upon analysis of composite spectra created by stacking the spectra of galaxies, binned by their velocity dispersion and redshift. The trends of spectral indices as measured from the stacked spectra, with respect to velocity dispersion, are compared in different environments. We find a lack of dependence of the IMF on the environment for intermediate-mass galaxy regime. We verify this finding by providing a more quantitative measurement of the IMF variations among galactic environments using MILES stellar population models with a precision of ΔΓb ∼ 0.2.

Topological charge influence on self-action of femtosecond optical vortices in the range of anomalous group velocity dispersion

The self-action of femtosecond optical vortices in LiF crystal at wavelength 1800 nm in the range of anomalous group velocity dispersion is considered. The influence of the topological charge on the spatio-temporal dynamics of the pulse and peak intensity values in the formation of ring light bullets is analyzed.

The Hydra I cluster core

Context. NGC 3311, the central galaxy of the Hydra I cluster, shows signatures of recent infall of satellite galaxies from the cluster environment. Previous work has shown that the line-of-sight velocity dispersion of the stars and globular clusters in the extended halo of NGC 3311 rises up to the value of the cluster velocity dispersion. In the context of Jeans models, a massive dark halo with a large core is needed to explain this finding. However, position dependent long-slit measurements show that the kinematics are still not understood. Aims. We aim to find kinematic signatures of sub-structures in the extended halo of NGC 3311. Methods. We performed multi-object spectroscopic observations of the diffuse stellar halo of NGC 3311 using VLT/FORS2 in MXU mode to mimic a coarse “IFU”. The slits of the outermost masks reach out to about 35 kpc of galactocentric distance. We use PPXF to extract the kinematic information of velocities, velocity dispersions and the high-order moments h3 and h4. Results. We find a homogeneous velocity field and velocity dispersion field within a radius of about 10 kpc. Beyond this radius, both the velocities and the velocity dispersion start to depend on azimuth angle and show a significant intrinsic scatter. The inner spheroid of NGC 3311 can be described as a slow rotator. Outside 10 kpc the cumulative angular momentum is rising, however, without showing an ordered rotation signal. If the radial dependence alone is considered, the velocity dispersion does not simply rise but fills an increasingly large range of dispersion values with two well defined envelopes. The lower envelope is about constant at 200 km s−1. The upper envelope rises smoothly, joining the velocity dispersion of the outer globular clusters and the cluster galaxies. We interpret this behaviour as the superposition of tracer populations with increasingly shallower radial distributions between the extremes of the inner stellar populations and the cluster galaxies. Simple Jeans models illustrate that a range of mass profiles can account for all observed velocity dispersions, including radial MOND models. Conclusions. The rising velocity dispersion of NGC 3311 apparently is a result of averaging over a range of velocity dispersions related to different tracer populations in the sense of different density profiles and anisotropies. Jeans models using one tracer population with a unique density profile are not able to explain the large range of the observed kinematics. Previous claims about the cored dark halo of NGC 3311 are therefore probably not valid. This may in general apply to central cluster galaxies with rising velocity dispersion profiles, where infall processes are important.

Dark Matter in Ultra-diffuse Galaxies in the Virgo Cluster from Their Globular Cluster Populations

Abstract We present Keck/DEIMOS spectroscopy of globular clusters (GCs) around the ultra-diffuse galaxies (UDGs) VLSB−B, VLSB−D, and VCC615 located in the central regions of the Virgo cluster. We spectroscopically identify 4, 12, and 7 GC satellites of these UDGs, respectively. We find that the three UDGs have systemic velocities (V sys) consistent with being in the Virgo cluster, and that they span a wide range of velocity dispersions, from ∼16 to ∼47 km s−1, and high dynamical mass-to-light ratios within the radius that contains half the number of GCs ( , , , respectively). VLSB−D shows possible evidence for rotation along the stellar major axis and its V sys is consistent with that of the massive galaxy M84 and the center of the Virgo cluster itself. These findings, in addition to having a dynamically and spatially (∼1 kpc) off-centered nucleus and being extremely elongated, suggest that VLSB−D could be tidally perturbed. On the contrary, VLSB−B and VCC615 show no signs of tidal deformation. Whereas the dynamics of VLSB−D suggest that it has a less massive dark matter halo than expected for its stellar mass, VLSB−B and VCC615 are consistent with a ∼1012 M ⊙ dark matter halo. Although our samples of galaxies and GCs are small, these results suggest that UDGs may be a diverse population, with their low surface brightnesses being the result of very early formation, tidal disruption, or a combination of the two.

Cold dark matter plus not-so-clumpy dark relics

Various particle physics models suggest that, besides the (nearly) cold dark matter that accounts for current observations, additional but sub-dominant dark relics might exist. These could be warm, hot, or even contribute as dark radiation. We present here a comprehensive study of two-component dark matter scenarios, where the first component is assumed to be cold, and the second is a non-cold thermal relic. Considering the cases where the non-cold dark matter species could be either a fermion or a boson, we derive consistent upper limits on the non-cold dark relic energy density for a very large range of velocity dispersions, covering the entire range from dark radiation to cold dark matter. To this end, we employ the latest Planck Cosmic Microwave Background data, the recent BOSS DR11 and other Baryon Acoustic Oscillation measurements, and also constraints on the number of Milky Way satellites, the latter of which provides a measure of the suppression of the matter power spectrum at the smallest scales due to the free-streaming of the non-cold dark matter component. We present the results on the fraction fncdm of non-cold dark matter with respect to the total dark matter for different ranges of the non-cold dark matter masses. We find that the 2σ limits for non-cold dark matter particles with masses in the range 1–10 keV are fncdm⩽0.29 (0.23) for fermions (bosons), and for masses in the 10–100 keV range they are fncdm⩽0.43 (0.45), respectively.

Comparative study of multioctave supercontinuum generation in fused silica, YAG, and LiF in the range of anomalous group velocity dispersion

We present spectral measurements that uncover the detailed dynamics of the supercontinuum generation in fused silica, YAG, and LiF crystals when pumped with 100 fs pulses with a central wavelength of 2.3 μm, which falls into the range of anomalous group velocity dispersion of the media. The multi-octave supercontinuum spectra, which span from the ultraviolet to the mid-infrared, are recorded by means of high-dynamic range measurements over the entire wavelength range covered by the supercontinuum radiation. The spectral dynamics versus the input pulse energy uncovers different mechanisms of spectral broadening, which are characterized by the occurrence of specific but well-distinguished spectral signatures and which are interpreted in terms of plasma-induced and anomalous group velocity dispersion-induced compression of the driving pulse.

Spatiotemporal light bullets and supercontinuum generation in β-BBO crystal with competing quadratic and cubic nonlinearities

We experimentally study filamentation and supercontinuum generation in a birefringent medium [beta-barium borate (β-BBO) crystal] pumped by intense 90 fs, 1.8 μm laser pulses whose carrier wavelength falls in the range of anomalous group velocity dispersion of the crystal. We demonstrate that the competition between the intrinsic cubic and cascaded-quadratic nonlinearities may serve as a useful tool for controlling the self-action effects via phase matching condition. In particular, we found that spectral superbroadening of the ordinary polarization is linked to three-dimensional self-focusing and formation of self-compressed spatiotemporal light bullets that could be accessed within a certain range of either positive or negative phase mismatch. In the extraordinary polarization, we detect giant spectral shifts of the second harmonic radiation, which are attributed to a light bullet-induced self-phase matching.

Molecular gas kinematics within the central 250 pc of the Milky Way

Using spectral-line observations of HNCO, N2H+, and HNC, we investigate the kinematics of dense gas in the central ~250 pc of the Galaxy. We present SCOUSE (Semi-automated multi-COmponent Universal Spectral-line fitting Engine), a line fitting algorithm designed to analyse large volumes of spectral-line data efficiently and systematically. Unlike techniques which do not account for complex line profiles, SCOUSE accurately describes the {l, b, v_LSR} distribution of CMZ gas, which is asymmetric about Sgr A* in both position and velocity. Velocity dispersions range from 2.6 km/s<\sigma<53.1 km/s. A median dispersion of 9.8 km/s, translates to a Mach number, M_3D>28. The gas is distributed throughout several "streams", with projected lengths ~100-250 pc. We link the streams to individual clouds and sub-regions, including Sgr C, the 20 and 50 km/s clouds, the dust ridge, and Sgr B2. Shell-like emission features can be explained by the projection of independent molecular clouds in Sgr C and the newly identified conical profile of Sgr B2 in {l ,b, v_LSR} space. These features have previously invoked supernova-driven shells and cloud-cloud collisions as explanations. We instead caution against structure identification in velocity-integrated emission maps. Three geometries describing the 3-D structure of the CMZ are investigated: i) two spiral arms; ii) a closed elliptical orbit; iii) an open stream. While two spiral arms and an open stream qualitatively reproduce the gas distribution, the most recent parameterisation of the closed elliptical orbit does not. Finally, we discuss how proper motion measurements of masers can distinguish between these geometries, and suggest that this effort should be focused on the 20 km/s and 50 km/s clouds and Sgr C.

The initial mass function of early-type galaxies: no correlation with [Mg/Fe

Abstract The initial mass function (IMF) of early-type galaxies (ETGs) has been found to feature systematic variations by both dynamical and spectroscopic studies. In particular, spectral line strengths, based on gravity-sensitive features, suggest an excess of low-mass stars in massive ETGs, i.e. a bottom-heavy IMF. The physical drivers of IMF variations are currently unknown. The abundance ratio of α elements, such as [Mg/Fe], has been suggested as a possible driver of the IMF changes, although dynamical constraints do not support this claim. In this letter, we take advantage of the large Sloan Digital Sky Survey data base. Our sample comprises 24 781 high-quality spectra, covering a large range in velocity dispersion (100 &amp;lt; σ0 &amp;lt; 320 km s−1) and abundance ratio ( − 0.1 &amp;lt; [Mg/Fe] &amp;lt; +0.4). The large volume of data allows us to stack the spectra at fixed values of σ0 and [Mg/Fe]. Our analysis – based on gravity-sensitive line strengths – gives a strong correlation with central velocity dispersion and a negligible variation with [Mg/Fe] at fixed σ0. This result is robust against individual elemental abundance variations, and seems not to raise any apparent inconsistency with the alternative method based on galaxy dynamics.