Effective Velocity Dispersion Research Articles

THE FUNDAMENTAL PLANE OF MASSIVE QUIESCENT GALAXIES OUT TO z ∼ 2

The Fundamental Plane (FP) of early-type galaxies, relating the effective radius, velocity dispersion, and surface brightness, has long been recognized as a unique tool for analyzing galaxy structure and evolution. With the discovery of distant quiescent galaxies and the introduction of high sensitivity near-infrared spectrographs, it is now possible to explore the FP out to z~2. In this Letter we study the evolution of the FP out to z~2 using kinematic measurements of massive quiescent galaxies ($M_{*}>10^{11} M_{\odot}$). We find preliminary evidence for the existence of an FP out to z~2. The scatter of the FP, however, increases from z~0 to z~2, even when taking into account the larger measurement uncertainties at higher redshifts. We find a strong evolution of the zero point from z~2 to z~0: $\Delta\log_{10}M/L_g\propto(-0.49\pm0.03)~z$. In order to assess whether our spectroscopic sample is representative of the early-type galaxy population at all redshifts, we compare their rest-frame g-z colors with those from a larger mass complete sample of quiescent galaxies. At z>1 we find that the spectroscopic sample is bluer. We use the color offsets to estimate a mass-to-light ratio (M/L) correction. The implied FP zero point evolution after correction is significantly smaller: $\Delta\log_{10}M/L_g\propto(-0.39\pm 0.02)~z$. This is consistent with an apparent formation redshift of $z_{\rm{form}}=6.62^{+3.19}_{-1.44}$ for the underlying population, ignoring the effects of progenitor bias. A more complete spectroscopic sample is required at z~2 to properly measure the M/L evolution from the FP evolution.

Understanding the structural scaling relations of early-type galaxies

We use a large suite of hydrodynamical simulations of binary galaxy mergers to construct and calibrate a physical prescription for computing the effective radii and velocity dispersions of spheroids. We implement this prescription within a semi-analytic model embedded in merger trees extracted from the Bolshoi Lambda-CDM N-body simulation, accounting for spheroid growth via major and minor mergers as well as disk instabilities. We find that without disk instabilities, our model does not predict sufficient numbers of intermediate mass early-type galaxies in the local universe. Spheroids also form earlier in models with spheroid growth via disk instabilities. Our model correctly predicts the normalization, slope, and scatter of the low-redshift size-mass and Fundamental Plane relations for early type galaxies. It predicts a degree of curvature in the Faber-Jackson relation that is not seen in local observations, but this could be alleviated if higher mass spheroids have more bottom-heavy initial mass functions. The model also correctly predicts the observed strong evolution of the size-mass relation for spheroids out to higher redshifts, as well as the slower evolution in the normalization of the Faber-Jackson relation. We emphasize that these are genuine predictions of the model since it was tuned to match hydrodynamical simulations and not these observations.

CLASH: EXTENDING GALAXY STRONG LENSING TO SMALL PHYSICAL SCALES WITH DISTANT SOURCES HIGHLY MAGNIFIED BY GALAXY CLUSTER MEMBERS

We present a strong lensing system in which a double source is imaged 5 times by 2 early-type galaxies. We take advantage in this target of the multi-band photometry obtained as part of the CLASH program, complemented by the spectroscopic data of the VLT/VIMOS and FORS2 follow-up campaign. We use a photometric redshift of 3.7 for the source and confirm spectroscopically the membership of the 2 lenses to the galaxy cluster MACS J1206.2-0847 at redshift 0.44. We exploit the excellent angular resolution of the HST/ACS images to model the 2 lenses in terms of singular isothermal sphere profiles and derive robust effective velocity dispersions of (97 +/- 3) and (240 +/- 6) km/s. The total mass distribution of the cluster is also well characterized by using only the local information contained in this lensing system, that is located at a projected distance of more than 300 kpc from the cluster luminosity center. According to our best-fitting lensing and composite stellar population models, the source is magnified by a total factor of 50 and has a luminous mass of about (1.0 +/- 0.5) x 10^{9} M_{Sun}. By combining the total and luminous mass estimates of the 2 lenses, we measure luminous over total mass fractions projected within the effective radii of 0.51 +/- 0.21 and 0.80 +/- 0.32. With these lenses we can extend the analysis of the mass properties of lens early-type galaxies by factors that are about 2 and 3 times smaller than previously done with regard to, respectively, velocity dispersion and luminous mass. The comparison of the total and luminous quantities of our lenses with those of astrophysical objects with different physical scales reveals the potential of studies of this kind for investigating the internal structure of galaxies. These studies, made possible thanks to the CLASH survey, will allow us to go beyond the current limits posed by the available lens samples in the field.

First gravitational lensing mass estimate of a damped Lyman α galaxy at z = 2.2

Abstract We present the first lensing total mass estimate of a galaxy, at redshift 2.207, that acts as a gravitational deflector and damped Lyman α absorber on the background QSO SDSS J1135−0010, at redshift 2.888. The remarkably small projected distance, or impact parameter, between the lens and the source has been estimated to be 0.8 ± 0.1 kpc in a recent work. By exploiting the Sloan Digital Sky Survey data base, we establish a likely lensing magnification signal in the photometry of the QSO. This is determined to be 2.2 mag brighter (or eight times more luminous) than the median QSO at comparable redshifts. We describe the total mass distribution of the lens galaxy with a one-component singular isothermal sphere model and contrast the values of the observed and model-predicted magnification factors. For the former, we use conservatively the photometric data of the 95 per cent of the available distant QSO population. We estimate that the values of the lens effective velocity dispersion and two-dimensional total mass, projected within a cylinder with radius equal to the impact parameter, are included between 60 and 170 km s−1 and 2.1 × 109 and 1.8 × 1010 M⊙, respectively. We conclude by remarking that analyses of this kind are crucial to exploring the relation between the luminous and dark-matter components of galaxies in the high-redshift Universe.

A simple way to classify supermassive black holes

AbstractWe propose a classification of supermassive black holes (SMBHs) based on their efficiency in the conversion of infalling mass in emitted radiation. We use a theoretical model that assumes a conservation of angular momentum between the gas falling inside the hole and the photons emitted outwards, and suggests the existence of the scaling relation M•‐Reσ3, where M• is the mass of the central SMBH, whereas Re and σ are the effective radius and velocity dispersion of the host galaxies (bulges), respectively. We apply our model on a data set of 57 galaxies of different morphological types and with M• measurements, obtained through the analysis of Spitzer /IRAC 3.6‐µ m images. In order to find the best fit of the corresponding scaling law, we use the FITEXY routine to perform a least‐squares regression of M• on Reσ3 for the considered sample of galaxies. Our analysis shows that the relation is tight and our theoretical model allows to easily estimate the efficiency of mass conversion into radiation of the central SMBHs. Finally we propose a new appealing way to classify the SMBHs in terms of this parameter. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

M• − σrelation for intermediate-mass black holes in globular clusters

For galaxies hosting supermassive black holes (SMBHs), it has been observed that the mass of the central black hole (M_BH) tightly correlates with the effective or central velocity dispersion (sigma) of the host galaxy. The origin of this M_BH - sigma scaling relation is assumed to lie in the merging history of the galaxies but many open questions about its origin and the behavior in different mass ranges still need to be addressed. The goal of this work is to study the black-hole scaling relations for low black-hole masses, where the regime of intermediate-mass black holes (IMBHs) in globular clusters (GCs) is entered. We collect all existing reports of dynamical black-hole measurements in globular clusters, providing black-hole masses or upper limits for 14 candidates. We plot the black-hole masses versus different cluster parameters including total mass, velocity dispersion, concentration and half-mass radius. We search for trends and test the correlations in order to quantify their significance using a set of different statistical approaches. For correlations showing a large significance we perform a linear fit, accounting for uncertainties and upper limits. We find a clear correlation between the mass of the IMBH and the velocity dispersion of the globular cluster. As expected, the total mass of the globular cluster then also correlates with the mass of the IMBH. While the slope of the M_BH - sigma correlation differs strongly from the one observed for SMBHs, the other scaling relations M_BH - M_TOT, and M_BH - L are similar to the correlations in galaxies. Significant correlations of black-hole mass with other cluster properties were not found in the present sample.

Measuring the slopes of mass profiles for dwarf spheroidals in triaxial cold dark matter potentials

Abstract We generate stellar distribution functions (DFs) in triaxial haloes in order to examine the reliability of slopes Γ ≡ Δlog M/Δlog r inferred by applying mass estimators of the form M∝Reσ2 (i.e. assuming spherical symmetry, where Re and σ are luminous effective radius and global velocity dispersion, respectively) to two stellar subpopulations independently tracing the same gravitational potential. The DFs take the form f(E), are dynamically stable and are generated within triaxial potentials corresponding directly to subhaloes formed in cosmological dark-matter-only simulations of Milky Way and galaxy cluster haloes. Additionally, we consider the effect of different tracer number density profiles (cuspy and cored) on the inferred slopes of mass profiles. For the isotropic DFs considered here, we find that halo triaxiality tends to introduce an anticorrelation between Re and σ when estimated for a variety of viewing angles. The net effect is a negligible contribution to the systematic error associated with the slope of the mass profile, which continues to be dominated by a bias towards greater overestimation of masses for more concentrated tracer populations. We demonstrate that simple mass estimates for two distinct tracer populations can give reliable lower limits for Γ, irrespective of the degree of triaxiality or shape of the tracer number density profile.

Upscaling of solute transport in heterogeneous media with non-uniform flow and dispersion fields

An analytical and computational model for non-reactive solute transport in periodic heterogeneous media with arbitrary non-uniform flow and dispersion fields within the unit cell of length ε is described. The model lumps the effect of non-uniform flow and dispersion into an effective advection velocity Ve and an effective dispersion coefficient De. It is shown that both Ve and De are scale-dependent (dependent on the length scale of the microscopic heterogeneity, ε), dependent on the Péclet number Pe, and on a dimensionless parameter α that represents the effects of microscopic heterogeneity. The parameter α, confined to the range of [−0.5, 0.5] for the numerical example presented, depends on the flow direction and non-uniform flow and dispersion fields. Effective advection velocity Ve and dispersion coefficient De can be derived for any given flow and dispersion fields, and ε. Homogenized solutions describing the macroscopic variations can be obtained from the effective model. Solutions with sub-unit-cell accuracy can be constructed by homogenized solutions and its spatial derivatives. A numerical implementation of the model compared with direct numerical solutions using a fine grid, demonstrated that the new method was in good agreement with direct solutions, but with significant computational savings.

SPIDER - VI. The central dark matter content of luminous early-type galaxies: Benchmark correlations with mass, structural parameters and environment

We analyze the central dark-matter (DM) content of \sim 4,500 massive (M* \gsim 10^{10} Msun), low-redshift (z<0.1), early-type galaxies (ETGs), with high-quality ugrizYJHK photometry and optical spectroscopy from SDSS and UKIDSS. We estimate the "central" fraction of DM within the K-band effective radius, \Re, using spherically symmetric isotropic galaxy models. We discuss the role of systematics. The main results of the present work are the following: (1) DM fractions increase systematically with both structural parameters and mass proxies, as in previous studies, and decrease with central stellar density. 2) All correlations involving DM fractions are caused by two fundamental ones with galaxy effective radius and central velocity dispersion. These correlations are independent of each other, so that ETGs populate a central-DM plane (DMP), i.e. a correlation among fraction of total-to-stellar mass, effective radius, and velocity dispersion, whose scatter along the total-to-stellar mass axis amounts to \sim 0.15 dex. (3) In general, under the assumption of an isothermal or a constant M/L profile for the total mass distribution, a Chabrier IMF is favoured with respect to a bottom-heavier Salpeter IMF, as the latter produces negative (i.e. unphysical) DM fractions for more than 50% of the galaxies in our sample. For a Chabrier IMF, the DM estimates agree with \LambdaCDM toy-galaxy models based on contracted DM-halo density profiles. We also find agreement with predictions from hydrodynamical simulations. (4) The central DM content of ETGs does not depend significantly on the environment where galaxies reside, with group and field ETGs having similar DM trends. (Abridged)

An Oxford SWIFT integral field spectroscopy study of 14 early-type galaxies in the Coma cluster

As a demonstration of the capabilities of the new Oxford SWIFT integral field spectrograph, we present first observations for a set of 14 early-type galaxies in the core of the Coma cluster. Our data consist of I- and z-band spatially resolved spectroscopy obtained with the Oxford SWIFT spectrograph, combined with r-band photometry from the SDSS archive for 14 early- type galaxies. We derive spatially resolved kinematics for all objects from observations of the calcium triplet absorption features at \sim 8500 {AA} . Using this kinematic information we classify galaxies as either Fast Rotators or Slow Rotators. We compare the fraction of fast and slow rotators in our sample, representing the densest environment in the nearby Universe, to results from the ATLAS3D survey, finding the slow rotator fraction is \sim 50 per cent larger in the core of the Coma cluster than in the Virgo cluster or field, a 1.2 {\sigma} increase given our selection criteria. Comparing our sample to the Virgo cluster core only (which is 24 times less dense than the Coma core) we find no evidence of an increase in the slow rotator fraction. Combining measurements of the effective velocity dispersion {\sigma_e} with the photometric data we determine the Fundamental Plane for our sample of galaxies. We find the use of the average velocity dispersion within 1 effective radius, {\sigma_e}, reduces the residuals by 13 per cent with respect to comparable studies using central velocity dispersions, consistent with other recent integral field Fundamental Plane determinations.

A NEARBY ANALOG OF z ∼ 2 COMPACT QUIESCENT GALAXIES WITH A ROTATING DISK

Recent studies have identified a population of compact quiescent galaxies at z\sim2. These galaxies are very rare today and establishing the existence of a nearby analog could allow us to study its structure in greater detail than is possible at high redshift. Here we present such a local analog, NGC 5845, which has a dynamical mass of M_dyn = 4.3\pm0.6\times10^10 M_sun and an effective radius of only r_e = 0.45\pm0.05kpc. We study the structure and kinematics with HST/WFPC2 data and previously published spatially resolved kinematics. We find that NGC 5845 is similar to compact quiescent galaxies at z\sim2 in terms of size versus dynamical mass (r_e-M_dyn), effective velocity dispersion versus size (sigma_e-r_e), and effective velocity dispersion versus dynamical mass (sigma_e-M_dyn). The galaxy has a prominent rotating disk evident in both the photometry and the kinematics: it extends to well beyond \geq1/3 effective radius and contribute to \geq1/4 of the total light of the galaxy. Our results lend support to the idea that a fraction of z\sim2 compact galaxies have prominent disks and positive mass-to-light ratio gradients, although we caution that NGC 5845 may have had a different formation history than the more massive compact quiescent galaxies at z\sim2.

The 6dF Galaxy Survey: stellar population trends across and through the Fundamental Plane

We present results from an analysis of stellar population parameters for 7132 galaxies in the 6dFGS Fundamental Plane (FP) sample. We bin the galaxies along the axes, $v_1$, $v_2$, and $v_3$, of the tri-variate Gaussian to which we have fit the galaxy distribution in effective radius, surface brightness, and central velocity dispersion (FP space), and compute median values of stellar age, [Fe/H], [Z/H], and [$\alpha$/Fe]. We determine the directions of the vectors in FP space along which each of the binned stellar population parameters vary most strongly. In contrast to previous work, we find stellar population trends not just with velocity dispersion and FP residual, but with radius and surface brightness as well. The most remarkable finding is that the stellar population parameters vary through the plane ($v_1$ direction) and across the plane ($v_3$ direction), but show no variation at all along the plane ($v_2$ direction). The $v_2$ direction in FP space roughly corresponds to `luminosity density'. We interpret a galaxy's position along this vector as being closely tied to its merger history, such that early-type galaxies with lower luminosity density are more likely to have undergone major mergers. This conclusion is reinforced by an examination of the simulations of Kobayashi (2005), which show clear trends of merger history with $v_2$.

The SAURON project - XX. The Spitzer [3.6] − [4.5] colour in early-type galaxies: colours, colour gradients and inverted scaling relations

We investigate the [3.6] - [4.5] Spitzer-IRAC colour behaviour of the early-type galaxies of the SAURON survey, a representative sample of 48 nearby ellipticals and lenticulars. We investigate how this colour, which is unaffected by dust extinction, can be used to constrain the stellar populations in these galaxies. We find a tight relation between the [3.6]-[4.5] colour and effective velocity dispersion, a good mass-indicator in early-type galaxies. Contrary to other colours in the optical and near-infrared, we find that the colours become bluer for larger galaxies. The relations are tighter when using the colour inside r_e, rather than the much smaller r_e/8 aperture, due to the presence of young populations in the central regions. We also obtain strong correlations between the [3.6]-[4.5] colour and 3 strong absorption lines (H beta, Mg b and Fe 5015). Comparing our data with the models of Marigo et al., which show that more metal rich galaxies are bluer, we can explain our results in a way consistent with results from the optical, by stating that larger galaxies are more metal rich. The blueing is caused by a strong CO absorption band, whose line strength increases strongly with decreasing temperature and which covers a considerable fraction of the 4.5 micron filter. In galaxies that contain a compact radio source, the [3.6]-[4.5] colour is generally slightly redder than in the other galaxies, indicating small amounts of either hot dust, non-thermal emission, or young stars near the center. We find that the large majority of the galaxies show redder colours with increasing radius. abbreviated...

Dark matter-rich early-type galaxies in the CASSOWARY 5 strong lensing system

We study the strong gravitational lensing system number 5 identified by the CAmbridge Sloan Survey Of Wide ARcs in the skY (CASSOWARY). In this system, a source at redshift 1.069 is lensed into four detected images by two early-type galaxies at redshift 0.388. The average projected angular distance of the multiple images from the primary lens is 12.6 kpc, corresponding to approximately 1.3 times the value of the galaxy effective radius. The observed positions of the multiple images are well reproduced by a model in which the total mass distribution of the deflector is described in terms of two singular isothermal sphere profiles and a small external shear component. The values of the effective velocity dispersions of the two lens galaxies are 328+7− 8 and 350+17− 18 km s−1. The best-fitting lensing model predicts magnification values larger than 2 for each multiple image and a total magnification factor of 17. By modelling the lens galaxy spectral energy distributions, we measure lens luminous masses of (3.09 ± 0.30) × 1011 and (5.87 ± 0.58) × 1011 M⊙ and stellar mass-to-light ratios of 2.5 ± 0.3 and 2.8 ± 0.3 M⊙ L−1⊙, i (in the observed i band). These values are used to disentangle the luminous and dark matter components in the vicinity of the multiple images. We estimate that the dark over total mass ratio projected within a cylinder centred on the primary lens and with a radius of 12.6 kpc is 0.8 ± 0.1. Inside the effective radii of the two galaxies, we measure projected total mass-to-light ratios of 12.6 ± 1.4 and 13.1 ± 1.7 M⊙ L−1⊙, i. We contrast these measurements with the typical values found at similar distances (in units of the effective radius) in isolated lens galaxies and show that the amount of dark matter present in these lens galaxies is almost a factor 4 larger than in field lens galaxies with comparable luminous masses. Data and models are therefore consistent with interpreting the lens of this system as a galaxy group. We infer that the overdense environment and dark matter concentration in these galaxies must have affected the assembly of the lens luminous mass components, resulting in the large values of the galaxy effective radii. We conclude that further multidiagnostics analyses on the internal properties of galaxy groups have the potential of providing us a unique insight into the complex baryonic and dark matter physics interplay that rules the formation of cosmological structures.

Evolution of the fundamental plane of 0.2 &lt; z &lt; 1.2 early-type galaxies in the EGS

The Fundamental Plane relates the structural properties of early-type galaxies such as its surface brightness and effective radius with its dynamics. The study of its evolution has therefore important implications for models of galaxy formation and evolution. This work aims to identify signs of evolution of early-type galaxies through the study of parameter correlations using a sample of 135 field galaxies extracted from the Extended Groth Strip in the redshift range 0.2<z<1.2. Using DEEP2 data, we calculate the internal velocity dispersions by extracting the stellar kinematics from absorption line spectra, using a maximum penalized likelihood approach. Morphology was determined through visual classification using the V+I images of ACS. The structural parameters of these galaxies were obtained by fitting de Vaucouleurs stellar profiles to the ACS I-band images, using the GALFIT code. S\'ersic and bulge-to-disc decomposition models were also fitted to our sample of galaxies, and we found a good agreement in the Fundamental Plane derived from the three models. Assuming that effective radii and velocity dispersions do not evolve with redshift, we have found a brightening of 0.68 mag in the B-band and 0.52 mag in the g-band at <z>=0.7. However, the scatter in the FP is reduced by half when we allow the FP slope to evolve, suggesting a different evolution of early-type galaxies according to their intrinsic properties. The study of the Kormendy relation shows the existence of a population of very compact (Re<2 Kpc) and bright galaxies (-21.5>Mg>-22.5), of which there are only a small fraction (0.4%) at z=0. The evolution of these compact objects is mainly caused by an increase in size that could be explained by the action of dry minor mergers, and this population is responsible for the evolution detected in the Fundamental Plane.

PROJECTED CENTRAL DARK MATTER FRACTIONS AND DENSITIES IN MASSIVE EARLY-TYPE GALAXIES FROM THE SLOAN DIGITAL SKY SURVEY

We investigate in massive early-type galaxies the variation of their two-dimensional central fraction of dark over total mass and dark matter density as a function of stellar mass, central stellar velocity dispersion, effective radius, and central surface stellar mass density. We use a sample of approximately 1.7 × 105 galaxies from the Sloan Digital Sky Survey Data Release Seven (SDSS DR7) at redshift smaller than 0.33. We apply conservative photometric and spectroscopic cuts on the SDSS DR7 and the MPA/JHU value-added galaxy catalogs, to select galaxies with physical properties similar to those of the lenses studied in the Sloan Lens ACS Survey. The values of the galaxy stellar and total mass projected inside a cylinder of radius equal to the effective radius are obtained, respectively, by fitting the SDSS multicolor photometry with stellar population synthesis models, under the assumption of a Chabrier stellar initial mass function (IMF), and adopting a one-component isothermal total mass model with effective velocity dispersion approximated by the central stellar velocity dispersion. The plausibility of an isothermal model to represent the galaxy total mass distribution is supported by independent gravitational lensing and stellar-dynamical analyses performed in the lens subsample, which is found here to represent nicely the entire galaxy sample. We find that within the effective radius the stellar mass estimates differ from the total ones by only a relatively constant proportionality factor. In detail, we observe that the values of the projected fraction of dark over total mass and the logarithmic values of the central surface dark matter density (measured in M☉ kpc−2) have almost Gaussian probability distribution functions, with median values of 0.64+0.08−0.11 and 9.1+0.2−0.2, respectively. We discuss the observed correlations between these quantities and other galaxy global parameters and show that our results disfavor an interpretation of the tilt of the fundamental plane in terms of differences in the galaxy dark matter content and give useful information on the possible variations of the galaxy stellar IMF and dark matter density profile. Finally, we provide some observational evidence on the likely significant contribution of dry minor mergers, feedback from active galactic nuclei, and/or coalescence of binary black holes on the formation and evolution of massive early-type galaxies.

MOND and the lensing fundamental plane: no need for dark matter on galaxy scales

Bolton et al. have derived a mass-based fundamental plane using photometric and spectroscopic observations of 36 strong gravitational lenses. The lensing allows a direct determination of the mass-surface density and so avoids the usual dependence on mass-to-light ratio. We consider this same sample in the context of Modified Newtonian dynamics (MOND) and demonstrate that the observed mass-based fundamental plane coincides with the MOND fundamental plane determined previously for a set of polytropic spheres chosen to match the observed range of effective radii and velocity dispersions in elliptical galaxies. Moreover, the observed projected mass within one-half of an effective radius is consistent with the mass in visible stars plus a small additional component of ‘phantom dark matter’ resulting from the MOND contribution to photon deflection.

Dynamical Models of Elliptical Galaxies inz = 0.5 Clusters. II. Mass‐to‐Light Ratio Evolution without Fundamental Plane Assumptions

We study M/L evolution of early-type galaxies using dynamical modeling of resolved internal kinematics. This makes fewer assumptions than Fundamental Plane (FP) studies and provides a powerful new approach for studying galaxy evolution. We focus on the sample of 25 galaxies in clusters at z=0.5 modeled in Paper I. For comparison we compile and homogenize M/L literature data for 60 nearby galaxies that were modeled in comparable detail. The nearby sample obeys log(M/L)_B = Z + S log(sigma_eff/[200 km/s]), with Z = 0.896 +/- 0.010, S = 0.992 +/- 0.054, and sigma_eff the effective velocity dispersion. The z=0.5 sample follows a similar relation but with lower zeropoint. The implied M/L evolution is Delta log(M/L) / Delta z = -0.457 +/- 0.046(random) +/- 0.078(systematic), consistent with passive evolution following high-redshift formation. This agrees with the FP results for this sample by van Dokkum & van der Marel. This confirms that FP evolution tracks M/L evolution, which is an important verification of the assumptions that underly FP studies. However, while we find more FP evolution for galaxies of low sigma_eff (or low mass), the dynamical M/L evolution instead shows little trend with sigma_eff. We argue that this difference can be plausibly attributed to a combination of two effects: (a) evolution in structural galaxy properties other than M/L; and (b) the neglect of rotational support in studies of FP evolution. The results leave the question open whether the low-mass galaxies in the sample have younger population ages than the high-mass galaxies. This highlights the general importance in the study of population ages for complementing dynamical measurements with broad-band colors or spectroscopic population diagnostics.

Luminosity dependence in the Fundamental Plane projections of elliptical galaxies

We analyse the Fundamental Plane projections of elliptical galaxies as a function of luminosity, using a sample of ≈80 000 galaxies drawn from Data Release 4 (DR4) of the Sloan Digital Sky Survey (SDSS). We separate brightest cluster galaxies (BCGs) from our main sample and reanalyse their photometry due to a problem with the default pipeline sky subtraction for BCGs. The observables we consider are effective radius (Re), velocity dispersion (σ), dynamical mass (Mdyn∝Reσ2), effective density (σ2/R2e) and effective surface brightness (μe). With the exception of the L–Mdyn correlation, we find evidence of variations in the slope (i.e. the power-law index) of the Fundamental Plane projections with luminosity for our normal elliptical galaxy population. In particular, the radius–luminosity and Faber–Jackson relations are steeper at high luminosity relative to low luminosity, and the more luminous ellipticals become progressively less dense and have lower surface brightnesses than lower luminosity ellipticals. These variations can be understood as arising from differing formation histories, with more luminous galaxies having less dissipation. Data from the literature and our reanalysis of BCGs show that BCGs have radius–luminosity and Faber–Jackson relations steeper than the brightest non-BCG ellipticals in our sample, consistent with significant growth of BCGs via dissipationless mergers. The variations in slope we find in the Faber–Jackson relation of non-BCGs are qualitatively similar to that reported in the black hole mass–velocity dispersion (MBH–σ) correlation. This similarity is consistent with a roughly constant value of MBH/M★ over a wide range of early-type galaxies, where M★ is the stellar mass.

Design of tunable bandgap guidance in high-index filled microstructure fibers

Tunable photonic bandgap (PBG) microstructure fibers, which were filled nematic liquid crystals (NLC), were theoretically investigated based on bandgap theory. By means of the modified plane-wave method, it is found that PBGs shift to the longer wavelength with increasing refractive index of NLC [ny(θ)] for y-polarized light. Fundamental modes are found in these PBG reigns, whose effective mode area, leakage loss and group velocity dispersion (GVD) have been calculated by using the full-vector finite-element method with anisotropic perfectly matched layers. The mode fields become larger with the increase of ny(θ), whereas the leakage loss varies slightly. Moreover, GVD is strongly dependent on ny(θ) and wavelength, which is much larger than the material dispersion of silica.