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 Physics , 2013, DOI: 10.1088/2041-8205/779/2/L21 Abstract: The Fundamental Plane (FP) is an empirical relation between the size, surface brightness, and velocity dispersion of early-type galaxies. This relation has been studied extensively for early-type galaxies in the local universe to constrain galaxy formation mechanisms. The evolution of the zeropoint of this plane has been extended to high redshifts to study the luminosity evolution of massive galaxies, under the assumption of structural homology. In this work, we assess this assumption by replacing surface brightness with stellar mass density and present the evolution of the "mass FP" for massive, quiescent galaxies since z~2. By accounting for stellar populations, we thereby isolate and trace structural and dynamical evolution. Despite the observed dramatic evolution in the sizes and morphologies of massive galaxies since z~3, we find that quiescent galaxies lie on the mass FP out to z~2. In contrast with ~1.4 dex evolution in the luminosity FP, average residuals from the z~0 mass FP are less than ~0.15 dex since z~2. Assuming the Hyde & Bernardi (2009) mass FP slope, we find that this minimal offset scales as (1+z)^{-0.095+/-0.043}. This result lends credence to previous studies that derived luminosity evolution from the FP. Therefore, despite their compact sizes and suggestions that massive galaxies are more disk-like at z~2, the relationship between their dynamics and structural properties are consistent with local early-type galaxies. Finally, we find no strong evidence for a tilt of the mass FP relative to the Virial plane, but emphasize the need for full models including selection biases to fully investigate this issue.
 Physics , 1993, DOI: 10.1093/mnras/263.1.21L Abstract: Velocity dispersion $\sigma$, radius $R$ and luminosity $L$ of elliptical galaxies are known to be related, leaving only two degrees of freedom and defining the so-called fundamental plane". In this {\em Letter} we present observational evidence that rich galaxy clusters exhibit a similar behaviour. Assuming a relation $L \propto R^{\alpha}\sigma^{2 \beta}$, the best-fit values of $\alpha$ and $\beta$ are very close to those defined by galaxies. The dispersion of this relation is lower than 10 percent, i.e. significantly smaller than the dispersion observed in the $L-\sigma$ and $L-R$ relations. We briefly suggest some possible implications on the spread of formation times of objects and on peculiar velocities of galaxy clusters.
 Physics , 2012, Abstract: We present a series of hundreds of collisionless simulations of galaxy group mergers. These simulations are designed to test whether the properties of elliptical galaxies - including the key fundamental plane scaling relation, morphology and kinematics - can be simultaneously reproduced by dry multiple mergers in galaxy groups. Preliminary results indicate that galaxy group mergers can produce elliptical remnants lying on a tilted fundamental plane, even without a central dissipational component from a starburst. This suggests that multiple mergers in groups are an alternate avenue for the formation of elliptical galaxies which could well dominate for luminous ellipticals.
 Kenji Bekki Physics , 1998, DOI: 10.1086/305411 Abstract: We perform numerical simulations of galaxy mergers between star-forming and gas-rich spirals in order to explore the origin of the Fundamental Plane (FP) of elliptical galaxies. We consider particularly that the origin of the slope of the FP is essentially due to the non-homology in structure and kinematics of elliptical galaxies and accordingly investigate structural and kinematical properties of elliptical galaxies formed by dissipative galaxy merging with star formation. We found that the rapidity of star formation, which is defined as the ratio of dynamical time-scale of merger progenitor to the time-scale of gas consumption by star formation, is a key determinant for nonhomology parameters, such as the density profile of stellar component, the relative importance of global rotation in kinematics, and the ratio of total dynamical mass to luminous mass, in merger remnants. We furthermore found that this result does not depend so strongly on initial intrinsic spins of progenitor disks and orbital energy and angular momentum of mergers. These results strongly suggest that the structural and kinematical nonhomology observed in elliptical galaxies can be closely associated with the difference in star formation history between elliptical galaxies formed by dissipative galaxy merging. Based upon these results, we discuss a close physical relation between the origin of the FP and the star formation history of elliptical galaxies.
 Physics , 2002, DOI: 10.1046/j.1365-8711.2002.05356.x Abstract: The existence of the Fundamental Plane (FP) 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 FP thinness and tilt and the amount of radial orbital anisotropy. 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 halos, we explore the impact of radial orbital anisotropy and instability on the FP properties. The numerical results confirm a previous semi--analytical finding: the requirement of stability matches almost exactly the thinness of the FP. In other words, galaxy models that are radially anisotropic enough to be found outside the observed FP (with their isotropic parent models lying on the FP) are unstable, and their end--products fall back on the FP itself. We also find that a systematic increase of radial orbit anisotropy with galaxy luminosity cannot explain by itself the whole tilt of the FP, becoming the galaxy models unstable at moderately high luminosities: at variance with the previous case their end--products are found well outside the FP itself (abridged).
 Physics , 1998, DOI: 10.1086/311715 Abstract: The fundamental plane (FP) has an intrinsic scatter that can not be explained purely by observational errors. Using recently available age estimates for nearby early type galaxies, we show that a galaxy's position relative to the FP depends on its age. In particular, the mean FP corresponds to ellipticals with an age of ~10 Gyr. Younger galaxies are systematically brighter with higher surface brightness relative to the mean relation. Old ellipticals form an upper envelope' to the FP. For our sample of mostly non-cluster galaxies, age can account for almost half of the scatter in the B band FP. Distance determinations based on the FP may have a systematic bias, if the mean age of the sample varies with redshift. We also show that fundamental plane residuals, B-V colors and Mg_2 line strength are consistent with an ageing central burst superposed on an old stellar population. This reinforces the view that these age estimates are tracing the last major episode of star formation induced by a gaseous merger event. We briefly discuss the empirical evolutionary tracks' of merger-remnants and young ellipticals in terms of their key observational parameters.
 R. H. Sanders Physics , 1999, DOI: 10.1046/j.1365-8711.2000.03272.x Abstract: 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 the fourth power of the velocity dispersion. 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, 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 global 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 which may differ from that implied by the traditional virial theorem. Scatter about this plane is relatively insensitive to the necessary deviations from homology.
 Physics , 1999, DOI: 10.1086/312290 Abstract: We suggest the radii and luminosities of the X-ray emitting halos of elliptical galaxies define a fundamental plane with the star velocity dispersions, as for the corresponding optical observables. Since the X-ray emitting material usually is at larger radius than the stars this can be interpreted as additional evidence for a relation between the space distributions of stellar and dark mass, in analogy to the Tully-Fisher relation and flat rotation curves for spiral galaxies. The picture is complicated, however, by ellipticals with relatively low X-ray luminosities that appear to have modest dark halos, quite unlike the standard picture for spirals.
 Physics , 1999, DOI: 10.1086/312371 Abstract: Galaxy clusters approximate a planar (FP) distribution in a three-dimensional parameter space which can be characterized by optical luminosity, half-light radius, and X-ray luminosity. Using a high-quality catalog of cluster redshifts, we find the nearest neighbor cluster for those common to an FP study and the cluster catalog. Examining scatter about the FP, we find 99.2% confidence that it is dependent on nearest neighbor distance. Our study of X-Ray clusters finds that those with high central gas densities are systematically closer to neighbor clusters. If we combine results here with those of Fritsch and Buchert, we find an explanation for some of our previous conclusions: Clusters in close proximity to other clusters are more likely to have massive cooling flows because they are more relaxed and have higher central gas densities.
 Physics , 2015, DOI: 10.1088/0004-637X/813/1/77 Abstract: Diffuse radio emission in galaxy clusters is known to be related to cluster mass and cluster dynamical state. We collect the observed fluxes of radio halos, relics, and mini-halos for a sample of galaxy clusters from the literature, and calculate their radio powers. We then obtain the values of cluster mass or mass proxies from previous observations, and also obtain the various dynamical parameters of these galaxy clusters from optical and X-ray data. The radio powers of relics, halos, and mini-halos are correlated with the cluster masses or mass proxies, as found by previous authors, with the correlations concerning giant radio halos being, in general, the strongest ones. We found that the inclusion of dynamical parameters as the third dimension can significantly reduce the data scatter for the scaling relations, especially for radio halos. We therefore conclude that the substructures in X-ray images of galaxy clusters and the irregular distributions of optical brightness of member galaxies can be used to quantitatively characterize the shock waves and turbulence in the intracluster medium responsible for re-accelerating particles to generate the observed diffuse radio emission. The power of radio halos and relics is correlated with cluster mass proxies and dynamical parameters in the form of a fundamental plane.
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