The integral Newton's and MacLaurin's theorems in tensor form

Caimmi, R.

doi:10.1002/asna.200310083

Cited by 7 publications

(20 citation statements)

References 15 publications

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“…(1) is formally correct, it is incomplete and imprecise because it does not explicitly separate the mass of the stars and gas (baryonic mass in general) and the mass of dark matter, it does not specify the mass-radius relationship, and it also neglects the possibility that other terms due to other effects are present. To improve upon this issue, we can derive another expression for the theoretical log(L)−log(σ) relation based on the virial theorem developed by Caimmi (2003Caimmi ( , 2009 in which dark matter (DM) and baryonic matter (BM) are treated separately. The details are given in Appendix A.…”

Section: Theoretical Introductionmentioning

confidence: 99%

The parallelism between galaxy clusters and early-type galaxies

D’Onofrio

Chiosi

Sciarratta

et al. 2020

A&A

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Context. This is the second work dedicated to the observed parallelism between galaxy clusters (GCs) and early-type galaxies (ETGs). The focus is on the distribution of these systems in the scaling relations (SRs) observed when effective radii, effective surface brightness, total luminosities, and velocity dispersions are mutually correlated. Aims. Using the data of the Illustris simulation we speculate on the origin of the observed SRs. Methods. We compare the observational SRs extracted from the database of the WIde-field Nearby Galaxy-cluster Survey with the relevant parameters coming from the Illustris simulations. Then we use the simulated data at different redshift to infer the evolution of the SRs. Results. The comparison demonstrate that GCs at z ∼ 0 follow the same log(L)−log(σ) relation of ETGs and that both in the log(⟨I⟩e)−log(Re) and log(Re)−log(M*) planes the distribution of GCs is along the sequence defined by the brightest and massive early-type galaxies (BCGs). The Illustris simulation reproduces the tails of the massive galaxies visible both in the log(⟨I⟩e)−log(Re) and log(Re)−log(M*) planes, but fails to give the correct estimate of the effective radii of the dwarf galaxies that appear too large and those of GCs that are too small. The evolution of the SRs up to z = 4 permits to reveal the complex evolutionary paths of galaxies in the SRs and indicate that the line marking the zone of exclusion, visible in the log(⟨I⟩e)−log(Re) and the log(Re)−log(M*) planes, is the trend followed by virialized and passively evolving systems. Conclusions. We speculate that the observed SRs originate from the intersection of the virial theorem and a relation L = L0′σβ where the luminosities depend on the star formation history.

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Section: Theoretical Introductionmentioning

confidence: 99%

The parallelism between galaxy clusters and early-type galaxies

D’Onofrio

Chiosi

Sciarratta

et al. 2020

A&A

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“…The relations between current and polytropic dimensionless density and radial coordinate, may be deduced by comparison of Eqs. (8) and (9) with (44) and (43), respectively. The result is:…”

Section: Polytropic Density Profilesmentioning

confidence: 99%

“…To this aim, the current paper takes into consideration a restricted number of density profiles, part obeying an equilibrium equation and part being purely descriptive. For sake of simplicity, attention shall be restricted to spherical-symmetric configurations, even if the formulation maintains for homeoidally striated ellipsoidal configurations as far as radial properties are concerned (e.g., Caimmi 1993Caimmi , 2003Caimmi and Marmo 2003). To emphasize the above mentioned property, sphericalsymmetric density profiles shall be quoted henceforth as homeoidally striated spherical density profiles.…”

Section: Introductionmentioning

confidence: 99%

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Gravitational acceleration and tidal effects in spherical-symmetric density profiles

Caimmi¹

2015

ams

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Pure power-law density profiles, ρ(r) ∝ r b−3 , are classified in connection with the following reference cases: (i) isodensity, b = 3, ρ = const; (ii) isogravity, b = 2, g = const; (iii) isothermal, b = 1, v = [GM (r)/r] 1/2 = const; (iv) isomass, b = 0, M = const. A restricted number of different families of density profiles including, in addition, cored power-law, generalized power-law, polytropes, are studied in detail with regard to both one-component and two-component systems. Considerable effort is devoted to the existence of an extremum point (maximum absolute value) in the gravitational acceleration within the matter distribution. Predicted velocity curves are compared to the data inferred from observations. Tidal effects on an inner subsystem are investigated and an application is made to globular clusters within the Galaxy. To this aim, the tidal radius is defined by balancing the opposite gravitational forces from the Galaxy and the selected cluster on a special point of the cluster boundary, lying between related centres of mass. The position of 17 globular clusters with respect to the stability region, where the tidal radius exceeds the observed radius, is shown for assigned dark-to-visible mass ratios and density profiles, among those considered, which are currently used for the description of galaxies and/or dark matter haloes.

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“…(6)and (109)-(112), the potential-energy tensor takes the equivalent form:(E sel ) pq = −kπGρ c I pq A p ; sel ν mas Ξ 3 ν inr ;(113b)being k, by definition, a profile factor. Owing to Eqs (8),(19),(21),(31),(32),. (113b), the normalized rotation parameter, defined by Eq.…”

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confidence: 99%

Why there are no elliptical galaxies more flattened than E7: Thirty years later

Caimmi

2006

SERBIAN ASTRON J

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Elliptical galaxies are modelled as homeoidally striated Jacobi ellipsoids (Caimmi & Marmo 2005) where the peculiar velocity distribution is anisotropic, or equivalently as their adjoints configurations i.e. classical Jacobi ellipsoids of equal mass and axes, in real or imaginary rotation (Caimmi 2006). Reasons for the coincidence of bifurcation points from axisymmetric to triaxial configurations in both the sequences (Caimmi 2006), contrary to earlier findings (Wiegandt 1982a,b;Caimmi & Marmo 2005) are presented and discussed. The effect of centrifugal support at the ends of the major equatorial axis, is briefly outlined. The existence of a lower limit to the flattening of elliptical galaxies is investigated in dealing with a number of limiting situations. More specifically, (i) elliptical galaxies are considered as isolated systems, and an allowed region within Ellipsoidland (Hunter & de Zeeuw 1997), related to the occurrence of bifurcation points from ellipsoidal to pear-shaped configurations, is shown to be consistent with observations; (ii) elliptical galaxies are considered as embedded within dark matter haloes and, under reasonable assumptions, it is 1 shown that tidal effects from hosting haloes have little influence on the above mentioned results; (iii) dark matter haloes and embedded elliptical galaxies, idealized as a single homeoidally striated Jacobi ellipsoid, are considered in connection with the cosmological transition from expansion to relaxation, by generalizing an earlier model (Thuan & Gott 1975), and the existence of a lower limit to the flattening of relaxed (oblate-like) configurations, is established. On the other hand, no lower limit is found to the elongation of relaxed (prolate-like) configurations, and the observed lack of elliptical galaxies more elongated than E7 needs a different physical interpretation, such as the occurrence of bending instabilities (Polyachenko

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The integral Newton's and MacLaurin's theorems in tensor form

Cited by 7 publications

References 15 publications

The parallelism between galaxy clusters and early-type galaxies

The parallelism between galaxy clusters and early-type galaxies

Gravitational acceleration and tidal effects in spherical-symmetric density profiles

Why there are no elliptical galaxies more flattened than E7: Thirty years later

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