Generalized isochrone models for spherical stellar systems

Kuzmin, G. G.; Veltmann, Ü. I. K.

doi:10.1007/978-94-011-0922-2_55

Cited by 6 publications

(10 citation statements)

References 3 publications

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“…The halo component is represented by the Hernquist (1990) potential, which is a special case of the formula proposed by Kuzmin and Veltmann (1973):…”

Section: Model Vmentioning

confidence: 99%

Parameters of Six Selected Galactic Potential Models

Bajkova

Бобылев

2017

Open Astronomy

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This paper is devoted to the refinement of the parameters of the six three-component (bulge, disk, halo) axisymmetric Galactic gravitational potential models on the basis of modern data on circular velocities of Galactic objects located at distances up to 200 kpc from the Galactic center. In all models the bulge and disk are described by the Miyamoto-Nagai expressions. To describe the halo, the models of Allen-Santillán (I), Wilkinson-Evans (II), NavarroFrenk-White (III), Binney (IV), Plummer (V), and Hernquist (VI) are used. The sought-for parameters of potential models are determined by fitting the model rotation curves to the measured velocities, taking into account restrictions on the local dynamical matter density ρ ⊙ = 0.1M ⊙ pc −3 and the vertical force |K z=1.1 |/2πG = 77M ⊙ pc −2 . A comparative analysis of the refined potential models is made and for each of the models the estimates of a number of the Galactic characteristics are presented.

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“…The halo component is represented by the Hernquist (1990) potential, which is a special case of the formula proposed by Kuzmin and Veltmann (1973):…”

Section: Model Vmentioning

confidence: 99%

Parameters of Six Selected Galactic Potential Models

Bajkova

Бобылев

2017

Open Astronomy

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“…When c = 1, (32) is the anisotropic DF of Ossipkov-Merritt type (OM). It was found earlier by Kuzmin and Veltmann (1967a). the smaller the anisotropic parameter c, the more anisotropic the model.…”

Section: Anisotropic Plummer Modelsmentioning

confidence: 77%

Anisotropic distribution functions for spherical galaxies

Jiang¹,

Ossipkov

2007

Celestial Mech Dyn Astr

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A method is presented for finding anisotropic distribution functions for stellar systems with known, spherically symmetric, densities, which depends only on the two classical integrals of the energy and the magnitude of the angular momentum. It requires the density to be expressed as a sum of products of functions of the potential and of the radial coordinate. The solution corresponding to this type of density is in turn a sum of products of functions of the energy and of the magnitude of the angular momentum. The products of the density and its radial and transverse velocity dispersions can be also expressed as a sum of products of functions of the potential and of the radial coordinate. Several examples are given, including some of new anisotropic distribution functions. This device can be extended further to the related problem of finding two-integral distribution functions for axisymmetric galaxies.Comment: 5 figure

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“…∆ vir = 0.907 • 323 = 292.961 ; (27) can be used to an acceptable extent 3 . As clearly pointed out in RTM, owing to the random criterion used for selection, their sample haloes are characterized by varying dynamical proper-ties: at the present time, some are more relaxed, while others are dynamically perturbed.…”

Section: The Rfsmmethodsmentioning

confidence: 99%

“…(iv) Different criterions in fitting GPL to SDH density profiles, such as minimizing the maximum fractional deviations of the fit, max | log(ρ GP L /ρ h )− log(ρ SDH /ρ h )| (e.g., Klypin et al 2001); the sum of the squares of was first defined by Hernquist [1990, Eq. ( 43) therein], even if his attention was restricted to the special case, (α, β, γ) = (1, 4, 1) which, in turn, was earlier proposed by Kuzmin & Veltmann (1973). A family of density profiles including the special case studied by Hernquist, the so called γ models, where (α, β, γ) = (1, 4, γ), was given independently by Dehnen (1993) and Tremaine et al (1994).…”

Section: Introductionmentioning

confidence: 99%

A numerical fit of analytical to simulated density profiles in dark matter haloes

2005

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Analytical and geometrical properties of generalized power-law (GPL) density profiles are investigated in detail. In particular, a one-to-one correspondence is found between mathematical parameters (a scaling radius, r_0, a scaling density, rho_0, and three exponents, alpha, beta, gamma), and geometrical parameters (the coordinates of the intersection of the asymptotes, x_C, y_C, and three vertical intercepts, b, b_beta, b_gamma, related to the curve and the asymptotes, respectively): (r_0,rho_0,alpha,beta,gamma) <--> (x_C,y_C,b,b_beta,b_gamma). Then GPL density profiles are compared with simulated dark haloes (SDH) density profiles, and nonlinear least-absolute values and least-squares fits involving the above mentioned five parameters (RFSM5 method) are prescribed. More specifically, the sum of absolute values or squares of absolute logarithmic residuals, R_i= log rhoSDH(r_i)-log rhoGPL(r_i), is evaluated on 10^5 points making a 5- dimension hypergrid, through a few iterations. The size is progressively reduced around a fiducial minimum, and superpositions on nodes of earlier hypergrids are avoided. An application is made to a sample of 17 SDHs on the scale of cluster of galaxies, within a flat LambdaCDM cosmological model (Rasia et al. 2004). In dealing with the mean SDH density profile, a virial radius, rvir, averaged over the whole sample, is assigned, which allows the calculation of the remaining parameters. Using a RFSM5 method provides a better fit with respect to other methods. The geometrical parameters, averaged over the whole sample of best fitting GPL density profiles, yield (alpha,beta,gamma) approx(0.6,3.1,1.0), to be compared with (alpha,beta,gamma)=(1,3,1), i.e. the NFW density profile (Navarro et al. 1995, 1996, 1997), (alpha,beta,gamma)=(1.5,3,1.5) (Moore et al. 1998, 1999), (alpha,beta,gamma)=(1,2.5,1) (Rasia et al. 2004); and, in addition, gamma approx 1.5 (Hiotelis 2003), deduced from the application of a RFSM5 method, but using a different definition of scaled radius, or concentration; and gamma approx 1.2-1.3 deduced from more recent high-resolution simulations (Diemand et al. 2004, Reed et al. 2005). No evident correlation is found between SDH dynamical state (relaxed or merging) and asymptotic inner slope of the fitting logarithmic density profile or (for SDH comparable virial masses) scaled radius. Mean values and standard deviations of some parameters are calculated, and in particular the decimal logarithm of the scaled radius, xivir, reads < log xivir >=0.74 and sigma_s log xivir=0.15-0.17, consistent with previous results related to NFW density profiles. It provides additional support to the idea, that NFW density profiles may be considered as a convenient way to parametrize SDH density profiles, without implying that it necessarily produces the best possible fit (Bullock et al. 2001). A certain degree of degeneracy is found in fitting GPL to SDH density profiles. If it is intrinsic to the RFSM5 method or it could be reduced by the next generation of high-resolution simulations, stil...

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Generalized isochrone models for spherical stellar systems

Cited by 6 publications

References 3 publications

Parameters of Six Selected Galactic Potential Models

Parameters of Six Selected Galactic Potential Models

Anisotropic distribution functions for spherical galaxies

A numerical fit of analytical to simulated density profiles in dark matter haloes

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