Phase-space consistency of stellar dynamical models determined by separable augmented densities

An, J.; Hese, E. Van; Baes, M.

doi:10.1111/j.1365-2966.2012.20642.x

Cited by 24 publications

(18 citation statements)

References 25 publications

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“…Note that the solution of the Jeans equation does not guarantee on general grounds a physical phase-space distribution function. In order to meet the known criteria for non-negative phase-space distributions, in our analysis we restrict β(r = 0) ≤ 0 according to the result in [37] and assume r β 1 pc, since radial anisotropy close to the center of the system may underly unphysical phase-space densities [38]. Moreover, the adopted binned kinematic dataset does not probe smaller scales.…”

Section: Methodsmentioning

confidence: 99%

Dark matter self-interactions from the internal dynamics of dwarf spheroidals

Valli

2018

Nat Astron

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Dwarf spheroidal galaxies provide well-known challenges to the standard cold and collisionless dark matter scenario [1, 2]: The too-big-to-fail problem, namely the mismatch between the observed mass enclosed within the half-light radius of dwarf spheroidals [3, 4] and cold dark matter N-body predictions [5,6]; The hints for inner constant-density cores [7][8][9][10]. While these controversies may be alleviated by baryonic physics and environmental effects [11][12][13][14][15], revisiting the standard lore of cold and collisionless dark matter remains an intriguing possibility. Self-interacting dark matter [16,17] may be the successful proposal to such a small-scale crisis [18,19]. Self-interactions correlate dark matter and baryon distributions, allowing for constant-density cores in low surface brightness galaxies [20][21][22][23]. Here we report the first data-driven study of the too-bigto-fail of Milky Way dwarf spheroidals within the self-interacting dark matter paradigm. We find good description of stellar kinematics and compatibility with the concentration-mass relation from the pure cold dark matter simulation in [24]. Within the latter, a subset of Milky Way dwarfs are well fitted by cross sections of 0.5-3 cm 2 /g, while others point to values greater than 10 cm 2 /g. The internal dynamics of dwarf spheroidal galaxies (dSphs) of the Milky Way (MW)is commonly studied exploiting the kinematics of a stellar population of density ρ , in dynamical equilibrium under the gravitational potential governed by dark matter (DM), Φ DM . For a spherically symmetric steady-state system, the first moment of the collisionless Boltzmann equation for the stellar phase-space distribution takes the form:where the prime denotes logarithmic derivative in r. The stellar orbital anisotropy, β ≡ 1 − σ 2 t /σ 2 r , measures the deviation from isotropy in the stellar velocity dispersion tensor. Photometric observations of the surface brightness of these systems constrain ρ . Supplying

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Section: Methodsmentioning

confidence: 99%

Dark matter self-interactions from the internal dynamics of dwarf spheroidals

Valli

2018

Nat Astron

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“…which at leading order behaves like the equation of state of an isothermal gas 13 . Incidentally, this is also the famous equation of state usually considered in cosmology, p = ωρc 2 , with ω being a dimensionless constant.…”

Section: Pressure and The Equation Of Statementioning

confidence: 98%

“…A number of methods to construct self-consistent stellar models have appeared in the literature over the years [7,8,9,10,11,12,13]. A first approach consists in starting with known profiles for the matter distribution and gravitational fields (which can be inferred directly from photometric and kinematic observations).…”

Section: Introductionmentioning

confidence: 99%

Anisotropic models for globular clusters, Galactic bulges, and dark halos

Nguyen¹,

Pedraza²

2013

Phys. Rev. D

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Spherical systems with polytropic equations of state are of great interest in astrophysics. They are widely used to describe neutron stars, red giants, white dwarfs, brown dwarfs, main sequence stars, galactic halos, and globular clusters of diverse sizes. In this paper we construct analytically a family of self-gravitating spherical models in the post-Newtonian approximation of general relativity. These models present interesting cusps in their density profiles which are appropriate for the modeling of galaxies and dark matter halos. The systems described here are anisotropic in the sense that their equiprobability surfaces in velocity space are nonspherical, leading to an overabundance of radial or circular orbits, depending on the parameters of the model under consideration. Among the family of models, we find the post-Newtonian generalization of the Plummer and Hernquist models. A close inspection of their equation of state reveals that these solutions interpolate smoothly between a polytropic sphere in the asymptotic region and an inner core that resembles an isothermal sphere. Finally, we study the thermodynamics of these models and argue for their stability. 1

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“…The Mittag-Leffler functions are special functions playing a fundamental role in fractional calculus. Applications of the generalized Mittag-Leffler function have been recognized in several fields, ranging from astronomy 34 to physics, 35 quantum mechanics, 36 economics, 8 engineering, and applied sciences. Furthermore, new definitions of generalized fractional derivatives for the fractional differential and integral equations were introduced, and solutions of the Cauchy-type initial and boundary value problems were presented in terms of the generalized Mittag-Leffler functions.…”

Section: The Generalized Mittag-leffler Functionmentioning

confidence: 99%

Stability and chaos control of regularized Prabhakar fractional dynamical systems without and with delay

Eshaghi

Ghaziani

Ansari

2019

Math Methods in App Sciences

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In this paper, we studied the stabilization of nonlinear regularized Prabhakar fractional dynamical systems without and with time delay. We establish a Lyapunov stabiliy theorem for these systems and study the asymptotic stability of these systems without design a positive definite function V (without considering the fractional derivative of function V is negative). We design a linear feedback controller to control and stabilize the nonautonomous and autonomous chaotic regularized Prabhakar fractional dynamical systems without and with time delay. By means of the Lyapunov stability, we obtain the control parameters for these type of systems. We further present a numerical method to solve and analyze regularized Prabhakar fractional systems. Furthermore, by employing numerical simulation, we reveal chaotic attractors and asymptotic stability behaviors for four systems to illustrate the presented theorem.

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Phase-space consistency of stellar dynamical models determined by separable augmented densities

Cited by 24 publications

References 25 publications

Dark matter self-interactions from the internal dynamics of dwarf spheroidals

Dark matter self-interactions from the internal dynamics of dwarf spheroidals

Anisotropic models for globular clusters, Galactic bulges, and dark halos

Stability and chaos control of regularized Prabhakar fractional dynamical systems without and with delay

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