General polytropic Larson–Penston-type collapses

Lou, Yu‐Qing; Shi, Chenwei

doi:10.1093/mnras/stu1568

Cited by 13 publications

(8 citation statements)

References 81 publications

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“…After integrating the Poisson equation, the evolution equations can be reduced to a system of two coupled nonlinear partial differential equations, which can subsequently be reduced to a single nonlinear second order partial differential equations for the mass of the condensate M (r, t). For many hydrodynamic flow models in gravitational fields, with matter obeying a polytropic equation of state the equations of motion admit semi-analytical selfsimilar or homologously collapsing solutions [195][196][197][198][199].…”

Section: Discussion and Final Remarksmentioning

confidence: 99%

“…The homologous solutions are stable against linear nonspherical perturbations, a result which can explains the remarkable stability of the galactic dark matter halos. However, in the case of index n = 1 polytropes no self-similar solution does exist, and the solutions of the equations of motion cannot be written in the form Φ(r, t) = f (t)g (r/t) [195][196][197][198][199]. This means that during their evolution the physical quantities describing Bose-Einstein Condensate dark matter halos are not scale and time invariant.…”

Section: (147)mentioning

confidence: 99%

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Jeans instability and turbulent gravitational collapse of Bose–Einstein condensate dark matter halos

Harkó

2019

Eur. Phys. J. C

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We consider the Jeans instability and the gravitational collapse of the rotating Bose-Einstein Condensate dark matter halos, described by the zero temperature non-relativistic Gross-Pitaevskii equation, with repulsive inter-particle interactions. In the Madelung representation of the wave function, the dynamical evolution of the galactic halos is described by the continuity and the hydrodynamic Euler equations, with the condensed dark matter satisfying a polytropic equation of state with index n = 1. By considering small perturbations of the quantum hydrodynamical equations we obtain the dispersion relation and the Jeans wave number, which includes the effects of the vortices (turbulence), of the quantum pressure and of the quantum potential, respectively. The critical scales above which condensate dark matter collapses (the Jeans radius and mass) are discussed in detail. We also investigate the collapse/expansion of rotating condensed dark matter halos, and we find a family of exact semi-analytical solutions of the hydrodynamic evolution equations, derived by using the method of separation of variables. An approximate first order solution of the fluid flow equations is also obtained. The radial coordinate dependent mass, density and velocity profiles of the collapsing/expanding condensate dark matter halos are obtained by using numerical methods.

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Section: Discussion and Final Remarksmentioning

confidence: 99%

Section: (147)mentioning

confidence: 99%

Jeans instability and turbulent gravitational collapse of Bose–Einstein condensate dark matter halos

Harkó

2019

Eur. Phys. J. C

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“…A physically-motivated, well-studied (see, e.g., Penston 1969a; Fatuzzo et al 2004;Lou & Shi 2014) initial mass profile (i.e., before the loss of pressure support) of a collapsing cloud is that of a polytrope -one in which the pressure scales as p = Kρ γ , where p is the pressure, γ is the polytropic index, and K is a constant that scales with the specific entropy of the gas. With this form for the pressure, the equation of hydrostatic equilibrium combined with the Poisson equation gives the Lane-Emden equation (e.g., Hansen et al 2004):…”

Section: Polytropesmentioning

confidence: 99%

Spherically Symmetric, Cold Collapse: The Exact Solutions and a Comparison With Self-Similar Solutions

Coughlin

2017

ApJ

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We present the exact solutions for the collapse of a spherically-symmetric, cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These solutions exhibit a number of remarkable features, including the self-consistent formation of and subsequent accretion onto a central point mass. A number of specific examples are provided, and we show that Penston's solution of pressureless, self-similar collapse is recovered for polytropic density profiles; importantly, however, we demonstrate that the time over which this solution holds is fleetingly narrow, implying that much of the collapse proceeds non-self-similarly. We show-eps-converted-to.pdf that our solutions can naturally incorporate turbulent pressure support, and we investigate the evolution of overdensities -potentially generated by such turbulence -as the collapse proceeds. Finally, we analyze the evolution of the angular velocity and magnetic fields in the limit that their dynamical influence is small, and we recover exact solutions for these quantities. Our results may provide important constraints on numerical models that attempt to elucidate the details of protostellar collapse when the initial conditions are far less idealized.

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“…To present physical properties of star-forming MCs and to compare them with observations, the general polytropic (GP) self-similar protostar formation model (Wang & Lou 2008;Cao & Lou 2009;Lou & Hu 2010, Lou & Shi 2014) is adopted here without magnetic field. Hydrodynamic partial differential equations (PDEs) of spherical symmetry are:…”

Section: Dynamic Polytropic Gas Spheresmentioning

confidence: 99%

“…where A and B are two integration constants (Lou & Shi 2014). The last one is the dynamic asymptotic free-fall solution towards the MC core centre as x → 0 + :…”

Section: Dynamic Polytropic Gas Spheresmentioning

confidence: 99%

Variable protostellar mass accretion rates in cloud cores

Lou

2016

Monthly Notices of the Royal Astronomical Society: Letters

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Spherical hydrodynamic models with a polytropic equation of state (EoS) of forming protostars are revisited for the so-called luminosity conundrum highlighted by observations. For a molecular cloud (MC) core with such an EoS of a polytropic index γ > 1, the central mass accretion rate (MAR) decreases with increasing time as a protostar emerges, offering a sensible solution to this luminosity problem. As the MAR decreases, the protostellar luminosity also diminishes, making it improper to infer the star formation time by currently observed luminosity using an isothermal model. By observations of radial density profiles and radio continua of numerous MC cores evolving towards protostars, polytropic dynamic spheres of γ > 1 are also preferred.

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General polytropic Larson–Penston-type collapses

Cited by 13 publications

References 81 publications

Jeans instability and turbulent gravitational collapse of Bose–Einstein condensate dark matter halos

Jeans instability and turbulent gravitational collapse of Bose–Einstein condensate dark matter halos

Spherically Symmetric, Cold Collapse: The Exact Solutions and a Comparison With Self-Similar Solutions

Variable protostellar mass accretion rates in cloud cores

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