An SPH simulation for cooling and self-gravitating protoplanetary disks

Faghei, Kazem

doi:10.1088/1674-4527/13/2/004

Cited by 3 publications

(9 citation statements)

References 34 publications

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“…However, the study on self-gravitating discs has received more attention recently in numerous publications (e.g. Nelson et al 1998Nelson et al , 2000Gammie 2001;Rice et al 2003Rice et al , 2005Pickett and Durisen 2007;Kley and Nelson 2008;Durisen et al 2008;Cossins et al 2010;Faghei 2012Faghei , 2013Kimura and Tsuribe 2012;Zhang et al 2014). Observational evidence has confirmed the existence of selfgravitating accretion discs in AGNs (Greenhill and Gwinn 1997;Lodato and Bertin 2003;Kondratko et al 2005) and in protostellar and protoplanetary discs (Larson 1984;Lin and Pringle 1987;Beltrán et al 2004;Chini et al 2004;Rodríguez et al 2005;Zhou et al 2005).…”

Section: Introductionmentioning

confidence: 99%

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A two-dimensional study for cooling and self-gravitating accretion discs

Faghei

Pak

2014

Astrophys Space Sci

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The importance of cooling for the structure and evolution of self-gravitating accretion discs has been confirmed through the use of direct numerical simulations. In this paper, we present a two-dimensional study for selfgravitating accretion discs, to investigate the influence of the cooling rate on the latitudinal structure of such accretion discs. The disc is cooled using a simple parametrization for the cooling function, (de/dt) cool = −e/t cool with e as the internal energy and t cool as the cooling timescale. The cooling timescale is in units of the dynamical timescale, t dyn [= Ω −1 ], is Ωt cool = β, where β is a free parameter. The mechanism of energy dissipation is assumed to be turbulent viscosity in the disc and an α-prescription is applied for the kinematic coefficient of viscosity. To study the gravitational stability of the self-gravitating disc, we use the Toomre parameter. We obtain the radial dependence of the physical variables through the use of a self-similar method and we numerically solve the equations to obtain the latitudinal dependence of the physical variables. The solutions show that the radial velocity is smaller than the Keplerian rotational velocity; however, the disc, dependent on the values of parameters α and β and only near the zone close to the equatorial plane, can rotate in a super-Keplerian manner. With the magnitude of both parameters α and β, the disc thickness increases due to the increase of the vertical pressure gradient. The dependence of the gas density on the parameters α and β indicates two zones in the accretion disc. In the first zone near the equatorial plane, the mass density decreases by increasing these parameters. However, in the second zone, the regions with higher latitude, the mass density increases with the magnitude of parameters α and β.

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Section: Introductionmentioning

confidence: 99%

“…Many simulations have been performed in order to obtain the value of β crit (e.g. Rice et al 2003Rice et al , 2005Cossins et al 2010;Bate 2011, 2012;Faghei 2013Faghei , 2014. The simulations represent the different values for β crit .…”

Section: Introductionmentioning

confidence: 99%

A two-dimensional study for cooling and self-gravitating accretion discs

Faghei

Pak

2014

Astrophys Space Sci

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“…The critical cooling timescale has attracted more attention recently in numerous publications (Rice et al 2003(Rice et al , 2005Cossins et al 2010;Meru & Bate 2011a,b;Faghei 2012Faghei , 2013Meru & Bate 2012). For T Tauri disks, Rice et al (2003) found that the fragments can form for a cooling timescale close to t cool = 3Ω −1 .…”

Section: Introductionmentioning

confidence: 99%

“…They mentioned that, although the quadratic term in the SPH artificial viscosity (β sph ) has very small effects on the dissipation of a gravitationally unstable disk, it can be an important parameter for disk fragmentation. Faghei (2013) investigated the effects of the cooling function in formation of clumps in protoplanetary disks through the use of two-dimensional SPH simulations. He assumed the ratio of local cooling to dynamical timescales to be a constant and also a function of the local temperature.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, he found that by increasing the temperature dependence of cooling timescale, the mass accretion rate decreases, the population of clumps/fragments increases, and the clumps/fragments can also form at smaller radii. In recent studies of cooling protoplanetary disks, the cooling timescale expressed in terms of dynamical timescale is assumed to only be a function of temperature and its dependence on density has been ignored (Cossins et al 2010;Faghei 2012Faghei , 2013. Thus, in the present paper, we are going to investigate how cooling timescale is dependent on density and also dependent on both density and temperature in the fragmentation of protoplanetary disks.…”

Section: Introductionmentioning

confidence: 99%

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The density and temperature dependence of the cooling timescale for fragmentation of self-gravitating disks

Faghei¹

2014

Res. Astron. Astrophys.

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The purpose of this paper is to explore the influences of cooling timescale on fragmentation of self-gravitating protoplanetary disks. We assume the cooling timescale, expressed in terms of the dynamical timescale Ω tcool, has a power-law dependence on temperature and density, Ω tcool ∝ Σ−aT−b, where a and b are constants. We use this cooling timescale in a simple prescription for the cooling rate, du/dt = −u/tcool, where u is the internal energy. We perform our simulations using the smoothed particle hydrodynamics method. The simulations demonstrate that the disk is very sensitive to the cooling timescale, which depends on density and temperature. Under such a cooling timescale, the disk becomes gravitationally unstable and clumps form in the disk. This property even occurs for cooling timescales which are much longer than the critical cooling timescale, Ω tcool ≳ 7. We show that by adding the dependence of a cooling timescale on temperature and density, the number of clumps increases and the clumps can also form at smaller radii. The simulations imply that the sensitivity of a cooling timescale to density is more than to temperature, because even for a small dependence of the cooling timescale on density, clumps can still form in the disk. However, when the cooling timescale has a large dependence on temperature, clumps form in the disk. We also consider the effects of artificial viscosity parameters on fragmentation conditions. This consideration is performed in two cases, where Ω tcool is a constant and Ω tcool is a function of density and temperature. The simulations consider both cases, and results show the artificial viscosity parameters have rather similar effects. For example, using too small of values for linear and quadratic terms in artificial viscosity can suppress the gravitational instability and consequently the efficiency of the clump formation process decreases. This property is consistent with recent simulations of self-gravitating disks. We perform simulations with and without the Balsara form of artificial viscosity. We find that in the cooling and self-gravitating disks without the Balsara switch, the clumps can form more easily than those with the Balsara switch. Moreover, in both cases where the Balsara switch is present or absent, the simulations show that the cooling timescale strongly depends on density and temperature.

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Structure of the self-gravitating accretion discs in the presence of outflow

Ghanbarnejad

Ghasemnezhad

2020

Monthly Notices of the Royal Astronomical Society

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Numerical simulations of self-gravitating accretion discs have shown that the evolution of such systems depends strongly on the rate at which it cools. In this work, we study the vertical structure of the self-gravitating accretion discs and also investigate the effect of the cooling rate on the latitudinal structure of such accretion discs. In the spherical coordinates, we write the hydrodynamics equations and simplify the basic equations based on the assumptions of axisymmetric and steady state. We use the self-similar method for solving the equations in the radial direction and we find proper boundary conditions. We find inflow–outflow solutions by considering the meridional component of the velocity field. In order to formulate the cooling term in energy equation, we introduce the new parameter β as a free constant that is the cooling time-scale in units of the dynamical time-scale. Our numerical solutions show that the thickness of the disc decreases with smaller β (or increasing the cooling term in energy equation) and it makes the disc colder and outflows form in the regions with lower latitude. So by increasing the cooling rate in the disc, the regions which belong to inflow decrease.

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An SPH simulation for cooling and self-gravitating protoplanetary disks

Cited by 3 publications

References 34 publications

A two-dimensional study for cooling and self-gravitating accretion discs

A two-dimensional study for cooling and self-gravitating accretion discs

The density and temperature dependence of the cooling timescale for fragmentation of self-gravitating disks

Structure of the self-gravitating accretion discs in the presence of outflow

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