On the thermal stability of slabs, cylinders, and spheres

Ibanez, M.; Plachco, Florencio P.

doi:10.1086/169857

Cited by 2 publications

(4 citation statements)

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“…The functions Γ(ρ, T ) and Λ(ρ, T ) represent the heating and cooling rates per unit volume, respectively. In many astrophysical situations the quantities κ, Γ and Λ can be approximated as being proportional to power laws of the form ∼ ρ α T β [18]. Under the assumption of isobaricity, we can eliminate the density as an independent variable and write…”

Section: Basic Equationsmentioning

confidence: 99%

“…where the constants κ 0 , Γ 0 , Λ 0 and the indices k, m and n are given by the physical processes involved. For instance, a typical interstellar region in the range of temperature 10 2 < ∼ T < ∼ 10 4 K with thermal conduction by neutral particles, heating proportional to the density, and cooled by collisions between particles, may be characterized by k = 1/2, m = −1 and n = −3/2 [12,18].…”

Section: Basic Equationsmentioning

confidence: 99%

“…Then, for convenience, we assume exactly the same boundary conditions used in Refs. [10,11,12,13,15,18]:…”

Section: Basic Equationsmentioning

confidence: 99%

“…[10] (see also Refs. [17,18,23]), the positive slope branch can be identified as the stable branch. Therefore, stationary solutions located on the positive (negative) slopes branches are expected to be linearly stable (unstable).…”

Section: Stability Criterionmentioning

confidence: 99%

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Stability of thermal structures with an internal heating source

Sanchez,

Lopez

2008

Preprint

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We study the thermal equilibrium and stability of isobaric, spherical structures having a radiation source located at its center. The thermal conduction coefficient, external heating and cooling rates are represented as power laws of the temperature. The internal heating decreases with distance from the source r approximately as ∼ exp(−τ )/r 2 , being τ the optical depth. We find that the influence of the radiation source is important only in the central region, but its effect is enough to make the system thermally unstable above a certain threshold central temperature. This threshold temperature decreases as the internal heating efficiency increases, but, otherwise, it does not depend on the structure size. Our results suggest that a solar-like star migrating into a diffuse interstellar region may destabilize the surrounding medium.Estabilidad de estructuras térmicas con una fuente interna de calentamiento.Resumen: En este trabajo estudiamos el equilibrio térmico y la estabilidad de estructuras isobáricas y esféricas que tienen una fuente de radiación en su centro. La conducción térmica y las tasas de calentamiento externo y enfriamiento son representadas como leyes de potencia de la temperatura. El calentamiento interno disminuye con la distancia a la fuente r aproximadamente como ∼ exp(−τ )/r 2 , siendo τ la profundidad óptica. Los resultados indican que la influencia de la fuente de radiación es importante solamente en la región central, pero su efecto es suficiente para que el sistema se vuelva térmicamente inestable por encima de una cierta temperatura umbral en el centro. Esta temperatura umbral disminuye a medida que la eficiencia del calentamiento interno aumenta, pero por otro lado la misma no depende del tamaño de la estructura. Nuestros resultados sugieren que una estrella de tipo solar que migre a través del medio interestelar difuso puede llegar a desestabilizarlo.

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Section: Basic Equationsmentioning

confidence: 99%

Section: Basic Equationsmentioning

confidence: 99%

“…Then, for convenience, we assume exactly the same boundary conditions used in Refs. [10,11,12,13,15,18]:…”

Section: Basic Equationsmentioning

confidence: 99%

Section: Stability Criterionmentioning

confidence: 99%

See 2 more Smart Citations