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Self‐Similar Gravitational Collapse of Radiatively Cooling Spheres

Masakatsu Murakami, Katsunobu Nishihara, Tomoyuki Hanawa

2004
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Astrophysical Journal
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Self-similar solutions play a crucial role in many branches of physics, in particular, for such fields as hydrodynamic phenomena in astrophysics. For example, the Larson-Penston (LP) solution 1,2 facilitates qualitative analysis of complex hydrodynamic flows of gravitational collapse of an isothermal gaseous sphere, 3,4 which is proposed to explain the qualitative dynamics in the early stage of star formation. However, the effect of radiative heat conduction is expected to play an important
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... ay an important role in such a temporal domain that substantial dissociation and ionization of molecules and atoms proceed with contraction of the system and that the isothermal assumption is not appropriate any more. Still, among a large variety of self-similar solutions of the hydrodynamic equations, those which include heat conduction are relatively few. 5-7 Still more, to the best of our knowledge, there has been no other publications on the self-similar solution, which simultaneously treats both the self-gravity and the non-linear heat conductivity. A striking difference between the outputs of the LP model, for example, and the present model is found in the physical picture of the core formation. The former and the latter respectively describe a decreasing and increasing core mass with time. Figure 1 highlights the output of the present work showing the temporal evolution of the density and velocity profiles at sequential times. As can be seen in Fig. 1 , the core shrinks with time, where t = 0 corresponds to the collapse time. The central density increases in proportion to t -2 , that is the universal scaling regardless of the degree of the heat conductivity. At the same time, the core mass also increases due to mass accretion. One more important feature of the present model, which is essentially different from the conventional ones obtained under the isothermal or the adiabatic assumptions, is that all the scales of the physical quantities are uniquely determined as a function of time only. The one-dimensional spherical gas-dynamical equations with both self-gravity and heat conductivity are ∂ρ ∂ ∂ ∂ ρ t r r ru += 1 0 2 2 () ,

doi:10.1086/383606
fatcat:ftkyjq7s6zbzxddwe4lcyr5gdi