Structure and Stability of Steady Protostellar Accretion Flows - Part Two - Linear Stability Analysis

Details Structure and Stability of Steady Protostellar Accretion Flows - Part Two - Linear Stability Analysis Structure and Stability of Steady Protostellar Accretion Flows - Part Two - Linear Stability Analysis

Mar 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991a%26a...243..187b&link_type=abstract

Astronomy and Astrophysics, Vol.243, NO. 1/MAR, P. 187, 1991

Astronomy and Astrophysics

Astrophysics

5

Star Formation, Protostellar Accretion, Linear Stability Analysis

Scientific paper

Recent developments concerning spherically symmetric (1D-) numerical models of protostellar evolution show that steady protostellar accretion flows (resp. their shockfronts) may be unstable at least in the very early (Tscharnuter 1987a) and late stages (Balluch 1988) of accretion. A global, linear stability analysis of the structure of steady protostellar accretion flows with a shock discontinuity (Balluch 1990) is therefore presented to investigate such flows by different methods. Thereby three characteristic wave types, the radiation-, radiation diffusion- and acoustic modes were found.
In the `ideal case' of a perfect gas law and constant opacity, the shockfront appears to be oscillatory unstable due to critical cooling as long as the mass flux rate is larger than a critical one of Mṡcrit = 10-6 Msun yr-1. In the `real case' with more realistic constitutive relations, an additional vibrational instability occurs due to the κ-mechanism in the outer layers of the core. This is shown to be the case in the whole range of core masses between 0.01 and 1 Msun, mass flow rates between 10-3 and 10-7 Msun yr-1 and different outer boundary conditions (corresponding to different states of the surrounding interstellar cloud).
Analysing the first, outer protostellar cores before they get dynamically unstable due to H2-dissociation in their interiors, similar instabilities as mentioned above were found. Now the unstable κ-behaviour is due to dust instead of the deep ionisation zone as in the case of second, inner cores.
According to the linear analysis, the instabilities should first appear in the velocity and the radiation flux in the settling zone. In the case of first, outer cores, these variations should be accompanied by an oscillation of the radiation flux in the region upstream from the shock up to r = 1014 cm. Sooner or later, the shockfront should oscillate in both cases too.
These results are finally compared with the characteristics of the accretion shock instabilities in the late stages of protostellar evolution, described by Balluch (1988). Agreement is found as far as the two models are comparable.

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