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The Role of Accretion in Binary Star Formation

Matthew R. Bate

Ph.D. Thesis, University of Cambridge, U.K. (1995)


The effects of accretion on the formation of a binary stellar system are studied. When a molecular cloud core undergoes gravitational collapse it may fragment into several protostars. This process is a promising mechanism for the formation of most binary systems and has been the subject of many numerical calculations. These demonstrate that protobinary systems can be formed with a wide variety of mass ratios, orbital separations and eccentricities. However, all these calculations must be halted soon after the protostars form, as the computation time required to evolve them further becomes prohibitive. Most of the computations are spent evolving the internal dynamics of the protostars, and the accretion of the rest of the collapsing cloud on to the protostellar system cannot be followed. Typically, the protostars contain only a few percent of the initial cloud when the calculations must be stopped. Thus, it is impossible to compare the results of the calculations with observations, as the parameters of the final stellar system depend upon the accretion of, or the interaction with, the rest of the cloud.

In this thesis, a new method for following fragmentation calculations beyond the formation of protostars is presented. The numerical technique of Smoothed Particle Hydrodynamics (SPH) is modified to incorporate sink particles. In standard SPH, high-density regions of gas are represented by many particles in a small volume of space. Short time steps are required to evolve these particles correctly, and this results in fragmentation calculations being halted soon after protostars are formed due to their high densities. In the new method, the many gas particles representing each protostar are replaced by a single, non-gaseous particle, with appropriate boundary conditions. These sink particles contain all the mass of the particles they replace, and accrete any infalling mass. This enables a collapse calculation to be followed to an arbitrary time after the protostars are formed, and, thus, for the final results to be determined.

Using this method, the effects of accretion on a forming binary system are studied. A binary is placed within a gaseous cloud from which it accretes. The effects of this accretion on the mass ratio and orbital separation of the system are studied. This study is performed first in the ballistic case, where the gas is modelled by non-interacting particles, and then by gaseous accretion using SPH with pressure and viscous forces. The effects of the accretion are found to depend primarily on the mass ratio of the binary and the angular momentum of the infalling cloud. For the accretion of low-angular-momentum material, the binary's separation deceases, and its mass ratio is lowered. For high-angular-momentum accretion, the binary's separation increases, and its mass ratio is forced toward unity. The magnitude of the effects depends on the mass ratio. The formation of circumstellar and circumbinary discs is also studied. It is found that circumstellar discs are formed around only the primary for low-angular-momentum material, around both protostars for intermediate-angular-momentum material, and around both protostars for the highest-angular-momentum material with a circumbinary disc also present. Finally, conclusions are drawn on how accretion may help to explain the mass-ratio distributions and the presence of discs that are observed for binary systems.


Chapters 1-5 and 8 are available as gzipped postscript files.

1 Introduction (includes Abstract)

    1.1 Introduction to Star Formation
    1.2 Binary Star Formation: Observations
    1.3 Binary Star Formation: Theory
    1.4 The Role of Accretion During Binary Star Formation
    1.5 Thesis Outline

2 Smoothed Particle Hydrodynamics

    2.1 General Principles of SPH
    2.2 SPH Implementation

3 Testing of the SPH Code

    3.1 Shocks and Particle Interpenetration
    3.2 Formation of Polytropes
    3.3 Oscillation of Polytropes
    3.4 Spherical Collapse

4 Modelling Accretion on to Protobinary Systems

    4.1 Problems of Modelling Multiple Star Formation
    4.2 Inclusion of Non-Gaseous, Accreting Particles in SPH
    4.3 Tests of Sink Particle Boundary Conditions
    4.4 Standard Isothermal Test Case
    4.5 Conclusions

5 The Effects of Ballistic Accretion on a Protobinary System

    5.1 Method
    5.2 Effects of Ballistic Accretion on Binary Masses
    5.3 Effects of Ballistic Accretion on Binary Separation
    5.4 Effects of Ballistic Accretion on Protostellar Spin
    5.5 Conclusions

6 The Effects of Gaseous Accretion on a Protobinary System

    6.1 Method
    6.2 Disc Formation
    6.3 Effects of Ballistic Accretion on Binary Masses
    6.4 Effects of Ballistic Accretion on Binary Separation
    6.5 Conclusions

7 Protobinary Evolution Under Massive Accretion

    7.1 Method
    7.2 Final States after Massive Accretion
    7.3 Inclusion of Initial Protostellar Spin
    7.4 Caveats to Massive Accretion
    7.5 Conclusions

8 Conclusions and Observational Implications (includes Bibliography)

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