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Chandrasekhar connects stellar gravitational fluctuations to systematic velocity deceleration and derives an approximate dynamical-friction coefficient from binary encounters in an isotropic stellar background. A star passing through other stars receives many small gravitational deflections. Random kicks alone would keep spreading the velocity distribution without limit. Chandrasekhar explains why the same statistical description must also contain systematic slowing if a Maxwellian equilibrium is to remain unchanged. He then calculates this slowing by summing idealized two-star encounters. The calculation needs a finite maximum impact parameter and a leading logarithmic approximation. In that approximation, the friction depends on the number of background stars moving more slowly than the star being considered; it does not say that faster stars have exactly zero effect in every encounter calculation. A Maxwellian background gives a familiar error-function velocity dependence. The coefficient is of the order of the inverse relaxation time. The paper also identifies limitations in its isotropic fluctuation model and leaves a more complete statistical treatment for later work. This provides a major stellar-dynamics tool, with a declared range rather than a universal drag law for every galaxy or gas.
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Scientific scope
The coefficient uses local isotropic stellar velocities and binary Newtonian encounters with a finite impact-parameter cutoff. The leading large-log approximation does not imply exactly zero contribution from every faster star. Maxwellian and diffusion assumptions constrain the result. Inhomogeneous cores, gas drag, collective wakes and a uniquely justified cutoff are outside this target. Later core-stalling results caution against universal application.
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- S. Chandrasekhar1943DynamicalfrictionI original255-262completewebtext
- Readetal2006: Dynamicalfrictioninconstantdensitycores, explicitmodel-limit evidence
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S. Chandrasekhar
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English catalogue narrative
Chandrasekhar: gravitational encounters produce systematic stellar slowing
Chandrasekhar connects stellar gravitational fluctuations to systematic velocity deceleration and derives an approximate dynamical-friction coefficient from binary encounters in an isotropic stellar background.
A star passing through other stars receives many small gravitational deflections. Random kicks alone would keep spreading the velocity distribution without limit. Chandrasekhar explains why the same statistical description must also contain systematic slowing if a Maxwellian equilibrium is to remain unchanged. He then calculates this slowing by summing idealized two-star encounters. The calculation needs a finite maximum impact parameter and a leading logarithmic approximation. In that approximation, the friction depends on the number of background stars moving more slowly than the star being considered; it does not say that faster stars have exactly zero effect in every encounter calculation. A Maxwellian background gives a familiar error-function velocity dependence. The coefficient is of the order of the inverse relaxation time. The paper also identifies limitations in its isotropic fluctuation model and leaves a more complete statistical treatment for later work. This provides a major stellar-dynamics tool, with a declared range rather than a universal drag law for every galaxy or gas.
Scientific scope
The coefficient uses local isotropic stellar velocities and binary Newtonian encounters with a finite impact-parameter cutoff. The leading large-log approximation does not imply exactly zero contribution from every faster star. Maxwellian and diffusion assumptions constrain the result. Inhomogeneous cores, gas drag, collective wakes and a uniquely justified cutoff are outside this target. Later core-stalling results caution against universal application.
People and systems
S. Chandrasekhar