'The Angular Momentum Problem' of Sink Particles

So I think I digested the Krumholz accretion paper sufficiently well and will attempt to distill its key points regarding angular momentum accretion onto a sub-grid sink particle, as well as how this may ultimately connect to outflows and jets launched from sink particles.

The Krumholz accretion algorithm is fairly sophisticated in that it calculates a modified Bondi accretion rate for rotating gas within the accretion volume, and then only removes gas from each grid point that is bound to the sink particle ().

Currently, in AstroBEAR, the Bondi accretion routine also removes linear momentum and specific internal energy from each grid point based on the fraction of mass this drho constitutes. In doing so, each component of the linear momentum is reduced by the same fraction. This reduces the magnitude of the momentum vector in the ith cell, but not its orientation. In other words, this results in the loss of angular momentum within that zone, and thus over the kernel:

where is the total angular momentum over the kernel, and the subscripts denote the given quantity in the ith cell. Note the radial vector points along a line connecting the cell center to the sink particle.

This loss in angular momentum is stored in the sink particle, which enables the accretion algorithm to effectively conserve mass, linear momentum, and angular momentum between the grid and the sink particle over an accretion step.

Now, onto the angular momentum problem of this routine…

Krumholz makes the argument (and after some thought I think I agree with him) that given the sink particle represents an object much smaller than the grid scale (i.e. think single star compared to protostellar core) the angular momentum of the sink particle is negligible to that of the gas on the scale of the accretion volume. For a rough idea, let's assume the accretion volume represents a protostellar core, than its angular momentum is approximately:

whereas the angular momentum of the sun is roughly:

This argument (known as the 'angular momentum problem of star formation,' c.f. this ​review) implies single stars simply cannot acquire the enormous angular momentum of their host cores and clouds: else they would rotate faster than their break up speed.

Thus, Krumholz decomposes the linear momentum vectors of each cell into a parallel component and a transverse components (wrt to the line connecting the sink particle and cell center) and only accretes the radial component of the momentum. That is, since the angular momentum of the object the sink particle represents is negligible compared to that of the accretion volume, it should be ignored. By only accreting the radial component of the momentum vector the angular momentum of the gas is preserved (as well as the radial velocity).

Connection to outflows

If one does not accrete angular momentum from the grid, then one cannot inject angular momentum into the grid from sink particles upon the jet launching step. Thus, if we choose to adopt this way of looking at things, our injected protostellar jets will not be rotating on their own (but perhaps will spin up due to the bulk motion of gas within the accretion volume).

This contrasts with the other school of thought, namely Federrath's sink particle algorithms (which are currently implemented in the code). This method DOES accrete angular momentum from the grid (as described above for the Bondi accretion routine), and thus under those conditions, injecting a rotating jet back into the grid should (hypothetically) be self-consistent and conservative.

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