Recent papers, Episode 2

Still catching up with some previous papers, this time it is Paolas first paper:

Trapping dust particles in the outer regions of protoplanetary disks
P. Pinilla et al., A&A (2012) vol. 538, A114

Dust particles in circumstellar disks are expected to collide and stick to each other, thus growing from sub-micrometer in size to planets. However this is not as easy as it sounds because apart from growth barriers (see last post), there is also an effect, called radial drift. Once particles have reached a certain size, they start to decouple from the gas flow and as a consequence they spiral inward. The size at which that happens reaches from roughly one meter in the inner disk (for example at the distance of the Earth) to particles of only millimeters or less in the outer disk (say around 100 times the Earth-Sun distance).

Now this effect of radial drift is quite simple physics, so we would be quite certain that this should indeed be at work in disks (possibly slightly weaker or stronger than we might expect), but the real problem comes from observations: observatories like the SMA, CARMA, or also the upcoming ALMA are used to detect and characterize these disks in the (sub-)millimeter wavelength range, which is sensitive to dust emission, particularly to grains of around millimeters in size. Several people have found that particularly the outer disk is full of mm or cm sized particles, exactly those which shouldn't be there according to the expectations of radial drift, so something has to halt or suppress radial drift.

The most straightforward way to stop radial drift is changing the pressure gradient in the disk: the closer you get to the star, the denser and hotter the gas becomes, so pressure is increasing as you get closer to the central star. Now the drift speed scales linear with the pressure gradient, which is the rate at which the pressure de- or increases. Therefore, if you have a region in the disk, where the pressure is constant, there is no drift. Taking this one step further, if there is a region where pressure is increasing with distance to the star, then particles should drift outwards instead of inwards.

But how do you do that? Now there are a few ideas out there ranging from turbulent over-densities, or spiral arms to more complicated effects such as zonal flows. All these effects are disturbances to the density structure of the disk, so our idea with this paper was to parameterize the disturbances and test what size and strength of the perturbation is needed to influence radial drift and growth of dust particles and how observable quantities are influenced.

What we found was the following: the best option to have efficient trapping of dust particles are sizes of around one pressure scale height (this is just a typical length scale for disk physics) and an over density of at least 30%. With values like these, exactly those grains are kept in the disk which are needed to explain observations. The plot shows the spectral index, which is a proxy for grain size (lower alpha means larger grains) versus the total flux, which is a measure of dust mass (more flux means more dust). The dots represent the observational data, the red area is what our theoretical models can cover if there is no drift at all. If radial drift were active, then our models would predict larger alpha and less flux as time proceeds - this obviously goes in the wrong direction, as you can see by looking at the orange arrow. Our new models with particle trapping (symbolized by the green arrow) manage to get both quantities right: the dust mass decreases slowly with time (since the flux goes down) while at the same time, particles are allowed to grow to larger sizes and keeping this size over time.

spectral slope vs millimeter flux

This paper was also selected as Highlight Paper by Astronomy & Astrophysics. Check out the A&A website for their shorter summary.