# Thesis Anthology Part 5: The Viscous Trick – Behind the Magic

Onward ho with part 5 of my thesis anthology.  Last time we talked about discs lighting up in outbursts after a second star passes nearby.  Now we’re going back to the isolated disc, and we’re going to look at angular momentum in more detail.  Take a deep breath!

You might remember from all the way back in part one how angular momentum is critical to the formation of discs.  If there wasn’t any angular momentum to start with, there would be no disc – simple as that.  We can think of angular momentum moving about in the disc, just like we might think of mass moving about.  Discs around stars are what is known as accretion discs – that means that the angular momentum moves outward, and the mass moves inward, and is accreted by the star.

Remember that when the star is “born”, it’s not reached its full mass.  A lot of the mass is going to come from the disc itself, due to accretion.  If we want to know how stars are assembled, then we need to know how the mass moves in the disc.  That means we need to know how the angular momentum in the disc moves too.

I’ve been studying this process in self-gravitating discs – discs that are massive enough that their own gravitational field is too important to ignore.  So we need to know how angular momentum is moved by the force of gravity itself.  Luckily, scientists have been thinking of this problem for quite a long time (it has other applications, including to spiral galaxies!).  Most approaches use an approximation to solve it – it involves treating the disc as viscous.  The action of gravity in these discs tends to produce turbulence, stirring up the disc.  This stirring makes the disc “syrupy”, and this is what pushes the angular momentum out and the mass in.

I’ve been testing this viscous approximation using simulations.  What I’ve discovered is that for this viscous approximation to work, we need to think about spirals, as they might spoil everything.

Take this disc for example.  It’s a moderate disc (about 1/4 of the mass of its star).  The spirals are neatly organised, there’s plenty of them, and no set of spirals dominate the gravitational field.  The more spirals in a disc, the more orderly the angular momentum transport, and the more likely our viscous trick will work.  But what happens if the disc is very massive?

This monster starts out at 1.5 times the mass of the star.  The spiral structure is a mess, there’s less of them, and the whole picture is dominated by a two-armed spiral.   This two-armed spiral twists and pulls the gravitational field, and the angular momentum responds to it.  This global feature wrecks the viscous trick – instead of a nice, orderly transport of mass caused by small scale spirals, this disc gets chaotic, bursty transport of mass caused by global spiral waves.

That’s no bad thing of course – we expect chaotic bursty transport in some young stars, and might be a useful explanation for outbursts – it’s just bad news for the viscous trick.  Unless your disc is small enough, that trick won’t work, and you’ll have to be more careful when modelling it.  The more you know…