Doing the Statistics on Top Down Planet Formation

I’m currently at the RAS National Astronomy Meeting 2013, and the back of my neck is burning, as I’m giving two talks on papers I’ve recently published, and I haven’t blogged about either of them (this post is coming back to bite me in the bottom once more).

Regular readers will know that a main research interest of mine has been the fragmentation of self-gravitating protostellar discs.  When stars are formed, they form a disc also, and it seems to be the case that in the very earliest stages of the star’s life, the mass of the disc it hosts is about the same as the mass of the star itself.

When the conditions are right, the disc becomes catastrophically unstable, and breaks up into fragments more massive than Jupiter.  It has long been suggested that these fragments can evolve into gas giant planets, providing an alternative theory of planet formation, as opposed to the standard theory of planet formation called core accretion, where planets are formed from growing dust grains in the disc into pebbles, boulders and eventually protoplanets.

Fragments being born in a self-gravitating protostellar disc.  But what happens next?
Fragments being born in a self-gravitating protostellar disc. But what happens next?

The very large mass of the disc fragments has led most theorists to rule out disc fragmentation as a means of making Earthlike planets, and an uneasy truce has developed between the two theories.  Core accretion seems to form low mass planets close to their star, and disc fragmentation seems to form massive planets (and brown dwarfs) at large distances from their star.

This truce is now at breaking point, as disc fragmentation theorists have proposed that disc fragments could be the progenitors of Earths after all,  via a process dubbed tidal downsizing.

When the disc fragment is born, it possesses a swarm of dust grains entrained in its gas.  Just like in core accretion, this swarm can collide and grow the grains, and begin to settle towards the centre of the fragment (for a nice analogy, think sediments settling in river beds).  If enough of this dust reaches the centre of the fragment, it collapses under its own gravity to form a core.

At the same time, the fragment is migrating, moving closer to the star, as the disc gravity begins to act on it.  The fragment is also trying to collapse under its own gravity, squeezing the gas as well as the dust into a smaller size.  The fragment is racing against time to compress to a small size before it gets too close to the star – if it fails, then the upper layers of the fragment are stripped off (this is the tidal downsizing in question).

Hopefully you can see that there are many different resulting objects you can make, depending on how quickly these different physical processes act.  Fragments that can compress quickly make giant planets and brown dwarfs (with and without solid cores).  Fragments that compress slowly, but allow dust to settle and become a core quickly will lose most of their gas and become terrestrial planets.  Fragments that compress slowly but don’t allow dust to settle quickly are destroyed, sometimes leaving behind half-grown dust and asteroid belts.

The real question we now have to ask: Which of these objects is made the most often? How often should we expect terrestrial planets to be formed via tidal downsizing, or do disc fragments still end up as massive planets and brown dwarfs?

We attempted to answer this question using population synthesis modelling.  Core accretion theory has been using population synthesis for many years, but disc fragmentation has lacked this capability until now.  Our work in fragmentation criteria allowed us to plug several theoretical gaps and create a model that investigates the fragmentation process and the crucial first million years after fragmentation.

Despite generating over a million disc fragments, we made only one Earthlike object.  To make it, we had to slow down the fragment migration process to a crawl, which is probably not particularly reflective of reality.  In fact, we discovered that the tidal downsizing process often results in complete destruction of the fragment (this happened for nearly half of all the fragments we generated).  The fragments that survived this process are (you guessed it) massive objects at large distances from the star.

Our one in a million Earthlike planet formed by tidal downsizing, all alone at the bottom of the plot.
Our one-in-a-million Earthlike planet formed by tidal downsizing, all alone at the bottom of the plot.  The rest are giant planets, brown dwarfs and low mass stars.

So it seems that the truce between disc fragmentation and core accretion remains.  For now.  We haven’t yet managed to put in all the physics we want to, and some of the physics we included was quite simple.  Any of these additions or changes to the model could produce more Earths, and put the two formation theories into direct competition.  Watch this space…


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