How Do We Find Interesting Things in Very Large Simulations?

It’s a growing problem in computational astrophysics.  Hydrodynamic simulations (say of giant molecular clouds and star forming regions) are getting very large.  When we want to analyse them and find interesting features to compare to the physical Universe, simply searching them “by eye” is becoming an enormous task.

One simple solution to this is to farm out the problem to citizen scientists, essentially doing the “by eye” hundreds of thousands of times in a few days.  This technique is great if you can break up the simulation into easily viewable chunks for each citizen scientist to look at.  But what if you can’t do this, or you don’t have access to millions of enthusiastic people?

We must rely on algorithms to solve this problem.  Luckily cosmologists came across similar issues in N-Body simulations of dark matter quite some time ago (click here for some images and movies of simulations done around 15 years ago).  These simulations have slightly less physics inside, and hence grew to large data sizes much quicker, which was essential to modelling the growth of structure on cosmic scales.  They used something called tensor classification to analyse the mass distribution.

This is a technique which relies on computing a rank 2 tensor, a matrix, which contains information about how the simulation changes with position over all 3 dimensions.

For example, we can compute a tidal tensor, which is two derivatives of the gravitational potential.  This measures how the gravitational force changes as a function of position.  Manipulation of the tensor (finding its eigenvalues and eigenvectors) allows us to say what shapes and geometries the gravitational force is trying to build.  Is it making pancake-like sheets? Rope-like filaments? Or is it squeezing everything into a sphere? Or is it doing none of this, and is instead creating a void?

This technique gives cosmologists useful information about the filamentary structure of dark matter on very large scales.  In a recent paper, I investigated how these N-Body methods (where the only force active is gravity) could be ported into hydrodynamic calculations (where pressure forces, radiation and perhaps magnetic fields also play a role).

As we work with smoothed particle hydrodynamics (SPH), which also simulates a fluid using particles, these methods are easy to apply, with the advantage that there are less free parameters in the calculation.

And it has some stunning uses.  Want to find the spiral arms in a self-gravitating disc? Presto:

sgdisc

sgdisc_tidalcluster.png

Want to trace the blast wave of a supernova as it travels through interstellar gas? Sure:

SN.png

SN_filamentsV.png

It is also quite good at detecting filaments in molecular clouds, but the results aren’t quite as impressive – yet.  I have a student working on this problem as we speak, and I’m hoping for exciting results.

We’ve really only just begun using tensor classification for problems like this, and there are some great possibilities for analysing other fields such as the magnetic field and radiation fields.  We might even be able to generalise this to fully relativistic calculations and compute structures in distorted space-time.

Hopefully you’ll be reading future posts on how I’ve put this technique to great use!

Squishier moons are better for life

My more eager readers will have noticed a sudden flurry of submissions to the arXiv since Christmas. I’ll try and bring you up to date with what I’ve been publishing recently, which is hitting a variety of topics.

The first is a return to a favourite area of research for me: exomoon habitability. As you can see from earlier posts, I’ve been looking at this subject for a while now, focusing in particular how an Earthlike object would fare orbiting a giant planet, which in turn orbits a star like our Sun.

I’ve been using a simple, 1D climate model to follow the temperature changes on this Earth copy, and discover what sort of orbital parameters might be needed for it to possess surface liquid water. But we’ve known from the start that these climate models have been overly simple, and in some cases they’ve missed out important physics that might affect our answers.

In our latest work, we took aim at two aspects of the model that we felt were lacking. In the first, we investigated the issue of atmospheric composition. Up until now, we had assumed a fixed composition, but we know that the Earth has adjusted its atmosphere over time. Sometimes, this is due to the presence of life (like the great oxygenation events that are responsible for the good stuff filling your lungs), but other processes play a role.

In fact, we can identify a complete cycle of processes that affect the total amount of carbon dioxide. CO2 is emitted into the atmosphere via volcanic eruptions. It then precipitates into rain, which falls into the sea, and gets incorporated into rocks and seashells on the ocean floor. This ocean floor is eventually sub ducted at a tectonic plate boundary, and returned to the mantle, where the whole cycle begins again.

carbon-dioxide-cycle-AW

It’s known as the carbonate-silicate cycle (because the rocks in play are carbonate and silicate rocks). What’s rather clever about this system is that it acts as a thermostat. If the planet starts to warm, then more Co2 rains out of the atmosphere and into the oceans than is expelled by volcanoes, which reduces the amount of Co2 in the atmosphere. As Co2 is a greenhouse gas, getting rid of it allows the planet to cool more easily. If the planet cools, less co2 rains out and is added to by volcanism. A little extra greenhouse gas helps the planet keep its heat. This is why scientists are worried about manmade co2 production, as we’re mucking around with the thermostat, and too much fiddling could break it.

We never considered this process before, so we changed our model to allow the co2 levels of our moon to vary to help keep the temperature warm and stable.

We then turned to the tidal heating of our moon, which until this point was done using a rather simple model. As you may already know, tidal heating is generated by the planet’s gravity stretching and squeezing the moon as it goes around its orbit. Crucially, the amount of heat the planet can generate in the moon depends on the material the moon is made of, as well as what state it’s in. If the heating is intense enough to allow melting, this can reduce the tidal heating, and stop moons from becoming too hot for life.

We found that when we added both effects, the habitable zone for the moon moves further away from the star.  It also gets wider around the planet as well – moons can orbit closer without being roasted, and changing CO2 levels lets the moon stay warm further away from heat sources by boosting its greenhouse effect.

We’re far from the final answer here: one day I hope to be telling you about fully 3D models of exomoon atmospheres.  Even 1D models like ours still need some extra physics, like investigating how changing the spectrum of incoming radiation affects this answer.  But every step is a step forward!

The power myth will soon be all that’s left of modern politics

The latest episode of This American Life has got me thinking about the dynamics of modern politics, and not just the 2016 American presidential elections, but the upcoming referendum on the UK’s place in the EU.

In the episode, we’re introduced to Alex Chalgren, a young Trump supporter with a troubled background. A gay black man adopted by an evangelical, Cruz-supporting Christian family, who loves Alex but cannot reconcile this with his sexuality, his life has been described as an “impotent man [seeking] power”, a person whose circumstances have never been entirely in their control.

That last sentence describes us all, doesn’t it? We are the captains of our souls, but we are not the masters of our fate. Disenfranchisement is the cloud that hangs over all of Western politics, hiding the silent masses of people sick-and-tired of political business-as-usual. The politician that harnesses this swirling vortex of despair, hate and fear has an almost unlimited power source, if they can transmute it into a seemingly positive force.

The SNP have been extremely successful in this practice in Scotland, capitalising on the independence referendum to engage sectors of the electorate who had never seen the inside of a polling booth, and destroy the competition in last year’s elections. Donald Trump is crushing his rivals in the Republican primaries, scooping up voters from almost every demographic, and Bernie Sanders is a strong second to Clinton, an unthinkable socialist in the top tier of US politics.

A common theme to all these successes is empowerment. Alex Chalgren paraphrases Frank Underwood in House of Cards, when he says

a fool goes after money. But someone that really seeks to control goes after power…

The message is pretty simple. You feel powerless.  I have power, vote for me and let me give you some of it. Trump’s power-persona, carefully constructed in simple sentences, spiced with hatred and accented by bullying and insults, is attracting the disempowered vote and dumbfounding the GOP establishment. The SNP’s principal cause of Scottish independence is the ultimate empowerment for a small nation, with historical baggage and a Tory government that very few Scots voted for. Even Sanders’ roaring rhetoric against the 1% imbues him with similar tough-talking attributes as Trump.

What will decide the EU referendum in the UK is the fight for the disempowered. The Out campaigns have a simple message of returning UK “sovereignty” and repealing apparently unending legislation. The In campaign have a much tougher job.  Firstly, they need to prick this “sovereignty” balloon (how can you have true freedom to legislate in a market economy, when you need to satisfy regulations to export goods to Europe? And will being out of Europe really protect us from the dreaded TTIP?).  Michael Gove’s recent statement supporting Out is typical of those made by the Out campaign, and this response is an excellent example of how to completely invalidate them.

Secondly, the In campaigners need to convince us that regulations exist to facilitate fair and free markets while protecting our social, human and natural capital.  A post-Brexit Britain would be far more prone to lobbying resulting in deregulation, destroying the environment and eroding UK citizens’ rights.  In fact, studies indicate it would have to do this to mitigate losses to GDP on Brexit.

We bought into the EEC ideal in the 70s (and the EU latterly) because we thought it would empower us to create a peaceful and prosperous Europe, free of continental war at last, with a cleaner environment, healthier and happier citizens and a better future for our children. The world has changed a lot since then, and we’re facing unprecedented migration, climate change and dangerous extremism, challenges on a scale we haven’t faced since the Second World War.  It’s not surprising that the EU is showing signs of strain. It may have its failings, but to leave it is to ignore its great successes and its potential for further success, throw the baby out with the bathwater, and step back from our closest allies when they need our support the most.

The challenge now for the In campaign is to win the disenfranchised – I wish them the very best of luck.  But it leaves the future of political discourse looking fairly bleak. It feels like the old practice of debating individual policies is rapidly disappearing, and the election victories are going to the man who looks best when they don the purple (and yes, I use the word “man” deliberately).  And if it finally goes, we’ll just be voting for the “strongman” – and history has taught us where that will lead.