See also the publications page for links to animations and images. For a good general overview of my research in laymans terms, you might also want to take a look at the lay report for my Royal Society Fellowship.
Below you can find laymans descriptions of some of my research publications: The effect of magnetic fields and radiation on star formation, Magnetic fields in star cluster formation, Kelvin-Helmholtz instabilities, Magnetic fields in star formation, Magnetic fields in neutron star mergers, Adaptive Gravitational force softening, Smoothed Particle Magnetohydrodynamics, Toy Stars, Jets/Relativistic winds
The effect of magnetic fields and radiation on star formation
A follow up to our work on understanding the role magnetic fields play in forming star clusters (see below) has been to combine the magnetic fields calculations with other important physics, the next most important of which is the radiation. In our previous calculations we "faked" the effect of radiation by using an approximate equation of state (which basically just assumes that the gas has a constant temperature until it reaches a certain density and then starts to heat up beyond that density, halting the collapse and forming a "star"). However there are important aspects of the physics which are missed by making this approximation, mainly that radiation does not "travel" (if the gas is optically thin) or "diffuse" (if the gas is optically thick) from hot regions to heat up nearby cold regions (whereas it should), which can have a significant effect on the fragmentation (that is, whether or not the gas breaks up under gravity into small pieces or large pieces). More recently, based on work done in Exeter over the last few years by Matthew Bate and Stuart Whitehouse, we have been able to incorporate the full effect of radiation into the calculations and thus we have been able to perform the first simulations of star cluster formation in the world that account for both effects, both of which are crucial ingredients in the star formation process.
The dramatic effect of adding a proper treatment of radiation to the calculations can be seen in the movies. Once a star has been formed, it heats the surrounding material to such a degree that no further star formation occurs in the vicinity, in stark contrast to the previous approximation. Whereas calculations with no magnetic fields and only approximate treatment of radiation form upwards of 17 stars from our 50 solar mass cloud, with these effects included (to approximately the correct observed degree compared to real molecular clouds) only a few regions are able to collapse. This actually brings our theoretical calculations into much better agreement with observations, since it has long been known that star formation is a highly inefficient process, where only a few percent of the mass in a molecular cloud will actually end up in stars.
The paper is submitted to Monthly Notices of the Royal Astronomical Society
Magnetic fields in star cluster formation
One of the key objectives of my PPARC fellowship was to perform the worlds first simulations of star cluster formation which incorporate the effects of magnetic fields. Thus we have recently completed some of the world's most advanced computer simulations of the process of star cluster formation from turbulent, magnetised, molecular clouds similar to those we observe in the Milky Way (e.g. the Orion Nebula). It is believed that our own Sun was formed in a similar process, so understanding how stars form in general is a crucial part of the story of how we got here. By understanding star formation we can also understand the initial conditions for planet formation in the swirling discs of gas (accretion discs) which gather around the newly formed protostars.The problem for us as humans is that star formation is a relatively long process, taking of order 1-10 million years, simply because it involves gathering material over huge distances by the gentle but steady pull of gravity. Thus when we observe the Milky Way's "dark clouds" (where star formation is currently taking place), all we get is a momentary snapshot of what is really a highly dynamic process. We therefore use computer simulations to speed up the process to a few months inside a supercomputer, by solving the equations which govern the basic physical processes, ie. gravity, gas dynamics and, through my research, the effects of magnetic fields.
Magnetic fields are a key ingredient in most astrophysical problems simply because most gas in space is ionised (that is, the electrons are not bound to their parent atoms and can move around freely -- and we know that moving charges around creates a magnetic field). The magnetic fields present in interstellar space have a significant impact on the gas dynamics because ionised gas can only flow *along* magnetic field lines, not across them (this is best illustrated by the wonderful loops and filaments seen in X-ray pictures of the Sun, where the gas motions are being controlled by the Sun's magnetic field). In star forming regions magnetic fields are ubiquitously observed with strengths strong enough to control the gas motions, so it is critical to take their effect into account (in fact one of the key problems for star formation is how to get rid of the magnetic field so that it does not prevent stars forming altogether).
click for movie
In our calculations we have found that magnetic fields can substantially change the picture of star cluster formation -- they strongly reduce the rate at which stars form (by stopping the gas from collapsing under its own gravity) and subsequently star formation is less vigourous, leading to fewer low mass objects known as "brown dwarfs" (failed stars). This is good, because the number of low mass objects formed in calculations which did not include magnetic fields was too high. We also found that magnetic fields leave a visible imprint in the cloud structure - for example a "stripiness" in the gas which we actually observe in one of the closest star forming regions in our own Galaxy in the Taurus constellation.
We are currently making our simulations more realistic by properly modelling the effect of the radiation from the stars after they have formed (which heats the gas around them). I am also improving aspects of the magnetic fields algorithm to be closer to reality (for example including effects which cause the magnetic fields to diffuse away in dense regions). With our new supercomputer we will also be able to perform much larger calculations, closer to the real size of the molecular clouds we observe in the Milky Way.
Simulating Kelvin-Helmholtz instabilities
The Kelvin-Helmholtz instability (named after Lord Kelvin and Hermann von Helmholtz who first studied it) is a very well known instability in fluids which occurs at the interface between two fluids flow past each other in opposite directions. The result is that one of the fluids starts to "curl" at the interface and mix into the opposing flow (as in the movie above). Examples of the Kelvin-Helmholtz instability occur all around us in everyday life - for example wind blowing across the surface of a lake creating ripples, or stirring milk into your coffee.
Recently a somewhat provocative paper was published highlighting the fact that certain problems occur when you try to model the Kelvin-Helmholtz instability on a computer using the method we use a lot for simulating gas flow in astrophysics (Smoothed Particle Hydrodynamics) and thus that the method was somehow "fundamentally broken". This is where you represent the fluid by a set of moving particles instead of the usual approach which is to represent the fluid on a fixed grid.
In response to the paper I spent a bit of time investigating the problem which turned out to be related to the way that you treat discontinuities in the flow (ie. a place where the fluid properties suddenly jump from one value to another). In this case the problem occurred when you try to simulate the Kelvin-Helmholtz instability across a big step change in density. The problem was related to the fact that the fluid pressures were not being kept equal at the interface, the next result being that the two fluids do not mix properly (in fact they act as if they have a surface tension - though not of physical origin). Happily enough there was a reasonably easy fix, so we can now move gratefully on with our lives, sleeping safe in the knowledge that Kelvin-Helmholtz instabilities will be treated properly when we simulate things. The paper is submitted to the Journal of Computational Physics. More movies can also be found here.
The impact of magnetic fields on single and binary star formation
In galaxies like the Milky Way, gas behind the spiral arms resides in clumps known as "molecular clouds" in which new stars are born. In our own galaxy we can observe several of these "stellar nurseries" up close, a famous example being the Orion nebula. Observations of such molecular clouds can give us a detailed insight into the physics necessary for the birth of stars, the most obvious components being gas and gravity. However most gas in astrophysics is, at least partially, ionised, meaning that electrons are not bound to their atoms and are free to move and create electric and magnetic fields.
It has been known for many years that magnetic fields are an important ingredient in the star formation process, both in understanding the dynamics of the turbulence present in molecular clouds but also affecting the way that the gas collapses to form stars. However modelling the effects of magnetic fields on the computer has proven to be far from easy. Using a new method which I have developed over the last few years, we have recently performed a series of detailed simulations of the formation of single and binary stars from rotating molecular cloud "cores" (that is, small pockets of gas within the much larger cloud), including the effects of magnetic fields.
The results of one of our sets of simulations is shown below, where the strength of the initial magnetic field has been increased from left to right, top to bottom. With no magnetic fields (top left) the cloud fragments to form a binary system which then subfragments further. As the magnetic field strength increases, the binary star formation is suppressed due to the increased support provided to the gas cloud by the magnetic field (although in some cases magnetic fields can also assist binary formation by making a "magnetic cushion" in the gas between the two stars, preventing them from merging to form a single object). Movies of these simulations and a preprint of the paper (accepted to Monthly Notices of the Royal Astronomical Society) are available here.
Producing ultra-strong magnetic fields in neutron star mergers
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see here for the press release
see here for images/movies see here for a preprint of the paper examples of articles which have appeared in the press about this work: bbc.co.uk, newscientist.com, spiegel.de (in German) |
Adaptive Gravitational force softening
One of the simplest (but also the most difficult) areas of astrophysics is the simulation of a number of bodies interacting under the influence of their own gravity (this is called the N-body problem, since there are N bodies...). There are two types of N-body simulation. The first type is where each particle in the computer represents a real star (treated as a point mass). An example would be simulations of star clusters like those done by Sverre Aarseth. The second type of problem is simulating things like galaxies (or even the whole universe) which in reality have of order 10 billion stars (or 10 billion galaxies with 10 billion stars each), which is far above the number of particles you can use in a computer simulation. Somewhat surprisingly, the most difficult of these two types of simulation is the first one, because the close range interactions between the bodies are incredibly difficult to simulate accurately (this is because the force gets stronger like 1/distance squared, so if the bodies get twice as close, the force gets four times larger etc).
In the second type of simulation (galaxies, the universe) these strong short range encounters between the simulated particles are unphysical because one point in the computer represents very many stars, not just one. A way of removing these effects is to modify the gravitational force at short range to remove the strong forces associated with close encounters. This is known as "force softening". For systems which are very inhomogeneous (ie clumpy, like for example the universe) it is an advantage to "soften" the forces differently for each particle in a simulation (this is called "adaptive softening", as opposed to "fixed softening" which uses the same force softening for all the particles). The problem with this is that important physical quantities like momentum and energy are in general no longer conserved. The error is not usually large, but large enough to make people not use adaptive softening, even though it improves the simulation resolution substantially. Thus our work has been to come up with a way of doing adaptive softening that conserves all the important things like momentum, angular momentum and energy. The paper is currently submitted to Monthly Notices of the Royal Astronomical Society.
Smoothed Particle Magnetohydrodynamics
Smoothed Particle Hydrodynamics (SPH) is a method for solving the equations of gas dynamics. Most methods used for fluid dynamics divide the region to be simulated up into even grid cells. SPH is unique because instead of doing this fluid quantities (such as density, pressure and temperature) are interpolated onto a set of `particles' which move with the fluid. This has lots of advantages, particularly in astrophysics, as it places to prior constraint on how complicated the flow can become (for example if you set up a grid with some gas in it, what happens if it flies off the side?) and can also be made to conserve important physical quantities (e.g. momentum, energy, angular momentum) exactly.
I have been developing and testing a Smoothed Particle
Hydrodynamics (SPH) which can handle magnetic fields (that is, magnetohydrodynamics
or MHD). There have been some issues in the past with attempts to do this,
which have now been overcome. The resulting algorithm gives very good results
on all the problems I have tested it on so far. The latest update on this work has been published in a
recent paper,
and also in my PhD
thesis. A picture
of the gas density one of the two dimensional tests (the Orszag-Tang vortex) is shown below at resolutions of 128x146,
256x294 and 512x590 particles. See a
movie of this simulation here (14Mb Quicktime format).
The pictures shown above were plotted using an interactive visualisation tool for SPH (and SPMHD) that I have developed based on kernel interpolations which is freely available here.
Some other Smoothed Particle Magnetohydrodynamics (SPMHD) resources can be found here (i.e. PhD's from Joe Morris, Zdislaw Meglicki and Steinar Borve, obtained from the author's web sites.)
Toy stars
As part of the testing of the magnetic fields code, I have been running some simple models of `stars', with a force law proportional to the distance away from the origin. The main point is that you can derive analytic solutions which can be compared with the results from the Smoothed Particle (Magneto)hydrodynamics code. Some animations of the toy star can be seen here.
Relativistic Winds
Near the start of my PhD I worked on a simple numerical model of outflow from stars which is related to astrophysical jets. This involves setting up an atmosphere above a gravitating body, heating a thin layer of this atmosphere (resulting in ejection of the gas) and seeing what velocities you can acclerate the gas to. The idea is to compare this to a relativistic simulation (that is, in general relativity, which would be necessary for winds or jets near a neutron star or black hole) and observe the different in velocities between the two simulations. The result we found was that the only difference between the two types of jets is that one is accelerated in a relativistic environment (ie. where the gravity is strong).
This is important for astrophysical jets because they are found in both young stars (where Newton's gravity law is valid) and in the central regions of galaxies near supermassive black holes (where the gravity is very strong and requires a relativistic treatment). The observed velocities of these jets are very different, but the idea of this work was to answer whether the different velocities can be accounted for (at least in part) by the different descriptions of gravity.
A beautiful example of a jet produced in the centre of
a galaxy is show below. The jet extends from the centre of a very powerful
galaxy known as a quasar for over one million light years (the galaxy is
not visible in this radio image).
Jets are also found near young stars that are just forming, such as this jet imaged by the Hubble Space telescope in the young stellar object known as HH111. The jet shown extends for 12 light years from one of two stars in a binary system.
