I started out studying physics in Amsterdam. My master thesis research project was about the combinatorics of lattice models of interacting electron (-like) particles, and how insights from the mathematics of super symmetry could aid in enumerating the possible energy states of such systems. I also stumbled across some interesting mathematics, but by the time the pros figured that one out I had long since switched fields to astrophysics.
For the past five years or so I have been involved in theoretical and computational research into gamma-ray bursts, the immense cosmic explosions that follow the collapse of a heavy star or the merger of neutron stars.
Gamma-ray bursts and their afterglows
Gamma-ray bursts were originally discovered by accident in 1967 by the Vela satellites. Although it was immediately understood that the bursts weren’t man-made, it took some decades for it to become clear that what was seen was actually the sudden flash produced by some cataclysmic event occurring literally galaxies away. What made this breakthrough in the late nineties possible was the discovery of a different type of radiation from a later stage of the event. As was theoretically predicted, gamma-ray bursts signal the type of event that typically produce a blast wave wave going out from the source into the interstellar medium, sweeping up matter as it goes along. At this stage, the blast wave (or shell, or jet) was predicted to radiate too, albeit not as strong as the explosion of gamma-rays that corresponded to its initial outbreak. And as time goes on, the radiation was expected and confirmed to become weaker and weaker, peaking first in X-rays and optical and gradually becoming visible as long wavelength radio emission.
This phenomenon has been labeled the afterglow of the gamma-ray burst. From the study of these afterglows a wealth of information can be gained about gamma-ray bursts, their origin and the galaxies in which they occur (for example, it was an afterglow that first made it possible to pinpoint the origin of an observed gamma-ray flash as a distant galaxy, because the precise direction of an afterglow is easier to determine than that of the gamma-rays)
The basic model of afterglow jets is fairly straightforward and reasonably well understood. There is the decelerating relativistic (i.e. moving close to light speed) jet, and both small magnetic fields and strongly accelerated individual electrons are generated at the shock front. The jet moves into some medium around the star and at some point spreads out and eventually becomes non-relativistic (such that their dynamics can be described using Newtonian mechanics rather than the special theory of relativity). But although analytical models were very helpful in getting the above big picture roughly right, they lack the detail to correctly capture many of the details of this process. In order to prevent all these details (e.g. “how does the jet evolve between these stages?”, or “what if the medium isn’t simply homogeneous?”) from swamping our theoretical understanding, it is very helpful to examine the evolution of the jet by using numerical simulations. Especially, if you take extra care to accurately calculate the predicted radiation from such hydrodynamical jet simulations.
The circumstellar environment
This brings me to my PhD research at the Astronomical Institute of the University of Amsterdam, which was largely devoted to developing the numerical tools to calculate synchrotron radiation from relativistic jet simulations for observers measuring at arbitrary distance, times and frequencies. As a consistency check on the radiation code and first application, we calculated what the afterglow would look like not just for a jet going into a homogeneous interstellar medium or a medium shaped by the steady outflow (“stellar wind”) of gas from the yet unexploded star, but also for density profiles in between. In a separate numerical study we found that, even when the environment of the star suddenly transitions between stellar wind and interstellar medium, the observed effect in the afterglow signal (the “light curve”) is gradual, resolving a discrepancy between studies that predicted a sudden jump in brightness and that disputed the rebrightening. A later project (in collaboration with a plasma physics group at the K.U. Leuven) confirmed numerically an alternative theory, that the sudden rebrightenings (that actually had been observed in the data, so they had to come from somewhere!) can be explained from late time ejected material catching up with the forward shock.
The visibility of the density transition was not the only effect that turned out to be more gradual than expected. Our studies of 1D models (of conic jets taking only radial flow into account) also show that the transition from relativistic to non-relativistic jet takes a very long time, with the transition point occurring noticeably later than analytically predicted. At the same time, our more detailed radiation code revealed that the shape of the light curve is sensitive to subtle changes in the assumptions about the details the relation between gas pressure and density, and about the generation of magnetic fields and particle acceleration in the shock.
Afterglow jets and jet breaks
Later research in Amsterdam and, more recently, at the Center for Cosmology and Particle Physics of New York University, focused a lot on the jet nature of the outflow. Afterglow blast waves are initially strongly collimated and confined to narrow jets. Because gamma-ray bursts occur at such vast distances, the shape of these jets cannot be observed directly (unlike, say, jets from active galactic nuclei). Instead, this property is inferred from the observed drop in afterglow flux usually observed after a few days or so. There are two theoretical reasons to expect this drop in flux (the “jet break”). First, the jet will at some point start to spread out once it has slowed down sufficiently. As it becomes wider, it will encounter more material is has to push against and as a result it will slow down even further. From this additional deceleration also follows an additional weakening of the emission therefore of the afterglow signal. Second, even if the jet doesn’t spread sideways, the edges of the are at first invisible due to the relativistic analog of Doppler shifts, applied to light instead of sound (the analogous effect for sound would be the increase in pitch and volume for noise coming towards you, like that from an approaching ambulance). Because the afterglow jet is aimed directly towards us, at first we see only the center of the jet, with the outer parts of the outflow that make a (very) small angle with respect to the observer remaining invisible on account of being beamed slightly away from us. Theory predicted that the first effect would overwhelm the second, and also that these jet breaks would become visible in each frequency at the same time, since their causes were linked to the dynamics of the outflow, rather than the processes generating the radiation.
What we found was that those theoretical predictions were either grossly oversimplified or wrong. The final paper for my thesis reports a study of the jet break seen at different frequencies, calculated with our radiation code which also takes into account that the jet becomes opaque to light at low frequencies (radio emission is partially blocked by “synchrotron self-absorption”). Although the the jet break is caused by changes in the jet outflow that are dynamical in origin, we show that the observer frequency still plays a crucial role: due to frequency-dependent opacity, different regions of the jet dominate the emission at different frequencies. And only if the region near the jet edge dominates, the jet break is seen directly. In practice, this means that optical and X-ray breaks are seen well before the radio break, something which had puzzled observers.
jet breaks and observer angle
Both our work in Amsterdam and numerical work of the NYU group before I joined was showing that in high resolution hydrodynamics simulations the jet did not spread sideways as quickly as analytically expected. In fact, this was already hinted at by earlier numerical work at lower resolution. This has a number of interesting consequences, aside from demonstrating that the dynamics of relativistic outflows are more complex than originally thought. It means that the jet does not decelerate as quickly as expected, and neither does it become roughly spherical as quickly as expected. Both confirm that the more elaborate 2D simulations do not fundamentally alter our earlier conclusions based on 1D models. It also means that of the two causes for the jet break mentioned above -jet spreading vs. edges becoming visible- there is no longer reason to believe that the first cause overwhelms the second. The second effect is far more sensitive to the precise orientation of the jet with respect to the observer, for if the jet is tilted slightly one edge becomes visible before the other and the whole jet break becomes only apparent in two phases. Although seemingly a small effect, it turns out to be strong enough to delay the complete jet break until the light curves flux has dropped below the detection threshold of Swift, one of the premier afterglow observational satellites. Thus it provides a natural answer to an issue that had puzzled astronomers working with Swift data: “where are the afterglow jet breaks?”
A library of afterglow light curves
Aside from helping to address specific research questions, the simulations also more generally provide a means to calculate realistic light curves for a wide range of input parameters for the explosion and radiation physics. This is a helpful tool for exploring what can be expected on average for telescope surveys, and our recent work has been aimed at quickly providing light curves at all sorts of wavelengths, from radio to X-ray, both in publications and directly on-line.
Written September 5, 2011 and describing my research until that date.