ay's ets
Simulations of Gamma-ray Burst
Afterglow Jet Evolution
Welcome to Jay Salmonson's jet page. Herein you will find a series of movies of simulations of the evolution of Gamma-ray Burst afterglow jets along with predicted flux and polarization curves. The purpose of these movies is primarily to build intuition about the dependence of observable quantities, in particular flux decay curves and polarization, on the physical features of jet morphology and evolution, such as viewing angle and energy distribution. Since the evolution of Gamma-ray Burst (GRB) afterglow jets is extremely special relativistic, it can be quite counter-intuitive and difficult to understand. Thus, these movies are an attempt to train one's relativistic intuition and move toward answering the question: "what does a GRB afterglow look like?"
To jump right into the data, go to the
What follows is a description of what the movies show. This is an equation-free page intended to inform both experts and lay-people about how to understand the data contained in these simulations and their representation of the relativistic afterglows. The extreme relativistic nature of these phenomena makes them an interesting case study of some of the counter-intuitive effects of Einstein's theory of special relativity.
0. What is a Gamma-ray Burst afterglow?
There
are numerous good websites discussing gamma-ray burts including the Introduction
to GRBs and Edo
Berger's GRB FAQ.
The discussion here begins with the so-called "afterglow" of the
GRB, which is subsequent to the actual gamma-ray burst and can be seen
in X-rays, optical and radio waves from hours to months after the
burst. The idea is that the gamma-ray burst event, lasting a few
seconds, ejects a jet of matter at extreme relativistic velocity; very
near the speed of light. This material slams into the tenuous gas and
dust surrounding the burst progenitor, thus shocking and heating it.
This hot, excited gas then emits the radiation observed by astronomers
in X-rays, optical and radio. As the shock expands into, and
sweeps up, the circumburst medium, it decelerates and cools. The goal of
these movies of simulations is to visualize the evolution of this
afterglow jet shock and to better understand how it works.
Basic understanding of the movies and how relativistic afterglow jets work is as easy as 1-2-3...
1. Relativistic Aberration.
Stuff moving directly at an observer is seen to evolve more quickly than stuff moving at an angle with respect to the line-of-sight.
An afterglow shock, represented by the polar grid, moves outward from a central explosion. The
top figures describe the non-relativistic expansion, which fits with one's intuition. The bottom figures
describe the relativistic case, where the region of the shock that moves directly at the observer evolves
most rapidly, thus achieving larger radii than other regions. In this case, the shock surface becomes distorted
and even folds back, hiding the edge of the shock from view.
Observer and Side views of the shock surface of the simulation of a homogeneous jet with opening angle of 5 degrees as seen at 3.35 degrees from the line of sight. The views are (artificially) rotating about the z-axis to maximize perspective. One can see the surface begin with a highly relativistic shape, in which the portion of the afterglow shock surface moving directly at the observer evolves and expands most quickly, thus creating the oblong morphology. As the shock surface decelerates to non-relativistic velocities (i.e. much less than the velocity of light) the surface becomes more in keeping with our (non-relativistic) intuition of what a shock expanding from a central explosion should look like. The grid lines correspond to 0.5 degree in latitude and 10 degrees in longitude. The surface is deliberately centered in the frames, but the true shape is preserved.
2. Afterglow Evolution.
As the afterglow shock expands away from the central GRB explosion, it sweeps up gas in the circumburst medium, much like a snowplow. As it does so, as one might expect, it decelerates. Therefore, as shown in the above movie of a simulated shock surface, the afterglow transitions from highly relativistic expansion to more pedestrian, non-relativistic expansion.Because it is the shock's job to excite the circumburst medium it plows into, the entire surface of the afterglow shock emits light. How much light is emitted toward the observer by a patch of the shock depends on how fast that patch is moving toward the observer; the faster the patch moves toward the observer, the more light is received by the observer from said patch.
Thus we have an interesting conceptual twist: since, as discussed in Step 1, the patch of shock moving toward the observer evolves most rapidly, it expands the furthest. Therefore, as explained here in Step 2, this patch will have plowed up the most circumburst material and will have decelerated the most. So it will emit less light toward the observer! Patches of the shock that move not quite directly at the observer, but at a small inclination angle from the observer line of sight will be less evolved, and thus will be expanding faster, and therefore will emit more light. So, if we could look at an afterglow, it would have a bright ring surrounding dark center.
A plot of the shock surface (top) with relativistic aberration, as discussed in Step 1, and the flux
surface (bottom) introduced here in Step 2, which is what is shown in the simulations. The point A
that moves toward the observer is furthest evolved and thus slower and dimmer than a point B which
is seen at an earlier, less evolved, brighter time. Finally at C the shock is moving at such a large angle
with respect to the observer that its radiation is beamed away from the observer.
The simulations on this webpage display the amount of light (flux) received from each point on the afterglow shock surface. So the z-axis represents the flux and the x & y-axes are the observer's view plane. An example surface at the top of this page demonstrates what I call a "molar morphology" because of its similarity to our grinding teeth. Why do we care about the flux surface? The flux surface describes where the shock is bright and dim; what the shock looks like to an observer. By analogy, we aren't interested in the shape of a movie screen or TV screen, but rather the image upon it (i.e. a flux surface map of bright and dim regions which makes up the images we see).
Adding all of flux from this surface together gives the total flux received by an observer and this is plotted on the right-hand-side of the movie frame. Also plotted is a caclulated polarization which describes a net orientation of the received flux.
3. Afterglow Structure.
There are currently two ideas for the structure of the afterglow. The first, chronologically in their inception, is the Homogeneous Jet Model that describes the afterglow shock as a simple, homogenous surface. In order to satisfy correlations in the data, this model requires that there be narrow, energetic shocks and wide, less energetic shocks and all intermediates as well (see figure below). Thus, this model implies a wide array of very different types of afterglows to account for observations.The second, the so-called Structured Jet Model asserts that it is plausible that an afterglow will have a hot core of highly energetic material flanked by progressively cooler material. An appealing attribute of this model is that it holds the potential to roll up all Homogeneous Jets into a single, universal jet. As such, the observed variety of afterglows that makes necessary a wide range of Homogeneous Jets might be accommodated by a much narrower range of Structured Jets, whereby the observed variety stems from our viewing angle of a universal structured afterglow. Thus if we were to observe the Structured jet straight on, we would see a very energetic, short-lived afterglow, but if instead we observed the afterglow at a progressively higher angle of inclination from the jet axis, we would see a progressively less energetic, long-lived afterglow. This idea that observer perspective on a universal jet is the primary source of the variety of afterglows observed, coupled with the physical plausibility of nature making such a jet, with an energetic core and less energetic wings, makes this model quite appealing. The drawback is that it is much more difficult to calculate. Indeed, performing detailed structured jet afterglow calculations was my primary motivation for developing the simulations found here.
A schematic of the difference
between the two afterglow jet models highlighted on this page. The
first is
the Homogeneous Jet Model, in which an afterglow shock is a simple, constant, homogeneous surface.
To accomodate observations, this jet must be narrow and energetic (red) or wide and less energetic (blue) or somewhere
in between (green). Thus, a wide variety of physical jets must be produced by nature. The Structured Jet Model tries
to explain the existence of all of these different Homogeneous Jets with a single, universal jet with an energetic
core flanked by progressively less energetic material. In the Structured Jet model, the observed variety of
afterglows is not inherent in the population, as in the Homogeneous Model, but derives solely from observer
perspective on the jet. , cons
the Homogeneous Jet Model, in which an afterglow shock is a simple, constant, homogeneous surface.
To accomodate observations, this jet must be narrow and energetic (red) or wide and less energetic (blue) or somewhere
in between (green). Thus, a wide variety of physical jets must be produced by nature. The Structured Jet Model tries
to explain the existence of all of these different Homogeneous Jets with a single, universal jet with an energetic
core flanked by progressively less energetic material. In the Structured Jet model, the observed variety of
afterglows is not inherent in the population, as in the Homogeneous Model, but derives solely from observer
perspective on the jet. , cons
Having read through this page, you are welcome to adjourn to the theater to view the afterglow movies at the...
Jay D. Salmonson
July 14, 2003