Lets try and get a better feel for how a simple SED might change as some parameters change. Let us assume a circumstellar disk made of perfect blackbody grains. Remember this means that they are perfect emitters and absorbers of radiation. Let's also assume that the disk is geometrically thin and optically thick (this will mean more later).
What do you think an SED of a disk that has a radius of 100 AU would look like? Click here to find out!
What do you think an SED of the same disk with an inner hole of 0.3 AU would look like? Click here to find out!
What if this disk had a gap in it as well?Click here to find out!
From these plots, you can begin to see how the SED of a disk might be different depending on its shape. We see that the inner radius, outer radius, and any gaps in the disk play a large role in the appearance of the SED. These gaps are interesting to us because they may correspond to forming planets. As the circumstellar disk rotates around the star, small clumps begin to form and these clumps sweep up more and more dust as they get larger thus producing a gap in the disk. These clumps, we believe, are the beginnings of planets. So if we can find the gaps in the disk, we can pinpoint where possible planets might be forming. The planet itself does not produce enough radiation for us to detect it but the planet does produce a tracer in the form of a gap that allows us to determine where it might be!
The temperature and radius of the star also effect how an SED appears because it plays a vital role in the temperature of the dust. In addition, the disk's distance from us is important because it effects how much light we receive from the object. But what about the dust grains themselves? Shouldn't the material, size, and shape of the grains play a role in how the disk absorbs and re-emits radiation? The answer is yes.
This brings up some interesting questions. What do we need to assume about the dust grains in order to make an effective model? And are different factors about the dust grains important in different types of disks? Different factors or "parameters" are, in fact, important in different types of disks. Circumstellar disks can basically be broken down into two groups: optically thick and optically thin. An optically thick disk is a disk that absorbs the radiation from the central star at the surface of the disk. As soon as the grains absorb this radiation and emit their own, it immediately is absorbed again by the surrounding grains. This absorption and re-emission takes place throughout the entire disk. We, therefore, only see the radiation that is being emitted by the outer most grains in the disk. Optically thin disks, on the other hand, do not have this property. The energy emitted from the grains within the disk is not immediately absorbed again by the surrounding grains. This means that we observe energy emission from grains throughout the disk, not just the ones present at the surface.
Because we only see the emission from grains at the surface of an optically thick disk, the material of the grains and the density of the disk do not play a very large role in the appearance of the SED. The size of the grains is the dominant factor. Dust grains that are larger than the wavelength of incoming radiation absorb that radiation very efficiently. Likewise, grains that are larger than the peak wavelength they emit, emit that radiation effectively. Grains smaller than the wavelength of incoming radiation, on the other hand, do not absorb that radiation very well. Those same grains, in turn, do not efficiently emit radiation at wavelengths larger than their diameter. So smaller interstellar medium-like grains will be very poor absorbers and emitters of radiation. This means smaller grains will not be able to emit the radiation that they absorb efficiently. As a result, they will remain hotter at larger radii (corresponding to smaller values of "p" in the power law temperature distribution). Very large grains behave just the opposite. They emit radiation very efficiently, so they tend to cool off closer to the star (corresponding to larger values of "p"). Above and below are SED's of optically thick disks that illustrate this well. Both disks have an inner hole that extends to .05 AU and a gap between 2.5 and 10 AU. Notice how the p=0.5 plot, the plot that allows dust to be hotter at larger radii, shows a significantly larger amount of infrared emission.
In an optically thin disk there are more parameters to worry about. The density of the disk and the material of the disk play a larger role because we are able to observe emission from grains throughout the disk, not just on the surface. We are also able to account for the material of the disk using another power law similar to the temperature distribution power law.
The density of a circumstellar disk also plays a large role in the appearance of an optically thin SED because we are able to see radiation emitted from grains throughout the disk, not just grains on the surface. So, obviously, if there are more grains per square centimeter, we are going to have more energy emission. The density of the disk also follows a power law
To get a better idea of how these factors effect an SED click here. These three plots are all SEDs modeling the same disk and comparing it to actual data. Notice, however, that all three models make different assumptions about the disk but all fit the data quite well. One assumes that the grains are small (less than 1 micron in radius), one assumes the grains are medium sized (around 1 micron in radius), and one assumes that the grains are large (around 1000 microns in radius). The parameters are listed at the top of the graph. The Greek letter sigma stands for the density and "Ri" and "Ro" stand for the inner and outer radii of the disk. The temperature distributions are also listed at the top of the graphs. Notice how the power law changes as the assumptions of the grain size changes. Also notice where the Kv power law takes effect. How might you be able to tell this simply from the SED? Do Kv power laws appear to be the same for all three temperature distributions? Should they be the same?
So what conclusions can we draw from all of this? First, it should be clear that studying circumstellar disks in just the optical range does not tell the whole story. By observing circumstellar disks in the infrared, we gain more insight into the geometry and composition of these disks. Furthermore, by using the spectral energy distribution as a tool, we are able to make models that allow us to determine what might be happening inside a particular disk. However, one should be weary because model parameters do play off on each other in such a way that many models are able to fit the same data. Finally, by studying these disks, we begin to learn more about other forming planetary systems and are able to place our own solar system within a context of others. We may finally be able to determine if our own solar system is unique and if there are other planetary systems such as our own that might support life!
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