# Maurice Wilson's

## Dusty Disk Density Distribution

The equations in my previous post show that my dust density distribution function $$\rho(r,z)$$ cannot be used unless we have information about the protoplanetary disk (e.g., $$M_{disk}, R_c$$ and $$\gamma$$) and its central star (e.g., $$M_{\star}, R_{\star}$$ and $$L_{\star}$$). To make this hypothetical disk realistic, I used values attributing to the star DoAr 25 and its circumstellar disk for the parameters in my equations. If you're interested, these parameter values can be found in "The Structure of the DoAr 25 Circumstellar Disk" paper.

This is the structure of my protoplanetary disk after cranking out those calculations.
Figure 1: Dust density distribution.

I used the VisIt software to visualize the result of my calculations. Before I go into how the laws of physics derived this structure, I will first mention a few important features in this visualization. The colors represent the density of the dust grains. The regions with the greatest density are colored red and the density decreases as the colors change from red to green to blue. Also note that the star at the center of the protoplanetary disk is not actually shown in my depiction of a protoplanetary disk. Instead, the center of my structure has a blank region that is transparent. These next images will help wrap your head around this structure even more.

Figures 2 and 3 really show how much this disk is flared. Flaring occurs for a variety of reasons but there are two concepts in particular that I used which are responsible for this flaring.
1) The scale height affects the height (above or below the midplane) at which the density becomes zero and no more dust grains exist beyond that height. This scale height gradually increases with radial distance away from the star. (Refer to the scale height $$H$$ equation in my previous post.)
2) At any given distance away from the star, the star's gravitational pull is strongest at the midplane than at any other height. (Refer to the cylindrical $$F_{grav}$$ equation in my previous post.) This means that dust, at a given distance, will gravitate toward the midplane and accumulate along that plane. This is why in all of my graphics thus far, you've seen that the midplane is super dense, in comparison to the density at other heights.

Now that I've explained a few characteristics of the structure vertically, I should mention how the density is distributed horizontally. If you look closely at Figure 3, you'll notice that at each layer the color changes from blue to green to yellow to red going from the inside out. Apparently, at a given height, the density of the dust grains increases as you get further away from the star. This is, again, due to the scale height. I already mentioned that the scale height increases with radial distance away from the star. Additionally, an increase in scale height increases the density of the dust grains along any given height, and this is exactly what Figure 3 reveals. (Refer to exponential factor $$exp$$ in the $$\rho(r,z)$$ equation of my previous post.)

Thanks to the equations and imagery I have introduced you to, you have now witnessed one way to deduce the structure formed by the dust grains of a protoplanetary disk. We can now move on to determining the temperature of dust throughout the disk. In my next post, I'll show visualizations for the 3D temperature profile that I'm sure you've been so desperately waiting to see.

to be continued ...

Posted: June 18, 2017

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