# Maurice Wilson's

## Protoplanetary Disks

Today I will discuss protoplanetary disks. This is nothing like the previous topics I have written about. But, there's a first for everything, so why not?

Our solar system consists of 8 planets. Over the past ~30 years, astronomers have found a ton of evidence proving that most of the stars we see in the night sky have their own "solar system." These stellar systems vary in the amount and type of planets they contain. However, one similarity that these planets of distinct stellar systems have is that they were born out of protoplanetary disks. A protoplanetary disk is full of gas and dust that serve as the primary building blocks for planets.

The gas and dust of a protoplanetary disk comes from a giant molecular cloud. Giant molecular clouds, like the Orion Nebula, are stellar nurseries. A portion of the giant molecular cloud can come together to form its own molecular cloud clump. The clump has its own gravity that makes it contract and its own internal pressure that helps it expand. Once the gravity overcomes the internal pressure and all other outward-pushing forces, the molecular cloud eventually collapses into a very hot and dense core of gas. This core indicates the birth of a new star, i.e. the formation of protostar. The outer region of the molecular cloud that is no longer touching the core is still affected by the gravitational pull of this young star. The remaining nearby gas and dust orbits the young star, forming a circumstellar disk that is more commonly known as a protoplanetary disk. This disk is also referred to as an accretion disk because the star is continuously pulling in and feeding off of the material in the disk.

By observing these disks in micrometer, millimeter and infrared wavelengths, a wealth of information about their structure, age and orbital mechanics have been inferred. One important detail that astronomers have learned is that these disks actually aren't disks. The structure is not flat. The gas and dust vertically disperses more as their distance away from the central star increases. Although the structure is close to being flat, it is actually a flared disk. Another fun fact is that these disks can live up to 10 million years. They are often a few hundred astronomical units (AU) in diameter. The inner portion of these disks can have temperatures above 2000 Kelvin (K) because of the central star. (As a relevant comparison, recall that the Sun's temperature is about 6000 K.) In the midplane of these flared disks, the temperatures are usually between 10 and 30 K in the outer regions of the disks. (In comparison, the temperature in the cold vacuum of empty space is 2.7 K. Apparently, these disks are quite chilly!) These temperatures vary as the disk ages. Over time, the hot radiation from the central star can evaporate the inner region of the protoplanetary disk out to 1 AU. A massive, second star that is nearby might destroy outer regions of this disk via its radiation too.

The temperature of the gas and dust can also depend on how they collide and how often they coagulate. Gas particles are pretty much always colliding with dust grains. If you think of the dust grain as a baseball and the gas as the wind, it is easy to see that gas can affect the speed of the dust grains. The grains succumb to the drag and friction caused by the gas and this affects the temperature of the local area, especially if the dust grains are large. Not all collisions result in the particles sticking together though. Therefore, it can be tough for chemists to determine when a dust grain, moving at a certain speed, will let other gas or dust stick to it. Here, I referred to chemists instead of astronomers because the study of protoplanetary disks heavily depends on knowledge from multiple disciplines. Dust grains are accumulations of molecules (like MgSiO$$_3$$ or FeSiO$$_3$$) that may or may not chemically react to the gas and dust that collides with it. This is why astronomers heavily depend on chemists (and astrochemists) who conduct experiments on Earth in a lab. Their experiments with dust grain collisions help us figure out how often the molecules coagulate and how grains—only the size of 0.1 microns ($$\mu$$m)—eventually become the size of baseballs, asteroids and finally planets. (For reference, note that 0.1 microns is about 50 times smaller than the average size of bacteria.)

Simulation of dust collision in protoplanetary disk.

Apparently, the dust collisions affect the protoplanetary disk temperature and the probability of creating a planet. It seems like collisions are a pretty big deal then. Unfortunately, these myriad amount of collisions cannot be directly detected. Despite this, the temperature of the gas and dust can still be determined. This is done by measuring the radiation of dust continuum emission and gas line emisssion. Studying these two sources of radiation requires distinct sets of equations. This is because the velocity of the gas is extremely important for knowing how often the gas collides with other gas. Gas collisions in (cold) protoplanetary disks cause a gas atom to de-excite, i.e. cause an electron of the atom to drop in energy level, which makes the gas emit a photon. The dust, on the other hand, moves so slowly in comparison to the gas that its velocity doesn't significantly alter its temperature. We can ignore the super slow velocity of the dust and still find a good estimate for its temperature. However, the velocity of the gas can affect the temperature of the dust. So, in theory, the dust temperature calculations would be even better if that information were included too.

Although gas and dust have very different characteristics, their important similarity is that they both are sources of radiation, and the light they emit behaves similarly as it travels from the protoplanetary disk to telescopes on Earth. The intensity of the light we measure is affected by the trajectory it took through the protoplanetary disk to reach us. This intensity is described by the radiative transfer equation. Simply put, this equation explains how the intensity changes as the radiation is transferred through a medium, such as dust grains or gas. Once the radiative transfer is understood, the temperature of various regions in the medium can be determined. Calculating this temperature profile is very important because it determines where gas and dust will be too hot and evaporate or where gas will be too cold and freeze/stick onto grains.

During radiative transfer, the intensity can change once the photons are absorbed, scattered or re-emitted by gas and dust. If a photon is absorbed by gas or dust then it won't reach the telescopes on Earth. As a result, this would decrease the intensity of the light we detect. Dust often scatters (blue) light that comes from the central star. This redirects the light's original path. Dust can also absorb then re-emit the star light. This would redirect the photons and alter their intensity. The radiative transfer calculations should account for these three events regardless of whether the photon originated from the central star, the gas, or the dust. In order to calculate this accurately, we need to know how much gas and dust the protoplanetary disk has and how this gas and dust is distributed throughout the disk. For this reason, I will talk about the density distribution of a protoplanetary disk in my next post.

to be continued ...

Posted: May 26, 2017

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