Today we have a guest post from Colette Salyk. Colette is the Leo Goldberg Postdoctoral Fellow at the National Optical Astronomy Observatory in Tucson, Arizona. She studies the evolution and chemistry of protoplanetary disks (the birthplace of planets) using a variety of ground and space-based telescopes.

Welcome to Part II of my three-part post about studying the chemistry in protoplanetary disks!  (You can find Part I here.) In the last post I talked about techniques for detecting molecules. But once we detect them, what do we do with these detections? Ultimately, we want to make chemical “maps” of the protoplanetary disks, so we can understand what kinds of environments planets are forming in at different distances from their host star. In this post I’ll explain how we use the Doppler shift (yet again!) plus Kepler’s law to locate molecules in protoplanetary disks. (In Part III, I’ll discuss some of the connections between disk chemistry and the formation of planets.)
In the figure below, I’ve reproduced the observed water emission line that I discussed in my first post, but have converted wavelength to velocity using the Doppler shift equation, (λ−λ0)/λ0 = v/c , and centered the line at zero velocity. Note that in the first post, I focused on the shift of the entire line relative to the theoretical line center; here I am repositioning the line to account for this new center, and we’ll be discussing Doppler shifts relative to this new center.
Although molecules emit/absorb at very specific wavelengths, the water vapor emission line we observed is clearly not thin and pointy. Instead, it has a rounded shape — something we refer to as “line broadening.” This broadening occurs for all spectra, due to two reasons. One reason is that the instrument optics always blur out the signal somewhat — this is called the “instrument response function.” The other reason is that the molecules themselves are always moving, and the motion of each molecule produces a Doppler shift. Collectively, they produce emission at a range of wavelengths. In our case, the instrument response function (plotted in the figure) is much narrower than our line. Therefore, the broadening is dominated by the motion of the molecules.

The molecules are moving around due to a variety of reasons, including bouncing around due to their temperature, being kicked around by turbulence, and being in orbit around the star. The last effect dominates in our case, and I’m going to focus on that motion in this post. A simple example that may help you picture how orbital motion broadens the emission line is to consider a thin ring of molecules orbiting a star, oriented edge-on to our view. The molecules on one side of the star are moving away from us, and are redshifted; the molecules on the other side are moving towards us and are blueshifted. The amount of Doppler shift also depends on the orientation of the motion — as we examine parts of the ring that appear “closer” to the star from our point of view, we see progressively more transerve motion, and progressively less radial (and therefore Doppler shift-producing) motion. This collection of Doppler shifts turns a thin theoretical emission line into something broader, with symmetric blueshifted and redshifted components.

How fast are the molecules moving in the disk as they orbit their host star? If you’ve taken Astronomy 101, you’ve probably heard of Kepler’s laws — they are a set of relatively simple rules that dictate how the planets of the solar system orbit around the sun. Kepler’s third law relates the period (P) and semi-major axis (a) of planetary orbits, stating that P^2 ∝ a^3. Alternatively, astronomers often convert period to velocity (using v = 2πa/P), and put in the correct constants so that the law applies to stars of all masses (not just ones like the sun), to obtain: v = sqrt(GM⋆/a), where G is the gravitational constant and M⋆ is the mass of the star. This is a very powerful statement, because it means that we can directly relate velocity (v) to distance from the star (a). Since we can use the Doppler shift to measure velocity, we can therefore use the line broadening to measure the location of the molecules.

In contrast to the simple ring example I gave above, real emission lines originate from a range of disk radii, and the amount of light emitted at each radius also depends on the temperature and density of molecules. Also, the line width depends on how inclined the disk is with respect to our view. The figure below shows example emission lines originating from a disk where I’ve assumed the molecules are located between two radii, Rin and Rout, and that the disk is inclined by 30°. Have a look at the plots to see how the line shape depends on both Rin and Rout.

What I find especially cool about this technique is that it works especially well when the molecules are at small radii. For example, it’s really easy to tell the difference between molecules located at 0.1 AU vs. molecules located at 1 AU! It’s not currently possible to obtain this kind of detailed spatial information through imaging alone, and so we sometimes say that we’re achieving “super-resolution”. I think this is a neat parallel to the Kepler mission, in which the transit observations are used to obtain detailed information about the sizes and orbital radii of planets, even though we cannot directly image the planets.

Now some questions for you. Have a look at the detected water emission line in the first figure. Assuming this disk is inclined by 30°, as I assumed in my models, where do you think the molecules are located in this disk?

Today we have a guest post from Colette Salyk. Colette is the Leo Goldberg Postdoctoral Fellow at the National Optical Astronomy Observatory in Tucson, Arizona. She studies the evolution and chemistry of protoplanetary disks (the birthplace of planets) using a variety of ground and space-based telescopes.

One of the most interesting results to emerge from planet-hunting surveys is that planets and planetary systems are really diverse. I am trying to understand this diversity by studying the birthplace of planets – disks of gas and dust around young stars that we call “protoplanetary disks”. In particular, I study the chemistry in protoplanetary disks. In this post, I’m going to explain some of the techniques we use to detect and study molecules in protoplanetary disks using ground-based telescopes. In particular, I’m going to discuss the importance of the Doppler shift.

To detect molecules, we look for their unique spectral fingerprints. So we use spectrographs, usually on a large telescope like Keck or Gemini Observatory, or the Very Large Telescope. These observations require a lot of photons! But one challenge for these types of observations is that, if we’re observing simple molecules like water, carbon monoxide or methane, for example, these same molecules sit in the earth’s atmosphere and preferentially absorb the very photons we’re trying to detect.

This is where Doppler shifts come to the rescue. You may be familiar with Doppler shifts in the context of radial velocity searches for planets, in which the periodic Doppler shift in stellar absorption lines is produced by the gravitational pull of an orbiting planet. Recall that Doppler shifts are shifts in wavelength that are produced by relative motions between a source emitting photons, and an observer. If the source and observer are moving towards each other, the source looks blueshifted — its spectrum moves towards shorter wavelengths; if they are moving away from each other, the spectrum looks redshifted, like it has moved to longer wavelengths.

In our case, because both the protoplanetary disks and the earth are moving in space, the light emitted by molecules in the disk are seen at earth to be shifted in wavelength. Therefore, the wavelength of light we’re trying to detect is no longer exactly where molecules in our atmosphere want to absorb light.

The figure below shows an example of this. The red line shows the percent transmission of light through the earth’s atmosphere as a function of wavelength, as observed at the top of Mauna Kea. Note that at some wavelengths, the transmission is significantly less than 100%, meaning that the atmosphere absorbs a significant fraction of the light it receives from space. These regions are where water vapor molecules in the earth’s atmosphere are sucking up photons. In black is a spectrum of emission from a protoplanetary disk, obtained with the TEXES spectrograph on the Gemini North telescope. The peak in this spectrum was emitted by water vapor molecules in a protoplanetary disk. Note that it’s shifted relative to the sky absorption line due to the Doppler shift. In this case, the shift of the source line relative to the earth is consistent with a relative velocity of 18 km/s (∼40,000 miles/hour).

 

Spectrum of emission from a protoplanetary disk (black), obtained with the TEXES spectrograph on the Gemini North telescope. The peak in this spectrum was emitted by water vapor molecules in a protoplanetary disk. Image credit: Colette Salyk

This Doppler shift wasn’t just obtained by chance. Because it’s the relative motion of the earth and the disk that determines the observed Doppler shift, this shift actually changes throughout the year, as the earth orbits around the sun. The diagram below is a schematic representing a top-down view of the earth’s orbit, with the location of the Earth at four hypothetical dates, as well as a possible location on the celestial sphere of a protoplanetary disk. Note that while the Earth orbits the sun at a nearly constant speed, the direction of its velocity (represented by the arrows) changes. So there are times of the year when the spectrum of this protoplanetary disk is shifted towards longer wavelengths, other times when it is shifted towards shorter wavelengths, and times when it is not shifted at all.

Assuming the geometry in this schematic, what time(s) of year might you expect the Doppler shift shown in the first figure? When do you think would be the ideal time(s) of year to plan observations of molecules in this disk? When would be the worst times of year?

Image credit: Colette Salyk

Once we detect the molecules, what do we learn from them about planet formation? I’ll discuss this in more detail in a future post. But here’s some food for thought. The architecture of the solar system has a very clear division between terrestrial planets (at 1.5 AU and within) and giant planets (at 5 AU and beyond). What might have caused this dichotomy, and should we expect to see it in exo-planetary systems as well?