*** Still a draft! ***
Posted by: Meredith MacGregor (4/18/13)
When discussing young stellar objects and protoplanetary disks, astronomers continually throw out the term ‘SED.’ For the past week, I have been at a conference titled ‘Transformational Science with ALMA: From Dust to Rocks to Planets– Formation and Evolution of Planetary Systems.’ And, I can attest to the fact that the term ‘SED’ has come up in a very significant fraction of the contributed talks. For those not intimately familiar with this sub-field, this rampant use of abbreviations can be confusing, making it difficult to glean any useful take-aways from a talk. So, in addition to summarizing the article by Robitaille et al. (2007), the goal of this post is to give a bit of an introduction to the terminology and motivation for the growing field of star and planetary system formation.
SEDs: What They Are and Why We Care So Much
The abbreviation ‘SED’ stands for ‘Spectral Energy Distribution.’ If you want to sound like an expert, this should be pronounced exactly as it appears (analogous to the non-acronym ‘said’). A SED is essentially a graph of how the flux of emission from an object depends on the wavelength the object is observed at– flux plotted versus wavelength. In the context of the Robitaille et al. article, we are most interested in the SEDs for young stars and the envelopes and disks surrounding them. So, why exactly does the flux from a young stellar object (YSO) vary with wavelength? As it turns out, different regions of the YSO emit at different wavelengths. This means that when we observe at different wavelengths, we are actually probing distinct regions of the star, envelope, disk, etc. By tracing out the entire SED for a YSO, we can actually determine what the geometry, structure, and constituents are for that object.
SEDs for pre-main sequence stars are often seen to have a bump or excess in the infrared. This bump is generally interpreted as being due to thermal emission from warm dust and gas surrounding the central star. As an illustrative example, let’s consider a protoplanetary disk around a young star. The image below is taken from a review article by Dullemond & Monnier (2010) and shows a graphical representation of the emission spectrum from such a disk.
In this case, emission in the Near-IR traces the warmer inner regions of the disk. As you move into submillimeter wavelengths, you start to probe the outer, cooler regions of the disk. By modeling the observed SED of a pre-main sequence star, you can determine what components of the source are contributing to the observed flux. The second figure below is taken from a paper by Guarcello et al. (2010). The left panel of this figure shows the observed SED of a BWE star (in line with other ridiculous astronomy acronyms, this stands from ‘blue stars with excesses’), while the right panel shows a model fit to this data. The authors describe the observed SED using a model with four distinct components: (1) emission from the reddened photosphere of the central star, (2) radiation scattered into the line of sight from dust grains in the disk, (3) emission from a collapsing outer envelope, and (4) thermal emission from a circumstellar disk. The summation of these four component makes up the complete SED for this BWE.
Describing and Classifying the Evolution of a Protostar
As a protostar evolves towards the Zero Age Main Sequence (ZAMS), the system geometry and, as a result, the SED will evolve as well. Thus, the stage of evolution of such a protostar is often classified according to features seen in the SED. A graphical overview of the four stages of protostar evolution are shown below (Andrea Isella’s thesis, 2006). Class 0 objects are characterized by a very embedded central core in a much larger accreting envelope. The mass of the central core grows in Class I objects and a flattened circumstellar accretion disk develops. For Class II objects, the majority of circumstellar material is now found in a disk of gas and dust. Finally, for Class III objects, the emission from the disk becomes negligible and the SED resembles a pure stellar photosphere.
2. The Article Itself
One common method of fitting SEDs is to assume a given gas and circumstellar dust geometry and set of dust parameters and then use radiative transfer models to find a set of parameters that best reproduce the observations. However, fitting SEDs by trial and error is a time consuming way to explore a large parameter space. The problem is even worse if you want to consider thousands of sources. So, what’s to be done? Enter Robitaille et al. In order to attempt to make SED fitting more efficient, they have pre-calculated a large number of radiative transfer models that cover a reasonable amount of parameter space. Then, for any given source, they can quickly find all of the combinations of parameters that could explain the observations.
Let’s Get Technical
The online version of this fitting tool draws from 20,000 sets of physical parameters and 10 viewing angles (if you are particularly curious, the online tool is available here). A brief overview of the parameter space covered is as follows:
- Stellar mass between 0.1 and 50 solar masses
- Stellar ages between 10^3 and 10^7 years
- Stellar radii and temperatures from evolutionary tracks given mass
- Disk and envelope parameters sampled given age of source
However, there are truly a vast number of parameters that could be varied in models of YSOs. Thus, for simplicity, the authors are forced to make a number of assumptions. What are some of the biggest assumptions involved?
- All stars form via accretion through a disk and an envelope.
- The gas-to-dust ratio in the disk is 100.
- The apparent size of the source is not larger than the given aperture.
The last constraint is not required, but it allows a number of model SEDs to be cut out and thus speeds up the process. Furthermore, the authors make a point of saying that the results can always be scaled to account for varying gas-to-dust ratios, since only the dust is taken into account in the actual radiative transfer calculations.
Does This Method Really Work?
If this tool works well, it should be able to correctly reproduce previous results. In order to test this out, the authors turn to the Taurus-Auriga star forming region. They select a sample of 30 sources from Kenyon & Hartman (1995) that are spatially resolved, meaning that there is prior knowledge of their evolutionary stage from direct observations (i.e. there is a known result that astronomers are fairly certain of to compare the model fits against). In the context of this particular star forming region, the authors throw in a few additional assumptions:
- All sources are within a distance range of 120 – 160 AU.
- The foreground interstellar extinction is no more that 20.
The authors then assign an arbitrary cut-off in chi-squared for the best-fit model. They even say themselves that this is arbitrary: ‘Athough this cut-off is arbitrary, it provides a range of acceptable fits to the eye.’ After taking Jim Moran’s Noise and Data Analysis class, I for one would like to see the authors try a Monte Carlo Markov Chain (MCMC) analysis of their 14-dimensional space. That might make the analysis a bit less ‘by eye’ and more ‘by statistics.’
The upshot of this study is that for the vast majority of the sources considered, the best-fit values obtained by this new SED fitting tool are close to the previously known values. Check.
It is also worth mentioning here, that there are many other sets of SED modeling codes. One set of codes of particular note are those written by Paola D’Alessio (D’Alessio et al., 1998; D’Alessio et al., 1999; D’Alessio et al, 2001). These codes were the most frequently used in the results presented at the ALMA conference I attended. The distinct change in the D’Alessio models is that they solve for the detailed hydrostatic vertical disk structure in order to account for observations of ‘flared’ disks around T Tauri stars (flaring refers to an increase in disk thickness at larger radii).
But, Wait! There are Caveats!
Although the overall conclusion is that this method fits SEDs with reasonable accuracy, there are a number of caveats that are raised. First of all, the models tend to overestimate the mid-IR fluxes for DM Tau and GM Aur (two sources known to have inner regions cleared of dust). The authors explain that this is most likely due to the fact that their models for central holes assume that there is no dust remaining in the hole. In reality, there is most likely a small amount of dust that remains. Second, the models do not currently account for the possibility of young binary systems and circumbinary disks (relevant for CoKu Tau 1).
The paper also addresses estimating parameters such as stellar temperature, disk mass, and accretion rate from SED fits. And, yes, you guessed it, these calculations raise several more issues. For very young objects, it is difficult to disentangle the envelope and disk, making it very challenging to estimate a total disk mass. To make these complications clearer, the set of two plots below from the paper show calculated values for the disk mass plotted against the accepted values from the literature. It is easily seen that the disk masses for the embedded sources are the most dissimilar from the literature values.
Furthermore, even if the disk can be isolated, the dust mass in the disk is affected by the choice of dust opacity. That’s a pretty big caveat! A whole debate was started at the ALMA conference over exactly this issue and the authors have swept it under the rug in just one sentence. In addition, the calculated accretion rates from SED fitting are systematically larger than what is presented in the literature. The authors conclude that future models should include disk emission inside the dust destruction radius, the radius inside which it is too hot for dust to survive. A great example of the complications that arise from a disk with a central hole can be seen in LkCa 15 (Espaillat et al., 2010; Andrews et al., 2011). The figure below shows the observed and simulated SEDs for the source (left) as well as the millimeter image (right). The double ansae seen in the millimeter contours are indicative of a disk with a central cavity.
In this case, a population of sub-micron sized dust within the hole is needed in order to produce the observed silicate feature at 10 microns. Furthermore, an inner ring is required to produce the strong near-IR excess shortward of 10 microns. A cartoon image of the predicted disk geometry is shown below. To make things even more complicated, the flux at shorter wavelengths appears to vary inversely with the flux at longer wavelengths over time (Espaillat et al., 2010). This phenomenon is explained by changing the height of the inner disk wall over time.
Finally, the authors discuss how well parameters are constrained given different combinations of data points for two example sources: AA Tau and IRAS 04361+2547. In both sources, if only IRAC (Infrared Array Camera on the Spitzer Space Telescope) fluxes are used, the stellar mass, stellar temperature, disk mass, disk accretion rate, and envelope accretion rate are all poorly constrained. Things are particularly bad for AA Tau in this scenario, where only using IRAC data results in ~5% of all SED models meeting the imposed goodness of fit criterion (yikes!). Adding in optical data to the mix helps to rule out models that have low central source temperatures and disk accretion rates. Adding data at wavelengths longer than ~ 20 microns helps to constrain the evolutionary stage of the YSO, because that is where any infrared excess is most apparent. And, adding submillimeter data helps to pin down the disk mass, since the emission at these longer wavelengths is dominated by the dust. This just goes to show how necessary it is to obtain multi-wavelength data is we really want to understand YSOs, disks, and the like.
Where to look if you want to read more about anything mentioned here…
- Andrews et al. (2011)
- D’Alessio et al. (1998)
- D’Alessio et al. (1999)
- D’Alessio et al. (2001)
- Dullemond & Monnier (2010)
- Espaillat et al. (2010)
- Isella (2006)
- Kenyon & Hartman (1995)
- Robitaille et al. (2007)