1. Bayesian Source Separation Applied to Identifying Complex Organic Molecules in Space Kevin H. Knuth A,B, Man Kit Tse A, Joshua Choinsky A, Haley A. Maunu A, Duane F. Carbon C
A Department of Physics, University at Albany, Albany NY, B Department of Information Sciences, University at Albany, Albany NY C NASA Advanced Supercomputing Division, NASA Ames Research Center, Moffett Field CA
Modeling Spectra
Nested Sampling
Abstract
The infrared spectra we work with has been collected by the Infrared Space Observatory, and is currently being collected by the Spitzer Space Telescope. These spectra contain light from not only PAHs, but also Planck Blackbody radiation from thermal emissions of the dust cloud, and any others in the line of sight. In addition, there are spectral features of unknown origin.
For us to accurately identify the PAHs and their contributions, we must also estimate these additional spectral features. The spectral model we employ is
The first term describes the PAH contributions, as well as other atomic, ionic, and molecular lines. These spectra are known a priori and are provided in a database generated by colleagues at NASA Ames Research Center. A binary-valued parameter dp enables us to turn PAHs ON and OFF, and the parameter cp, enables us to estimate the probability that a PAH is present independent of its contribution.
The second term describes the Planck blackbody radiation, which is given by
where
The last term describes a mixture of Gaussians, which is used to model the unknown sources.
We employ Bayesian probability theory, but at present make straightforward probability assignments, which lead to a Student-t distribution
We employ a new sampling method called Nested Sampling (Sivia and Skilling, 2006). Nested sampling works by sampling directly from the prior probability, with a hard likelihood constraint. Poor samples are removed, and the likelihood is adjusted to that sample’s likelihood. The result is a nested set of likelihood boundaries that enable one to estimate the evidence as well as the mean parameter values.
Emission from a class of benzene-based molecules known as Polycyclic Aromatic Hydrocarbons (PAHs) dominates the infrared spectrum of star-forming regions. The observed emission appears to arise from the combined emission of numerous PAH species, each with its unique spectrum. Linear superposition of the PAH spectra identifies this problem as a source separation problem. It is, however, of a formidable class of source separation problems given that different PAH sources potentially number in the hundreds, even thousands, and there is only one measured spectral signal for a given astrophysical site. Fortunately, the source spectra of the PAHs are known, but the signal is also contaminated by other spectral sources. We describe our ongoing work in developing Bayesian source separation techniques relying on nested sampling in conjunction with an ON/OFF mechanism enabling simultaneous estimation of the probability that a particular PAH species is present and its contribution to the spectrum.
Discarded samples are used to represent points in the space at different likelihood boundaries. These are used in a numerical integration scheme to obtain both the evidence and the posterior.
Figure 1 The Orion Nebula is a star forming region rich in organic molecules. The infrared spectrum, taken from the Orion Bar, displays typical PAH features (indicated by arrows).
Figure 2 Below shows several PAHs and their spectra.
Organic Molecules in Space
Our Sun is powered by nuclear fusion where Hydrogen is fused into Helium. Eventually, this fuel runs out and the star swells into a Red Giant and begins fusing higher elements such as Carbon, Nitrogen, and Oxygen. These elements are dredged up from deep within the star and blown off in the stellar winds. It was discovered only about 15 years ago that as soon as these gases cool, complex organic molecules coalesce. These molecular species are collectively known as polycyclic aromatic hydrocarbons. At this stage, we now very little about the organic chemistry that ensues.
These molecules are often found in star-forming regions, which are rich in gases from old dead stars. One such region is the Orion Bar in the Orion Nebula shown in Figure 1. The ultraviolet light from nearby young stars excite these organic molecules, which then emit infrared radiation.
Figure Figure 4
Polycyclic Aromatic Hydrocarbons
Preliminary Results
The enormous class of molecules based on the simple benzene ring are known as polycyclic aromatic hydrocarbons (PAHS). These molecules possess distinctive infrared emission lines due to the various vibrational modes of the molecule. These lines are typically in the ranges of 3.3, 6.2, 7.7, 8.6 and 11.2 mm. Each PAH species has its own unique emission spectrum. Figure 2 shows several examples of PAHs.
In a physical environment, these PAHs interact via collisions, and can stick together as well as break apart. This quickly leads to a distribution of PAH species, and in a given mixture there can be hundreds of PAH species present. This results in spectral features that are the result of a mixture of PAHs (as seen in Figure 1). To identify a specific PAH species in the mixture is a formidable task, but a critical one if we are to understand the organic chemistry that takes place in the interstellar environ.
Accurate background estimation (without PAHs) is critical to this endeavor. Figure 3 shows a spectrum taken from the Orion Bar (Figure 1). The black curve is the original data, the blue curve is the background estimation. One blackbody radiator is at a temperature of  K, and there is possibly a second (36.3% chance), at a temperature around 18.8 K.
Figure 4 shows the results of 7 early experiments to estimate the contributions of 47 PAHs. The x-axis represents the PAH labels. The vertical lines indicate PAHs that were actually present in the synthetic data set. The squares represent their true contributions, and the stars the estimates. Most present PAHs have been detected. The ON-OFF technique is not being applied here, so all PAHs are estimated to have some, albeit very small, contribution.
Supported by NASA AISRP NNH05ZDA001N