We commonly use images and kinematic information from spectroscopic observations as constraints for 3D reconstructions of expanding circumstellar nebulae or supernovae. The measurements of the Doppler-velocity are crucial, since in expanding nebulae they can usually be mapped to position along the line of sight (with the caveats that we have discussed in earlier posts and in a recent conference talk).
But kinematic information can also be obtained from measurements of motion in the plane of the sky, yielding the velocity component that is not accessible to spectroscopy. Unfortunately, such proper motion measurements within a nebula are more difficult than their counterparts of the motion of stars on the sky, since the position is more diffuse compared to that of the image of a star.
An second problem is that the measured motion may represent the displacement of a pattern, that has little to do with the actual gas flow (which is what the Doppler-effect delivers in spectroscopic velocity measurements). For instance, such patterns can be shock waves or ionization fronts or combinations of those. Deducing a flow speed that can then be combined in an overall model that includes velocity information from spectroscopy can be tricky. Mellema (2004) has studied the phenomenon to estabilish a quantitative difference between the advancing ionization front and the gas flow.
Another problem may be the superposition of more than one flow due to projection on the sky, creating a mixture of motions that can produce fake patterns, such as the famous Moiré patterns of superimposed systems of lines (see Figure). Mertens & Lobanov (2016) explored how to separate multiple flows in VLBI-observations of relativistic jets from Active Galactic Nuclei (AGN). They used wavelength decomposition to separate a faster smooth flow through the center of the jet (the “spine”), from a more irregular region that is the envelope of the spine.
A similar approach was taken by Riera et al. (2014) to analyze the proper motion in the nebula CRL618 and hydrodynamic simulations that aimed at reproducing the observed proper motion. This approach seemed to have worked well in this object, since it consisted of rather discrete knots that had traveled a substantial angular distance compared to their size.
García-Díaz et al. (2015) compared two different methods to determine the internal proper motion in the planetary nebula NGC 2392 (the “Eskimo Nebula”). They based their analysis on several hundred manually set rectangular regions within Hubble Space Telescope images that where taken with a time separation of about 8 years. Instead of using a wavelet decomposition, they used cross-correlation and least-square methods, similar the one used by Szyszka et al. (2011) for NGC 6302. The difference in the results for the two methods was not huge, but significant if one wants to use proper motion measurements as constraints for 3D-reconstructions.
In observations of filamentary planetary nebulae such as NGC6302 or NGC2392, the issue of superposition of more than one filament (for instance from the front and back walls) is likely to generate locally spurious results. If superimposed filaments move at an angle to each other, non-radial patterns can appear that propagate much faster than the actual flow speed, not unlike the Moiré-phenomenon.
So, until now proper motion analysis in planetary nebulae has been a bit disappointing as a tool for contraining 3D reconstructions. Hopefully new methods can improve this situation. There is a research problem for image process experts, since new approaches to measuring the internal proper motions in astrophysical nebulae need to be introduced.