promos: proper motion software

NASA USRP – Internship Final Report

PRO-MOTIONS: PROper MOTION Software

John C. Wherry1

Austin Peay State University, Clarksville, TN, 37044, USA

We report on the development of a software tool (PRO-MOTIONS) to streamline the process of measuring proper motions of material in expanding nebulae. Our tool makes use of IDL's widget programming capabilities to design a unique GUI that is used to compare images of the objects from two epochs. The software allows us to first orient and register the images to a common frame of reference and pixel scale, using field stars in each of the images. We then cross-correlate specific morphological features in order to determine their proper motions, which consist of the proper motion of the nebula as a whole (PM-neb), and expansion motions of the features relative to the center. If the central star is not visible (quite common in bipolar nebulae with dense dusty waists), we assume point-symmetric expansion, and use the average motion of high-quality symmetric pairs of features on opposite sides of the nebular center to compute PM-neb, which is then subtracted out to determine the individual movements of these and additional features relative to the nebular center. PRO-MOTIONS should find wide applicability in measuring proper motions in astrophysical objects such as the expanding outflows/jets commonly seen around young and dying stars. We present first results from using PRO-MOTIONS to successfully measure proper motions in several pre-planetary nebulae (transition objects between the red giant and planetary nebula phases), using images taken 7-10 years apart with the WFPC2 and ACS instruments on board HST.

I. Introductionhe study of circumstellar matter around dying Sun-like stars (i.e., Asymptotic Giant Branch [AGB] stars, pre-planetary nebulae [PPNs] and planetary nebulae [PN]) is of great interest in the astrophysical world

today. These aspherical, yet highly geometric, shapes of the nebulae challenge professional astronomers to find mechanisms that produce these dazzling shapes. Mathematical models and analyses of images taken by the Hubble Space Telescope (HST) can help provide insight into the formation of these complex geometries.

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The morphological transitions during the dying stages of Sun-like stars are currently poorly understood. These models and analysis techniques will help to formulate a more unified view of the system as a whole. There exist many conjectures as to why the transition from an AGB star to a planetary nebula results in complex and intricate geometries, but no universal theory has been formulated that can encompass all the different shapes observed in these nebulae.

We are mainly focused on understanding the dynamical evolution of PPNs. This evolution is believed to be driven by jets, an exciting, dramatic, and integral feature of many astrophysical environments. These jets are amazingly similar to those found in young stellar objects. A better understanding of these jets will improve our comprehension of the formation of the intricate geometries of PPNs.

In our research, we will be studying the expansion motions of material in PPNs. One of the problems with studying and measuring these motions is that there are two types of movement that the material in the nebula is experiencing. First is the nebula's proper motion (PM-neb) as a whole across the sky. The other movement is that of the material relative to the center of the nebula (PM-cen). PM-neb needs to be removed in order to determine PM-cen. PM-cen consists mostly of radial expansion of material outward from the central star. These two types of movements may be directly observable by cross-correlating 2 images of the PPN taken anywhere between 5 and 10 years apart (Epoch1 and Epoch2). Although material in the PPN may experience non-radial expansion motions also, these are generally much smaller. We focus on observing the proper motion and radial expansion in this study.

1 Research Assistant, Undergraduate Student Research Program, Jet Propulsion Laboratory, CalTech.

Summer 2008 Session1


II. Methods1. Interactive Data Language (IDL)

PRO-MOTIONS was developed using the IDL programming language and environment. IDL is an extremely useful astronomical programming environment because it provides the user with many robust routines that can be used to manipulate, interpret, and analyze large data sets. IDL also provides an environment that can easily deal with the unique data formats that NASA instruments adhere to. This allows us to quickly and easily process data without having the overhead of reading data in on a lower system level. High-language capabilities makes this an ideal language to develop astronomical software with.

One drawback to using IDL to develop an entire software system is the fact that IDL was not originally built to handle development of large scale software applications. Event handling, error handling, and program states all have to be specifically written in IDL. This makes it cumbersome to develop an environment that is both user friendly and agile to code upgrades. Time was taken in carefully constructing a solid code platform that can easily be upgraded and added to. This allows for new features to be implemented with ease. This type of programming style is essential to creating a software system which can be distributed and added to by the scientific community. The first portion of our developed software package is pictured below (Fig. 1).

Figure 1: PRO-MOTIONS. Our Graphical User Interface (GUI) developed in IDL. This is our first tab: Image Registration. We have displayed the unregistered Epoch1 and Epoch2 images of the PPN IRAS22036.

2. Measurements of MotionsWhen dealing with measurements of motions of nebulae, there are certain difficulties we have to overcome

before we perform any image analyses between the images. Since the images we are using (Epoch1[Fig 2.] and Epoch2 [Fig. 3]) are taken 5-10 years apart, there is a good chance that the images will have been taken by different cameras. We therefore have to register Epoch1 to the same pixel scale and rotation as Epoch2 before we can do any analyses between the images. We do this by picking field stars in both images. The average proper motion of a random sample of field stars can be assumed to be zero. PRO-MOTIONS rejects stars that appear to have anomalously large proper motions. A gaussian routine then locates the star's position on the image accurately (to



better then a tenth of a pixel accuracy). Now that we have the centers calculated, we calculate a transformation matrix that allows us to accurately transform the Epoch1 image to the same orientation and pixel scale as Epoch2. To calculate this transformation matrix, we use a bicubic spline interpolation routine that generates a pixel scale change and rotation. We now have a newly registered Epoch1 (Fig. 4) image in which the average proper motion of our sample of field stars is close to zero (within a few tenths of a pixel).

Figure 2: IRAS22036 Epoch1. Epoch1 for IRAS- Figure 3: IRAS22036 Epoch2. Epoch2 for IRAS- 22036. The blue boxes represent the field stars we 22036. As in Fig. 2, the blue boxes represent the will be using to calculate our transformation matrix. field stars we will be using to calculate our

transformation matrix.

Figure 4: Epoch1 Shifted. This is our output image that has been transformed by PRO-MOTIONS. If you look closely, you can tell that the stars in this image match up with those in Fig 3.

Once we have the images registered to each other, a center needs to be determined. In most cases, this proves to be a problem because the central star is masked by dust in the nebula or is highly saturated. We use three techniques to solve this problem. Since radially symmetric expansion is assumed in the nebula, we use this to our advantage. Our first technique is to overlay a circle on the target image. We resize and align this circle to match up with features in the image which are circularly symmetric about the center. From here we calculate the center of the circle and get an approximate center for the nebula. Our second technique is to use diffraction spikes from the center star when it



is highly saturated. We align two vectors along the diffraction spikes and the intersection of these vectors is the approximate center of the nebula. The last technique used to find the approximate center of the nebula is the simplest. We can overlay just one vector by connecting diametrically-opposed symmetric features on either side of the nebular center and calculate the midpoint of the vector. All three of these techniques yield approximate nebular centers.

The technique we use to calculate the proper motion of the nebula focuses on the cross-correlations of fiducial features in the nebula. We select features of the nebula that are of "good" quality, meaning features that are localized and distinctly visible with the human eye and which appear to be point-symmetrically distributed around the center. Once we have chosen a pair of symmetric features, we then have to determine the optimum size of a box that will yield a reliable XY-Offset between the two images. The algorithm we use to cross-correlate our images is the CORREL_OPTIMIZE procedure from the IDL Astronomical Library.

We need to test and make sure that this procedure works correctly and produces correct results. So, we first take Epoch2 and cross-correlate it with itself. As you would expect, this should give an XY-Offset of (0,0) and it does. We now take Epoch2 and shift it ourselves by a non-integral number of pixels and name this image Epoch2_Shift. We then cross-correlate this new image as a whole with the original and see if our procedure can produce the correct offset we applied. This test yields results that match our applied offset. We now test to see the offsets when we do multiple cross-correlations on fiducial features of the nebula. We select eight features and run cross-correlations between these features. We begin with a uniform box size of 20x20 pixels to encompass each feature. Ideally, each feature's XY-Offset should match the applied offset. However, this will not be the case unless the fiducial feature is properly centered and has a padding of good "non-bright" pixels surrounding it. With uniform box size of 20x20 pixels, we may not correctly capture all of the features. The box sizes need to be adjusted to accurately encompass each of the features. Since we know the offset of Epoch2_Shift with respect to Epoch2 is some non-integral value we set, we can vary the box size and get a range of values that yield a derived offset which is within +/- 0.2 pixels of the applied offset. After testing many box sizes, we came up with set of box sizes that work best for each feature.

Once we have these optimized box sizes, we then apply them to the cross-correlation of nebula features in Epoch1 to Epoch2. Since we know these box sizes give correct offsets between Epoch2_Shift and Epoch2, we assume it will give accurate offsets between Epoch1 and Epoch2 also. Figure 5 shows examples of selected features used for the cross-correlation and radial vectors.

Figure 5: Cross-Correlation of Epoch1 and Epoch2. This image comprises the selected areas that the cross correlation routine will be run on. Each blue box encompasses a feature selected for cross-correlation and each yellow box is an estimate of where the diametrically-opposed counterpart is located.

We take the XY-Offsets of all the fiducial features and average them. This gives us the average movement of ALL of the features. This is the proper motion of the nebula as a whole (PM-neb). We then subtract the X and Y components of PM-neb from the individual XY-Offsets of each feature. We are thus left with the proper motion of each feature relative to the center of the nebula (PM-cen).



III. Proper Motions in the PPN, the Red Rectangle

Figure 6: Red Rectangle. An image of the PPN, the Red Rectangle, which we have analyzed for proper motions. A typical knot, used as a cross-correlation feature, is shown. Such knots rather than diffuse features are appropriate for calculating proper motion. The specific features selected appear in Fig. 5 and their results appear in Fig. 7.

1. Image RegistrationAs stated above, the image registration component of PRO-MOTIONS works within our needed accuracy range.

After transforming Epoch1 to the same pixel scale and rotation of Epoch2, the resultant image's field stars are within a fraction of a pixel offset to the original Epoch2's field stars. This allows us to confidently move onto the measuring of proper motion.

2. Proper MotionFrom preliminary tests of the Red Rectangle (Fig 6.) using radial intensity cuts, we have concluded that the

range of total proper motion of each feature that is acceptable lies within +/- 2-3 pixels. Any proper motions that fall within this range are referred to as “expected results.” Features that yield motions outside of this range are designated “poor” quality and their proper motions are not used to calculate PM-neb.

Using the testing processes described in earlier sections, we have determined the box sizes that yield expected results fall within the range of 14-30 pixels. We showed earlier that the size of the box must be regulated in order to accurately encompass the feature. Thus far, we have identified 8 fiducial features (some containing more than 1 knot) that are distinct enough to run cross-correlations on. These features, if of good quality, are represented by a capital letter (i.e., A, B, C, etc.). Their symmetric pair is also represented with a capital letter but notated with a prime (A', B', C', etc.). If we have a feature that we deem "of poor quality", then the naming scheme is the same as previously stated but the letters are now lowercase (i.e., a, b, c, etc.). The same goes for their symmetric pair (i.e., a', b', c', etc.). Our selected box sizes are below (Table 1).



Name Box Size Range (Pixels) Box Size Used (Pixels) Avg. Pair Proper Motion (Pixels)

A 14-26 20 --

A' 14-22 20 < -0.938, -0.875>

B 14-24 20 --

b' 10 10 <-0.812, -1.000>

C 14-36 26 --

C' 14-40 30 <-0.938,-0.875>

D 18-34 26 --

D' 36 36 <-1.000,-1.125>

Table 1: Selected Fiducial Feature's Box Sizes. These are the calculated box sizes that yielded expected results for optimum offsets. Box sizes are dependent on the area of “non-bright” pixels that surround the fiducial feature and if the feature is completely encompassed and centered in the box. These are the main criteria in selecting box sizes. The red sections are features that yield motions beyond the standard deviation of box sizes but these sizes were the closes to the overall average proper motion of the nebula.

We describe below how we determine the quality of each feature. The first image for each feature is from Epoch1 and the second is from Epoch2.

A: From the images, we can see that the structure of this feature is quite good. It has a padding of non-bright pixels around it and the feature is central to the geometry of the box.

A': This feature is not as well defined as feature A. It is diffuse along the edges of the box which could skew results when running the cross-correlation routine.

B: This feature, just as A, has a centralized fiducial feature that as adequate padding of non-bright pixels around it.

b': We label this feature as having "poor" quality (notice the lowercase lettering). The reason for this is because we do not have a well defined feature. The feature is diffuse. We give it a box size of 10 because making the box bigger did not give us expected offset result, neither did shrinking the box. A box size of 10 was the only size that yielded results close to the expected outcome. At this point in time, we are going to categorize this feature as of poor quality. It might become necessary at some point to disregard this point all together in calculations because of it's anomalous characteristics and potential of throwing off the entire proper motion of the nebula.



C: We now come to a fiducial feature that is comprised of 2 very noticeable knots on the outside of the feature and a very faint knot between them. If we try and run cross-correlations on each of these knots individually, we see results that are skewed because of what was mentioned earlier (i.e., feature takes up too much of the box size). So, we include all three of these knots as a feature. This, contrary to our belief before running these tests, gives a better XY-Offset. The feature is nicely centralized and has plenty of "non-bright" pixels surrounding it.

C': As with it's symmetric pair (C), this feature is comprised of 3 knots. In this feature, we can distinctly see all three knots; while in C we could only faintly see the middle knot. This could be grounds for an inaccurate cross correlation but we observe an expected XY-Offset. As with C, this feature is extremely well defined and can be accurately represented by multiple box sizes.

D: This feature is almost identical to C and C'. Seeing features that are similar is good since we assume symmetric radial expansion. We would hope features would evolve similarly.

D': This feature is very similar in box size with that of feature b', although we do not give it poor quality just yet. To the naked eye this seems to be a feature of good quality but the tests do not back up this observed data. Just as in b', we only get expected results with a certain box size, 36 pixels. Any deviations from this size gives us non-expected results. This could be from the extension of the feature from one side of the box to the other. Just as on b', this feature might have to be thrown out if it skews the calculation of PM-neb.

These eight features are the basis for our calculations of proper motion of the Red Rectangle. From these results, we observe an average XY-offset of <-0.828, -1.031> pixels. This is our calculated proper motion of the Red Rectangle as a whole across the sky, i.e., PM-neb. Using this refined PM-neb we can then calculate the PM-cen of each fiducial feature. Once we have the PM-cen of each of the features, we can begin to do analyses on the movement of the nebula in 3D and estimate the age of the nebula itself.



IV. Using Proper Motion for Scientific Analysis There are two applications of PRO-MOTIONS that make it essential to the arsenal of a researcher studying

PPNs or other expanding nebulae. The first application of PRO-MOTIONS is the calculation of the age of a nebula – expansion proper motions are the only direct way of measuring the latter. Furthermore, these do not require knowledge of the distance to the object (which are hard to determine). The age of a feature is given by the radial offset of that feature from the center divided by the proper motion per unit time. The total nebular age can then be estimated by proportionately extrapolating to the full size of the nebula.

The second application is related to measuring the 3D movement of material in the nebula as a whole. PRO-MOTIONS allows us to measure the proper motion of features in nebula. This proper motion is one of the two orthogonal components needed to calculate the 3D radial expansion of the feature (the other component being the velocity calculated by observing the Doppler shift of an emission line from that feature). These two vectors combined yield the radial expansion of the feature.

AcknowledgmentsThe authors are grateful to NASA's Undergraduate Students Research Program (USRP) for supporting this

research. A special thanks also goes out to Dr. Raghvendra Sahai at NASA's Jet Propulsion Laboratory for his expertise and mentorship on this project.

References1Balick, B., Adam, F., 2002. “Shapes and Shaping of Planetary Nebulae” Annual Review of Astronomy and Astrophysics,

Vol. 40, p. 439-486.2Cohen, M., Van Winckel, H., Bond, H.~E., Gull, T.~R., 2004. “Hubble Space Telescope Imaging of HD 44179. The Red

Rectangle” Astronomical Journal, 127, 2362.3Sahai, R., Morris, M., Sanchez Contreras, C., Claussen, M., 2007. “Preplanetary Nebulae: A Hubble Space Telescope

Imaging Survey and a New Morphological Classification System” Astronomical Journal, 134, 2200.4Ueta, T., Murakawa, K., Mexiner, M., 2005. “Proper-Motion Measurements of the Cygnus Egg Nebula” ApJ, 641, 1113.


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