IntroductionIntroduction

PRO-MOTIONS is a handy tool for calculating the age of a nebula because expansion proper motions are the only direct way of measuring this age. 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.

PRO-MOTIONS allows us to measure the proper motion of features in nebulae. 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 in 3D.

PRO-MOTIONS is still under development and a number of improvements are currently being implemented. For example, making PRO-MOTIONS cross-platform and adding geometric tools that allow us to estimate the center of the nebula based on symmetric features such as circular arcs and searchlight beams in the nebula. Further, spatially extended features are not well handled by the cross-correlation routine for determining proper motions, we intend to include software to make and compare radial and angular intensity cuts which are more suited to the analysis of such features.

PRO-MOTIONS: PROper MOTION SoftwarePRO-MOTIONS: PROper MOTION SoftwareJohn C. WherryJohn C. Wherry11, Raghvendra Sahai, Raghvendra Sahai22

11Austin Peay State University, Clarksville, TN, USAAustin Peay State University, Clarksville, TN, USA22Jet Propulsion Laboratory, California Institute of Technology, PasadenaJet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, CA, USA

Figure 1: PRO-MOTIONS Graphical user interface (GUI) for Image Registration section of the application. The object displayed is the PPN (pre-planetary nebula), IRAS22036. PRO-MOTIONS is very dynamic in that users can interactively update and change the color tables, contrast, and brightness of the images displayed. All of the analysis results are displayed on the screen for convenience of the user.

´ 1The IDL Astronomy User's Library is publicly available through http://idlastro.gsfc.nasa.gov/.

We report on the development of a software tool (PRO-MOTIONS) to determine the proper motions of material in expanding nebulae. This tool registers and compares images of an object from two epochs.

PRO-MOTIONS is built with the Interactive Data Language (IDL) programming environment with certain subroutines developed in C++. IDL provides a stable platform on which to develop widget-style software applications and bind different code bases together. C++ offers a programming environment for fast processing of data.

We have three main objectives while developing PRO-MOTIONS:

Build an application that can easily and efficiently register astrophysical objects to a common frame of reference between two epochs and calculate their proper motions.

Create a complete, integrated software system for measuring proper motions.

Construct a completely platform independent software package. These objectives have led to the development of a software package that is both robust and agile to code enhancements.

PROMOTIONS should find wide applicability in measuring proper motions in astrophysical objects such as the expanding outflows/jets commonly seen around young and dying stars (e.g., Sahai et al. 2007).

Software MethodsSoftware MethodsPRO-MOTIONS allows us to first orient and register images to a common frame of reference and pixel scale, using field stars in each of the images. We use a bicubic spline interpolation routine written in C++ developed by Dwight Moody (JPL) to correctly carry out this process. Stars that are designated as outliers are flagged and not used in calculations.

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. We use routines from the IDL Astronomy User's Library to help with these calculations.1

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.

Our main interface (Fig. 1) shows you the basic design of our software package.

Care has been taken to implement features that allow users to change contrasts, rotate, and annotate images, among other things. This simplifies the process of producing a finished product.

For example, after proper motions have been computed, the user can produce publication-quality plots of the proper motion vectors superimposed on the nebular image (Fig. 2-7).

All error handling is dealt with in a “loopback” format. If an error occurs during the running of PRO-MOTIONS, the state of the program is reverted back to the previous state before the error occurred. This allows PRO-MOTIONS to keep running when errors occur and allows the user to continue with his/her analysis without loss of previous work.

Results: Red RectangleResults: Red Rectangle Results: Egg NebulaResults: Egg Nebula

Summary & Work In ProgressSummary & Work In Progress

The first object we studied was the PPN (pre-planetary nebula), the Red Rectangle (Cohen et al. 2004). Figure 2 shows the proper motions of each feature. PM-neb was measured to be 8.9 mas/yr.

The proper motions of the symmetric pairs (i.e., PM-exp) lie in the range 8.6 to 10.1 mas/yr with a mean value of 9.3 ± 0.5 mas/yr. We use the mean from symmetric pairs to calculate the age and tangential expansion velocity of the nebula.

The proper motions of lower quality features not used in calculating PM-neb (i.e., Non-Pairs [features that have no radially symmetric pair]) lies in the range 5.6 to 11.3 mas/yr with a mean value of 8.8 ± 2.1 mas/yr.

We assume a distance of 0.7 kpc (Cohen et al. 2004) to this object.

Figure 2: Red Rectangle Selected features in theRed Rectangle with PM-neb subtracted out. Red vectors show the proper motion of the features.

Figure 3: Selected Features Two examples of selected featuresused to calculate PM-neb. We pick features that are centrallylocated in our box and have paddings of non-bright pixels.

Figure 4: Egg Nebula Selected symmetric features used in calculation of PM-neb. Red vectors represent proper motions of individual features.

The object in figures 4 and 5 is the PPN, CRL 2688 (Egg Nebula). Figure 4 shows you the proper motions of each feature. PM-neb was measured to be 14.6 mas/yr, which compares reasonably well with Ueta et al's value (17.1 mas/yr).

The proper motions of the symmetric pairs lie in the range 10.3 mas/yr – 12.8 mas/yr with a mean value of 11.3 ± 0.5 mas/yr. We use this mean value to calculate the age and tangential expansion velocity of the nebula.

The proper motions of lower quality features not used in calculating PM-neb (i.e., Non-Pairs) lies in the range 6.9 to 13.9 mas/yr with a mean value of 11.0 ± 2.4 mas/yr.

Figure 5: Selected Inner Features Selected features with no symmetric pairs. Proper motion vectors obtained by subtracting out PM-neb.

Acknowledgements: This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, and was sponsored by the Undergraduate Student Research Program (USRP) and the National Aeronautics and Space Administration. We also want to thank Dwight Moody (JPL) for contributing his code for the bicubic spline interpolation routine.

PM-exp = 9.35 mas/yrAge = 1,400 yr at radius of 13” (i.e., 9,100 AU at D = 0.7 kpc)

Vtang

= 31 km/s (D/0.7 kpc)

PM-exp = 11.3 mas/yr

Age = 2,000 yr at radius of 22.5” (i.e., 22,500 AU at D = 1 kpc)

Vtang

= 54 km/s (D/1 kpc)

Figure 7: Selected Outer Features Selected features That are located further away from the nebular center. The naming scheme here is not the same as in fig. 5.

Figure 6: Selected Features Two examples of selected features used to calculate PM-neb. Just as with the Red Rectangle, we pick features that are centrally located inour box and have paddings of non-bright pixels. Feature names as in figure 4.

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A major uncertainty in calculating the tangential expansion velocity is that it's derived value is proportional to the distance to the object. In the above calculation, we take the commonly assumed value of the distance (1 kpc). In the outer region, the outflow is known to be spherical with an expansion velocity of about 20 km/s. Therefore, a smaller value of the distance, such as that inferred by Ueta et al (420 pc), is likely to be correct.

Our argument for a smaller distance is quite robust because, unlike Ueta et al, it does not require a knowledge of the inclination angle of the bipolar outflow (which dominates in the inner region).

The features we are analyzing are at a much further radial distance from the central star than the features analyzed by Ueta et al. (2005). Our symmetric pairs lie between 8” and 14” and the features analyzed by Ueta et al. lie between 1” and 7” away from the central star.

For the inner region (Fig. 5: c,d,e,f,g,h), which has also been analyzed by Ueta et al., our calculated value of the average proper motion (9.3 mas/yr) is somewhat lower than Ueta et al's value (14.3 mas/yr).

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ReferencesReferences- Balick, B., Adam, F., 2002. “Shapes and Shaping of Planetary Nebulae” Annual Review of Astronomy and Astrophysics,Vol. 40, p. 439-486.- Cohen, 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.- Sahai, 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.- Ueta, T., Murakawa, K., Mexiner, M., 2005. “Proper-Motion Measurements of the Cygnus Egg Nebula” ApJ, 641, 1113.