Proper Motions of Water Masers in Ceph A HW 2 Jack F. Gallimore, Bucknell University Richard Cool, University of Wyoming Michele D. Thornley, Bucknell University (Poster presented at the 199th AAS Meeting, January 2002) Abstract Galactic water vapor masers are commonly associated with jets and outflows from nascent stars. Recent VLA observations of a handful of star-forming regions have resolved compact maser spot distributions that align nearly at right angles to a larger-scale molecular outflow axis. The interpretation has been that these masers may actually trace motions in a protoplanetary disk surrounding the protostar. We obtained new MERLIN observations of one promising disk candidate, Ceph A HW2 (Torrelles et al. 1996, 2001; Figure 1, below). We have found that that the R4 ring of maser spots may trace material in a disk surrounding a forming A or B star. The maser ring has been expanding between 1996 and 2001 (Figure 2, below). We interpret the origin of the masers and the expansion of the ring as owing to a spherical shock-wave emanating from the central star and perhaps disrupting the disk.   Figure 1: The (2000) MERLIN H2O maser spot positions atop a VLA 1.3 cm continuum image, shown as contours (originally published by Torrelles et al. 1996).  Several key maser groups are identified following the naming convention of Torrelles et al. (2001).   Figure 2: The R4 maser spots. The spots are color-coded according to their radial velocity relative to the LSR (see scale bar at right). The (1996) VLBA data of Torrelles et al. (2001) are plotted as squares, and our new (2000) MERLIN data are plotted as circles. The relative astrometry between epochs was deduced by cross-correlation of the maser spot positions over the entire Ceph A HW2 field (see also Torrelles et al. 2001) and tweaked by < 5 mas to ensure that the 1996 and 2000 epochs share a common center of curvature.   Model 1: Jet-Induced Bow Shocks The R4 masers appear to trace partially an elliptical ring with a velocity gradient compatible with rotation. Modeling the spot pattern as an inclined, circular ring, we find that the radius of curvature has increased from about 15 AU to about 30 AU between April 1996 and April 2000. We aligned the two epochs by cross-correlation of the brighter maser spot positions and found that the data are compatible with both epochs having a common center of curvature. Given the large proper motions, corresponding to about 20 km/sec expansion, the simplest explanation would seem to be outflow, and perhaps the maser arcs might trace the limbs of a cooling front behind a jet-induced bow shock. However, maser emission is not limb-brightened without radial velocity coherence. The question remains, should we expect the observed radial velocity pattern along velocity-coherent limbs of a bow shock? To answer this question, we generated a simple model of a strong, parabolic shock front (based on the analysis of Hartigan, Raymond, & Meaburn 1990). We calculated the expected post-shock velocities at points on a uniformly spaced grid over the post-shock shell. The results are shown in Figure 3, below. The shell edges are coherent in radial velocity, but the expected velocities are identically the systemic velocity, with no velocity gradient around the shell. It appears that a bow shock model is not compatible with the observed position-velocity distribution. Figure 3: The expected radial velocity pattern of masers uniformly covering a post-shock shell. In this simulation, the jet axis is inclined by 45° to the sight-line, and the shock velocity is 60 km/sec. Spots on the near side overlap spots on the far side. The spots are color-coded by radial velocity. Bottom line: the shock model cannot explain the observed position-velocity distribution of maser spots.   Model 2: Spherical Expansion into a Disk Viewed at any single epoch, the arcuate structures of R4 resemble an inclined ring, rotating, presumably, around a central protostar. To explain the apparent expansion of the ring, we propose that the protostar has released a shockwave into the disk, and the masers originate in the cooling, post-shock gas. As a result, the maser kinematics should comprise both a rotational component and an expansion component. We fit the multi-epoch data using a rotating ring model. The results are provided in Table 1 and Figure 4. Notice that many maser spots associated with the R4 region do not fall along the arcuate structures. We incorporated a > 3-sigma-rejection algorithm to reduce the effect of these outlying spots. The fitting results are broadly compatible with the proposed model, but there remain significant radial velocity outliers (even after the positional sigma-rejection). This model assumes, however, an infinitely thin disk with no intrinsic random motion. Radial velocity outliers might be explained by shock-acceleration out of the plane of the disk owing to the curvature of the shockwave in the disk-vertical direction. The fitted expansion velocities are of order 5 – 10 km/sec, as much as half the observed proper motion. Neglecting radiative losses, the Mach number of the shockwave should be at least 1.2 – 1.8. The average sound speed of the disk must be less than ~ 15 km/sec, corresponding to pre-shock temperatures of order 50 K.   Figure 4: Results of the rotating ring model for the R4 maser arcs. Each epoch is color-coded according to the legend in the bottom figure, and the models are plotted as continuous dark lines. Open symbols represent data that were rejected after the first fitting attempt. From top to bottom, the plots are: (1) relative sky positions, (2) position-velocity diagram taken along the ring major axis, and (3) position-velocity diagram taken along the ring minor axis. Parameter 1996 (VLBA) 2000 (MERLIN) Systemic V (km/s) -11.0 (0.5) -12.2 (0.2) Radius (AU) 13.6 (0.4) 27.8 (0.1) Central Mass (solar units) 2.6 (0.3) 3.1 (0.2) Expansion V (km/s) 7 (1) 5 (1) Inclination (degs) 50 (1) 49 (1) Position Angle (degs) 150 (4) 142 (2) Table 1: Results of the rotating ring model. Parameter uncertainties are listed in parentheses. For each epoch, we allowed the systemic velocity, inclination, and position angle to vary as a check of the consistency between epochs; there appears to be no significant change in these parameters. Summary The apparent proper motion of the R4 masers of Ceph A HW 2 might be explained not as true sky motions of persistent maser clumps but instead as the motion of a shock front propagating outward through a protoplanetary disk. The central mass, presumably dominated by an as-yet-unseen protostar, is roughly 3 solar masses, the A0/B9 boundary of main-sequence stars. One issue with the present data is the uncertainty in the relative astrometry between the VLBA data, which are not phase-referenced, and the MERLIN data, which are phase referenced. To improve the relative astrometry, we are planning to obtain 2002 epoch MERLIN observations again with phase-referencing. The new observations will therefore eliminate the systematic uncertainties owing to the cross-correlation technique and improve our proper motion measurements. References Hartigan, P., Raymond, J., & Meaburn, J. 1990, ApJ, 362, 24 Torrelles, J. M., et al. 2001, ApJ, 560, 853 Torrelles, J. M. et al. 1996, ApJ, 457, L107   Acknowledgements R. Cool acknowledges support from the National Science Foundation REU program to Bucknell University, grant number 0097424. Additional travel support provided by the National Radio Astronomy Observatory (NRAO). The MERLIN telescope is operated by the University of Manchester on behalf of the PPARC