AAS 207th Meeting, 8-12 January 2006
Session 22 Evolution of Galaxies, Galaxies Surveys I
Poster, Monday, 9:20am-7:00pm, January 9, 2006, Exhibit Hall

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[22.17] Studies of Radially Varying Spiral Pattern Speeds with a Modified Tremaine-Weinberg Method

S. E. Meidt, R. J. Rand (Univ. of New Mexico), M. R. Merrifield (Univ. of Nottingham, UK), P. Rautiainen (Univ. of Oulu, Finland)

One of the most elusive measurements associated with spiral density waves has been the angular frequency with which the pattern rotates. A potentially very powerful method was developed by Tremaine & Weinberg (1984; hereafter TW) who showed, as long as a tracer can be found that obeys continuity as it orbits through the pattern, that measurement of the mean velocity and surface density of the tracer along any line parallel to the major axis of a galaxy gives an estimate of the pattern speed \OmegaP along that line. The TW method, however, is not well formulated for studies of galaxies with radially varying or multiple distinct pattern speeds: the TW calculations combine data from a wide range of radii, producing spatially averaged estimates of such pattern speeds. A generalized version of the TW method, which has the capacity to extract pattern speeds that vary radially, can be solved (with discretization) by matrix inversion. This approach produces solutions \OmegaP(r) that map to the original measurements with considerable accuracy, but such a solution is susceptible to ‘instability,’ displaying oscillatory behavior at inner radii; inversion by back substitution propagates small variations from the pattern (as a result of noise in the data) inward, degrading the solution at smaller and smaller radii. However, solving the inverse problem with regularization using a stabilizing/regularizing functional that reflects \textit{a priori} judgments about the form of a galaxy’s pattern speed returns a “smoothed” solution. We present studies on the effect of several orders of regularization on the behavior of the solution as applied to both simulated and observed galaxies. We also present results on the effectiveness of a regularizing functional that parameterizes \textit{a priori} assumptions regarding the location and height of a discontinuity as applied to galaxies where at least two distinct patterns are suspected to exist.

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