  The grand-design spiral galaxy M51 has long been a crucial target for
theories of spiral structure. Studies of this iconic spiral can address the
question of whether strong spiral structure is transient (e.g.
interaction-driven) or long-lasting. As a clue to the origin of the structure
in M51, we investigate evidence for radial variation in the spiral pattern
speed using the radial Tremaine-Weinberg (TWR) method. We implement the method
on CO observations tracing the ISM-dominant molecular component. Results from
the method's numerical implementation--combined with regularization, which
smooths intrinsically noisy solutions--indicate two distinct patterns speeds
inside 4 kpc at our derived major axis PA=170 deg., both ending at corotation
and both significantly higher than the conventionally adopted global value.
Inspection of the rotation curve suggests that the pattern speed interior to 2
kpc lacks an ILR, consistent with the leading structure seen in HST near-IR
observations. We also find tentative evidence for a lower pattern speed between
4 and 5.3 kpc measured by extending the regularized zone. As with the original
TW method, uncertainty in major axis position angle (PA) is the largest source
of error in the calculation; in this study, where \delta PA=+/-5 deg. a ~20%
error is introduced to the parameters of the speeds at PA=170 deg. Accessory to
this standard uncertainty, solutions with PA=175 deg. (also admitted by the
data) exhibit only one pattern speed inside 4 kpc, and we consider this
circumstance under the semblance of a radially varying PA.
