11 ther to collapse or expansion suggest that it sits at the threshold. Furthermore that a single parameter is suffi- cient to stabilize the solution suggests that there is a sin- gle unstable mode. In contrast, sometimes one can tune multiple parameters to find a threshold solution [61]. If these suggestions hold up, these would suggest that at least some of these unstable solutions might serve as Type I critical solutions. Indeed, previous work [62] perturbed stable TOV stars in spherical symmetry and found unstable TOV stars at criticality in Type I collapse. In that work, they were able to achieve phenomenal resolution and tuning. In contrast, while they perturbed a self-consistent stable solution and saw the tuned evolution driven to the unstable branch of solutions, here we begin with the unstable solution and perturb around it. Here, we have only been able to tune to about one part in a million, being prevented from tuning further because successive evolutions stop the trend towards longer lived solutions. That such searches are prevented from continuing might indicate some new phenomena, or, more likely, that boundary effects and numerical error begin to spoil the threshold behavior. We have looked for a scaling law in the survival times of these tuned unstable stars. To the extent that this rough tuning is representative of the overall behavior, we find that the different solutions appear to scale as expected. However, because our searches have terminated so far from criticality, we cannot have much confidence in a precise scaling relationship. There has been recent work in the axisymmetric collision of neutron stars [63, 64] which appears to demonstrate the same type of critical behavior as observed in [62]. We find the same type of behavior about a magne- tized star as shown in Fig. 8. Here we have carried out three searches by varying a different parameter all per- turbing the same solution. The figure makes apparent the same ringing for all three families, although the ampli- tude varies across the different tuning families. It seems reasonable to take the results of these tunings as further evidence that only a single mode is unstable since if there were more unstable modes, these different tunings would produce solutions more varied from each other. We have begun to look at the geometry of the purported unstable mode by looking at the difference Δ = ρ$_{0}$ ( t ) − ρ$_{0}$ (0) at late times for near-critical evolutions. These calculations indicate the the mode is likely axisymmetric with differ- ences between Δ on the x = 0 plane and on the y = 0 plane being at about the 10% level. We study the evolution of rotating stellar configura- tions and examine different phenomenology related to stability and magnetic field influence in their dynamical behavior. The stars are constructed assuming a poly- tropic equation of state using the code Magstar which We would like to thank J. Novak for his gracious assis- tance with Magstar and Lorene . SLL thanks Matthew Choptuik and Scott Noble for valuable discussions con- cerning the apparent critical behavior. We also would like to thank Matthew Anderson, Eric Hirschmann, Miguel Megevand, Patrick Motl, Joel Tohline and Travis Gar- Acknowledgments VII. CONCLUSIONS is part of the publicly available Lorene package. We present several studies which indicate our code reliably and robustly evolves astrophysically relevant scenarios including magnetic field effects. We study the dynamical effect of perturbations of stars on the unstable branch of solutions. We find evidence that these unstable solutions may play a similar role as the unstable TOV stars play in spherically symmetric evolutions as studied in [62]. This is significant because it suggests that the addition of an- gular momentum, magnetic field, and three dimensions do not allow for a multitude of unstable modes. Needless to say, the phenomena associated with the threshold of gravitational collapse merit further study. Beyond the studies considered in this work, further in- teresting phenomenology to consider include the impact of magnetic fields in the stability of the star, a thor- ough analysis of the possible critical phenomena observed and differences due to more realistic equations of state. The investigation of such scenarios will be presented else- where. FIG. 8: Results of three critical searches for a magnetized, ro- tating star with central enthalpy of 0 . 8 and a radial magnetic field at the pole of 1 , 000 GT . One search varied the ampli- tude of the pressure perturbation A$_{p}$ with m = 7 (black and cyan), another with m = 3 (blue and magenta), and another varied the density perturbation A$_{ρ}$ . In solid line are shown the super-critical evolutions which collapse to black holes, while sub-critical solutions for the two searches are shown with dot- ted lines. The search over pressure with m = 7 achieved tun- ing to about one part in 10 $^{3}$, that with m = 3, one part in 10 $^{4}$, and that over density achieved about one part in 10$^{5}$.