0 0.5 1 1.5 2 2.5 3 3.5 4 −12 −10 −8 −6 −4 −2 0 2 4 6 log$_{10}$ t / M log 10 | $_{ψ}$ L=2 | t −7 5 0 0.5 1 1.5 2 2.5 3 3.5 4 −10 −8 −6 −4 −2 0 2 log$_{10}$ t / M log 10 | $_{ψ}$ L=2 | t −7 t −5 IV. EXCITATION OF “UP” MODES FIG. 1: The quadrapole projection of the full field as a function of time, for initial data of a pure quadrapole field, then injected at T = 250 M with a pure quadrapole field. The late–time field behavior is computationally found to be given by ψ ∼ t − 7 . $^{05}$. The power law index, and all the indices in this Paper, were calculated by extrapolating the local power-law index to infinite time. FIG. 2: The quadrapole projection of the full field as a function of time, for initial data of a pure quadrapole field, then injected at T = 250 M with a pure monopole field. The late–time field behavior is computationally found to be given by ψ ∼ t − 5 . $^{03}$. between the two cases: the excited monopole is not an arbitrary field: it is carefully chosen by the dynamics of the problem, and may be viewed as a fine tuned field; the injected monopole is arbitrary, and is not fine tuned to lead to a different late–time decay rate. Most interest has been devoted to finding the decay rate of the slowest decaying mode, for obvious reasons. Specif- ically, the slowest decaying mode determines the late–time behavior of the full field. As lower multipole modes typically have a slower decay rate, most interest has naturally focused on the excitation of “down” modes, specifically the excitation of lower multipole modes starting with higher multipole modes. Here, we are interested in the converse, i.e., in the excitation and decay rate of “up” modes, i.e., the excitation and decay rate of a higher multipole mode than the one initially excited. Such modes are typically sub-dominant, and do not dominate the late–time behavior of the full field. Our interest in the “up” modes is therefore only tangentially