At intermediate masses Sample Clauses

At intermediate masses. (i.e. if tm < tpix < tc), this gradually gives way to many oscillations inside a single pixel. We have to average the os- cillation term and compute the Xxxxx profile by Eq. 3.4. In this case, the Xxxxx profile is simply broadened, but the broadening is not fixed de- terministically by ρ φ .3 In this case, we draw φ r from the Rayleigh dis- tribution for each coherence time traveled along the line of sight, and rescale it according to the local dilaton density. This scheme is approx- imate: a complete picture could be found only by full simulation of the field on sub-coherence timescales (e.g. Refs. [87, 88], although ap- 2This is approximately 10 32 eV, below which field oscillations freeze and are no longer dynamical. However spatial variations of non-oscillating could still be detected, similarly to [86].‌ 3In principle this step could be computed deterministically by recomputing P(k;t) on the pixel crossing time, but this would be computationally prohibitive. proximate methods such as Ref. [89] might suffice on the quasi-linear scales probed). Our treatment of this case is inspired by Ref. [55] who consider the same regime of scales for direct detection experiments.
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