tokens: (). While p obs does not depend on the longitude, the diurnal cycle can still introduce a systematic bias. This is because the Sun will be systematically out of phase with the northern maximum of the antenna pattern (Figure 2 ). We find that this typically produces an increase in p obs of a few percent for mid-latitudes in the north, even though their analogs in the south have larger p obs because of the shorter solar exposure over an entire year. We note that p obs reflects the amount of localization probability that is observable in the limit of many detections. Outside of this limit, we consider an analogous quantity () defined for a finite number of detections ( N d ) with the correspondence (see the Appendix for more details). Statistical fluctuations in , caused by variations in which events occur, can be large, particularly with events. We expect the uncertainty in this estimate to scale inversely with , and Figure 3 reports as error bars along with the mean. Typical values are between 6% and 10%. We also note that the intrinsic distribution for single events ( N d = 1) may not be Gaussian but, in the limit of many detections, the distribution of the mean will be. 3.2. Minimum Zenith Distance While equatorial observatories may be able to access the largest integrated probability, and thereby have the largest probability of being able to image a source, this does not necessarily imply that they will have the best conditions for observing. An important consideration is the closest approach of each field to an observatory’s zenith (minimum zenith distance). Sources at large angles from an observatory’s zenith can be difficult to observe because of high air mass and mechanical limitations. In Figure 4, we present the mean minimum zenith distance, as a function of latitude, weighted by the probability that the source actually comes from each location: accounts for solar occlusion and incorporates when the EM facility will actually be able to observe. We find that observatories at extreme latitudes () will almost always have large D zen , with a gradual transition to lower values at lower latitudes. There is a difference in D zen between observatories at mid-latitudes, with northern sites preferred. This is because the diurnal cycle makes the Sun preferentially overlap the southern antenna pattern and forces southern facilities to observe closer to sunrise and sunset than their northern counterparts. This behavior is particularly evident at the northern winter solstice. Figure 4. D zen averaged over a year (black), near the northern summer solstice (blue), and near the northern winter soltice (red). Shaded regions correspond to the fluctuations from localization maps simulations (), and we note that 's distribution is quite broad. Figure 4 also shows the fluctuations in the analgous stastic defined for a finite number of detections (). We typically find –10 (see the Appendix for more details). Furthemore, D zen corresponds to the mean of
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O