### κ,γ parameter space properties

A selection of properties plotted in the κ,γ parameter space are presented here:

More detailed explanations can be found below.

Kolmogorov-Smirnov (KS) tests between pairs of MPDs   number of bins: 100 number of bins: 150 number of bins: 200
Are all maps for given κ,γ equivalent?
In these κ,γ parameter space plots we show the results of the KS test between pairs of individual magnification probability distributions (MPDs), using data from GD0. At each κ,γ location there are 15 individual MPDs available, calculated from maps with different microlens positions. The null hypothesis is that the MPDs are the same. We perform the KS test between all the possible pairs of MPDs, and we plot the percentage of pairs that failed the test, Nf . Increasing the number of bins used to calculate the MPDs is expected to increase the detailed features of the curves, leading to more of them failing the KS test.

These results have been reported in Vernardos & Fluke, 2013.

Kolmogorov-Smirnov (KS) tests between individual MPDs and the mean top»   number of bins: 100 number of bins: 150 number of bins: 200
Can we find a representative mean-MPD for each κ,γ?
In these κ,γ parameter space plots we show the results of the KS test between individual magnification probability distributions (MPDs) and the corresponding mean distribution, using data from GD0. At each κ,γ location there are 15 individual MPDs available, calculated from maps with different microlens positions. We derive the mean from the sample of 15 MPDs, the mean MPD, and test the null hypothesis that the MPDs are the same as the mean. This is a more fair test than comparing pairs of individual MPDs, because the mean is more representative than any individual MPD. We plot the number of MPDs that failed the test with the mean, Nf . Increasing the number of bins used to calculate the MPDs is expected to increase the detailed features of the curves, leading to more of them failing the KS test.

These results have been reported in Vernardos & Fluke, 2013.

Smooth matter induced magnification fluctuations top»  s for which max P3 (high) occurs s for which max P0.3 (low) occurs
How does including smooth matter effect the very high and very low magnifications?
In these κ,γ parameter space plots we show the effect of smooth matter on extreme - very high or very low - magnifications. For low magnifications, we define P0.3 , which is the sum of probabilities for μ < 0.3μth, where μth is the expected macromagnification. Similarly, we define P3 for μ > 3μth. The effect of changing the smooth matter fraction, s, on these probability sums is investigated. In the two plots above we show the s for which P0.3 and P3 are maximized, across the range of κ,γ, using data from GD1.

These results have been reported in Vernardos et al., 2014.