In week 348 we looked at the results of simulations we have run on how likely we are to find periodic signals in our data depending on the amplitudes and periods. It turns out that the detection rate only really depends on the amplitudes of the signals and not on the period (at least for the periods we are interested in). The amplitudes scale nicely linearly with the spot size.
In the above histogram we show the size distribution of spots found in all of the HOYS data. The red histogram is for cold spots and the blue histogram for the warm/hot spots. We experimented with trying to fit this distribution to see what the underlying size distribution is. This can be simply done by using a distribution, multiplying it by the detection rates as a function of spot size and over plotting the best fit. This is done as the black line in the plot.
We can see, the the black fit is pretty close to the histogram of the observed spot sizes. The best model is an exponential distribution with a scale height of 0.08. It turns out that a power-law distribution or a log-normal distribution cannot be fit to the data. They both predict far too many large spots compared to small ones. Now we need to find an explanation for this 🙂