Default value of mtry for random forests
The textbook 'The Elements of Statistical Learning' by authors Trevor Hastie, Robert Tibshirani, and Jerome Friedman discuss how to tune the number of variables to sample as you build the trees in Chapter 15, Section 3. The pdf of the text is freely available and can be found here.

Note that the values you have listed are in fact default values, as you have mentioned. In practice, it is best to tune the value of 'mtry', as the best value will depend on the specific problem and dataset you are working with.