A three-parameter magnitude phase function for asteroids

We develop a three-parameter H, G₁, G₂ magnitude phase function for asteroids starting from the current two-parameter , H, G phase function. We describe stochastic optimization of the basis functions of the magnitude phase function based on a carefully chosen set of asteroid photometric observations covering the principal types of phase dependencies. We then illustrate the magnitude phase function with a chosen set of observations. It is shown that the H, G₁, G₂ phase function systematically improves fits to the existing data and considerably so, warranting the utilization of three parameters instead of two. With the help of the linear three-parameter phase function, we derive a nonlinear two-parameter H, G₁₂ phase function, and demonstrate its applicability in predicting phase dependencies based on small numbers of observations.