Phase integral of asteroids

¹ Department of Astronomy and Space Informatics, V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 61022, Ukraine
e-mail: shevchenko@astron.kharkov.ua
² Institute of Astronomy, V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 61022, Ukraine
³ Department of Physics, University of Helsinki, Gustaf Hällströmin katu 2, 00560 Helsinki, Finland
⁴ Finnish Geospatial Research Institute FGI, Geodeetinrinne 2, 02430 Masala, Finland
⁵ Institute of Physics and Technology, Ural Federal University, Mira str. 19, 620002 Ekaterinburg, Russia
⁶ Space Science Institute, 4750 Walnut St. Suite 205, Boulder CO 80301, USA

Received: 31 March 2019
Accepted: 20 May 2019

Abstract

The values of the phase integral q were determined for asteroids using a numerical integration of the brightness phase functions over a wide phase-angle range and the relations between q and the G parameter of the HG function and q and the G₁, G₂ parameters of the HG₁G₂ function. The phase-integral values for asteroids of different geometric albedo range from 0.34 to 0.54 with an average value of 0.44. These values can be used for the determination of the Bond albedo of asteroids. Estimates for the phase-integral values using the G₁ and G₂ parameters are in very good agreement with the available observational data. We recommend using the HG₁G₂ function for the determination of the phase integral. Comparison of the phase integrals of asteroids and planetary satellites shows that asteroids have systematically lower values of q.