Hachisu Self-Consistent-Field Technique
In 1986, Izumi Hachisu published two papers in The Astrophysical Journal Supplement Series (vol. 61, pp. 479-507, and vol. 62, pp. 461-499) describing "A Versatile Method for Obtaining Structures of Rapidly Rotating Stars." (Henceforth, we will refer to this method as the Hachisu Self-Consistent-Field, or HSCF, technique.) We have found the HSCF technique to be an extremely powerful tool for constructing equilibrium configurations of self-gravitating fluid systems under a wide variety of different circumstances. This chapter has been built upon an (ca. 1999) outline of the HSCF technique that appeared in our original version of this HyperText Book (H_Book). The photo of Professor Izumi Hachisu shown here, on the left, dates from the mid-1980s — about the time he developed this remarkably useful numerical technique; a more recent photo can be found on the web page associated with Professor Hachisu's current faculty appointment at the University of Tokyo, Komaba.
Steps to Follow
- Choose a particular barotropic equation of state. More specifically, functionally define the density-enthalpy relationship, <math>~\rho(H)</math>, and identify what value, <math>~H_\mathrm{surface}</math>, the enthalpy will have at the surface of your configuration. For example, if a polytropic equation of state is adopted, <math>~H_\mathrm{surface} = 0</math> is a physically reasonable prescription.
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