Difference between revisions of "User:Tohline/AxisymmetricConfigurations/HSCF"
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<li>'''Choose a particular [[User:Tohline/SR#Barotropic_Structure|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.</li> | <li>'''Choose a particular [[User:Tohline/SR#Barotropic_Structure|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.</li> | ||
<li>Choosing from, for example, a list of astrophysical relevant ''[[User:Tohline/AxisymmetricConfigurations/SolutionStrategies#Simple_Rotation_Profile_and_Centrifugal_Potential|simple rotation profiles]],'' '''specify the corresponding functional form of the centrifugal potential''', <math>~\Psi(\varpi)</math>, that will define the radial distribution of specific angular momentum in your equilibrium configuration.</li> | |||
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Revision as of 20:50, 22 March 2018
Hachisu Self-Consistent-Field Technique
 I. Hachisu |
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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.
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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.
- Choosing from, for example, a list of astrophysical relevant simple rotation profiles, specify the corresponding functional form of the centrifugal potential, <math>~\Psi(\varpi)</math>, that will define the radial distribution of specific angular momentum in your equilibrium configuration.
Related Discussions
- Constructing BiPolytropes
- Analytic description of BiPolytrope with <math>(n_c, n_e) = (5,1)</math>
- Bonnor-Ebert spheres
- Bonnor-Ebert Mass according to Wikipedia
- A MATLAB script to determine the Bonnor-Ebert Mass coefficient developed by Che-Yu Chen as a graduate student in the University of Maryland Department of Astronomy
- Schönberg-Chandrasekhar limiting mass
- Relationship between Bonnor-Ebert and Schönberg-Chandrasekhar limiting masses
- Wikipedia introduction to the Lane-Emden equation
- Wikipedia introduction to Polytropes
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