skip to main content

Title: A THREE-DIMENSIONAL NUMERICAL SOLUTION FOR THE SHAPE OF A ROTATIONALLY DISTORTED POLYTROPE OF INDEX UNITY

We present a new three-dimensional numerical method for calculating the non-spherical shape and internal structure of a model of a rapidly rotating gaseous body with a polytropic index of unity. The calculation is based on a finite-element method and accounts for the full effects of rotation. After validating the numerical approach against the asymptotic solution of Chandrasekhar that is valid only for a slowly rotating gaseous body, we apply it to models of Jupiter and a rapidly rotating, highly flattened star ({alpha} Eridani). In the case of Jupiter, the two-dimensional distributions of density and pressure are determined via a hybrid inverse approach by adjusting an a priori unknown coefficient in the equation of state until the model shape matches the observed shape of Jupiter. After obtaining the two-dimensional distribution of density, we then compute the zonal gravity coefficients and the total mass from the non-spherical model that takes full account of rotation-induced shape change. Our non-spherical model with a polytropic index of unity is able to produce the known mass of Jupiter with about 4% accuracy and the zonal gravitational coefficient J {sub 2} of Jupiter with better than 2% accuracy, a reasonable result considering that there is only onemore » parameter in the model. For {alpha} Eridani, we calculate its rotationally distorted shape and internal structure based on the observationally deduced rotation rate and size of the star by using a similar hybrid inverse approach. Our model of the star closely approximates the observed flattening.« less
Authors:
;  [1] ;  [2] ;  [3]
  1. Department of Mathematical Sciences, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF (United Kingdom)
  2. Department of Earth and Space Sciences, University of California, Los Angeles, CA 90095-1567 (United States)
  3. Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA 91109 (United States)
Publication Date:
OSTI Identifier:
22167114
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 763; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCURACY; ASYMPTOTIC SOLUTIONS; DENSITY; EQUATIONS OF STATE; FINITE ELEMENT METHOD; GRAVITATION; JUPITER PLANET; MASS; ROTATION; SATELLITES; SPHERICAL CONFIGURATION; SPHERICAL MODEL; STARS; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS