Rotating neutron star models with a toroidal magnetic field - SFB/TR7
Rotating neutron star models with a toroidal magnetic field - SFB/TR7
Rotating neutron star models with a toroidal magnetic field - SFB/TR7
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Numerical method<br />
5<br />
Problem: (1) sources of elliptic <strong>field</strong> equations fill all space,<br />
(2) exact boundary condition (of asymptotic flatness) only known at spatial infinity,<br />
(3) sources of elliptic equations involve quadratic terms of derivatives of metric<br />
potentials themselves.<br />
Approach: iterative procedure (relaxation) based on surface-adapted multi-domain<br />
spectral method derived from LORENE C++ class library for numerical relativity.<br />
Expand scalar and vector functions according to<br />
f (r,θ) =<br />
L∑<br />
a l (r)coslθ , U ˜φ (r,θ) =<br />
l=0<br />
L∑<br />
l=1<br />
a ˜φ<br />
l<br />
(r)sinlθ . (8)<br />
Angular expansion by Fourier series, radial expansion by Chebyshev polynomials.<br />
Use three domains: (1) spheroidal kernel containing all the matter,<br />
(2) intermediate domain covering the neighbourhood of the <strong>star</strong>,<br />
(3) outer (vacuum) domain stretching to spatial infinity, mapped onto finite grid.<br />
Code validation: (1) Full agreement <strong>with</strong> Newtonian results e.g. of Sinha (1968),<br />
(2) for each model, error estimate provided by GRV2/GRV3 (10 −6 to 10 −10 ).<br />
Joachim Frieben Golm, June 18, 2007
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