Numerical Relativity @ Parma

Bar-Mode instability in full General Relativity

The results of our studies of the bar-mode instability of rapidly rotating differentially rotating Neutron Star models are discussed HERE. The new results found were: a precise determination of the critical value of the parameter β=T/W for the onset of the instability for a wide range of compactness for polytropic neutron star models characterized by Γ=2, K=100 and a fixed differential rotation profile; the determination of the mode dynamics of the dynamical bar-mode instability and the evidence of the importance of mode coupling for the suppression of the bar-mode deformation in the dynamical time scale.

Here you may see an example of the development of the dynamical bar-mode instability for the simulated model Ub11 (β=0.2743, M₀=1.51M_Sun) simulated using 2 refiment level (CARPET driver).

Measure units

In Physics it is customs to chose a system of measures units such that the main physical quantity involved on the process are easily expressed. In numerical relativity is usually chosen a system such that: c=G=M_sun=1

In this unit system the main physical quantities are expresend as:

• Lenght= G c^-2 M_sun =1.47663 Km
• Time = G c^-3 M_sun =4.92549 10^-6 sec
• Mass = M_sun =1.98844 10³⁰ kg

Values from the PDG

• c=299792458 m s^-1
• G=6.6742 10^-11 m³ kg^-1 s^-2
• M_sun=1.98844 10³⁰ kg
• parsec =3.08568 10¹³ km