Calculating the moment of inertia of neutron stars

Jacobus Diener

Stellenbosch University, RSA

Dr Alan Dzhioev and Prof Victor Voronov

Bogoliubov Laboratory of Theoretical Physics, JINR

Pulsar: Quantity of interest

• Pulsars Rapidly rotating remnant star of massive star

that exploded in core-collapse supernovaRadius ~10 kmMass ~1.4 M (solar mass)Density ~1015 g/cm3 (few times nuclear density)Radio-emission from magnetic polesSudden spin-ups in frequency (glitches)

• Pulsars modelled as giant nucleiConstraining models proven difficult with

observational data

Models and constraints

• Models for nuclear matter• Equation of state

Mass-radius relationship for different models of nuclear matter. Observational constraints given by mass-radius relationship of EXO 0748-676 (purple) and General Relativity (black).

Glitch models

• Alpar et al. model glitch as two components differential rotating in the pulsar.

• Outer crust spin downs faster than superfluid interior due to magnetic torques

• Angular momentum transferred between two components resulting in spin-up of star.

• Size of spin-up related to moment of inertia of different layersres

crust

IA

I

Calculating moment of inertia• Rapidly rotating ultra-dense fluid• Framework proved by General Relativity• General expression for moment of inertia

• Relativistic effectsRotationBreaking of spherical symmetryFrame dragging

1( ) ( , , , ) ( , , , )tdrd d r rI T g

2 2 2

( )

0 0

1( )

( )

R

d dre

I e

South African context

• Hartebeesthoek Radio Astronomy Observatory26 m radio-telescopeVela glitch data spanning 20 years

• SA SKA/MeerKAT

26 m telescope at HartRAO

Furthermore…

• Presented a talk to students at the BLTP on the main aspects of my studies so far

• Discussed possible nuclear matter calculations with Dr V. V. Burov using the Bethe-Salpeter approach

Conclusion

• Expression for moment of inertia derived• To be able to solve more study of rotating,

axial symmetric relativistic fluid further study needs to be undertaken

• Could provide publishable results when compared with long-term glitch data of the Vela pulsar from HartRAO

For organising and financing this visit thanks to the• National Research Foundation (South Africa) and• the Joint Institute for Nuclear Research.

Acknowledgements

References• M.A. Alpar, H.F. Chau, K.S. Cheng & D. Pines, ApJ,

409, 345 (1993). • J.M. Lattimer & B.M. Schutz, ApJ, 629, 979 (2005). • B. Link, R.I. Epstein & J.M. Lattimer, Phys. Rev. Lett.,

83, 3362 (1999).• F. Weber, Prog. Pat. Nucl. Phys. 54, 193 (2005).