Rotating Neutron Stars Fridolin Weber San Diego State University San Diego, California USA

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1 Rotating Neutron Stars Fridolin Weber San Diego State University San Diego, California USA HYP 2006, October 2006, Mainz, Germany

2 Outline Neutron stars (Ultrafast) Rotation Compressed baryonic matter in rotating neutron stars Hyperons and quarks in neutron stars Gravitational radiation reaction driven instabilities Summary

3 Crab nebula Parkes VLA Isolated Rotating Neutron Stars (Pulsars)

4 Neutron Stars in X-ray Binaries (e.g. LMXBs) XMM Newton

5 A few most intriguing facts about neutron stars: All the ambient conditions that characterize neutron stars tend to the extreme!!!! N~1057 baryons M~1 2 Msun R~10 12 km } ~1015 g/cm3 B~ G, E ~ V/cm T~ K Total number ~ Currently known ~ 1600 Latest discovery: PSR in Terzan 5 PJ ad=1.39 ms (716 Hz)!! PB =1.58 ms (630 Hz) Accretion rates: 10-8 to Msun/yr

6 Σ,Λ,Ξ, Δ Neutron Star Composition in 2006 CFL 2SC LOFF strange quark matter F. Weber, Prog. Part. Nucl. Phys. 54 (2005) K

7 Einstein's Field Equations for Rotating Compact Objects Metric: ds2 = e2ν dt2 + e L dr + r dw Christoffel symbols: Гσμν= gσλ ( νgμλ + μgνλ λgμν) / 2 Riemann tensor: Rτμνσ = νгτμσ σгτμν + ГκμσГτκν ΓκμνΓτκσ Ricci tensor: Rμν = Rτμσν gστ Scalar curvature: R = Rμν gμν Einstein's equation: Gmn=Rmn gmn/2 = 8pTmn(e,P) => m 1 4 r 3 P / m 1 IP / dp = 2 dr r 1 2m/ r Tolman-Oppenheimer-Volkoff

8 Einstein's Field Equations for Rotating Compact Objects Metric: ds2 = e2ν dt2 + e2(α+β ) r2 sin2 (dφ Nφ dt)2 + e2(α β) (dr2 + r2 d ) Christoffel symbols: Гσμν= gσλ ( νgμλ + μgνλ λgμν) / 2 Riemann tensor: Rτμνσ = νгτμσ σгτμν + ГκμσГτκν ΓκμνΓτκσ Ricci tensor: Rμν = Rτμσν gστ Scalar curvature: R = Rμν gμν Limiting frequency? 1. Kepler frequency, ΩK = r 1 eν α β UK + Nφ 2. GRR driven instabilities I Differential rotation/uniform rotation?

9 Differentially Rotating Stellar Objects Ω 1.9 km M =1.4 Msun neq=290 Hz nc =140 νeq 5.5 km 14.3 km mixed phase of baryons and qarks Open issue: dynamical stability; secular stability

10 Pulsar's Composition depends on Spin Frequency! Pure quark matter 60% change!! F. Weber, Prog. Nucl. Part. Phys. 54 (2005)

11 Model Quark-Hadron Composition Ω~ΩKepler Ω=0

12 Quark-hybrid star losing its quark matter core due to changes in the rotation rate Ω Backbending Glendenning, Pei & Weber, PRL 79 (1997) 1603; Chubarian, Grigorian, Poghosyan, Blaschke A&A 357 (2000) 968; F. Weber, Prog. Nucl. Part. Phys. 54 (2005)

13 Backbending nuclear physics well known in... and from the Olympics Backbending predicted in 1960 by Mottelson & Valatin. Observed in 1972 by Stephens & Simon.

14 Model Composition of a M=1.7 Msun (Req=11.5 km, Ω=0) P. Rosenfield, SDSU, 2006 J ad Equation of state: DD RBHF, Bonn, Hofmann, Keil, Lenske. PRC 64 (2001)

15 Gravitational-Radiation Reaction Driven Instabilities... Driven by rotation at ν>νcritical Damped by Shear viscosity Bulk viscosity Classified in terms of Ylm

16 Gravitational-Radiation Reaction Driven Instabilities... Star rotates at Ω Perturbation rotates at ωm(ω) quadrupole mode A A0 e i m t i m t /

17 The underlying theory... i v i = 0 t vi v j j v i = i P i t i i = 4 Energy contained in perturbation: de 3 ij 2l 1 m m = d x 2 ij l N l D L D l dt Ansatz for amplitudes: A A0 e => i t i m t / 1 de = 2 E dt GR Final equation: = GR If 1/τ> 0: perturbation is damped If 1/τ< 0: perturbation grows

18 Gravitational-Radiation Reaction Driven Instabilities...

19 Critical Angular Velocity of Rotating Neutron Stars f-mode instability unstable rotation F. Weber, Prog. Part. Nucl. Phys. 54 (2005) r-mode instability unstable rotation From Lindblom & Owen. PRD 65 (2002)

20 Summary Cores of neutron stars are likely to contain significant amount of strangeness - confined in hyperons - unconfined quark matter Strangeness content will change dramatically with neutron star frequency. Backbending of isolated neutron stars r-modes damped by hyperons Need more neutron star data (SkA)

21 ... an observational windows on inner workings of neutron stars Sensitivity ~100 times higher than the VLA sensitivity ~ 20,000 pulsars expected to be discovered ~ 1000 MSPs Pulsars around black holes Testing GR Initial operations start ~2016 Final operations start ~2020

22 Interacting neutron gas fails(!), and so does a... MJ = 2.1±0.2 Msol Nice, Splaver, Stuirs, Loehmer, Jessner, Kramer, Cordes, astro-ph/ M4U =2.0±0.1 Msol Barret,Olive,Miller (2005)... non-interacting neutron gas!!

23 Overview of Sources Neutron Star & Black Hole Binaries inspiral merger Spinning NS s LMXBs Pulsars NS Birth (SN, AIC) tumbling convection Stochastic background big bang early universe Source: J. Hartle