Gravitational Waves from Neutron Stars

Gravitational Waves from Neutron Stars Astronomical Institute Anton Pannekoek

Elastic outer crust Neutron star modelling Elastic inner curst with superfluid neutrons Superfluid neutrons and superconducting protons in the outer core Exotic particles in the inner core Large magnetic fields, possibly arranged in flux tubes in (Type II) superconducting regions Rapid rotation

Theoretical relevance Probe the low temperature high density region of the QCD phase diagram! Uncertainties still large... Must model multi fluid superfluid and superconducting system (possibly in GR) Several inputs required besides EOS: shear modulus, vortex/flux tube interactions, dissipation, etc..

Astrophysical relevance X-ray (Magnetars, LMXBs...) Radio (Pulsar glitches...) Gravitational waves γ -ray, optical.. (Pulsars, bursts..)

GW emission mechanisms: Compact binary inspirals: NS/NS or NS/BH inspirals tidal signatures of EOS (Gold et al. 2011, Pannarale et al. 2011) chirps Supernovae / GRBs: bursts Simulations suggest unstable modes could be excited in the proto-ns after the collapse (Ferrari et al. 2003, Ott et al. 2006) Pulsars: periodic Deformations of isolated stars (Abbot et al. 2009) Modes of Oscillation (Gaertig & Kokkotas 2010) Pulsar glitches (Sidery et al. 2010, Bennett et al. 2010) Accreting systems (Watts et al. 2008) Cosmological signals: stochastic background Prime target for Pulsar Timing Arrays NS physics needed for detection! (Shannon & Cordes 2010)

GW emission mechanisms: Compact binary inspirals: chirps NS/NS or NS/BH inspirals tidal signatures of EOS (Gold et al. 2011, Pannarale et al. 2011) High frequency signals (khz) 3G(ET?) needed Supernovae / GRBs: bursts Simulations suggest unstable modes could be excited in the proto-ns after the collapse (Ferrari et al. 2003, Ott et al. 2006) Pulsars: periodic Deformations of isolated stars (Abbot et al. 2009) Modes of Oscillation (Gaertig & Kokkotas 2010) Pulsar glitches (Sidery et al. 2010, Bennett et al. 2010) Accreting systems (Watts et al. 2008) Cosmological signals: stochastic background Prime target for Pulsar Timing Arrays NS physics needed for detection! (Shannon & Cordes 2010)

GW emission mechanisms: Compact binary inspirals: chirps NS/NS or NS/BH inspirals tidal signatures of EOS (Gold et al. 2011, Pannarale et al. 2011) High frequency signals (khz) 3G(ET?) needed Supernovae / GRBs: bursts Simulations suggest unstable modes could be excited in the proto-ns after the collapse (Ferrari et al. 2003, Ott et al. 2006) Pulsars: periodic Deformations of isolated stars (Abbot et al. 2009) Modes of Oscillation (Gaertig & Kokkotas Low amplitude ET needed to constrain models 2010) Pulsar glitches (Sidery et al. 2010, Bennett et al. 2010) Accreting systems (Watts et al. 2008) Cosmological signals: stochastic background Prime target for Pulsar Timing Arrays NS physics needed for detection! (Shannon & Cordes 2010)

Low Mass X-ray Binaries Mass is stripped from the donor Forms a disc and spirals in Interacts with the magnetic field Transfers angular momentum to the central NS, spinning it up

GWs from LMXBs Cutoff of distribution at ~730 Hz Keplerian breakup at ~2000 Hz (Chakrabarty et al 2003, Patruno 2010) LMXB spin distribution points to a mechanism that halts the spin-up before the break up limit. GWs!: mountains, unstable modes, magnetic deformations.. (Papaloizou & Pringle 1978, Wagoner 1984, Bildsten 1998)

Spin equilibrium? Interaction at magnetospheric radius can lead to spin equilibrium Originally discarded (White & Zhang 1997) while recent results show it could be consistent with observations (Patruno, Haskell & D Angelo 2011)

Neutron star mountains ɛ = I xx I yy I zz Emission at ω =2Ω de dt ɛ2 Ω 6 Theoretical upper limit ɛ 10 6 (Haskell, Jones, Andersson 2006)

Neutron star mountains-ii Mountains from wavy capture layers in crust (Ushomirsky, Cutler, Bildsten 2000) Deep crustal heating consistent with cooling observations from X-ray transients. Small temperature deviations could be detected by ET

Magnetic mountains Magnetic field distorted by the accretion flow Possibility of confining a mountain (Haskell et al 2008, Payne & Melatos 2005, Priymak et al. 2011, Lander et al. 2012)

r-mode instability (Animation by Ben Owen) r-mode generically unstable to GW emission Rotating observer Emission at ω 4 3 Ω Viscosity damps the mode except in a window of temperatures and frequencies Inertial observer

r-mode instability window

r-mode instability window 0.8 0.7 0.6 1/2! c / ( G " # ) 0.5 0.4 0.3 0.2 0.1 0 1e+05 1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 Temperature (K) α s 10 5 [ Bondarescu, Teukolsky, Wasserman 2007]

r-mode instability window Duty cycle short (10% or less) for large saturation amplitudes 0.8 0.7 0.6 For small saturation amplitudes the system does not move far from the instability curve 1/2! c / ( G " # ) 0.5 0.4 0.3 0.2 For tiny saturation amplitudes the system can live IN the window 0.1 0 1e+05 1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 Temperature (K) α s 10 5 [ Bondarescu, Teukolsky, Wasserman 2007]

r-mode instability window - II 700 4U 1608 600 IGR J00291 SAX J1750.8 MXB 1659 Aql X-1 EXO 0748 Spin frequency (Hz) 500 400 300 SAX J1808 KS 1731 SWIFT J1749 SAX J1748.9 XTE J1751 HETE J1900.1 XTE J1814 IGR J1791 200 NGC 6440 PSR J2124 XTE J1807 IGR J17511 PSR J0030 PSR J0437 XTE J0929 SWIFT J1756 100 1e+06 1e+07 1e+08 1e+09 Temperature (K) [ Haskell, Degenaar & Ho, 2011]

r-mode instability window - II 700 Spin up 4U 1608 600 IGR J00291 SAX J1750.8 MXB 1659 Aql X-1 EXO 0748 Spin frequency (Hz) 500 400 300 Spin down KS 1731 SWIFT J1749 SAX J1748.9 XTE J1751 SAX J1808 HETE J1900.1 XTE J1814 IGR J1791 200 NGC 6440 PSR J2124 XTE J1807 IGR J17511 PSR J0030 PSR J0437 XTE J0929 SWIFT J1756 100 1e+06 1e+07 1e+08 1e+09 Temperature (K) [ Haskell, Degenaar & Ho, 2011]

Multifluid hydrodynamics t ρ x + i (ρ x v i x)=0 ( t + vx j j )(vi x + ε x w yx i )+ i ( µ x + Φ)+ε x wyx j i vj x = fi x /ρ x + j D j i D j i Dissipative terms (bulk viscosity, shear viscosity, etc..) f x i =2ρ n B ɛ ijk Ω j w k xy +2ρ n Bɛ ijk ˆΩj ɛ klm Ω l w xy m Mutual Friction

Mutual friction Superfluids rotate by forming quantised vortices Vortex density determines spin : vortices must move out to spin down the fluid! Balance of forces determines the dynamics v i n t +... = ɛijkˆkj (v v k v n k) v i c t +... = R(vi c v i v) Magnus Force FREE : ɛ ijkˆkj (v v k v n k)+r(v i c v i v) = 0

Strong Mutual Friction - vortex/flux tube cutting? 800 700 UNSTABLE R=0.02 800 700 R=0.02 UNSTABLE 600 IGR J00291 600 IGR J00291 Spin frequency (Hz) 500 400 300 200 R=0.01 Spin frequency (Hz) 500 400 300 200 R=0.01 100 STABLE 100 STABLE 0 1e+05 1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 Temperature (K) 0 1e+05 1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 Temperature (K) [ Haskell, Degenaar & Ho (2011) - Ho, Andersson & Haskell (2011)]

Hyperon/quark bulk viscosity? 800 700 UNSTABLE!=1 R=10 Km 700 600! s= 0.05 m = 100 MeV s IGR J00291 4U 1608 SAX J1750.8 600 IGR J00291 MXB 1659 Aql X-1 EXO 0748 Spin frequency (Hz) 500 400 300 200 100 STABLE!=0.01 R=10 Km!=0.01 R=12.5 Km Spin frequency (Hz) 500 400 300 200! s= 0.1 m = 200 MeV s KS 1731 SWIFT J1749 SAX J1748.9 XTE J1751 SAX J1808 HETE J1900.1 XTE J1814 IGR J1791 NGC 6440 PSR J2124 IGR J17511 XTE J1807 PSR J0030 PSR J0437 XTE J0929 SWIFT J1756 0 1e+05 1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 Temperature (K) 100 1e+06 1e+07 1e+08 1e+09 Temperature (K) [ Haskell & Andersson 2010, Haskell, Degenaar & Ho 2011]

Hyperon/quark bulk viscosity? 700 600! s= 0.05 m = 100 MeV s IGR J00291 4U 1608 SAX J1750.8 MXB 1659 Aql X-1 EXO 0748 Spin frequency (Hz) 500 400 300! s= 0.1 m = 200 MeV s SAX J1808 KS 1731 SWIFT J1749 SAX J1748.9 XTE J1751 HETE J1900.1 XTE J1814 IGR J1791 200 NGC 6440 PSR J2124 XTE J1807 IGR J17511 PSR J0030 PSR J0437 XTE J0929 SWIFT J1756 100 1e+06 1e+07 1e+08 1e+09 Temperature (K) [ Haskell & Andersson 2010, Haskell, Degenaar & Ho 2011]

Spin equilibrium Spin frequency (Hz) 700 600 500 400 300 200 4U 1608 IGR J00291 SAX J1750.8 MXB 1659 Aql X-1 EXO 0748 KS 1731 SWIFT J1749 SAX J1748.9 XTE J1751 SAX J1808 HETE J1900.1 XTE J1814 IGR J1791 NGC 6440 PSR J2124 XTE J1807 IGR J17511 PSR J0030 Is GW emission from an r-mode dictating spin equilibrium? Possible for hotter faster systems? GW emission excluded in 2 slower systems: SAX J1808, XTE J1814 [ Haskell & Patruno 2011] PSR J0437 XTE J0929 SWIFT J1756 100 1e+06 1e+07 1e+08 1e+09 Temperature (K) [ Haskell, Degenaar & Ho 2011]

Conclusions GW observations can constrain the physics of dense matter in NS Signals likely to be weak and (possibly) at high frequencies. Third generation detectors (ET) are needed to place real constraints of physical models Electromagnetic observations (X-ray, radio, gamma-ray) can provide important constraints NS modelling could impact on (and benefit from) GW searches with PTAs.