What can X-ray observations tell us about: The role of Gravitational Waves in Low Mass X-ray Binaries

Transcription

1 What can X-ray observations tell us about: The role of Gravitational Waves in Low Mass X-ray Binaries Astronomical Institute Anton Pannekoek

2 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

3 GWs from LMXBs Cutoff of distribution at ~730 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)

4 GWs from LMXBs Cutoff of distribution at ~730 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)

5 Spin equilibrium? Interaction at magnetospheric radius Accretion torque: spin up Magnetic torques and propeller: spin down

6 Spin equilibrium? 1e+09 B (G) 1e+08 khz QPOs X-ray PSRs Burst oscillations (White & Zhang 1997) M / M Edd

7 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)

8 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.

9 Magnetic mountains Magnetic field distorted by the accretion flow Possibility of confining a mountain (Payne & Melatos 2004, Melatos and Payne 2005)

10 The strange case of XTE J (& SAX J ) φ(t) =φ 0 +(t t 0 )ν 0 Flux correlated to phase? (Patruno, Wijnands & Van der Klis 2009) Constant frequency during outburst? ν < Where is the angular momentum going? GWs? [ Haskell & Patruno (2011)]

11 The strange case of XTE J (& SAX J ) Pulse phase residuals [cycles] X-ray Flux [mcrab] Flipped Pulse Phases X-ray Flux (Patruno, Wijnands & Van der Klis 2009) Flux correlated to phase? Constant frequency during outburst? ν < Where is the angular momentum going? GWs? [ Haskell & Patruno (2011)]

12 Gravitational waves? Crustal mountains. Ushomirsky, Cutler & Bildsten (2000) Not enough heat deposited in the crust δt 10 3 C 1 k p 1 30 Q n M 22 K Ushomirsky & Rutledge (2001) ( δtq )( Q ) 3 g cm 2 Q R K 30MeV Q (To balance accretion one would need )

13 Gravitational waves? Magnetic mountains. Cutler (2002), Melatos & Payne (2005) B field too weak. Spin-down too strong? Requires strong internal toroidal (or surface higher multipole) component of the order B G

14 Gravitational waves? Hyperon bulk viscosity (or quark bulk viscosity, mutual friction etc.) can halt the r-mode thermal run-away. Andersson, Jones & Kokkotas (2002) Nayyar & Owen (2006) Star too hot and spin-down in quiescence too strong? Haskell & Andersson (2010) Estimated core temperature: T c 10 7 K Would need strong direct URCA with no superfluidity

15 Spin equilibrium? XTE J SAX J1808 (2005) Flux [Crab] Flux [Crab] MJD [days] MJD [days] Assume a propeller phase with Rc=Rm [Haskell & Patruno (2011)] The simple model of Andersson et al gives spin equilibrium at approximately the mean accretion rate (Rm=0.8 Rc) Rm/Rc=0.75 XTE J1814, Rm/Rc= SAX J1808

16 Spin equilibrium? Faint model Close to Eddington Model B = L Spin Eq Msun/yr Spin Eq Msun/yr Spin Eq Msun/yr B [10 8 G] L/L Edd Correlation between B and L weak B [10 8 G] Spin Period [ms] Many systems may be close to spin equilibrium as set by the disc/magnetosphere interaction [ Patruno, Haskell & D Angelo (in preparation)]

17 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

18 r-mode instability window - I

19 r-mode instability window - I /2! c / ( G " # ) e+05 1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 Temperature (K)

20 r-mode instability window - I 0.8 Duty cycle short (10% or less) Effects of EOS? (Hyperons..) Effects of superfluidity? 1/2! c / ( G " # ) e+05 1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 Temperature (K)

21 r-mode instability window - II

22 r-mode instability window - II Spin up Spin down

23 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

24 Mutual friction Superfluids rotate by forming quantised vortices Vortex density determines spin : vortices must move out to spin down the fluid! Vortices could be strongly pinned in the crust Magnus Force PINNED : ɛ ijkˆkj (v v k v n k)+f i p =0 FREE : ɛ ijkˆkj (v v k v n k)+r(v i c v i v) = 0

25 r-mode instability window - III [ Haskell et al. (in preparation) - Ho, Andersson & Haskell (2011)]

26 r-mode instability window - III [ Haskell et al. (in preparation) - Ho, Andersson & Haskell (2011)]

27 Conclusions We have a problem with the r-mode. Can a system be inside the instability window? Need to model the accretion torque. Are some AMXPs emitting GWs? Precise timing and cooling measurements can guide us..(while we wait for GW measurements...) Important input for choosing targets for GW observations: persistent sources best targets?