Gravitational waves from neutron stars and the nuclear equation of state

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1 Gravitational waves from neutron stars and the nuclear equation of state Ian Jones School of Mathematics, University of Southampton, UK University of Surrey, 18th October 2011

2 Context: the hunt for gravitational waves The search for gravitational waves is ongoing. Motivation behind gravitational wave astronomy is two-fold: To confirm a key prediction of General Relativity To probe physics in extreme regimes I will talk about GWs from individual neutron stars

3 The nuclear physics inputs Overall pressure-density relation ( soft verses hard ) Thickness, shear modulus and breaking strain of crust Thermal and electrical conductivities & cooling mechanisms Shear and bulk viscosities Existence of superfluidity/superconductivity T heavy ion collider QGP hadronic non CFL gas liq CFL Figure: Dany Page nuclear superfluid neutron star µ Alford et al, arxiv:

4 Plan of talk 1. The compact object zoo 2. Electromagnetic astronomy: what we already know 3. Gravitational wave astronomy: what we d like to know

5 The compact object zoo Possible targets include: Pulsars LMXBs Magnetars Central Compact Objects Gravitars The Crab nebula (HST)

6 The compact object zoo Possible targets include: Pulsars LMXBs Magnetars Central Compact Objects Gravitars Artist s impression!

7 The compact object zoo Possible targets include: Pulsars LMXBs Magnetars Central Compact Objects Gravitars Ring surrounding SGR (Spitzer Space Telescope)

8 The compact object zoo Possible targets include: Pulsars LMXBs Magnetars Central Compact Objects Gravitars Cas A nebula (Spitzer Space Telescope)

9 The compact object zoo Possible targets include: Pulsars LMXBs Magnetars Central Compact Objects Gravitars Not seen electromagnetically!

10 Plan of talk 1. The compact object zoo 2. Electromagnetic astronomy: what we already know 3. Gravitational wave astronomy: what we d like to know

11 Glitches Most of the time pulsar spin frequencies gradually decrease Occcasionally some younger pulsars under-go sudden spin-ups 1% 2% of spin-down reversed in glitches Taken as evidence of a superfluid component penetrating inner crust

12 Binary pulsars Accurate timing of binary pulsars has provided indirect evidence for GWs Gives mass measurements too Recent highlight is measurement M = 1.97 ± 0.04M by Demorest et al (2010) Rules out softer equations of state: Lattimer & Prakash 2007

13 Cooling stars For most stars, cooling dominated by neutrino emission from core Density and state of matter determine exact reactions, e.g. (m)urca: n p + e + νe and p + e n + ν e Fast cooling can indicate presence of exotic component......or onset of superfluidity! Shternin et al 2011

14 Plan of talk 1. The compact object zoo 2. Electromagnetic astronomy: what we already know 3. Gravitational wave astronomy: what we d like to know

15 Emission mechanisms... Need time-varying mass or current multipoles for GW emission. e.g. for mass multipoles: h 1 r d l dt l Ilm where I lm ρ(y lm ) r l dv Possible GW emission mechanisms include: Rotation of non-axisymmetric stars ( mountains ) Oscillation modes Free precession

16 Mountains A spinning non-axisymmetric star radiates gravitational waves: Emission is at 2Ω. h 1 r Ω2 ɛi 3 where ɛ = I 2 I 1 I 3. An upper limit on h can be recast as an upper limit on ɛ. But what does modelling/nuclear physics have to say about maximum possible mountain size?

17 Theoretical upper limit: normal neutron stars Maximum elastic mountain size determined by balance between gravitational and elastic forces: ɛ µv ( crust GM 2 /R u break 10 7 u ) break Simple argument confirmed by rigorous calculation of Ushomirsky, Cutler & Bildsten (2000). Breaking strain a function of temperature and duration of applied stress (Chugunov & Horowitz 2010) Also expect magnetic mountain (estimate, not upper limit!): ɛ mag (B2 /8π)V star GM 2 /R B 2 12

18 Mountain building How might such an elastic mountain by formed in the first place? Bildsten (1998) investigated temperature/composition asymmetries. Viability of mechanism confirmed by Ushomirsky, Cutler & Bildsten (2000) But what creates temperature asymmetry? Open question! Figure: Ushomirsky, Cutler & Bildsten (2000)

19 More exotic scenarios Exotic states of matter might lead to solid cores giving larger maximum allowed ellipticites. ɛ max 10 4 possible for solid quark core (Owen 2005) Crystalline colour superconducting quark matter also relevant (Mannarelli et al 2007) leading to similarly large maximum ellipticities (Haskell et al 2007 and Lin 2007) Lack of detection of such a large mountain does not rule out such exotic states of matter. Superconductivity acts to increase magnetic mountain estimate: ɛ mag 10 9 B 12

20 Oscillation modes Neutron stars have a complex zoo of oscillation modes In a sufficiently rapidly rotating star, mode may go CFS unstable Instability is an example of a two-stream instability the two media are the stellar fluid and the spacetime! R-mode is a leading candidate for this instability; f GW 4f star /3 Figure: Chad Hanna & Ben Owen

21 Astrophysical manifestation of the r-mode Useful to think in terms of an instability curve break-up limit!/! k ! c core temperature Shear viscosity: Viscous boundary later forms at crust/core interface Bulk viscosity: Various weak-interactions relevant, e.g. (m)urca: n p + e + νe and p + e n + ν e Strangeness-violating reactions involving hyperons, e.g. Σ + p n + n Mutual friction between species, e.g. Scattering of electrons off neutron vortices Cutting of neutron flux tubes through magnetic vortices

22 Astrophysical manifestation of the r-mode cont... break-up limit!/! k ! c core temperature Trajectories computed using coupled ODEs linking temperature, spin rate and mode amplitude. Qualitative outcome depends upon shape of curve and position of minimum. Many aspects yet to be fully understood, including implications of non-linear mode coupling and multi-fluid dynamics.

23 Gravitational wave searches LIGO, Virgo & GEO600 detectors have collected large amounts of data at/near initial design sensitivity. 50 papers published, all upper limits. Advanced LIGO and Virgo will improve astrophysical reach (aligo expected 2015). In the meantime need to: Decide what further searches to carry out on data. Prepare for advanced detector era.

24 GW searches: a highlight result Searches have looked for GWs from known pulsars, assuming emission from a mountain. Relatively straightforward, as EM astronomy gives all but signal amplitude and phase. Upper limits placed on ɛ for many known radio pulsars. Highlight was Crab result (Abbott et al, Ap.J ), with upper limit ɛ Shows that Crab does not contain a maximally strained exotic core! Corresponding to no more than 2% of energy loss going in to GW channel.

25 Summary Nuclear physics helps guide gravitational wave astronomy by Probing viability of emission mechanisms prioritising effort Interpreting upper limits/eventual detection Many unanswered questions, including: What is state of matter at highest stellar densities? Is core fluid or crystalline? Are fluids normal or superfluid/superconducting? If superfluid, how do fluids/vortices/flux tubes interact? KEY MESSAGE: Need a lot more than the pressure-density relation!