1. Gravitational waves and neutron star matter (except oscillations) Ben Owen August 6, 2009PREx @ ECT* Trento arXiv:0903.2603

2. A gravitational wave Shear strain h 0 …is 2 nd t-derivative of quadrupole moment Luminosity is square of 3 rd derivative Passes through every- thing! Even horizons! Including detectors… Ben OwenGW from NS matter2

3. Gravitational wave observations Astrophysical targets Continuous waves Magnetar flares Pulsar glitches Binary mergers Supernova core collapse Magnetar birth NS physics affecting GW Equation of state Phase structure Shear modulus (crust, core) Breaking strain (crust, core) Magnetic field effects Neutrino cooling Viscosity (shear, bulk) Conductivity (both kinds) … Ben OwenGW from NS matter3

4. Ben OwenGW from NS matter Big science: LIGO and Virgo Images: LIGO/Caltech 4 Image: Virgo

5. Continuous GW searches Crab pulsar (Abbott et al. 2008) –One-timing search: h 0 < 3×10 -25, ε < 1×10 -4, 4% spin-down power –Range of timings: h 0 < 12×10 -25, ε < 6×10 -4, 70% spin-down power All-sky & band survey (Abbott et al. 2009) Cas A wide-band (Wette et al. 2008, Abbott et al. in prep.) Ben OwenGW from NS matter5 Image: Chandra/NASA

6. Continuous GW emission mechanisms Mountains – buried quadrupoles elastically supported Oscillations – mainly r-modes (Jones’ talk) Magnetically supported mountains Magnetic bottling Ben OwenGW from NS matter6

7. How big can elastic mountains get? Standard neutron star (Ushomirsky et al. 2000) –Thin crust, < 1/2  nuclear density:  < few  10 -7 But what about funny phases? (Owen 2005) –Some models have lots of solid at high density Mixed phase star (Glendenning 1990s) –Solid core up to 1/2 star, several  nuclear density:  < 10 -5 Quark star (Xu 2003) –Whole star solid, high density:  < few  10 -4 –Right range for some initial LIGO pulsar results! –Also color superconductor (Mannarelli et al. 2007) –Can get  above 10 -3 (Lin 2007, Haskell et al. 2007) Ben OwenGW from NS matter7

8. How big can elastic mountains get? Hydrostatic equilibrium tells you (dropping integral sign) Q = R 6 /(GM) × (geometry) × (shear modulus) × (strain) Geometry isn’t that big a (dimensionless) factor But high symmetry energy = high R = good Product means observational upper limits CANNOT constrain one factor like EOS (Lin 2007, Haskell et al. 2007, Knippel & Sedrakian 2009) But detection of high ε would (Owen 2005) Ben OwenGW from NS matter8

9. Ben OwenGW from NS matter9 Shear modulus Energy (density) needed for unit shear strain Electrostatics problem (Fuchs 1936) –Homogeneous bcc lattice –  = 0.11q 2 D 6 /S 4 Typical inner crust –Spacing S = 30fm –Diameter D = 20fm –Charge 50 (q is density) –  < 10 30 erg/cm 3

10. Breaking strain Assumed breaking strain < 10 -2 (terrestrial materials) Perfect crystal breaks around 10 -1, but that can’t be real… Horowitz & Kadau (2009): pressure makes perfect! Cracks (voids) can’t form (Some hint in Jones 2003) Grain boundaries no problem Impurities segregate out So ε up to 10 -5 for normal NS Also nice for magnetar flares Ben OwenGW from NS matter10

11. Questions for nuclear physics (and…) Are we sure about shear modulus and breaking strain? (Funny phases as well as normal crust) How long does it last? Viscoelastic creep? Plastic flow? Does it really look like that denser than n-drip? What does it look like in strong magnetic fields? What can drive them that big? (young neutron stars) Does supernova mess get frozen in? Details of accretion? Ben OwenGW from NS matter11

12. Magnetar flares Gamma-ray flares distributed w/Gutenberg-Richter law B-field ~10 15 G twists against crust (Duncan & Thompson) Giant flares up to 10 44 erg till 2004 Fits 10 44 erg crust elastic energy But then in 2004: flare > 10 45 erg Change shear modulus: quarks 10 47 erg (Owen 2005) Change breaking strain: 10 46 erg (Horowitz & Kadau 2009) Ben OwenGW from NS matter12 Image: R. Duncan

13. LIGO magnetar flare searches 2004 giant flare: QPO frequencies (Abbott et al. 2007) ~200 flares: f-modes, bucket (Abbott et al. 2008) 2006 storm, stacked: f-modes, bucket (Abbott et al. 2009) F-modes: 1.5-3kHz Depends on mean density! How much energy? Up to 10 49 erg (Ioka 2001) Magnetic tension model Ben OwenGW from NS matter13

14. Questions for nuclear physics (and…) How much energy is available in various models? (EOS, shear modulus, & breaking strain) How does it break? (B-field is definitely high enough to change things) Is GW energy correlated w/gamma-ray energy? Could they be completely decoupled? How fast/well will breaking crust transfer to f-modes? Ben OwenGW from NS matter14

15. Take-away Gravitational waves … directly probe matter at super-nuclear densities … are affected by more than just the equation of state … could be great evidence for a crystalline phase Ben OwenGW from NS matter15

16. Ben OwenGW from NS matter16 O’Shaughnessy & Owen (in prep.)