Gravitational waves and neutron star matter(except oscillations)

Ben Owen

August 6, 2009PREx @ ECT* Trento

arXiv:0903.2603

A gravitational wave

• Shear strain h0

• …is 2nd t-derivative of quadrupole moment

• Luminosity is square of 3rd derivative

• Passes through every-thing! Even horizons!

• Including detectors…Ben Owen GW from NS matter 2

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)• …

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GW from NS matterBen Owen

Big science: LIGO and Virgo

Images: LIGO/Caltech

4

Image: Virgo

Continuous GW searches

• Crab pulsar (Abbott et al. 2008)– One-timing search: h0 < 3×10-25, ε < 1×10-4, 4% spin-down power

– Range of timings: h0 < 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.)

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Image: Chandra/NASA

Continuous GW emission mechanisms

• Mountains – buried quadrupoles elastically supported• Oscillations – mainly r-modes (Jones’ talk)• Magnetically supported mountains• Magnetic bottling

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ela

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How big can elastic mountains get?

• Standard neutron star (Ushomirsky et al. 2000)– Thin crust, < 1/2 nuclear density: < few10-7

• 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: < few10-4

– 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)

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How big can elastic mountains get?

• Hydrostatic equilibrium tells you (dropping integral sign) Q = R6/(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)

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GW from NS matter 9Ben Owen

Shear modulus

• Energy (density) needed for unit shear strain

• Electrostatics problem (Fuchs 1936)– Homogeneous bcc lattice– m = 0.11q2D6/S4

• Typical inner crust– Spacing S = 30fm– Diameter D = 20fm– Charge 50 (q is density)– m < 1030erg/cm3

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

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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?

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Magnetar flares

• Gamma-ray flares distributed w/Gutenberg-Richter law• B-field ~1015G twists against crust (Duncan & Thompson)• Giant flares up to 1044erg till 2004• Fits 1044erg crust elastic energy

• But then in 2004: flare > 1045erg• Change shear modulus: quarks 1047erg (Owen 2005)• Change breaking strain: 1046erg (Horowitz & Kadau 2009)

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Image: R. Duncan

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 1049erg (Ioka 2001)• Magnetic tension model

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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?

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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

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O’Shaughnessy & Owen (in prep.)