arXiv:0903.2603
(except oscillations)
Ben Owen
PREx @ ECT* Trento August 6, 2009

Ben Owen
• Shear strain h
0
• …is 2 nd t-derivative of quadrupole moment
• Luminosity is square of 3 rd derivative
• Passes through everything! Even horizons!
• Including detectors…
GW from NS matter 2

Astrophysical targets
• Continuous waves
• Magnetar flares
• Pulsar glitches
• Binary mergers
• Supernova core collapse
• Magnetar birth
Ben Owen
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)
• …
GW from NS matter 3

Ben Owen
Images: LIGO/Caltech
GW from NS matter
Image: Virgo
4

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

• Mountains – buried quadrupoles elastically supported
• Oscillations – mainly r-modes (Jones’ talk)
•
• Magnetically supported mountains
Magnetic bottling
Ben Owen GW from NS matter 6

• 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 Owen GW from NS matter 7

• 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 Owen GW from NS matter 8

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

• 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 Owen GW from NS matter 10

• 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 Owen GW from NS matter 11

• 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
Image: R. Duncan
• 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 Owen GW from NS matter 12

• 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 Owen GW from NS matter 13

• 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 Owen GW from NS matter 14

• 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 Owen GW from NS matter 15

O’Shaughnessy & Owen (in prep.)
Ben Owen GW from NS matter 16