How high a hill can you make on a neutron star

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How high a hill can you make on a neutron star?

• Ben Owen

Owen PRL 2005 Owen CQG 2006
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Answer ( Outline)

• Higher than we used to think
• Craziest publishable theory 103 x standard
• Not so crazy theory 20 x standard
• What is the standard anyway?
• What does it mean?
• Initial LIGO is interesting, especially with
  upgrade
• A detection is (remotely) possible
• Therefore upper limits will mean something
• Pulsar glitches could come from starquakes again
• Biggest gamma-ray superflare explained

3
What kind of hill?(for GW)

• Quadrupole (lm2 density perturbation)
• Not m0 (centrifugal bulge)
• Not lm100 (Mt Everest)
• Ellipticity e (Ixx-Iyy)/Izz
• Quadrupole / moment of inertia
• Dimensionless number
• Tones down M and R dependence
• Comparable to hill height / radius

4
Three matter models

• Standard neutron star (lowest emax)
• Extrapolated from laboratory nuclei reactions
• Only calculation of ellipticity until recently
• Solid strange quark star (highest emax)
• Suspicious astrophysical phenomenology
• Possible in QCD though seems unlikely
• Not CFL (Alford Rajagopal Wilczek NPB 1999)
• Hybrid star w/solid core (intermediate emax)
• Gradual phase transition of nucleons to quarks
• Generic physical argument meson stars too

5
Standard neutron star (crust)

• Outer crust
• Density lt few x 1011 g/cm3
• N-rich nuclei in lattice
• Electron capture, pycnonuclear reactions
• Effective mass formula, laboratory cross sections
• Inner crust (neutron drip)
• Density lt 1.5 x 1014 g/cm3
• Free neutron fluid coexists
• 3 of M (of star)
• 100 of e

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Crust Monster
Ushomirsky Cutler Bildsten MNRAS 2000

• Chemically detailed crust w/shear modulus m
• Hydrostatic equilibrium (mountains sink)
• Newtonian gravity (including self-gravity)
• All strain in lm2 spherical harmonic
• Breaking strain smax10-2 (not 10-5)
• Result ?max ()msmaxR4/(GM2)
• emax 6 x 10-7
• () encodes structure, could change by 2
• Max. quadrupole 2.4 x 1038 g cm2

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Shear modulus

• Energy (density) stored in unit shear strain
• Electrostatics problem (Fuchs PRoyS 1936) (!)
• Homogeneous bcc lattice
• m ()q2D6/S4
• Typical inner crust
• Spacing S30fm
• Diameter D20fm
• Charge 50 (q is density)
• m lt 1030 erg/cm3

8
Solid strange star

• Strange Bodmer PRD 1971, Witten PRD 1984
• Ground-state matter is strange quark gas?
• Neutron stars become strange stars, R / 2
• Solid strange Xu ApJL 2003 (and ongoing)
• What if LMXB QPO are torsion modes of solid star?
• Fitting QPO frequencies means m 103
• Need quarks to cluster in groups up to 18
• Suspicious origins, but not a priori ruled out
• Result ?max 6 x 10-4
• Mainly due to shear modulus

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Hybrid star
Glendenning PRD 1992

• Nucleon to quark phase transition is gradual (2
  conserved numbers)
• Q droplets in N matter
• Q rods in N matter
• Alternating Q and N slabs
• N rods in Q matter
• N droplets in Q matter
• Mixed phase is solid
• Up to 8km of core
• emax 1 x 10-5

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Gradual phase transition

• Not the usual minimum-pressure criterion
• Nuclear matter has more neutrons than protons,
  costs isospin symmetry energy
• Can make protons if negative charge dumped into
  quark matter blob
• Blobs form lattice due to charge
• Volume fraction is function of pressure
• Size minimizes lattice energy (Coulomb surface)
• Shape (dimension) minimizes lattice energy
• Heiselberg Pethick Staubo PRL 1993

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Pulsar glitches

• 1969 Vela Crab seen to jump in frequency
• Ruderman Nature 1969 proposes crust, quakes
• Baym Pines AnnP 1971 show its not enough
• Glitch energy 1044 erg can be stored in crust,
  barely
• Takes too long to build up strain for another
  glitch
• Vela 108 yr predicted, few yr observed
• Crab 104 yr predicted, 10 yr observed
• The Crab is a solid strange star?
• Time / 103 since m 103

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Soft gamma repeaters

• Neutron stars that flare every few years
• Magnetars (Duncan Thompson ApJL 1992)
• B 1 x 1015 Gauss (spin age, steady x-rays,
  flares)
• Flares (since 1979) up to 1044 erg elastic
  crust
• Burton-Richter power law (earthquakes)
• Magnetic field strains crust, slowly builds,
  crack!
• Dec. 27, 2004 SGR 1806-20 superflare 1046 erg
• OK with large shear modulus
• Also explains lt 1ms rise time
• And excites gravitational waves? (Horvath 2005)

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Gravitational waves

• S2 upper limits (LIGO PRL 2005)
• Best ? few x 10-6 but spindown limit is lower
• Best globular cluster e few x 10-5 (no
  spindown)
• S5 (one year at design)
• Will beat Crab spindown by a few (nebula?)
• S6 (factor 2 upgrade) (Owen CQG 2006)
• Crab can get ? 5 x 10-5 (spindown 7 x 10-4)
• J19523252 ? 9 x 10-5 (spindown 11 x 10-5)
• J0537-6910 ? 9 x 10-5 ( spindown oops!)

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Whats it mean for LIGO?

• Factors of 2 matter
• Moment of inertia (Pitkin CQG 2006)
• Distance, multiple pieces, ?
• Instrument upgrade is good get rid of mystery
  noise
• Detection is possible
• Known pulsars w/initial LIGO only if exotic -
  hard evidence for strange quark stars
• Upper limits are interesting
• Cant rule out strange stars, but accumulate
  evidence (population studies?)

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Wrap

• Star quakes look interesting again (for both
  glitches and gammas)
• LIGO is interesting now - not just 2014
• Its worth doing this in more detail