Neutron star crust and crust breaking

• Plasma crystals in lab., white dwarfs, and neutron stars.

• MD simulations find breaking strain of crust is very large, even including effects of defects, impurities, and grain boundaries.

• Possible applications of crust breaking: glitches, magnetar flares, mountains and gravitational waves ...

1

Neutron star

JLAB

C. J. Horowitz, Indiana UniversityTransients Workshop, INT, Jul., 2011

Neutron Star

Casey Reed

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Electron screening cloud

How Stars Freeze

Plasma Crystals • Stars are plasmas, however interior of white dwarfs and crust of

neutron stars are so dense that they can freeze.

• Plasma crystals first observed in lab in 1994.

• In stars: plasma consists of ions plus very degenerate (relativistic) electron gas. Electrons slightly screen ion-ion interactions: V(r)=Z2e2/r exp(-r/λ). Electrons give large Thomas Fermi screening length λ.

• Complex (or dusty) plasma can have micron sized microparticles in weakly ionizing gas. Particles acquire large negative charge. Compared to a star:

• λ is shorter (fcc or hcp instead of bcc lattice)

• Also have fluctuating and friction interactions with background gas. In stars, e-ion interactions small because of very large Fermi energy.

• Overall confining potential.

Plasma Crystal on Space Station

Light colors (red, orange) indicate large bond angle metric (fcc, hcp lattice) while blue, green indicate small metric (amorphous)

Complex plasma in microgravity is observed to freeze (center) and melt (right) as control voltage changed.

B. A. Klumov, Physics-Uspekhi, 53, 1053 (2010)

White Dwarf Crystallization• As core of WD freezes, release of

latent heat slows cooling and leads to peak in luminosity function (# of WD stars with given luminosity).

• Freezing T can give info on C/O ratio in core, Phys. Rev. Let. 104, 231101 (2010)

Winget et al. ApJ693(2009)L6

Red: cooling curve with crystallization.Blue, green no latent heat

Luminosity

Globular cluster NGC 6397 (Hubble)

Neutron star crust microphysics• Shear modulus, shear speed• Breaking strain (strength)• Bulk modulus• Shear viscosity• Thermal conductivity• Electrical conductivity• Diffusion coefficients • Heat capacity• Pycnonuclear and electron capture

reaction rates• Phase diagram (melting point and

chemical separation) • ... 9

Casey Reed

Hypothesis

• Neutron star crust is an extremely good crystal that is remarkably free of defects such as vacancies, dislocations, and grain boundaries.

• Because imperfections diffuse very quickly.

• Neutron star crust is a “nearly perfect solid”.

Diffusion in Coulomb Crystals

• Ions in a star are completely pressure ionized. They have soft 1/r interactions. There are no hard cores!

• Diffusion may be much faster than in conventional materials because ions can get by one another.

• Example: quench a liquid configuration of 27648 ions by reducing T by a factor of 2.9. Then evolve amorphous system with MD for long time. System spontaneously crystallizes.

• Fast diffusion suggests WD interiors and neutron star crust are remarkably perfect crystals with few defects.

Amorphous becomes crystalline with MD evolution

arXiv:1104.4822, Phys. Rev. E in press

Diffusion examples

Diffusion in nearly perfect 3456 ion bcc lattice. Large disks are ions that have move more than 1.34a in time 250/plasma frequency

Liquid 27648 ion sample frozen into two micro-crystals. Diffusion mostly along grain boundaries.

Cooling of KS 1730-260 Surface After Extended Outburst

Neutron star cooling in KS 1731–260 5

Figure 2. Theoretical cooling curves for (a) M = 1.6 M! and (b) 1.4 M! neutron stars, and (c) for stars with both M compared withobservations. The curves are explained in Table 1 and in text.

idity can change the core heat capacity and neutrino lu-minosity, but the principal conclusions will be the same.Our calculations are not entirely self-consistent. For in-stance, the surface temperature was inferred from observa-tions (Cackett et al. 2006), assuming neutron star massesand radii di!erent from those used in our cooling models.This inconsistency cannot a!ect our main conclusions, butit would be desirable to infer T"

s for our neutron star mod-els. The thermal relaxation in the quiescent state has beenobserved also (Cackett et al. 2006) for another neutron starX-ray transient, MXB 1659–29. We hope to analyse thesedata in the next publication.

5 ACKNOWLEDGMENTS

We are grateful to A. I. Chugunov, O. Y. Gnedin, K. P.Levenfish and Yu. A. Shibanov for useful discussions, andto the referee, Ulrich Geppert, for valuable remarks. Thework was partly supported by the Russian Foundation forBasic Research (grants 05-02-16245, 05-02-22003), by theFederal Agency for Science and Innovations (grant NSh9879.2006.2), and by the Polish Ministry of Science andHigher Education (grant N20300632/0450). One of the au-thors (P.S.) acknowledges support of the Dynasty Founda-tion and perfect conditions of the Nicolaus Copernicus As-tronomical Center in Warsaw, where this work was partlyperformed. P.H. and A.P. thank the Institute for NuclearTheory at the University of Washington for hospitality andthe U.S. Department of Energy for partial support duringthe completion of this work.

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Sunyaev R. A. et al., 1990, SvA Lett., 16, 59Ushomirsky G., Rutledge R. E., 2001, MNRAS, 325, 1157Wambach J., Ainsworth T. L., Pines D., 1993, Nucl. Phys.A, 555, 128

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Yakovlev D. G., Pethick C. J., 2004, ARA&A, 42, 169Yakovlev D. G., Levenfish K. P., Haensel P., 2003, A&A,407, 265

Yakovlev D. G., Levenfish K. P., Shibanov Yu. A., 1999,Physics–Uspekhi, 42, 737

Yakovlev D. G., Kaminker A. D., Haensel P., Gnedin O. Y.,2001, Physics Reports, 354, 1

Observe cooling of NS crust after heating from accretion stops.

Rutledge et al. suggested cooling would measure crust properties. Also calculations by E. Brown and A. Cumming.

Curves 1-4 use high crust thermal conductivity (regular lattice) while 5 uses low conductivity (amorphous)

Data favor high thermal conductivity crystalline crust.

Shternin et al. 2007

amorphous crust

crystalline crust

Gravitational Waves from Mountains • Strong continuous GW sources (at

LIGO frequencies) place extraordinary demands on neutron rich matter and stress it to the limit.

• Place a mass on a stick and shake vigorously.

• May need both a large mass and a strong stick.

• Let me talk about the strong stick.

• Example: consider a large mountain (red) on a rapidly rotating neutron star. Gravity from the mountain causes space-time to oscillate, radiating gravitational waves. How do you hold the mountain up?

Mountain (red) on rotating neutron star.

Also GW from r modes that depend on damping (shear / bulk viscosity)

Neutron Star Quadrupole Moments and Gravitational Waves

• A solid crust can support a mass quadrupole moment, that on a rapidly rotating NS, efficiently radiates GW.

• Very active ongoing/ future searches for continuous GW at LIGO, Virgo ...

• How big can the quad. moment be? This depends on the strength of the crust (before mountain collapses under extreme gravity of a NS).

• We perform large scale MD simulations of the crust breaking including effects of defects, impurities, and grain boundaries...

• We find neutron star crust is the strongest material known. It is 10 billion times stronger than steel. Very promising for GW searches.

15CJH, Kai Kadau, Phys Rev Let. 102,191102 (2009)

Movie of breaking of 1.7 million ion crystal. Red indicates deformation of lattice.

MD Simulation of Stress vs Strain

• Shear stress vs. system size at a rate of 4 X 10-7 c/fm as calculated with the Scalable Parallel Short ranged Molecular dynamics (SPaSM) code.

• Stress tensor is force per unit area resisting strain (fractional deformation).

• Very long ranged tails of screened coulomb interactions between ions important for strength.

V (r) =Z2e2

re!r/!

Shear Stress vs Strain

• Shear stress versus strain for strain rates of (left to right) 0.125 (black), 0.25 (red), 0.5(green), 1(blue), 2(yellow), 4(brown), 8(gray), 16(violet), and 32(cyan) X10-8 c/fm.

N=9826 pure bcc lattice

Failure Mechanism• Fracture in brittle material such as

silicon involves propagation of cracks that open voids.

• Crack propagating in MD simulation of Silicon. Swadener et al., PRL89 (2002) 085503.

The dislocations and other damage on the crack surfacesresulted in atoms displaced from their lattice positions inthe wake of the crack as shown in Fig. 4. The excess energyassociated with these displaced atoms and surface atomswas calculated by completely relaxing the H ! 147 !Amodel at 0 K after the crack had run completely throughit. Then the energy of the atoms in ten bilayers above andbelow the crack faces was determined for a 100 A longregion where steady crack propagation had occurred. In theabsence of any other dissipation mechanism, the energy inexcess of the bulk potential energy is equal to the dynamicfracture toughness (Jd). A least squares regression of thedata from the H ! 147 !A model determined that Jd in-creased linearly with Js according to: Jd ! 1:15 J=m2 "0:337 Js (regression coefficient, r ! 0:99). Extrapolationof this linear relation to large values indicates Jd thatapproaches #1=3$ Js. Inserting Jd ! #1=3$ Js into Eq. (1)predicts a limiting value of the crack speed equal to#2=3$cR, as observed in the simulations and in agreementwith experimental results [1].

In order to test whether Eq. (1) holds for the stripgeometry, the results for v=cR are plotted versus Jd=Js inFig. 5. Plotted this way, the prediction from Eq. (1) is astraight line, as shown by the solid line in Fig. 5. The datumpoint for the lowest crack speed does not agree with theprediction, because the crack has probably not reachedsteady state. The rest of the data shows approximate agree-ment with Eq. (1).

The strain energy that is not consumed as Jd is convertedinto phonon vibrations. Using the modified SW potential,Hauch et al. [1] determined that most of the strain energywas converted into phonon vibrations during fracture.Gumbsch et al. [19] propose that each bond breaking eventleads to phonon vibrations. For a wide range of dynamicfracture toughness, the current results show that the phononvibration energy is approximately equal to the elastic waveenergy predicted by continuum theory for an infinite body.

This research was funded by the U.S. Department ofEnergy Office of Basic Energy Sciences. The authors

would like to acknowledge helpful discussions with R. G.Hoagland and M. Marder. Computer assistance fromF. Cherne is also acknowledged.

[1] J. A. Hauch, D. Holland, M. P. Marder, and H. L. Swinney,Phys. Rev. Lett. 82, 3823 (1999).

[2] T. Cramer, A. Wanner, and P. Gumbsch, Phys. Rev. Lett.85, 788 (2000).

[3] D. Holland and M. Marder, Phys. Rev. Lett. 80, 746(1998).

[4] D. Holland and M. Marder, Phys. Rev. Lett. 81, 4029(1998).

[5] F. F. Abraham, N. Bernstein, J. Q. Broughton, and D. Hess,Mater. Res. Soc. Bull. 25, 27 (2000).

[6] N. Bernstein and D. Hess, Mater. Res. Soc. Symp. Proc.653, 37 (2001).

[7] M. I. Baskes, Phys. Rev. Lett. 59, 2666 (1987).[8] M. I. Baskes, Phys. Rev. B 46, 2727 (1992).[9] J. J. Gilman, J. Appl. Phys. 31, 2208 (1960).

[10] R. J. Jacodine, J. Electrochem. Soc. 110, 524 (1963).[11] C. P. Chen and M. H. Liepold, Am. Ceram. Soc. Bull. 59,

469 (1980).[12] L. B. Freund, J. Mech. Phys. Solids 20, 129 (1972);

J. Appl. Mech. 39, 1027 (1972); Dynamic FractureMechanics (Cambridge University Press, Cambridge,United Kingdom, 1990).

[13] J. W. Hutchinson and Z. Suo, Adv. Appl. Mech. 29, 63(1992).

[14] S. Nose, Mol. Phys. 52, 255 (1984).[15] W. G. Hoover, Phys. Rev. A 31, 1695 (1985).[16] A. N. Darinskii, Wave Motion 25, 35 (1997).[17] W. G. Knauss, J. Appl. Mech. 33, 356 (1966).[18] J. R. Rice, J. Appl. Mech. 34, 248 (1967).[19] P. Gumbsch, S. J. Zhou, and B. L. Holian, Phys. Rev. B 55,

3445 (1997).

FIG. 5. Normalized crack speed (v=cR) as a function of Jd=Jsfor dynamic fracture in the H ! 147 !A silicon model. Solid lineis the prediction from Eq. (1).

[111]

[211]

FIG. 4. Detail of a crack propagating in the H ! 147 !A siliconmodel for Js ! 13:1 J=m2.

VOLUME 89, NUMBER 8 P H Y S I C A L R E V I E W L E T T E R S 19 AUGUST 2002

085503-4 085503-4

Simulation of neutron star crust with central defect using 1.7 million ions

• Neutron star crust is under great pressure which prevents formation of voids. Crust does not fracture.

Polycrystalline sample (bcc) with 12.8 million ions consisting of 8 differently oriented grains.

Extrapolation to long times

Fit MD results of breaking stress vs strain rate on left to phenomenological model of an activation energy and critical volume for breaking. Extrapolate model to very long times on right.

A. Chugunov, CJH, MNRAS 407, L54 (2010).

Breaking Strain is Large ~0.1• Often conventional materials fail as strain

causes defects to migrate and then collection of defects leads to fracture.

• Plasma crystals in neutron star crust

• Large pressure suppresses formation of vacancies and prevents fracture.

• Most defects diffuse rapidly away.

• Very few remaining defects and these have only a very small impact on the strength.

• Each ion has long range coulomb interactions with thousands of neighbors and is insensitive to a few out of place neighbors. --> Many redundant bounds give great strength.

Gravitational Wave Searches• Can gain sensitivity to weak continuous GW signals by

coherently integrating for long times. Searches are very computationally intensive! Must search over many parameter values: period, period derivative, location on sky...

• Einstein@home uses large # of volunteer computers. Sign up at http://einstein.phys.uwm.edu/

• Interesting neutron stars:– Fast rotating: GW power rapidly increases with frequency.– Large accretion: angular momentum gained from accretion

could be radiated in GW. Explains why fastest NS only spin at about half of breakup rate.

– Young and radio bright: example, direct limit on Crab, GW radiation is less than few % of observed rotational power.

– Unknown: vast majority of NS in galaxy are unknown but potentially observable in GW.

– Unexpected: Low mass NS can have large deformations and be uniquely strong GW sources. Solid quark matter could be even stronger and also support large deformations.

– ... 22

Near Shoemaker images of asteroid 433 Eros

Hubble images of dwarf planet Ceres

Low Mass Neutron Stars• Low mass neutron stars

(maximally deformed) are the answer to the following astro-engineering question: given material with the strength of neutron star crust, construct the strongest possible continuous gravitational wave source (at LIGO frequencies).

23

Ok, hot Jupiters can’t be formed, but doppler shift planet searches are most sensitive to them, so you should search anyway.

Maximum deformation and quadruple moment vs NS mass

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Magnetar Giant Flares and Star Quakes

• Magnetars are neutron stars with 1015 G fields [normal pulsars 1012 G]

• Giant flares are rare, extraordinarily energetic gamma ray bursts from magnetars that are thought to involve crust breaking.

• 27 Dec 2004 flare from SGR 1806-20, 30,000+ light years away.

Curst Breaking Mechanism for Giant Flares• Twisted magnetic field

diffuses and stresses crust.

• Crust breaks and moves allowing magnetic field to reconnect, releasing huge energy observed in giant flares.

• We find the crust is very strong and can control large energy in the magnetic field.

• Possibilities: 1) crust breaks allowing field to reconnect 2) field reconnects and breaks crust 3) field reconnects and does not break crust.

Thompson + Duncan

Glitches and crust breaking

• As star spins down, crust must break.

• What role does breaking of strong crust play in glitches?

• Perhaps some “classical glitches” just from crust breaking? Large but rare because crust so strong??

• Perhaps crust breaking leads to vortex unpinning?

Cracks on planet mercury.

• We performed large scale MD simulations of solids in white dwarfs and NS. Coulomb crystals are likely nearly perfect with few defects.

• We find breaking strain of neutron star crust is very large ~ 0.1 even including the effects of dislocations, impurities, and grain boundaries.

• This large strength can support large mountains that on a rapidly rotating stars will radiate strong gravitational waves.

• Large breaking strain has implications for glitches and magnetar flares.

• Collaborators D. Berry, E. Brown, A. Chugunov, K. Kadau, J. Piekarewicz. Students: L. Caballero, H. Dussan, J. Hughto, J. Mason, A. Schneider, and G. Shen.

• Supported in part by DOE.

28C. J. Horowitz, Indiana University, Transients Workshop, INT, Jul. 2011.

Neutron Star Crust and crust breaking