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The Nuclear of

Exotic Beam Summer School 2015 Tallahassee, FL - August 2015

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 1 / 21 My FSU Collaborators My Outside Collaborators Genaro Toledo-Sanchez B. Agrawal (Saha Inst.) Karim Hasnaoui M. Centelles (U. Barcelona) Bonnie Todd-Rutel G. Colò (U. Milano) Brad Futch C.J. Horowitz (Indiana U.) Jutri Taruna W. Nazarewicz (MSU) Farrukh Fattoyev N. Paar (U. Zagreb) Wei-Chia Chen M.A. Pérez-Garcia (U. Raditya Utama Salamanca) P.G.- Reinhard (U. Erlangen-Nürnberg) X. Roca-Maza (U. Milano) D. Vretenar (U. Zagreb)

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 2 / 21 S. Chandrasekhar and X-Ray Chandra White dwarfs resist gravitational collapse through degeneracy pressure rather than thermal pressure (Dirac and R.H. Fowler 1926) During his travel to graduate school at Cambridge under Fowler, Chandra works out the physics of the relativistic degenerate electron gas in white dwarf stars (at the age of 19!) For in excess of M =1.4 M becomes relativistic and the degeneracy pressure is insufficient to balance the ’s gravitational attraction (P n5/3 n4/3) ∼ → “For a star of small the white-dwarf stage is an initial step towards complete extinction. A star of large mass cannot pass into the white-dwarf stage and one is left speculating on other possibilities” (S. Chandrasekhar 1931) (1919 bending of ) publicly ridiculed Chandra’s on his discovery Awarded the in Physics (in 1983 with W.A. Fowler) In 1999, NASA lunches “Chandra” the premier USA X-ray observatory

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 3 / 21 Some Historical Facts Chandrasekhar shows that massive stars will collapse (1931) Chadwick discovers the neutron (1932) ... predicted earlier by but never published! Baade and Zwicky introduce the concept of neutron stars (1933) Oppenheimer-Volkoff compute masses of neutron stars using GR (1939) Predict M? '0.7 M as maximum NS mass or minimum mass

Jocelyn Bell discovers (1967) and Pacini propose basic lighthouse model (1968) Pulsars are rapidly rotating Neutron Stars!

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 4 / 21 Jocelyn Bell Worked with Anthony Hewish on constructing a radio telescope to study quasars In 1967 as a graduate student (at the age of 24!) detected a bit of “scruff”

Jocelyn Bell discovers amazing regularity in the radio signals( P =1.33730119 s) Speculated that the signal might be from another civilization (LGM-1) Paper announcing the first published in (February 1968) A Hewish, S J Bell, J D H Pilkington, P F Scott, R A Collins Antony Hewish and Martin Ryle awarded the in 1974 The “No-Bell” roundly condemned by many astronomers (Fred Hoyle) “I believe it would demean Nobel Prizes if they were awarded to research students, except in very exceptional cases, and I do not believe this is one of them”

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 5 / 21 Table of Contents 5

Neutron Star Crust: Preface by Jocelyn Bell

Table of Contents

Preface ...... 1 Introduction ...... 3 crust and simulation C. J. Horowitz, J. Hughto, A. Schneider, and D. K. Berry ...... 6 Nuclear in supernovae and neutron stars

Preface 1 G. Watanabe and2JocelynBellBurnell T. Maruyama ...... 26

Terrestrial andthe field, astrophysical both observational andsuperfluidity: theoretical, and identify coldsome of the critical and problems neutron on A. Gezerlis andwhich J. majorCarlson progress may . . .be . expected...... in . the . . next . .. decade...... 48 Dr. Carlos Bertulani’s and Dr. Jorge Piekarewicz’s goal has been to put together a Pairing correlationscomprehensive and review thermodynamic of some of the main theoretical properties ideas related of toinner the structure crust and matter dynamics of neutron stars, with special emphasis on the . I have found J. Margueron andthe idea N. very Sandulescu timely and have gladly . . . accepted . . . . . their . . . invitati . . . .on . . to . write. . .. the . . preface . . . . to. . this ...... 68 Preface The crust ofcollection spinning-down of review articles. neutron stars Ibelievethatthisbookwillhaveawidereadership.Mostarticles are accessible to a R. Negreiros, S.graduate Schramm, student, or to and a non-practitioner F. Weber researcher, . . . . wit . .hout . . much. . . . knowledge ...... of. . the . . field...... 87 Moreover, I expect that this book will become a useful resource for the many established Influence ofpractitioners. the nuclear I hope you symmetry agree with me, find the book enjoyabon thele tostructure read, and useful to and have composition of the Jocelyn Bell Burnell ∗ University of Oxford, Denys Wilkinson Building outer crust on your shelves. Keble Road, Oxford OX1 3RH, UK X. Roca-Maza, J. Piekarewicz, T. Garc´ıa-Galvez,´ and M. Centelles ...... 104 Jocelyn Bell Burnell Equation of stateUniversity for of Oxford -neutron star Ijudgemyselffortunatetobeworkinginanexcitingandfastmoving area January 2012 of science and at a time when the public has become fascinated by questions re- G.Shen ...... 129 garding the birth and evolution of stars, the nature of and dark en- From nuclei to ergy, the formation of black holes and the origin and evolution of the . C.O. Dorso, P.A. G´ımenez-Molinelli, and J.A. Lopez´ ...... 151 The physics of neutron stars is one of these fas- The structure of the neutron star crust within a semi-microscopic func- cinating subjects. Neutron stars are formed in su- pernova explosions of massive stars or by accretion- tional method induced collapse of smaller white dwarf stars. Their existence was confirmed through the discovery of ra- M. Baldo and E.E. Saperstein ...... 171 dio pulsars during my thesis work in 1967. Since The inner crust and its structure then this field has evolved enormously. Today we know of accretion-powered pulsars which are pre- D.P. Menezes, S.S. Avancini, C. Providencia,ˆ and M.D. Alloy ...... 194 dominantly bright X-ray sources, rotation-powered pulsars observed throughout the electromagnetic Neutron-star crusts and finite nuclei , radio-quiet neutron stars, and highly mag- S. Goriely, J. M. Pearson, and N. Chamel ...... 214 netized neutron stars or . No wonder there has been an explosion in the research activity related The nuclear symmetry energy, the inner crust, and global neutron star modeling to neutron stars! W.G. Newton, M. Gearheart, J. Hooker, and Bao-An Li ...... 236 It is now hard to collect in a single book what we already know about neutron stars along with some of Neutron starquakes and the dynamic crust the exciting new developments. In this volume ex- perts have been asked to articulate what they believe A.L.Watts ...... 266 are the critical, open questions in the field. In order for the book to be useful to a more Thermal and transport properties of the neutron star inner crust general audience, the presentations also aim to be as pedagogical as possible. This book is a collection of articles on the neutron stars themselves, written by well- D. Page and S. Reddy ...... 282 known . It is written with young researchers as thetargetaudience,tohelpthis new generation move the field forward. The invited authors summarize the current status of Quantum description of the low-density inner crust: finite size effects and linear re-

∗[email protected] sponse, superfluidity, vortices P. Avogadro, F. Barranco, R.A. Broglia, and E. Vigezzi ...... 309

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 6 / 21 Biography of a Neutron Star: The Crab Pulsar SN 1054 first observed as a new “star” in the sky on July 4, 1054 Event recorded in multiple Chinese and Japanese documents Event also recorded by Anasazi residents of Chaco Canyon, NM Crab nebula and pulsar became the SN remnants Name: PSR B0531+21 Distance: 6,500 ly POB: Taurus Temperature: 106 K Mass: 1.4 M Density: 1014g/cm3 Radius: 10 km Pressure: 1029 atm Period: 33 ms : 1012 G

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 7 / 21 A Grand Challenge: How does subatomic matter organize itself? “Nuclear Physics: Exploring the Heart of Matter” (2010 Committee on the Assessment and Outlook for Nuclear Physics) Consider A and Z in a fixed volume V at T ≡0 ... cold fully catalyzed matter in thermal and chemical equilibrium Enforce charge neutrality = electrons + Enforce chemical (i.e., ) equilibrium: n→p+e− +¯ν; p+e− →n+ν

Impossible to answer such a question under normal laboratory conditions — as such a system is in general unbound!

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 8 / 21 Neutron Stars as Nuclear Physics Gold Mines Neutron Stars are the remnants of massive stellar explosions Are bound by NOT by the strong Satisfy the Tolman-Oppenheimer-Volkoff equation( vesc/c ∼1/2) Only Physics sensitive to: Equation of state of neutron-rich matter EOS must span about 11 orders of magnitude in density Increase from 0.7→2M must be explained byLETTER NuclearRESEARCH Physics!

Received 7 July;dM accepted 1 September 2010. MS0 2 2.5 GR MPA1 = 4 r E(r) ∞ AP3 1. Lattimer, J. M. & Prakash, M. Theπ physics of neutron stars. Science 304, 536–542 < PAL1 P ENG (2004). dr AP4 MS2 2. Lattimer, J. M. & Prakash, M. Neutron star observations: prognosis for equation of  Causality state constraints.dP Phys. Rep. 442, 109–165E(r (2007).)M(r) P(r) 2.0 J1614-2230 3. Glendenning, N. K. &= Schaffner-Bielich,−G J. condensation and1 dynamical+ SQM3 MS1 nucleons in neutron stars. Phys. Rev. Lett. 81, 4564–45672 (1998). J1903+0327 FSU 4. Lackey, B. D.,dr Nayyar, M. & Owen, B. J. Observationalr constraints on hyperonsE in (r) )

( SQM1 PAL6 GM3 neutron stars. Phys. Rev. D 73, 024021 (2006). M 1.5 J1909-3744 5. Schulze, H., Polls, A., Ramos, A. & Vidan3 ˜a, I. Maximum mass of neutron stars. Phys.  1 GS1 − Double neutron sstar systemssy Rev. C 73, 058801 (2006).4πr P(r) 2GM(r)

Mass ( 6. Kurkela, A., Romatschke,1 + P. & Vuorinen, A. Cold matter.1 −Phys. Rev. D 81, 105021 (2010). 1.0 M(r) r 7. Shapiro, I. I. Fourth test of . Phys. Rev. Lett. 13, 789–791 (1964). 8. Jacoby, B. A., Hotan, A., Bailes, M., Ord, S. & Kulkarni, S. R. The mass of a millisecond pulsar. Astrophys. J. 629, L113–L116 (2005). 0.5 9. Verbiest,Need J. P. W. et al. Precision an timing EOS: of PSR J0437–4715:P =P an accurate(E) pulsarrelation Rotation distance, a high pulsar mass, and a limit on the variation of Newton’s gravitational constant. Astrophys. J. 679, 675–680 (2008). 10. Hessels, J. et al. in Binary Radio Pulsars (eds Rasio, F. A. & Stairs, I. H.) 395 (ASP Conf. 0.0 Ser. 328, AstronomicalNuclear Society of the Pacific, Physics 2005). Critical 7 8 9 10 11 12 13 14 15 11. Crawford, F. et al. A survey of 56 midlatitude EGRET error boxes for radio pulsars. Radius (km) Astrophys. J. 652, 1499–1507 (2006). 12. O¨ zel, F., Psaltis, D., Ransom, S., Demorest, P. & Alford, M. The massive pulsar PSR Figure 3 | Neutron star mass–radius diagram. The plot shows non-rotating J161422230: linking , -ray bursts, and mass versus physical radius for several typical EOSs27: blue, nucleons; pink, gravitational wave . Astrophys. J. (in the press). nucleonsJ. plus Piekarewicz ; green, (FSU) matter. The horizontal bands 13.Neutron Hobbs, G. Stars B., Edwards, R. T. & Manchester, R. N. TEMPO2, a new pulsar-timingEBSS 2015 9 / 21 package - I. An overview. Mon. Not. R. . Soc. 369, 655–672 (2006). show the observational constraint from our J1614-2230 mass measurement of 14. Damour, T. & Deruelle, N. General relativistic celestial of binary 8,28 (1.97 6 0.04)M[, similar measurements for two other millisecond pulsars systems. II. The post-Newtonian timing formula. Ann. Inst. Henri Poincare´ Phys. and the range of observed masses for double neutron star binaries2. Any EOS The´or. 44, 263–292 (1986). line that does not intersect the J1614-2230 band is ruled out by this 15. Freire, P. C. C. & Wex, N. The orthometric parameterisation of the Shapiro delay and measurement. In particular, most EOS curves involving exotic matter, such as an improved test of general relativity with binary pulsars. Mon. Not. R. Astron. Soc. kaon condensates or , tend to predict maximum masses well below (in the press). 16. Iben, I. Jr & Tutukov, A. V. On the evolution of close binaries with components of 2.0M[ and are therefore ruled out. Including the effect of neutron star rotation initial mass between 3 solar masses and 12 solar masses. Astrophys. J Suppl. Ser. increases the maximum possible mass for each EOS. For a 3.15-ms period, 58, 661–710 (1985). this is a =2% correction29 and does not significantly alter our conclusions. The 17. O¨ zel, F. Soft equations of state for neutron-star matter ruled out by EXO 0748 - grey regions show parameter space that is ruled out by other theoretical or 676. Nature 441, 1115–1117 (2006). observational constraints2. GR, general relativity; P, spin period. 18. Ransom, S. M. et al. Twenty-one millisecond pulsars in Terzan 5 using the Green Bank Telescope. Science 307, 892–896 (2005). 19. Freire, P. C. C. et al. Eight new millisecond pulsars in NGC 6440 and NGC 6441. Astrophys. J. 675, 670–682 (2008). common feature of models that include the appearance of ‘exotic’ 20. Freire, P. C. C., Wolszczan, A., van den Berg, M. & Hessels, J. W. T. A massive neutron 4,5 3 star in the globular cluster M5. Astrophys. J. 679, 1433–1442 (2008). hadronic matter such as hyperons or kaon condensates at densities 21. Alford,M.etal.:quarkmatterincompactstars?Nature445,E7–E8(2007). of a few times the nuclear saturation density (ns), for example models 22. Lattimer, J. M. & Prakash, M. Ultimate energy density of observable cold baryonic GS1 and GM3 in Fig. 3. Almost all such EOSs are ruled out by our matter. Phys. Rev. Lett. 94, 111101 (2005). 23. Podsiadlowski, P., Rappaport, S. & Pfahl, E. D. Evolutionary sequences for low- and results. Our mass measurement does not rule out condensed quark intermediate-mass X-ray binaries. Astrophys. J. 565, 1107–1133 (2002). matter as a component of the neutron star interior6,21, but it strongly 24. Podsiadlowski, P. & Rappaport, S. Cygnus X-2: the descendant of an intermediate- constrains quark matter model parameters12. For the range of allowed mass X-Ray binary. Astrophys. J. 529, 946–951 (2000). 25. Hotan, A. W., van Straten, W. & Manchester, R. N. PSRCHIVE and PSRFITS: an open EOS lines presented in Fig. 3, typical values for the physical parameters approach to radio pulsar data storage and analysis. Publ. Astron. Soc. Aust. 21, of J1614-2230 are a central baryon density of between 2ns and 5ns and a 302–309 (2004). radius of between 11 and 15 km, which is only 2–3 times the 26. Cordes, J. M. & Lazio, T. J. W. NE2001.I. A new model for the Galactic distribution of free electrons and its fluctuations. Preprint at Æhttp://arxiv.org/abs/astro-ph/ Schwarzschild radius for a 1.97M[ star. It has been proposed that 0207156æ (2002). the Tolman VII EOS-independent analytic solution of Einstein’s 27. Lattimer, J. M. & Prakash, M. Neutron star structure and the equation of state. equations marks an upper limit on the ultimate density of observable Astrophys. J. 550, 426–442 (2001). 22 28. Champion, D. J. et al. An eccentric binary millisecond pulsar in the Galactic plane. cold matter . If this argument is correct, it follows that our mass mea- Science 320, 1309–1312 (2008). surement sets an upper limit on this maximum density of 29. Berti, E., White, F., Maniopoulou, A. & Bruni, M. Rotating neutron stars: an invariant (3.74 6 0.15) 3 1015 g cm23, or ,10n . comparison of approximate and numerical space-time models. Mon. Not. R. s Astron. Soc. 358, 923–938 (2005). Evolutionary models resulting in companion masses .0.4M[ gen- erally predict that the neutron star accretes only a few hundredths of a Supplementary Information is linked to the online version of the paper at www.nature.com/nature. solar mass of material, and result in a mildly recycled pulsar23, that is one with a spin period .8 ms. A few models resulting in orbital para- Acknowledgements P.B.D. is a Jansky Fellow of the National Radio Astronomy 23,24 Observatory. J.W.T.H. is a Veni Fellow of The Netherlands Organisation for Scientific meters similar to those of J1614-2230 predict that the neutron star Research. We thank J. Lattimer for providing the EOS data plotted in Fig. 3, and P. Freire, ¨ could accrete up to 0.2M[, which is still significantly less than the F. Ozel and D. Psaltis for discussions. The National Radio Astronomy Observatory is a >0.6M needed to bring a neutron star formed at 1.4M up to the facility of the US National Science Foundation, operated under cooperative agreement [ [ by Associated Universities, Inc. observed mass of J1614-2230. A possible explanation is that some neutron stars are formed massive (,1.9M ). Alternatively, the trans- Author Contributions All authors contributed to collecting data, discussed the results [ and edited the manuscript. In addition, P.B.D. developed the MCMC code, reduced and fer of mass from the companion may be more efficient than current analysed data, and wrote the manuscript. T.P. wrote the observing proposal and models predict. This suggests that systems with shorter initial orbital created Fig. 3. J.W.T.H. originally discovered the pulsar. M.S.E.R. initiated the survey that periods and lower companion masses—those that produce the vast found the pulsar. S.M.R. initiated the high-precision timing proposal. majority of the fully recycled millisecond pulsar population23—may Author Information Reprints and permissions information is available at experience even greater amounts of mass transfer. In either case, our www.nature.com/reprints. The authors declare no competing financial interests. Readers are welcome to comment on the online version of this article at mass measurement for J1614-2230 suggests that many other milli- www.nature.com/nature. Correspondence and requests for materials should be second pulsars may also have masses much greater than 1.4M[. addressed to P.B.D. ([email protected]).

28 OCTOBER 2010 | VOL 467 | NATURE | 1083 ©2010 Macmillan Publishers Limited. All rights reserved The Anatomy of a Neutron Star (Figures courtesy of Dany Page and Sanjay Reddy) Atmosphere (10 cm): Shape of Thermal ( L=4πσR2T 4) Envelope (100 m): Huge Temperature Gradient (108K ↔106K ) Outer Crust (400 m): crystal of exotic neutron-rich nuclei Inner Crust (1 km): Coulomb frustrated “Nuclear Pasta” Outer Core (10 km): Neutron-rich uniform matter( n, p, e, µ) Inner Core (?): Exotic matter (Hyperons, condensates, quark matter, ...)

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 10 / 21 Bethe-Weizsäcker Mass Formula( circa 1935-36) Nuclear saturate ⇒ equilibrium density Nuclei penalized for developing a surface Nuclei penalized by Coulomb repulsion Nuclei penalized if N 6=Z 2/3 2 1/3 2 B(Z , N) = −avA + asA + acZ /A + aa(N −Z) /A + ... + shell corrections (2, 8, 20, 28, 50, 82, 126, ...)

av '16.0, as '17.2, ac '0.7, aa '23.3 (in MeV) Neutron stars are gravitationally bound!

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 11 / 21 The Composition of the Outer Crust Pearson et al., PRC 83, 065810 (2011) ; Wolf et al., PRL 110, 041101 (2013) Composition emerges from relatively simple dynamics: 4/3 E/Atot = M(N, Z)/A + 3/4Ye kFermi + lattice Subtle competition between electronic and symmetry energy High-precision mass measurements of exotic nuclei are essential!

I NTERNATIONAL JOURNAL OF HIGH-ENERGY PHYSICS CERNCOURIER

WELCOME V OLUME 53 NUMBER 3 A PRIL 2013 CERN Courier – digital edition Welcome to the digital edition of the April 2013 issue of CERN Courier.

Supernova explosions provide a natural laboratory for some interesting nuclear and physics, not least when they leave behind neutron stars, the densest known objects in the cosmos. Conversely, experiments ISOLTRAP casts light in physics laboratories can cast light on the nature of neutron stars, just as the ISOLTRAP collaboration is doing at CERN’s ISOLDE facility, as this on neutron stars month’s cover feature describes. Elsewhere at CERN, the long shutdown of the accelerators has begun and a big effort on maintenance and consolidation has started, not only on the LHC but also at the experiments. At Point 5, work is underway to prepare the CMS detector for the expected improvements to the collider. Meanwhile, the Worldwide LHC Computing Grid continues to provide high-performance computing for the experiments 24 hours a day, while it too undergoes a continual process of improvement.

To sign up to the new issue alert, please visit: http://cerncourier.com/cws/sign-up.

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SN BOSE EXPERIMENTS COMPUTING Kolkata honours How CMS is a great Indian preparing for AT THE LHC EDITOR: CHRISTINE SUTTON, CERN the future Work never stops for DIGITAL EDITION CREATED BY JESSE KARJALAINEN/IOP PUBLISHING, UK p35 p16 the WLCG p21

CERNCOURIER Starquakes—muchWWW. like earthquakes—may be used to probe the V OLUME 53 NUMBER 3 A PRIL 2013 composition of the stellar crust (Steiner, Strohmayer, Watts, ...)

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 12 / 21 The Inner Crust: Nuclear Pasta

Top Layers: Coulomb Crystal of neutron-rich nuclei immersed in e− gas ... and a superfluid neutron vapor (critical for glitches) Bottom Layers: Coulomb Frustration and “Nuclear Pasta” Frustration emerges from a dynamical (or geometrical) competition Impossibility to simultaneously minimize all elementary interactions Emergence of a multitude of competing (quasi-degenerate) ground states Emergence of complex topological shapes “Nuclear Pasta” Universal in complex systems ( low-D , strongly-correlated e−, ...) “In 2D-electron systems with Coulomb interactions, a direct transition—whether first or second order—from a liquid to a crystalline state is forbidden” (Spivak-Kivelson)

Nuclear Pasta may significantly affect transport properties!

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 13 / 21 The EOS of neutron-rich matter: Where do the extra go? h i The EOS of asymmetric matter α≡(N −Z)/A, x ≡(ρ−ρ0 )/3ρ0  1   1  E(ρ, α) ≈ E (ρ) + α2S(ρ) ≈  + K x 2 + J + L x + K x 2 α2 0 0 2 0 2 sym In 208Pb, 82 protons/neutrons form an symmetric spherical core Where do the extra 44 neutrons go? Competition between and density dependence of S(ρ)

Surface tension favors placing them in the core where S(ρ0 ) is large

Symm. energy favors pushing them to the surface where S(ρsurf ) is small

If difference S(ρ0 )−S(ρsurf )∝L is large, then neutrons move to the surface The larger the value of L the thicker the neutron skin of 208Pb

50 208 Rskin =0.12fm 208 Rskin =0.16fm 40 208 Rskin =0.28fm

30 [MeV] )

ρ 20 S(

10

0 0 0.2 0.4 0.6 0.8 1.0 1.2 ρ/ρ 0 J. Piekarewicz (FSU) Neutron Stars EBSS 2015 14 / 21 Relativistic Density Functional Theory: The Control Room

h  gρ e  i L = ψ¯ g φ− g V + τ · b + (1+τ )A γµ ψ int s v µ 2 µ 2 3 µ κ λ ζ    − (g φ)3 − (g φ)4 + g4(V V µ)2 + Λ g2 b · bµ g2V V ν 3! s 4! s 4! v µ v ρ µ v ν

Symmetric 1 2 ESNM = ε0 + 2 K0x + ... Symmetry Energy 1 2 S = J + Lx + 2 Ksymx + ...

Parameters EoS Constrained Ranking gs, gv ρ0, 0 Ground state properties of finite nuclei ? ? ?? gρ J Ground state properties of heavy nuclei ??? κ, λ K0 Isoscalar giant monopole ?? Λv L Neutron radius of heavy nuclei/stellar radii ? ζ — Maximum neutron-star mass ??

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 15 / 21 The Enormous Reach of the Neutron Skin Reinhard-Nazarewicz, PRC 81 (2010) 051303; Fattoyev-Piekarewicz, PRC 86 (2012) 015802; PRC 84 (2011) 064302 Neutron skin as proxy for neutron-star radii ... and more! Calibration of nuclear functional from optimization of a measure Predictions accompanied by meaningful theoretical errors Covariance analysis least biased approach to uncover correlations Neutron skin strongly correlated to a myriad of neutron star properties: Radii, Enhanced Cooling, Moment of , ...

14.5 FSUGold skin 208Pb RNS[0.8] skin 132Sn RNS[1.4] 14 skin 48Ca

] (km) R [0.8] CAB=0.988 NS

sun 13.5 RNS[1.4] Structure

Cooling MDUrca 13 Yt [M/M p Pasta NS t R 12.5 Glitches I [0.8] CAB=0.946 crust L 12 40 50 60 70 80 0 0.2 0.4 0.6 0.8 1 L (MeV) Correlation with skin of 208Pb

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 16 / 21 The Modern Approach: PV in Elastic Electron-Nucleus Donnelly, Dubach, Sick, NPA 503, 589 (1989); Abrahamyan et al., PRL 108, (2012) 112502 Charge () densities known with enormous precision charge density probed via -conserving eA scattering Weak-charge (neutron) densities very poorly known weak-charge density probed via parity-violating eA scattering   G Q2 F (Q2) = √F − 2 − n APV 1 4 sin θW 2  2 2πα | {z } Fp(Q ) 0 ≈

Use parity violation as Z0 couples preferentially to neutrons PV provides a clean measurement of neutron densities (and rn)

up-quark down-quark proton neutron γ-coupling +2/3 −1/3 +1 0 Z0-coupling ≈ +1/3 ≈ −2/3 ≈ 0 −1 2 gv =2tz − 4Q sin θW ≈2tz −Q

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 17 / 21 PREX: The Radius EXperiment Abrahamyan et al., PRL 108, (2012) 112502 Ran for 2 months: April-June 2010 First electroweak observation of a neutron-rich skin in 208Pb 208 Promised a 0.06 fm measurement of Rn ; error 3 times as large!

1 SV-min FSUGold 0.8 PREX

0.6 48Ca (q) w

F 0.4 Fw×10 208Pb 0.2 qCREX

F =0 0 w

0 0.4 0.8 1.2 1.6 q(fm-1) “One of the main science drivers of FRIB is the study of nuclei with neutron skins 3-4 times thicker than is currently possible ... Studies of neutron skins at JLab and FRIB will help pin down the behavior of nuclear matter at densities below twice typical nuclear density” A Physics case for PREX-II, CREX, and ... Coherent ν-nucleus scattering

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 18 / 21 Heaven on Earth: Radius of a M? =1.4 M

Same dynamical origin to neutron skin and NS radius Same pressure creates neutron skin and NS radius Correlation among observables differing by 18 orders of magnitude! NS radius sensitive to the EOS at moderate densities &1.5ρ0 Large neutron skin and small neutron radius? May be evidence in favor of a (quark matter?) The Neutron Star Radius

<11 km (99% conf). 15 +1.3 9.1 1.4 km NL3 14 (90%conf.) Models M-R 13by J. Lattimer FSUGold WFF1=12 Wiring, Fiks (km) and Fabrocini11 (1988)1.4 R phase transition? PREX is a fascinating experiment that uses parity 10 violation to accurately determine the neutron radius in 208Pb. This has broad applications to astrophysics, , atomic parity non- conservation and tests of the . The PREX-II conference will begin with introductory lectures qLMXB and we encourage new comers to attend. 9 For more information contact [email protected]

Topics Organizing Committee Parity Violation Contains Chuck Horowitz (Indiana) Theoretical descriptions of neutron-rich nuclei and 8from: Kees de Jager (JLAB) bulk matter Distance Laboratory measurements of neutron-rich nuclei Jim Lattimer (Stony Brook) and bulk matter All spectral Witold Nazarewicz (UTK, ORNL) parameters Neutron-rich matter in Compact Stars / Astrophysics Jorge Piekarewicz (FSU Calibration0.15 0.20 0.25 0.30 0.35 0.40 Website: http://conferences.jlab.org/PREX Sponsors: Jefferson Lab, JSA 208 Guillot et al (2013) Rskin(fm) Exciting times because of the tension between theory and experiment/observation J. Piekarewicz (FSU) Neutron Stars EBSS 2015 19 / 21 Addressing the Tension ... W.-C. Chen and JP (arXiv:1505.07436) Guillot et al., assumes all neutron stars have a common radius! Assumption on observable MR rather than on EOS One-to-one correspondence between MR and EOS TOV equation + EOS → MR

“Lindblom’s inversion algorithm” proves the inverse [APJ 398, 569 (1992)] TOV equation + MR → EOS Tension in reconciling NS with large masses and small radii Is the resulting EOS causal or superluminal? Stellar radius of 1.4 M must exceed 10.7 km! Astrophysical observations are imposing similar upper limits!

3 1750 R8 R8 R9 R9 2.5 BH R10 1500 R10 P Causality R11 & this work R11 ε L AV14+UVII

FSUGold ) AV14+UVII P=

3 1250 2 FSUGold2 NL3 FSUGarnet Superluminal

sun NL3 1000

1.4 8 9 10 11 13

M/M 750

1 P(MeV/fm 500

0.5 250

0 0 0 250 500 750 1000 1250 1500 1750 6 8 10 12 14 16 18 20 3 R(km) ε(MeV/fm ) J. Piekarewicz (FSU) Neutron Stars EBSS 2015 20 / 21 Conclusions and Outlook: The Physics of Neutron Stars Astrophysics: What is the minimum mass of a black hole? : Pure neutron matter as a Unitary Condensed-Matter Physics: Signatures for the liquid to crystalline state transition? General Relativity: Rapidly rotating neutrons stars as a source of gravitational waves? Nuclear Physics: What are the limits of nuclear existence and the EOS of nuclear matter? : QCD made simple — the CFL phase of dense quark matter QCD MADE SIMPLE uantum chromodynamics, Quantum chromodynamics is to the presence or of Qfamiliarly called QCD, is , very similar to the modern theory of the conceptually simple. Its realization the way respond to .1 Historic- in nature, however, is usually . ally its roots are in nuclear physics and the description of very complex. But not always. and ordinary matter—understand- One class of that ing what protons and neu- carry color charge are the trons are and how they inter- Frank Wilczek quarks. We know of six differ- act. Nowadays QCD is used to ent kinds, or “flavors,” of describe most of what goes on at high-energy accelerators. quarks—denoted u, d, s, c, b, and t, for: up, down, Twenty or even fifteen years ago, this activity was strange, charmed, bottom, and top. Of these, only u and d commonly called “testing QCD.” Such is the success of the quarks play a significant role in the structure of ordinary theory, that we now speak instead of “calculating QCD matter. The other, much heavier quarks are all unstable. backgrounds” for the investigation of more speculative Aquark of any one of the six flavors can also carry a unit phenomena. For example, discovery of the heavy W and Z of any of the three color charges. Although the different that mediate the , or of the flavors all have different masses, the theory is per- quark, would have been a much more difficult and uncer- fectly symmetrical with respect to the three colors. This tain affair if one did not have a precise, reliable under- color symmetry is described by the Lie SU(3). standing of the more common processes governed by Quarks are spin-1/2 point particles, very much like QCD. With regard to things still to be found, search electrons. But instead of electric charge, they carry color strategies for the Higgs particle and for manifestations of charge. To be more precise, quarks carry fractional elec- depend on detailed understanding of pro- tric charge (+ 2e/3 for the u, c, and t quarks, and – e/3 for duction mechanisms and backgrounds calculated by the d, s, and b quarks) in addition to their color charge. means of QCD. For all their similarities, however, there are a few Quantum chromodynamics is a precise and beautiful crucial differences between QCD and QED. First of all, theory. One of this elegance is that the essence the response of gluons to color charge, as measured by the of QCD can be portrayed, without severe distortion, in the QCD coupling constant, is much more vigorous than the few simple pictures at the bottom of the box on the next response of photons to electric charge. Second, as shown page. But first, for comparison, let me remind you that the in the box, in addition to just responding to color charge, essence of (QED), which is a gluons can also change one color charge into another. All generation older than QCD, can be portrayed by the sin- possible changes of this kind are allowed, and yet color gle picture at the top of the box, which represents the charge is conserved. So the gluons themselves must be interaction vertex at which a responds to the pres- able to carry unbalanced color charges. For example, if ence or motion of electric charge.2 This is not just a absorption of a changes a blue quark into a red metaphor. Quite definite and precise algorithms for calcu- quark, then the gluon itself must have carried one unit of lating physical processes are attached to the Feynman red charge and minus one unit of blue charge. graphs of QED, constructed by connecting just such inter- All this would seem to require 3 × 3=9 different action vertices. color gluons. But one particular combination of gluons— In the same pictorial language, QCD appears as an the color-SU(3) singlet—which responds equally to all expanded version of QED. Whereas in QED there is just charges, is different from the rest. We must remove it if one kind of charge, QCD has three different kinds of we are to have a perfectly color-symmetric theory. Then charge, labeled by “color.” Avoiding chauvinism, we might we are left with only 8 physical gluon states (forming a choose red, green, and blue. But, of course, the color color-SU(3) octet). Fortunately, this conclusion is vindicat- charges of QCD have nothing to do with physical colors. ed by experiment! Rather, they have properties analogous to electric charge. The third difference between QCD and QED, which is In particular, the color charges are conserved in all phys- the most profound, follows from the second. Because glu- ical processes, and there are photon-like massless parti- ons respond to the presence and motion of color charge cles, called color gluons, that respond in appropriate ways and they carry unbalanced color charge, it follows that gluons, quite unlike photons, respond directly to one another. Photons, of course, are electrically neutral. FRANKWILCZEK is the J. Robert Oppenheimer Professor of Physics at Therefore the laser sword fights you’ve seen in Star Wars the Institute for Advanced Study in Princeton, New Jersey. Next month wouldn’t work. But it’s a movie about the future, so maybe he moves to Cambridge, Massachusetts, to take up the Herman Feshbach Chair of Physics at the Massachusetts Institute of Technology. they’re using color gluon lasers. We can display QCD even more compactly, in terms of Neutron22 AUGUST 2000 PHYSICS TODAY Stars© 2000 American , are S-0031-9228-0008-010-8 the natural meeting place for fundamental and interesting Physics

J. Piekarewicz (FSU) Neutron Stars EBSS 2015 21 / 21