Neutron Skins in Nuclei31st Annual HUGS Program

(Jorge Piekarewicz - FSU)

Organizing Committee

Chuck Horowitz (Indiana)

Kees de Jager (JLAB)

Jim Lattimer (Stony Brook)

Witold Nazarewicz (UTK, ORNL)

Jorge Piekarewicz (FSU

Sponsors: Jefferson Lab, JSA

PREX is a fascinating experiment that uses parity

violation to accurately determine the neutron

radius in 208Pb. This has broad applications to

astrophysics, nuclear structure, atomic parity non-

conservation and tests of the standard model. The

conference will begin with introductory lectures

and we encourage new comers to attend.

For more information contact horowit@indiana.edu

Topics

Parity Violation

Theoretical descriptions of neutron-rich nuclei and

bulk matter

Laboratory measurements of neutron-rich nuclei

and bulk matter

Neutron-rich matter in Compact Stars / Astrophysics

Website: http://conferences.jlab.org/PREX

Heaven on EarthPREX informing Astrophysics

Outline

1 Historical Context

2 How does matter organize itself?

3 Gravitationally Bound Neutron Stars

4 Anatomy of a Neutron Star

5 The Nuclear Symmetry Energy

6 Laboratory Constraints on the EOS

7 Astrophysical Constraints on the EOS

8 Conclusions and Outlook

J. Piekarewicz (FSU) Neutron Stars Santa Tecla, September 2013 2 / 33

The impact of the neutron skin

of 208Pb on the physics of

neutron stars

Organizing Committee

Chuck Horowitz (Indiana)

Kees de Jager (JLAB)

Jim Lattimer (Stony Brook)

Witold Nazarewicz (UTK, ORNL)

Jorge Piekarewicz (FSU

Sponsors: Jefferson Lab, JSA

PREX is a fascinating experiment that uses parity

violation to accurately determine the neutron

radius in 208Pb. This has broad applications to

astrophysics, nuclear structure, atomic parity non-

conservation and tests of the standard model. The

conference will begin with introductory lectures

and we encourage new comers to attend.

For more information contact horowit@indiana.edu

Topics

Parity Violation

Theoretical descriptions of neutron-rich nuclei and

bulk matter

Laboratory measurements of neutron-rich nuclei

and bulk matter

Neutron-rich matter in Compact Stars / Astrophysics

Website: http://conferences.jlab.org/PREX

Neutron Stars: Unique Cosmic LaboratoriesNeutron stars are the remnants of massive stellar explosions (CCSN)

Bound by gravity — NOT by the strong forceCatalyst for the formation of exotic state of matter Satisfy the Tolman-Oppenheimer-Volkoff equation (vesc /c ~ 1/2)

Only Physics that the TOV equation is sensitive to: Equation of State EOS must span about 11 orders of magnitude in baryon density

Increase from 0.7/ 2 Msun transfers ownership to Nuclear Physics!Predictions on stellar radii differ by several kilometers!

Neutron Stars as Nuclear Physics Gold MinesNeutron Stars are the remnants of massive stellar explosions

Are bound by gravity NOT by the strong forceSatisfy the Tolman-Oppenheimer-Volkoff equation (v

esc

/c⇠1/2)Only Physics sensitive to: Equation of state of neutron-rich matter

EOS must span about 11 orders of magnitude in baryon densityIncrease from 0.7!2M� must be explained by Nuclear Physics!

common feature of models that include the appearance of ‘exotic’hadronic matter such as hyperons4,5 or kaon condensates3 at densitiesof a few times the nuclear saturation density (ns), for example modelsGS1 and GM3 in Fig. 3. Almost all such EOSs are ruled out by ourresults. Our mass measurement does not rule out condensed quarkmatter as a component of the neutron star interior6,21, but it stronglyconstrains quark matter model parameters12. For the range of allowedEOS lines presented in Fig. 3, typical values for the physical parametersof J1614-2230 are a central baryondensity of between 2ns and 5ns and aradius of between 11 and 15 km, which is only 2–3 times theSchwarzschild radius for a 1.97M[ star. It has been proposed thatthe Tolman VII EOS-independent analytic solution of Einstein’sequations marks an upper limit on the ultimate density of observablecold matter22. If this argument is correct, it follows that our mass mea-surement sets an upper limit on this maximum density of(3.746 0.15)3 1015 g cm23, or ,10ns.Evolutionary models resulting in companion masses.0.4M[ gen-

erally predict that the neutron star accretes only a few hundredths of asolar mass of material, and result in a mildly recycled pulsar23, that isone with a spin period.8ms. A few models resulting in orbital para-meters similar to those of J1614-223023,24 predict that the neutron starcould accrete up to 0.2M[, which is still significantly less than the>0.6M[ needed to bring a neutron star formed at 1.4M[ up to theobserved mass of J1614-2230. A possible explanation is that someneutron stars are formed massive (,1.9M[). Alternatively, the trans-fer of mass from the companion may be more efficient than currentmodels predict. This suggests that systems with shorter initial orbitalperiods and lower companion masses—those that produce the vastmajority of the fully recycled millisecond pulsar population23—mayexperience even greater amounts of mass transfer. In either case, ourmass measurement for J1614-2230 suggests that many other milli-second pulsars may also have masses much greater than 1.4M[.

Received 7 July; accepted 1 September 2010.

1. Lattimer, J. M. & Prakash, M. The physics of neutron stars. Science 304, 536–542(2004).

2. Lattimer, J. M. & Prakash, M. Neutron star observations: prognosis for equation ofstate constraints. Phys. Rep. 442, 109–165 (2007).

3. Glendenning, N. K. & Schaffner-Bielich, J. Kaon condensation and dynamicalnucleons in neutron stars. Phys. Rev. Lett. 81, 4564–4567 (1998).

4. Lackey, B. D., Nayyar, M. & Owen, B. J. Observational constraints on hyperons inneutron stars. Phys. Rev. D 73, 024021 (2006).

5. Schulze, H., Polls, A., Ramos, A. & Vidana, I. Maximummass of neutron stars. Phys.Rev. C 73, 058801 (2006).

6. Kurkela, A., Romatschke, P. & Vuorinen, A. Cold quark matter. Phys. Rev. D 81,105021 (2010).

7. Shapiro, I. I. Fourth test of general relativity. Phys. Rev. Lett. 13, 789–791 (1964).8. Jacoby, B.A., Hotan, A., Bailes,M., Ord, S. &Kulkarni, S.R. Themassof amillisecond

pulsar. Astrophys. J. 629, L113–L116 (2005).9. Verbiest, J. P. W. et al. Precision timing of PSR J0437–4715: an accurate pulsar

distance, a high pulsarmass, and a limit on the variation of Newton’s gravitationalconstant. Astrophys. J. 679, 675–680 (2008).

10. Hessels, J.et al. inBinaryRadio Pulsars (edsRasio, F. A.&Stairs, I. H.)395 (ASPConf.Ser. 328, Astronomical Society of the Pacific, 2005).

11. Crawford, F. et al. A survey of 56midlatitude EGRET error boxes for radio pulsars.Astrophys. J. 652, 1499–1507 (2006).

12. Ozel, F., Psaltis, D., Ransom, S., Demorest, P. & Alford, M. The massive pulsar PSRJ161422230: linking quantum chromodynamics, gamma-ray bursts, andgravitational wave astronomy. Astrophys. J. (in the press).

13. Hobbs, G. B., Edwards, R. T. & Manchester, R. N. TEMPO2, a new pulsar-timingpackage - I. An overview.Mon. Not. R. Astron. Soc. 369, 655–672 (2006).

14. Damour, T. & Deruelle, N. General relativistic celestial mechanics of binarysystems. II. The post-Newtonian timing formula. Ann. Inst. Henri Poincare Phys.Theor. 44, 263–292 (1986).

15. Freire, P.C.C.&Wex,N.Theorthometricparameterisationof theShapirodelay andan improved test of general relativity with binary pulsars.Mon. Not. R. Astron. Soc.(in the press).

16. Iben, I. Jr & Tutukov, A. V. On the evolution of close binaries with components ofinitial mass between 3 solar masses and 12 solar masses. Astrophys. J Suppl. Ser.58, 661–710 (1985).

17. Ozel, F. Soft equations of state for neutron-star matter ruled out by EXO 0748 -676. Nature 441, 1115–1117 (2006).

18. Ransom, S. M. et al. Twenty-one millisecond pulsars in Terzan 5 using the GreenBank 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).

20. Freire, P. C. C.,Wolszczan, A., vandenBerg,M.&Hessels, J.W. T. Amassiveneutronstar in the globular cluster M5. Astrophys. J. 679, 1433–1442 (2008).

21. Alford,M.etal.Astrophysics:quarkmatterincompactstars?Nature445,E7–E8(2007).22. Lattimer, J. M. & Prakash, M. Ultimate energy density of observable cold baryonic

matter. Phys. Rev. Lett. 94, 111101 (2005).23. Podsiadlowski, P., Rappaport, S. & Pfahl, E. D. Evolutionary sequences for low- and

intermediate-mass X-ray binaries. Astrophys. J. 565, 1107–1133 (2002).24. Podsiadlowski, P. & Rappaport, S. CygnusX-2: the descendant of an intermediate-

mass X-Ray binary. Astrophys. J. 529, 946–951 (2000).25. Hotan, A.W., van Straten,W. &Manchester, R. N. PSRCHIVE andPSRFITS: an open

approach to radio pulsar data storage and analysis. Publ. Astron. Soc. Aust. 21,302–309 (2004).

26. Cordes, J.M. & Lazio, T. J.W.NE2001.I. A newmodel for theGalactic distribution offree electrons and its fluctuations. Preprint at Æhttp://arxiv.org/abs/astro-ph/0207156æ (2002).

27. Lattimer, J. M. & Prakash, M. Neutron star structure and the equation of state.Astrophys. J. 550, 426–442 (2001).

28. Champion, D. J. et al. An eccentric binary millisecond pulsar in the Galactic plane.Science 320, 1309–1312 (2008).

29. Berti, E., White, F., Maniopoulou, A. & Bruni, M. Rotating neutron stars: an invariantcomparison of approximate and numerical space-time models.Mon. Not. R.Astron. Soc. 358, 923–938 (2005).

Supplementary Information is linked to the online version of the paper atwww.nature.com/nature.

Acknowledgements P.B.D. is a Jansky Fellow of the National Radio AstronomyObservatory. J.W.T.H. is a Veni Fellow of The Netherlands Organisation for ScientificResearch.We thankJ. Lattimer for providing theEOSdataplotted inFig. 3, andP. Freire,F. Ozel and D. Psaltis for discussions. The National Radio Astronomy Observatory is afacility of the USNational Science Foundation, operated under cooperative agreementby Associated Universities, Inc.

Author Contributions All authors contributed to collecting data, discussed the resultsand edited themanuscript. In addition, P.B.D. developed theMCMCcode, reduced andanalysed data, and wrote the manuscript. T.P. wrote the observing proposal andcreated Fig. 3. J.W.T.H. originally discovered thepulsar.M.S.E.R. initiated the survey thatfound the pulsar. S.M.R. initiated the high-precision timing proposal.

Author Information Reprints and permissions information is available atwww.nature.com/reprints. The authors declare no competing financial interests.Readers are welcome to comment on the online version of this article atwww.nature.com/nature. Correspondence and requests for materials should beaddressed to P.B.D. (pdemores@nrao.edu).

0.07 8 9 10 11

Radius (km)12 13 14 15

0.5

1.0

1.5

2.0

AP4

J1903+0327

J1909-3744

systemsDouble neutron sDouble neutron star sysy

J1614-2230

AP3

ENG

MPA1

GM3

GS1

PAL6

FSUSQM3

SQM1

PAL1

MS0

MS2

MS1

2.5 GR

Causality

Rotation

P < ∞

Mass

(M

()

Figure 3 | Neutron star mass–radius diagram. The plot shows non-rotatingmass versus physical radius for several typical EOSs27: blue, nucleons; pink,nucleons plus exoticmatter; green, strange quarkmatter. The horizontal bandsshow the observational constraint from our J1614-2230 mass measurement of(1.976 0.04)M[, similar measurements for two other millisecond pulsars8,28

and the range of observed masses for double neutron star binaries2. Any EOSline that does not intersect the J1614-2230 band is ruled out by thismeasurement. In particular, most EOS curves involving exotic matter, such askaon condensates or hyperons, tend to predict maximum masses well below2.0M[ and are therefore ruled out. Including the effect of neutron star rotationincreases themaximum possiblemass for each EOS. For a 3.15-ms spin period,this is a=2% correction29 and does not significantly alter our conclusions. Thegrey regions show parameter space that is ruled out by other theoretical orobservational constraints2. GR, general relativity; P, spin period.

LETTER RESEARCH

2 8 O C T O B E R 2 0 1 0 | V O L 4 6 7 | N A T U R E | 1 0 8 3

Macmillan Publishers Limited. All rights reserved©2010

dMdr

= 4⇡r2E(r)

dPdr

= �GE(r)M(r)

r2

1 +

P(r)E(r)

�

1 +

4⇡r3P(r)M(r)

� 1 � 2GM(r)

r

��1

Need an EOS: P=P(E) relation

Nuclear Physics Critical

J. Piekarewicz (FSU) Neutron Stars Mazurian Lakes 2015 4 / 15

The Equation of State of Neutron-Rich MatterThe EOS of asymmetric matter: a=(N-Z)/A; x=(r-r0)/3r0; T=0

r0 x0.15 fm-3 — saturation density 4 nuclear density

Symmetric nuclear matter saturates: e0 x-16 MeV — binding energy per nucleon 4 nuclear massesK0x230 MeV — nuclear incompressibility 4 nuclear “breathing” mode

Density dependence of symmetry poorly constrained: J x30 MeV — symmetry energy 4 masses of neutron-rich nucleiLx? — symmetry slope 4 neutron skin (Rn-Rp) of heavy nuclei ?

E(⇢,↵) ' E0(⇢) + ↵

2S(⇢) '⇣✏0 +

1

2K0x

2⌘+

⇣J + Lx+

1

2Ksymx

2⌘↵

2

0 2 4 6 8 10r (fm)

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

ρ(fm

-3)

ExperimentRskin=0.176 fmRskin=0.207 fmRskin=0.235 fmRskin=0.260 fmRskin=0.286 fm

-ρweak

ρcharge

208Pb

Bayes’ Theorem Thomas Bayes (1701-1761)

A simple example: “False Positives”A: Individual is infected with the HIV virusB: Individual tests positive to HIV test

The priors and the likelihood P(A) = 1/200 (“prior” knowledge; 0.5% of population is infected)P(B|A) = 98/100 (likelihood of the evidence; accuracy of test)P(B) = (1/200)*(98/100)+(199/200)*(2/100) = 496/(100*200)

The odds: the posterior probabilityP(A|B) = 49/248 x 20% (odds have increased from 0.5% but still very far away from 98%)

P (A|B) =P (B|A)P (A)

P (B)

Bayes’ Theorem: Application to Model Building

P (M |D) =P (D|M)P (M)

P (D)

PriorPosterior

LikelihoodMarginal

Likelihood

QCD is the fundamental theory of the strong interactions!M: A theoretical MODEL with parameters and biasesD: A collection of experimental and observational DATA

The Prior P(M): An insightful transformation in DFT

The Likelihood P(D|M)xexp(-c2/2)

The Marginal Likelihood; overall normalization factor

(gs, gv, g⇢,,�,⇤v) () (⇢0, ✏0,M⇤,K, J, L)

�2(D,M) =NX

n=1

⇣O

(th)

n (M)�O(exp)

n (D)⌘2

�O2

n

PHYSICAL REVIEW C 90, 044305 (2014)

Building relativistic mean field models for finite nuclei and neutron stars

Wei-Chia Chen* and J. Piekarewicz†

Department of Physics, Florida State University, Tallahassee, Florida 32306, USA(Received 18 August 2014; published 7 October 2014)

Background: Theoretical approaches based on density functional theory provide the only tractable method toincorporate the wide range of densities and isospin asymmetries required to describe finite nuclei, infinite nuclearmatter, and neutron stars.Purpose: A relativistic energy density functional (EDF) is developed to address the complexity of such diversenuclear systems. Moreover, a statistical perspective is adopted to describe the information content of variousphysical observables.Methods: We implement the model optimization by minimizing a suitably constructed χ2 objective functionusing various properties of finite nuclei and neutron stars. The minimization is then supplemented by a covarianceanalysis that includes both uncertainty estimates and correlation coefficients.Results: A new model, “FSUGold2,” is created that can well reproduce the ground-state properties of finite nuclei,their monopole response, and that accounts for the maximum neutron-star mass observed up to date. In particular,the model predicts both a stiff symmetry energy and a soft equation of state for symmetric nuclear matter,suggesting a fairly large neutron-skin thickness in 208Pb and a moderate value of the nuclear incompressibility.Conclusions: We conclude that without any meaningful constraint on the isovector sector, relativistic EDFswill continue to predict significantly large neutron skins. However, the calibration scheme adopted here isflexible enough to create models with different assumptions on various observables. Such a scheme—properlysupplemented by a covariance analysis—provides a powerful tool to identify the critical measurements requiredto place meaningful constraints on theoretical models.

DOI: 10.1103/PhysRevC.90.044305 PACS number(s): 21.60.Jz, 21.65.Cd, 21.65.Mn

I. INTRODUCTION

Finite nuclei, infinite nuclear matter, and neutron stars arecomplex, many-body systems governed largely by the strongnuclear force. Although quantum chromodynamics (QCD) isthe fundamental theory of the strong interaction, enormouschallenges have prevented us from solving the theory in thenonperturbative regime of relevance to nuclear systems. Todate, these complex systems can be investigated only in theframework of an effective theory with appropriate degrees offreedom. Among the effective approaches, the one based ondensity functional theory (DFT) is most promising, as it is theonly microscopic approach that may be applied to the entirenuclear landscape and to neutron stars. In the past decades nu-merous energy density functionals (EDFs) have been proposedwhich can be grouped into two main branches: nonrelativisticand relativistic. Skyrme-type functionals are the most popularones within the nonrelativistic domain, where nucleons inter-act via density-dependent effective potentials. Using such aframework, the Universal Nuclear Energy Density Functional(UNEDF) Collaboration [1] aims to achieve a comprehensiveunderstanding of finite nuclei and the reactions involving them[2–4]. On the other end, relativistic mean field (RMF) models,based on a quantum field theory having nucleons interactingvia the exchange of various mesons, have been successfullyused since the 1970s and provide a covariant description ofboth infinite nuclear matter and finite nuclei [5–10].

*wc09c@my.fsu.edu†jpiekarewicz@fsu.edu

In the traditional spirit of effective theories, both nonrel-ativistic and relativistic EDFs are calibrated from nuclearexperimental data that is obtained under normal laboratoryconditions, namely, at or slightly below nuclear saturationdensity and with small to moderate isospin asymmetries.The lack of experimental data at both higher densities andwith extreme isospin asymmetries leads to a large spreadin the predictions of the models, even when they may allbe calibrated to the same experimental data. Consequently,fundamental nuclear properties, such as the neutron densityof medium-to-heavy nuclei [11–14], proton and neutron driplines [15,16], and a variety of neutron-star properties [17–19],remain largely undetermined.

It has been a common practice for a long time to supplementexperimental results with uncertainty estimates. Indeed, noexperimental measurement could ever be published withoutproperly estimated “error bars.” Often, the most difficult partof an experiment is a reliable quantification of systematicerrors, and improving the precision of the measurementconsists of painstaking efforts at reducing the sources of suchuncertainties. On the contrary, theoretical predictions merelyinvolve reporting a “central value” without any information onthe uncertainties inherent in the formulation or the calculation.Thus, to determine whether a theory is successful or not, theonly required criterion is to reproduce the experimental data.Although this approach has certain value—especially if theexamined model reproduces a vast amount of experimentaldata—such a criterion is often neither helpful nor meaningful.The situation becomes even worse if the predictions of aneffective theory are extrapolated into unknown regions, suchas the boundaries of the nuclear landscape and the interior

0556-2813/2014/90(4)/044305(17) 044305-1 ©2014 American Physical Society

Searching for L: The StrategyPPNM xLr0 /3 is not a physical observable

Establish a powerful physical argument connecting L to Rskin Where do the extra 44 neutrons in 208Pb go? Competition between surface tension and the difference S(r0)-S(rsurf)xL. The larger the value of L, the thicker the neutron skin of 208Pb

Ensure that “your” accurately-calibrated DFT supports the correlation Statistical Uncertainty: Theoretical error bars and correlation coefficientsWhat precision in Rskin is required to constrain L to the desire accuracy?

Ensure that “all” accurately-calibrated DFT support the correlation Systematic Uncertainty: As with all systematic errors, much harder to quantify

(… “all models are equal but some models are more equal than others”)

v090MSk7

HFB-8SkP

HFB-17SkM

*DD-M

E2DD-M

E1FSUGoldDD-PC1Ska

PK1.s24Sk-Rs

NL3.s25Sk-T4G2

NL-SV2PK1NL3

NL3*NL2

NL1

0 50 100 150 L(MeV)

0.1

0.2

0.3

Rsk

in20

8(fm

)

Linear Fit, r = 0.979Mean Field

D1S

D1NSGII

Sk-T6SkX SLy5

SLy4

MSkA

MSL0

SIVSkSM

*SkM

P

SkI2SV

G1

TM1

NL-SHNL-RA1

PC-F1

BCP

RHF-PKO3Sk-GsRHF-PKA1

PC-PK1

SkI5

PREX-II

S-PREX

(63±16)Roca-Maza et al.

PRL106,252501(2011)

40 50 60 70 80L (MeV)

0.18

0.2

0.22

0.24

R ski

n[20

8 Pb] (

fm) 6L/2

lAB=0.995

6Lmin=1.18 MeV

0.01

5 fm

New era in Nuclear Theory

where predictability will be

typical and uncertainty

quantification will bedemanded …

Theory Informing ExperimentPREX@JLAB: First electroweak evidence in favor of Rskin in Pb (error bars too large!)

Precision required in the determination of the neutron radius/skin?

As precisely as “humanly possible” - fundamental nuclear structure property (cf. charge density) To strongly impact Astrophysics?

Is there a need for a systematic study over “many” nuclei?PREX, CREX, SREX, ZREX, …

Is there a need for more than one q-point? Radius and diffuseness … or the whole form factor?

0.0 0.5 1.0 1.5 2.0q (fm-1)

10-4

10-3

10-2

10-1

100

|F c(q

)|

Exp.rskin=0.176 fmrskin=0.207 fmrskin=0.235 fmrskin=0.260 fmrskin=0.286 fm

Rch=5.5012(13) fm

0.0 0.5 1.0 1.5 2.0q (fm-1)

10-3

10-2

10-1

100

|F wea

k(q)

|

PREXrskin=0.176 fmrskin=0.207 fmrskin=0.235 fmrskin=0.260 fmrskin=0.286 fm

Rwk=5.826(181) fm

These questions were just addressed at the MITP Program “Neutron Skins of Nuclei”

Mainz, May 17-27, 2016

Heaven and Earth The enormous reach of the neutron skin

Neutron-star radii are sensitive to the EOS near 2r0Neutron star masses sensitive to EOS at much higher density

Neutron skin correlated to a host of neutron-star propertiesStellar radii, proton fraction, enhanced cooling, moment of inertia

We are at a dawn of a new era … the train has left the station Predictability typical and uncertainty quantification demanded!

40 50 60 70 80L (MeV)

12

12.5

13

13.5

14

14.5

RN

S [M

/Msu

n] (k

m)

RNS[0.8]RNS[1.4]

CAB=0.988

FSUGold

CAB=0.946

0 0.2 0.4 0.6 0.8 1Correlation with skin of 208Pb

skin 132Sn

RNS[0.8]RNS[1.4]

skin 48Ca

lt

skin 208Pb

L

Ypt

MDUrca

Icrust[0.8]

Stru

ctur

ePa

sta

Cooling

Glitches

PHYSICAL REVIEW A 83, 040001 (2011)

Editorial: Uncertainty Estimates

Papers presenting the results of theoretical

calculations are expected to include

uncertainty estimates for the calculations

whenever practicable …

Have We Discovered Quark Stars?

Enhanced vs Minimal Cooling of Neutron Stars: Quark Stars?Core-collapse supernovae generates hot (proto) neutron star T '1012

K

Neutron stars cool promptly by ⌫-emission (URCA) n! p + e� + ⌫e . . .

Direct URCA process cools down the star until T '109K

Inefficient modified URCA takes over (n) + n! (n) + p + e� + ⌫e . . .

Neutrino “enhanced” cooling possible in exotic quark matter

Unless ... symmetry energy is stiff: large Yp , large neutron skin

J. Piekarewicz (FSU) Neutron-Rich Nuclei in Heaven and Earth CSM-2008 17 / 23

Have We Discovered Quarks Stars?

0.16 0.2 0.24 0.28

Rn-Rp (fm)

0.5

1

1.5

2

2.5

3

M!U

rca (M

sun

)

FSU-likeNL3-likeNLC-like

Threshold Direct Urca Mass

Max

imu

m M

ass

Experiment/Obervation (assumed!)

Assume Rn � Rp . 0.18 fm and M(3C58) . 1.3M�Then the pulsar in 3C58 may indeed be a quark starJ. Piekarewicz (FSU) Neutron-Rich Nuclei in Heaven and Earth CSM-2008 18 / 23

George Gamow andURCA cooling

George Gamow and URCA Cooling?URCA is not an acronym but rather, the name of a Casino in Rio de Janeiro where George Gamow commented to the Brazilian astrophysicist Mario Schonberg: “The energy disappears in the nucleus of the supernova as quickly as the money disappears at the roulette table”

In Gamow’s Russian dialect, “urca” also means a pickpocket, someone that can steel your money in a matter of seconds!

URCA Casino, Rio de Janeiro

Addressing Future ChallengesSame dynamical origin to neutron skin and NS radius

Same pressure pushes against surface tension and gravity!Correlation involves quantities differing by 18 orders of magnitude!NS radius may be constrained in the laboratory (PREX-II, CREX, …)

However, a significant tension has recently emerged! Stunning observations have established the existence of massive NSRecent observations has suggested that NS have small radiiExtremely difficult to reconcile both; perhaps evidence of a phase transition?

Time delay due to NS radiation dipping into gravitational well of WD!

The Neutron Star Radius

9.1+1.3�1.4 km

(90%conf.)

Guillot et al (2013)

<11 km (99% conf).

M-R by J. Lattimer

WFF1=Wiring, Fiks

and Fabrocini (1988)

Contains uncertainties from:

DistanceAll spectral parametersCalibration

WFF1 violates causality!

"We have detected gravitational waves. We did it"

David Reitze, February 11, 2016

The dawn of gravitational wave astronomy Initial black hole masses are 36 and 29 solar massesFinal black hole mass is 62 solar masses, 3 solar masses radiated in GW

properties of space-time in the strong-field, high-velocityregime and confirm predictions of general relativity for thenonlinear dynamics of highly disturbed black holes.

II. OBSERVATION

On September 14, 2015 at 09:50:45 UTC, the LIGOHanford, WA, and Livingston, LA, observatories detected

the coincident signal GW150914 shown in Fig. 1. The initialdetection was made by low-latency searches for genericgravitational-wave transients [41] and was reported withinthree minutes of data acquisition [43]. Subsequently,matched-filter analyses that use relativistic models of com-pact binary waveforms [44] recovered GW150914 as themost significant event from each detector for the observa-tions reported here. Occurring within the 10-ms intersite

FIG. 1. The gravitational-wave event GW150914 observed by the LIGO Hanford (H1, left column panels) and Livingston (L1, rightcolumn panels) detectors. Times are shown relative to September 14, 2015 at 09:50:45 UTC. For visualization, all time series are filteredwith a 35–350 Hz bandpass filter to suppress large fluctuations outside the detectors’ most sensitive frequency band, and band-rejectfilters to remove the strong instrumental spectral lines seen in the Fig. 3 spectra. Top row, left: H1 strain. Top row, right: L1 strain.GW150914 arrived first at L1 and 6.9þ0.5

−0.4 ms later at H1; for a visual comparison, the H1 data are also shown, shifted in time by thisamount and inverted (to account for the detectors’ relative orientations). Second row: Gravitational-wave strain projected onto eachdetector in the 35–350 Hz band. Solid lines show a numerical relativity waveform for a system with parameters consistent with thoserecovered from GW150914 [37,38] confirmed to 99.9% by an independent calculation based on [15]. Shaded areas show 90% credibleregions for two independent waveform reconstructions. One (dark gray) models the signal using binary black hole template waveforms[39]. The other (light gray) does not use an astrophysical model, but instead calculates the strain signal as a linear combination ofsine-Gaussian wavelets [40,41]. These reconstructions have a 94% overlap, as shown in [39]. Third row: Residuals after subtracting thefiltered numerical relativity waveform from the filtered detector time series. Bottom row:A time-frequency representation [42] of thestrain data, showing the signal frequency increasing over time.

PRL 116, 061102 (2016) P HY S I CA L R EV I EW LE T T ER S week ending12 FEBRUARY 2016

061102-2

Observation of Gravitational Waves from a Binary Black Hole Merger

B. P. Abbott et al.*

(LIGO Scientific Collaboration and Virgo Collaboration)(Received 21 January 2016; published 11 February 2016)

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-WaveObservatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards infrequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0 × 10−21. It matches the waveformpredicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of theresulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and afalse alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greaterthan 5.1σ. The source lies at a luminosity distance of 410þ160

−180 Mpc corresponding to a redshift z ¼ 0.09þ0.03−0.04 .

In the source frame, the initial black hole masses are 36þ5−4M⊙ and 29þ4

−4M⊙, and the final black hole mass is62þ4

−4M⊙, with 3.0þ0.5−0.5M⊙c2 radiated in gravitational waves. All uncertainties define 90% credible intervals.

These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first directdetection of gravitational waves and the first observation of a binary black hole merger.

DOI: 10.1103/PhysRevLett.116.061102

I. INTRODUCTION

In 1916, the year after the final formulation of the fieldequations of general relativity, Albert Einstein predictedthe existence of gravitational waves. He found thatthe linearized weak-field equations had wave solutions:transverse waves of spatial strain that travel at the speed oflight, generated by time variations of the mass quadrupolemoment of the source [1,2]. Einstein understood thatgravitational-wave amplitudes would be remarkablysmall; moreover, until the Chapel Hill conference in1957 there was significant debate about the physicalreality of gravitational waves [3].Also in 1916, Schwarzschild published a solution for the

field equations [4] that was later understood to describe ablack hole [5,6], and in 1963 Kerr generalized the solutionto rotating black holes [7]. Starting in the 1970s theoreticalwork led to the understanding of black hole quasinormalmodes [8–10], and in the 1990s higher-order post-Newtonian calculations [11] preceded extensive analyticalstudies of relativistic two-body dynamics [12,13]. Theseadvances, together with numerical relativity breakthroughsin the past decade [14–16], have enabled modeling ofbinary black hole mergers and accurate predictions oftheir gravitational waveforms. While numerous black holecandidates have now been identified through electromag-netic observations [17–19], black hole mergers have notpreviously been observed.

The discovery of the binary pulsar systemPSR B1913þ16by Hulse and Taylor [20] and subsequent observations ofits energy loss by Taylor and Weisberg [21] demonstratedthe existence of gravitational waves. This discovery,along with emerging astrophysical understanding [22],led to the recognition that direct observations of theamplitude and phase of gravitational waves would enablestudies of additional relativistic systems and provide newtests of general relativity, especially in the dynamicstrong-field regime.Experiments to detect gravitational waves began with

Weber and his resonant mass detectors in the 1960s [23],followed by an international network of cryogenic reso-nant detectors [24]. Interferometric detectors were firstsuggested in the early 1960s [25] and the 1970s [26]. Astudy of the noise and performance of such detectors [27],and further concepts to improve them [28], led toproposals for long-baseline broadband laser interferome-ters with the potential for significantly increased sensi-tivity [29–32]. By the early 2000s, a set of initial detectorswas completed, including TAMA 300 in Japan, GEO 600in Germany, the Laser Interferometer Gravitational-WaveObservatory (LIGO) in the United States, and Virgo inItaly. Combinations of these detectors made joint obser-vations from 2002 through 2011, setting upper limits on avariety of gravitational-wave sources while evolving intoa global network. In 2015, Advanced LIGO became thefirst of a significantly more sensitive network of advanceddetectors to begin observations [33–36].A century after the fundamental predictions of Einstein

and Schwarzschild, we report the first direct detection ofgravitational waves and the first direct observation of abinary black hole system merging to form a single blackhole. Our observations provide unique access to the

*Full author list given at the end of the article.

Published by the American Physical Society under the terms ofthe Creative Commons Attribution 3.0 License. Further distri-bution of this work must maintain attribution to the author(s) andthe published article’s title, journal citation, and DOI.

PRL 116, 061102 (2016)Selected for a Viewpoint in Physics

PHY S I CA L R EV I EW LE T T ER Sweek ending

12 FEBRUARY 2016

0031-9007=16=116(6)=061102(16) 061102-1 Published by the American Physical Society

What Will We Learn fromNeutron-Star Mergers

Tidal polarizability scales as R5 …observations and population synthesis studies suggestthese systems to be most abundant [40]. After energy andangular momentum losses by GWs have driven the inspiralof the NSs for several 100 Myrs, there are two differentoutcomes of the coalescence. Either the two stars directlyform a black hole (BH) shortly after they fuse (‘‘promptcollapse’’), or the merging leads to the formation of adifferentially rotating object (DRO) that is stabilizedagainst the gravitational collapse by rotation and thermal

pressure contributions. Continuous loss of angular momen-tum by GWs and redistribution to the outer merger remnantwill finally lead to a ‘‘delayed collapse’’ on time scales oftypically several 10–100 ms depending on the mass and theEoS. For EoSs with a sufficiently highMmax stable or verylong-lived rigidly rotating NSs are the final product.A prompt collapse occurs for three EoSs of our sample

(marked by x in Table I and Fig. 1). One observes thisscenario only for EoSs with small Rmax. In the simulationswith the remaining EoSs DROs are formed. The evolutionof these mergers is qualitatively similar. The dynamics aredescribed in [21,22].For all models that produce a DRO the GW signal is

analyzed by a post-Newtonian quadrupole formula [21].The inset of Fig. 2 shows the GW amplitude of the pluspolarization at a polar distance of 20 Mpc for NSs de-scribed by the Shen EoS. Clearly visible is the inspiralphase with an increasing amplitude and frequency (until5 ms), followed by the merging and the ringdown of thepostmerger remnant (from 6 ms). All DROs are stableagainst collapse well beyond the complete damping ofthe postmerger oscillations. In Fig. 2 we plot the spectraof the angle-averaged effective amplitude, hav¼0:4f~hzðfÞ(see, e.g., [16]), at a distance of 20 Mpc for the ShenEoS (solid black) and the eosUU (dash-dotted) togetherwith the anticipated sensitivity for Advanced LIGO [17]and the planned Einstein Telescope (ET) [41]. Here

~hzðfÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðj~hþj2 þ j~h%j2Þ=2

qis given by the Fourier trans-

forms, ~hþ=%, of the waveforms for both polarizationsobserved along the pole. As a characteristic feature of thespectra a pronounced peak at fpeak ¼ 2:19 kHz for theShen EoS and 3.50 kHz for eosUU is found, which isknown to be connected to the GW emission of the mergerremnant [7]. Recently, this peak has been identified as the

8 10 12 14 16 180

0.5

1

1.5

2

2.5

3

M [M

sun]

R [km]

FIG. 1 (color online). NS M-R relations for all consideredEoSs. Red curves (gray in print version) correspond to EoSsthat include thermal effects consistently, black lines indicateEoSs supplemented with a thermal ideal gas. The horizontalline corresponds to the 1:97M& NS [3].

0 1 2 3 4 510

−23

10−22

10−21

f [kHz]

h av(2

0 M

pc) 0 5 10 15 20

−1

0

1x 10

−21h + a

t 20

Mpc

t [ms]

fpeak

FIG. 2 (color online). Orientation-averaged spectra of the GWsignal for the Shen (solid) and the eosUU (black dash-dotted)EoSs and the Advanced LIGO [red dashed (gray in print ver-sion)] and ET (black dashed) unity SNR sensitivities. The insetshows the GW amplitude with þ polarization at a polar distanceof 20 Mpc for the Shen EoS.

TABLE I. Used EoSs. Mmax and Rmax are mass and radius ofthe maximum-mass TOV configuration, fpeak is the peak fre-

quency of the postmerger GWemission with the FWHM (a crossindicates prompt collapse of the remnant). f~hzðfpeakÞ is the

effective peak amplitude of the GW signal at a polar distanceof 20 Mpc. The tables of the first five and next seven EoSs aretaken from [25,26], respectively.

Mmax Rmax fpeak, FWHM f~hzðfpeakÞEoS with references [M&] [km] [kHz] [10'21]

Sly4 [27] þ!th 2.05 10.01 3.32, 0.20 2.33

APR [28] þ!th 2.19 9.90 3.46, 0.18 2.45

FPS [29] þ!th 1.80 9.30 x xBBB2 [30] þ!th 1.92 9.55 3.73, 0.22 1.33

Glendnh3 [31]þ!th 1.96 11.48 2.33, 0.13 1.27

eosAU [32] þ!th 2.14 9.45 x xeosC [33] þ!th 1.87 9.89 3.33, 0.22 1.27

eosL [34] þ!th 2.76 14.30 1.84, 0.10 1.38

eosO [35] þ!th 2.39 11.56 2.66, 0.11 2.30

eosUU [32] þ!th 2.21 9.84 3.50, 0.17 2.64

eosWS [32] þ!th 1.85 9.58 x xSKA [36] þ!th 2.21 11.17 2.64, 0.13 1.96

Shen [37] 2.24 12.63 2.19, 0.15 1.43

LS180 [36] 1.83 10.04 3.26, 0.25 1.19

LS220 [36] 2.04 10.61 2.89, 0.21 1.63

LS375 [36] 2.71 12.34 2.40, 0.13 1.82

GS1 [38] 2.75 13.27 2.10, 0.12 1.46

GS2 [39] 2.09 11.78 2.53, 0.12 2.15

PRL 108, 011101 (2012) P HY S I CA L R EV I EW LE T T E R Sweek ending

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011101-2

pð~dij~θi; ~E;H; IÞ ¼ pð~dij~θi;H; IÞ. (The waveform signaldepends on ~E only through ~Λi which is already included asa waveform parameter.)The marginalized PDF [Eq. (20)] is now

pð~EjD;H;IÞ ¼ 1

pðDjH;IÞ

Zd~θin;1…d~θin;n

× pð~EjH;IÞYn

i¼1

½pðm1i;m2ij~E;H;IÞ

× pð ~Λijm1i;m2i; ~E;H;IÞLð~di; ~θin;i;H;IÞ%;ð24Þ

where we have defined the quasilikelihood for the intrinsicparameters as

Lð~di; ~θin;i;H;IÞ ¼Z

d~θex;ipð~θex;ijH; IÞpð~dij~θi;H; IÞ:

ð25Þ

Because ~Λi is a deterministic function of m1i, m2i and theEOS parameters,

pð ~Λijm1i; m2i; ~E;H; IÞ ¼ δð ~Λi − ~Λðm1i; m2i; ~EÞÞ: ð26Þ

The marginalized PDF finally becomes

pð~EjD;H; IÞ ¼ 1

pðDjH; IÞ

Zdm11dm21…dm1ndm2n

× pð~EjH; IÞYn

i¼1

½pðm1i; m2ij~E;H; IÞ

× Lð~di; ~θin;i;H; IÞj ~Λi¼ ~Λðm1i;m2i; ~EÞ%: ð27Þ

The problem has now been reduced to computing thequasilikelihood [Eq. (25)] for each BNS event and thencomputing Eq. (27).

B. Likelihood and signal-to-noise ratio

The final ingredient we need to evaluate the marginalizedPDF is an expression for the likelihood pð~dij~θi;H; IÞ foreach GWevent.4 In this paper we assume that each detectorin the network has stationary, Gaussian noise and that thenoise between detectors is uncorrelated. This means thatthe power spectral density (PSD) SnðfÞa of the noise naðtÞin detector a is

h ~naðfÞ ~na&ðf0Þi ¼ 1

2δðf − f0ÞSnðfÞa; ð28Þ

where ~naðfÞ is the Fourier transform of the noise ofdetector a and h·i represents an ensemble average. For aGW event with true parameters θ, resulting in the GWsignal haðt; θÞ, the data stream of detector a will be

daðtÞ ¼ naðtÞ þ haðt; θÞ: ð29Þ

For stationary, Gaussian noise, it is well known that theprobability of obtaining the noise time series nðtÞ is

pn½nðtÞ% ∝ e−ðn;nÞ=2; ð30Þ

where ða; bÞ is the usual inner product between two timeseries aðtÞ and bðtÞ weighted by the PSD

ða; bÞ ¼ 4ReZ

∞

0

~aðfÞ ~b&ðfÞSnðfÞ

df: ð31Þ

FIG. 2 (color online). Radius and tidal deformability oftabulated EOS models (solid line) and the least-squares piece-wise-polytrope fits (dashed line) to those tabulated models givenin Table I. The 20 vertical lines represent the most likely NSmasses of the ten known BNS systems [38]. Some of thesemasses, however, have significant uncertainties. The overlappingvertical bands represent the 1σ uncertainty in the masses of thepulsars J1614-2230 (1.97( 0.04M⊙) [1] and J0348þ 0432(2.01( 0.04M⊙) [2], both in neutron-star–white-dwarf binaries.

4In the following subsections, when we discuss the likelihoodfor individual GW events, we omit the event index i for brevity.

RECONSTRUCTING THE NEUTRON-STAR EQUATION OF … PHYSICAL REVIEW D 91, 043002 (2015)

043002-7

Gravitational waves – EoS survey

characterize EoS by radius of nonrotating NS with 1.35 M

sun

Triangles: strange quark matter; red: temperature dependent EoS; others: ideal-gas for thermal effects

all 1.35-1.35 simulations

M1/M

2 known from

inspiral

Pure TOV property => Radius measurement via fpeak

Important: Simulations for the same binary mass, just with varied EoS

→ Empirical relation between GW frequency and radius of non-rotating NS

Dominant oscillation frequency

• Robust feature, which occurs in all models (which don't

collapse promptly to BH)

• Fundamental quadrupolar fluid mode of the remnant

Mode analysis at f=fpeak

Stergioulas et al. 2011

Re-excitation of f-mode (l=|m|=2)

in late-time remnant, Bauswein

et al. 2015

NS radius measured to better than 1km!

Conclusions: It is all Connected

Conclusions and Outlook: The Physics of Neutron StarsAstrophysics: What is the minimum mass of a black hole?Atomic Physics: Pure neutron matter as a Unitary Fermi GasCondensed-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?Particle Physics: QCD made simple — the CFL phase of dense quark matter

22 AUGUST 2000 PHYSICS TODAY © 2000 American Institute of Physics, S-0031-9228-0008-010-8

Quantum chromodynamics,familiarly called QCD, is

the modern theory of thestrong interaction.1 Historic-ally its roots are in nuclearphysics and the description ofordinary matter—understand-ing what protons and neu-trons are and how they inter-act. Nowadays QCD is used todescribe most of what goes on at high-energy accelerators.

Twenty or even fifteen years ago, this activity wascommonly called “testing QCD.” Such is the success of thetheory, that we now speak instead of “calculating QCDbackgrounds” for the investigation of more speculativephenomena. For example, discovery of the heavy W and Zbosons that mediate the weak interaction, or of the topquark, would have been a much more difficult and uncer-tain affair if one did not have a precise, reliable under-standing of the more common processes governed byQCD. With regard to things still to be found, searchstrategies for the Higgs particle and for manifestations ofsupersymmetry depend on detailed understanding of pro-duction mechanisms and backgrounds calculated bymeans of QCD.

Quantum chromodynamics is a precise and beautifultheory. One reflection of this elegance is that the essenceof QCD can be portrayed, without severe distortion, in thefew simple pictures at the bottom of the box on the nextpage. But first, for comparison, let me remind you that theessence of quantum electrodynamics (QED), which is ageneration older than QCD, can be portrayed by the sin-gle picture at the top of the box, which represents theinteraction vertex at which a photon responds to the pres-ence or motion of electric charge.2 This is not just ametaphor. Quite definite and precise algorithms for calcu-lating physical processes are attached to the Feynmangraphs of QED, constructed by connecting just such inter-action vertices.

In the same pictorial language, QCD appears as anexpanded version of QED. Whereas in QED there is justone kind of charge, QCD has three different kinds ofcharge, labeled by “color.” Avoiding chauvinism, we mightchoose red, green, and blue. But, of course, the colorcharges of QCD have nothing to do with physical colors.Rather, they have properties analogous to electric charge.In particular, the color charges are conserved in all phys-ical processes, and there are photon-like massless parti-cles, called color gluons, that respond in appropriate ways

to the presence or motion ofcolor charge, very similar tothe way photons respond toelectric charge.

Quarks and gluonsOne class of particles thatcarry color charge are thequarks. We know of six differ-ent kinds, or “flavors,” of

quarks—denoted u, d, s, c, b, and t, for: up, down,strange, charmed, bottom, and top. Of these, only u and dquarks play a significant role in the structure of ordinarymatter. The other, much heavier quarks are all unstable.A quark of any one of the six flavors can also carry a unitof any of the three color charges. Although the differentquark flavors all have different masses, the theory is per-fectly symmetrical with respect to the three colors. Thiscolor symmetry is described by the Lie group SU(3).

Quarks are spin-1/2 point particles, very much likeelectrons. But instead of electric charge, they carry colorcharge. To be more precise, quarks carry fractional elec-tric charge (+ 2e/3 for the u, c, and t quarks, and – e/3 forthe d, s, and b quarks) in addition to their color charge.

For all their similarities, however, there are a fewcrucial differences between QCD and QED. First of all,the response of gluons to color charge, as measured by theQCD coupling constant, is much more vigorous than theresponse of photons to electric charge. Second, as shownin the box, in addition to just responding to color charge,gluons can also change one color charge into another. Allpossible changes of this kind are allowed, and yet colorcharge is conserved. So the gluons themselves must beable to carry unbalanced color charges. For example, ifabsorption of a gluon changes a blue quark into a redquark, then the gluon itself must have carried one unit ofred charge and minus one unit of blue charge.

All this would seem to require 3 × 3 = 9 differentcolor gluons. But one particular combination of gluons—the color-SU(3) singlet—which responds equally to allcharges, is different from the rest. We must remove it ifwe are to have a perfectly color-symmetric theory. Thenwe are left with only 8 physical gluon states (forming acolor-SU(3) octet). Fortunately, this conclusion is vindicat-ed by experiment!

The third difference between QCD and QED, which isthe most profound, follows from the second. Because glu-ons respond to the presence and motion of color chargeand they carry unbalanced color charge, it follows thatgluons, quite unlike photons, respond directly to oneanother. Photons, of course, are electrically neutral.Therefore the laser sword fights you’ve seen in Star Warswouldn’t work. But it’s a movie about the future, so maybethey’re using color gluon lasers.

We can display QCD even more compactly, in terms of

FRANKWILCZEK is the J. Robert Oppenheimer Professor of Physics atthe Institute for Advanced Study in Princeton, New Jersey. Next monthhe moves to Cambridge, Massachusetts, to take up the Herman FeshbachChair of Physics at the Massachusetts Institute of Technology.

QCD MADE SIMPLEQuantum chromodynamics is

conceptually simple. Its realizationin nature, however, is usuallyvery complex. But not always.

Frank Wilczek

Neutron Stars are the natural meeting place forfundamental and interesting Physics

J. Piekarewicz (FSU) Neutron Stars Santa Tecla, September 2013 33 / 33

Astrophysics: What is the minimum mass of a black hole?Atomic Physics: Is pure neutron matter a unitary Fermi gas?C.Matter Physics: Is there a Coulomb crystal to Fermi liquid transition?General Relativity: Can NS mergers constrain stellar radii?Nuclear Physics: What is the EOS of neutron-rich matter?Particle Physics: What exotic phases inhabit the dense core?

Neutron Stars are the natural meeting place for interdisciplinary, fundamental, and fascinating physics!