Density Functional Theory meets Bayesian Neural Networks: A New - - PowerPoint PPT Presentation

SLIDE 1

Information and Statistics in Nuclear Experiment and Theory ISNET-3

Trento, November 16-20, 2015

Main Topics Estimation of statistical uncertainties of calculated quantities, assessment of systematic errors, validation and verification of extrapolations, information content of observables with respect to current theoretical models, statistical tools of nuclear theory and planning of future experiments, Bayesian methods and computational techniques, novel methods of optimization

Organizers

David Ireland (University of Glasgow) Witold Nazarewicz (FRIB/NSCL - Michigan State University) Bartlomiej Szpak (Insitute of Nuclear Physics PAN - Krakow) Director of the ECT*: Professor Wolfram Weise (ECT*) The ECT* is sponsored by the “Fondazione Bruno Kessler” in collaboration with the “Assessorato alla Cultura” (Provincia Autonoma di Trento), funding agencies of EU Member and Associated States and has the support of the Department of Physics of the University of Trento. For local organization please contact: Gianmaria Ziglio - ECT* Secretariat - Villa Tambosi - Strada delle Tabarelle 286 - 38123 Villazzano (Trento) - Italy Tel.:(+39-0461) 314721 Fax:(+39-0461) 314750, E-mail: ect@ectstar.eu or visit http://www.ectstar.eu Key Speakers Anatoli Afanasjev (Mississippi State University, USA), Enrique Ruiz Arriola (University of Granada, Spain), Julia Bliss (Technical University of Darmstadt, Germany), Rick Casten (Yale University, USA), Gianluca Colo (University of Milan and INFN, Italy), Andreas Ekstrom (University of Tennessee, USA), Christian Forssen (Chalmers University of Technology, Sweden), Dick Furnstahl (Ohio State University, USA), Krzysztof Graczyk (University of Wroclaw, Poland), Tiia Haverinen (University of Jyväskylä, Finland), Dave Ireland (University of Glasgow, UK), Yannen Jaganathen (Michigan State University, USA), Markus Kortelainen (University of Jyvaskyla and Helsinki Institute of Physics, Finland), Amy Lovell (Michigan State University, USA), Rodrigo Navarro-Perez (Lawrence Livermore National Laboratory, USA), Witold Nazarewicz (Michigan State University, USA), Nils Paar (University of Basel, Switzerland), Alessandro Pastore (University of York, UK), Jorge Piekarewicz (Florida State University, USA), Scott Pratt (Michigan State University, USA), David Regnier (CEA Bruyères, France), Paul-Gerhard Reinhard (University of Erlangen, Germany), David Richards (Jefferson Laboratory, USA), Xavier Roca-Maza (University of Milan and INFN, Italy), Jan Ryckebusch (Ghent University, Belgium), Nicolas Schunck (Lawrence Livermore National Laboratory, USA), Achim Schwenk (TU Darmstadt), Paul Stevenson (University of Surrey, UK), Rebecca Surman (University of Notre Dame, USA), Bartlomiej Szpak (Insitute of Nuclear Physics PAN - Krakow), Sarah Wesolowski (Ohio State University, USA), Stefan Wild (Argonne National Laboratory, USA)

Highlights of 2015

Welcome to JPhysG's 2015 highlights! Before you get to the articles, here are a few of my personal choices. First, the way the community reacted and engaged with our focus issue, Enhancing the interaction between nuclear experiment and theory through information and statistics was outstanding. Linking theory with experiment is vital for any field and I look forward to seeing more research on the topic in both nuclear and particle physics. Then, in mid-2015 Sir Tom Kibble kicked off our selection of 40th anniversary articles, a unique collection of works from renowned authors

Bayesian Methods in Nuclear Physics

INT Program 2016

Density Functional Theory meets 
 Bayesian Neural Networks: 
 A New Paradigm in the Study of Neutron Stars

Jorge Piekarewicz - Florida State University

2017 ICNT Program: Extracting Bulk Properties of Neutron-Rich Matter 
 with Transport Models in Bayesian Perspective. March 22 — April 12, 2017 at FRIB/MSU

SLIDE 2

Chandrasekhar shows that massive stars will collapse (1931) Chadwick discovers the neutron (1932)


(… predicted earlier by Majorana but never published)

Baade-Zwicky introduce the concept of a neutron star (1933)


(… Landau mentions dense stars that look like giant nuclei!)

Oppenheimer-Volkoff use GR to compute the structure of neutron stars (1939)


(… predict as maximum neutron star mass)

Jocelyn Bell discovers neutron stars (1967)

M? ' 0.7 M

Neutron Stars: Very Few Historical Facts

SLIDE 3

Neutron Stars: Unique Cosmic Laboratories

Neutron stars are the remnants of massive stellar explosions (CCSN)

Bound by gravity — NOT by the strong force Catalyst 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!

0.0 7 8 9 10 11 Radius (km) 12 13 14 15 0.5 1.0 1.5 2.0

AP4

J1903+0327 J1909-3744 systems Double neutron s Double neutron star sy sy

J1614-2230 AP3 ENG MPA1 GM3 GS1 PAL6 FSU SQM3 SQM1 PAL1 MS0 MS2 MS1

2.5 G R Causality Rotation P < ∞ Mass (M()

dM dr = 4πr 2E(r) dP dr = −GE(r)M(r) r 2  1 + P(r) E(r)

• 

1 + 4πr 3P(r) M(r)  1 − 2GM(r) r −1 Need an EOS: P =P(E) relation

Nuclear Physics Critical

SLIDE 4

The Composition of the Outer Crust


Enormous sensitivity to nuclear masses

System unstable to cluster formation

BCC lattice of neutron-rich nuclei imbedded in e-gas

Composition emerges from relatively simple dynamics Competition between electronic and symmetry energy

Precision mass measurements of exotic nuclei is essential

Both - for neutron-star crusts and r-process nucleosynthesis

E/Atot = M(N, Z)/A + 3 4Y 4/3

e

kF + lattice

V O L U M E 5 3 N U M B E R 3 A P R I L 2 0 1 3

CERNCOURIER

I N T E R N A T I O N A L J O U R N A L O F H I G H -E N E R G Y P H Y S I C S

ISOLTRAP casts light

• n neutron stars

COMPUTING

SLIDE 5

DFT meets BNN

PHYSICAL REVIEW C 93, 014311 (2016)

Nuclear mass predictions for the crustal composition of neutron stars: A Bayesian neural network approach

• R. Utama,* J. Piekarewicz,† and H. B. Prosper‡

Department of Physics, Florida State University, Tallahassee, Florida 32306, USA (Received 25 August 2015; revised manuscript received 14 December 2015; published 20 January 2016)

M(N, Z) = MDF T (N, Z) + δMBNN(N, Z)

Systematic scattering greatly reduced Predictions supplemented by theoretical errors

Use DFT to predict nuclear masses Train BNN by focusing on residuals

• The paradigm

Blume-2006

SLIDE 6

The 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 masses K0x230 MeV — nuclear incompressibility 4 nuclear “breathing” mode

Density dependence of symmetry poorly constrained:

J x30 MeV — symmetry energy 4 masses of neutron-rich nuclei Lx? — symmetry slope 4 neutron skin (Rn-Rp) of heavy nuclei ?

E(⇢, ↵) ' E0(⇢) + ↵2S(⇢) ' ⇣ ✏0 + 1 2K0x2⌘ + ⇣ J + Lx + 1 2Ksymx2⌘ ↵2

2 4 6 8 10

r(fm)

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

ρ(fm-3)

Experiment Rskin=0.176 fm Rskin=0.207 fm Rskin=0.235 fm Rskin=0.260 fm Rskin=0.286 fm

• ρ

weak

ρ

charge

208Pb

The Equation of State of Neutron-Rich Matter

SLIDE 7

LYukawa = ¯ ψ h gsφ− ⇣ gvVµ+ gρ 2 τ · bµ+ e 2(1+τ3)Aµ ⌘ γµi ψ

Lself = κ 3!(gsφ)3− λ 4!(gsφ)4+ ζ 4!g4

v(VµV µ)2 + Λv

⇣ g2

ρ bµ · bµ⌘⇣

g2

vVνV ν⌘

Nucleus TAMU RCNP NL3 FSU FSU2

90Zr

17.81 ± 0.35 — 18.76 17.86 17.93 ± 0.09

116Sn

15.90 ± 0.07 15.70 ± 0.10 17.19 16.39 16.47 ± 0.08

144Sm

15.25 ± 0.11 15.77 ± 0.17 16.29 15.55 15.59 ± 0.09

208Pb

14.18 ± 0.11 13.50 ± 0.10 14.32 13.72 13.76 ± 0.08

Nucleus Observable Experiment NL3 FSU FSU2

16O

B/A 7.98 8.06 7.98 8.00 Rch 2.70 2.75 2.71 2.73

40Ca

B/A 8.55 8.56 8.54 8.54 Rch 3.48 3.49 3.45 3.47

48Ca

B/A 8.67 8.66 8.58 8.63 Rch 3.48 3.49 3.48 3.47

68Ni

B/A 8.68 8.71 8.66 8.69 Rch — 3.88 3.88 3.86

90Zr

B/A 8.71 8.70 8.68 8.69 Rch 4.27 4.28 4.27 4.26

100Sn

B/A 8.25 8.30 8.24 8.28 Rch — 4.48 4.48 4.47

116Sn

B/A 8.52 8.50 8.50 8.49 Rch 4.63 4.63 4.63 4.61

132Sn

B/A 8.36 8.38 8.34 8.36 Rch 4.71 4.72 4.74 4.71

144Sm

B/A 8.30 8.32 8.32 8.31 Rch 4.95 4.96 4.96 4.94

208Pb

B/A 7.87 7.90 7.89 7.88 Rch 5.50 5.53 5.54 5.51

Nuclear Density Functional Theory (DFT)

Ab-initio calculations of heavy nuclei remains daunting task Search for energy functional valid over a large physics domain
 “from finite nuclei to neutron stars” Incorporate physics insights into the construction of the functional Accurately calibrated to various properties of finite nuclei
 masses, charge radii, and giant monopole resonances Empirical constants encode physics beyond mean field Empirical constants obtained from the optimization of a quality measure

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

Model Building: The Protocol

SLIDE 8

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

Prior Posterior Likelihood Marginal Likelihood

(gs, gv, gρ, , , Λv) ⇐ ⇒ (⇢0, ✏0, M ∗, K, J, L)

χ2(D, M) =

N

X

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

Bayes’ Theorem: Application to Model Building

QCD is the fundamental theory of the strong interactions!

M: A theoretical MODEL with parameters and biases D: A collection of experimental and observational DATA

The Prior P(M): An insightful transformation in DFT The Likelihood The Marginal Likelihood; overall normalization factor

P(D|M) = exp(−χ2/2)

SLIDE 9

Neutron-star radii are sensitive to the EOS near 2r0

Neutron star masses sensitive to EOS at much higher density

Neutron skin correlated to a host of neutron-star properties

Stellar radii, proton fraction, enhanced cooling, moment of inertia

Neutron skin of heavy nuclei and NS radii driven by same physics

Difference in length scales of 18 orders of magnitude!!

40 50 60 70 80

L (MeV)

12 12.5 13 13.5 14 14.5

RNS [M/Msun] (km)

RNS[0.8] RNS[1.4] CAB=0.988 FSUGold CAB=0.946 0.2 0.4 0.6 0.8 1

Correlation with skin of 208Pb skin 132Sn RNS[0.8] RNS[1.4] skin 48Ca

• t

skin 208Pb L Y

p t

MDUrca Icrust[0.8]

Structure Pasta Cooling Glitches

Heaven and Earth 


The enormous reach of the neutron skin

SLIDE 10

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” DFT supports the correlation Ensure that “all” accurately-calibrated DFT support the correlation

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

v090 MSk7 HFB-8 SkP HFB-17 SkM* DD-ME2 DD-ME1 FSUGold DD-PC1 Ska PK1.s24 Sk-Rs NL3.s25 Sk-T4 G2 NL-SV2 PK1 NL3 NL3* NL2 NL1

50 100 150

L(MeV)

0.1 0.2 0.3

Rskin

208 (fm)

Linear Fit, r = 0.979 Mean Field

D1S D1N SGII Sk-T6 SkX SLy5 SLy4 MSkA MSL0 SIV SkSM* SkMP SkI2 SV G1 TM1 NL-SH NL-RA1 PC-F1 BCP RHF-PKO3 Sk-Gs RHF-PKA1 PC-PK1 SkI5

PREX-II S-PREX (63±16)

Roca-Maza et al. PRL106,252501(2011)

40 50 60 70 80

L (MeV)

0.18 0.2 0.22 0.24

Rskin[208Pb] (fm)

L/2

• AB=0.995

Lmin=1.18 MeV

0.015 fm

Searching for L: The Strategy

SLIDE 11

0.0 0.5 1.0 1.5 2.0

q (fm-1)

10

• 4

10

• 3

10

• 2

10

• 1

10

|F

c(q)|

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

Rch =5.5012(13) fm

0.0 0.5 1.0 1.5 2.0

q (fm-1)

10

• 3

10

• 2

10

• 1

10

|F

weak(q)|

PREX rskin=0.176 fm rskin=0.207 fm rskin=0.235 fm rskin=0.260 fm rskin=0.286 fm

Rwk =5.826(181) fm

PREX@JLAB: First electroweak (clean!) evidence in favor of Rskin in Pb Precision hindered by radiation issues

Excellent control of systematic uncertainties Statistical uncertainties 3 times larger than promised

PREX-II and CREX to run in 2018

Original goal of 1% in neutron radius

APV = GFQ2 2 √ 2πα 2 41 − 4 sin2 θW | {z }

≈0

− Fn(Q2) Fp(Q2) 3 5 Neutral weak-vector boson 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 Z0-coupling ≈ +1/3 ≈ −2/3 ≈ 0 −1 gv =2tz − 4Q sin2 θW ≈2tz −Q

Electroweak Measurement of Neutron Densities

SLIDE 12

The incompressibility of neutron rich matter:
 Why is tin so fluffy?

K0(α) = K0 + Kτα2; Kτ = Ksym− 6L + . . .

PHYSICAL REVIEW C 76, 031301(R) (2007)

Why is the equation of state for tin so soft?

• J. Piekarewicz

Department of Physics, Florida State University, Tallahassee, Florida 32306, USA (Received 10 May 2007; published 4 September 2007) ution of isoscalar monopole strength in the neutron-even 112–124Sn isotopes has been random-phase-approximation approach. The accurately-calibrated model used successful in reproducing both ground-state observables as well as collective excitations—including resonance (GMR) in 90Zr, 144Sm, and 208Pb. Yet this same model significantly Sn isotopes. It is argued that the question of “Why is tin

• ne that should be answered without sacrificing the

vC.76.031301 PACS number(s):

(also known parameter fluctuations

PHYSICAL REVIEW C 79, 034309 (2009)

Description of the giant monopole resonance in the even-A 112–124Sn isotopes within a microscopic model including quasiparticle-phonon coupling

• V. Tselyaev,

1 , 2

• J. Speth,

1

• S. Krewald,

1

• E. Litvinova,

3 , 4 , 5

• S. Kamerdzhiev,

1 , 5

• N. Lyutorovich,

1 , 2

• A. Avdeenkov,

1 , 6

and F. Gr¨ ummer

1 1Institut f¨ ur Kernphysik, Forschungszentrum J¨ ulich, D-52425 J¨ ulich, Germany Nuclear Physics Department, V. A. Fock Institute of Physics, St. Petersburg State University, RU-198504 St. Petersburg, Russia 3Gesellschaft f¨ ur Schwerionenforschung mbH, D-64291 Darmstadt, Germany 4Frankfurt Institute for Advanced Studies, Universit¨ at Frankfurt, D-60438 Frankfurt am Main, Germany 5Institute of Physics and Power Engineering, RU-249033 Obninsk, Russia 6Skobeltsyn Institute of Nuclear Physics, Moscow State University, RU-119991 Moscow, Russia (Received 6 October 2008; published 10 March 2009) calculated the strength distributions of the isoscalar giant monopole resonance 112–124) that were recently measured in inelastic α scattering. The icroscopic models: the quasiparticle random phase approximation pproximation (QTBA), which is an extension of the Q elf-consistent calculational scheme based on the RPA the self-consistency is full. The single-particle elf-consistent mean field and the effecti two Skyrme force parametrizations modulus of infinite nuclear theoretical results esults of compared

PHYSICAL REVIEW C 86, 024303 (2012)

Giant monopole resonances and nuclear incompressibilities studied for the zero-range and separable pairing interactions

• P. Vesel´

y,1,* J. Toivanen,1 B. G. Carlsson,2 J. Dobaczewski,1,3 N. Michel,1 and A. Pastore4

1Department of Physics, University of Jyv¨

askyl¨ a, P.O. Box 35 (YFL) FI-40014, Finland

Isotopic Dependence of the Giant Monopole Resonance in the Even-A 112–124Sn Isotopes and the Asymmetry Term in Nuclear Incompressibility

• T. Li,1 U. Garg,1 Y. Liu,1 R. Marks,1 B. K. Nayak,1 P. V. Madhusudhana Rao,1 M. Fujiwara,2 H. Hashimoto,2 K. Kawase,2
• K. Nakanishi,2 S. Okumura,2 M. Yosoi,2 M. Itoh,3 M. Ichikawa,3 R. Matsuo,3 T. Terazono,3 M. Uchida,4 T. Kawabata,5
• H. Akimune,6 Y. Iwao,7 T. Murakami,7 H. Sakaguchi,7 S. Terashima,7 Y. Yasuda,7 J. Zenihiro,7 and M. N. Harakeh8

1

PRL 99, 162503 (2007) P H Y S I C A L R E V I E W L E T T E R S

week ending 19 OCTOBER 2007

The Giant Monopole Resonance in the Sn Isotopes: Why is Tin so “Fluffy”?

• U. Garg,a T. Li,a S. Okumura,b H. Akimunec M. Fujiwara,b M.N. Harakeh,d
• H. Hashimoto,b M. Itoh,e Y. Iwao,f T. Kawabata,g K. Kawase,b Y. Liu,a R. Marks,a
• T. Murakami,f K. Nakanishi,b B.K. Nayak,a P.V. Madhusudhana Rao,a H. Sakaguchi,f
• Y. Terashima,f M. Uchida,h Y. Yasuda,f M. Yosoi,b and J. Zenihirof

Nuclear Physics A 788 (2007) 36c–43c

PHYSICAL REVIEW C 78, 064304 (2008)

Microscopic linear response calculations based on the Skyrme functional plus the pairing contribution

J u n L i (

• )

,1,2,* G i a n l u c a C

• l

`

• ,1,†

a n d J i e M e n g (

• )2,3,4,5,‡

1Dipartimento di Fisica, Universit` a degli Studi and INFN Sez. di Milano, Via Celoria 16, 20133 Milano, Italy 2School of Physics, and State Key Laboratory of Nuclear Physics and Technology Peking University, Beijing 100871, People’s Republic of China 3Department of Physics, University of Stellenbosch, Stellenbosch, South Africa Institute of Theoretical Physics, Chinese Academy of Science, Beijing 100080, People’s Republic etical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000, ed 31 March 2008; revised manuscript received 23 June 2008; published 11 elf-consistent quasiparticle random-phase approximation (QRPA) model ck-Bogoliubov (HFB) basis and an energy-density functional w iring is used to study the monopole collective ex spurious state on the strength function of the fect of different kinds of pairing forces tation strength function. The nuclear incompressibility

10 15 20 25

(MeV)

2000 2000 2000 2000 2000 2000 2000

116Sn 112Sn 114Sn 118Sn 120Sn 122Sn 124Sn

R(;0) (fm4/MeV)

112 114 116 118 120 122 124

A

14 15 16 17 18

EGMR(MeV)

RCNP TAMU NL3 FSU Hybrid

Sn-Isotopes

min=10 MeV max=20 MeV

Workshop on Nuclear Incompressibility

University of Notre Dame July 14-15, 2005 The Joint Institute for Nuclear Astrophysics (JINA) will organize a 2-day Workshop focused on Nuclear Incompressibility and the Nuclear Equation of State, to be held at the University of Notre Dame during July 14-15, 2005. This meeting follows a similar Workshop held at Notre Dame in January 2001, and the Symposium on Nuclear Equation of State used in Astrophysics Models, held at the ACS meeting in Philadelphia last Summer. The primary aim of the Workshop is to bring together interested physicists from the areas of Astrophysics, Giant Resonances, and Heavy-Ion Reactions, to discuss current status of experiments and theoretical models related to nuclear incompressibility and the equation of state, and to explore what experiments might be needed to clarify some of the outstanding issues. Most of the Workshop will be devoted to talks, with a lot of time allowed for discussions and interactions. In that spirit, we will follow a somewhat flexible schedule for the talks. There is no registration fee but participants are requested to register via the webpage (www.jinaweb.org), so that we can make appropriate arrangements. For further information, please contact: Kathy Burgess (kburgess@nd.edu)

• r

Umesh Garg (garg@nd.edu) The Joint Institute for Nuclear Astrophysics May 18, 2005

Outcome: A window into L through systematic measurements of the GMR across a long isotopic chain

Onwards and upwards to GMRs in unstable nuclei!

SLIDE 13

Electric Dipole Polarizability

GSI: Adrich et al PRL95, 132501 (2005)

20 40 60 80 100 120 140

L(MeV)

5 6 7 8 9 10

10-2αD

208J (MeV fm3)

r=0.96 FSU NL3 DD-ME Skyrme SV SAMi TF

Electric dipole polarizability

IVGDR: The quintessential 
 nuclear excitation

Out-of-phase oscillation of neutrons vs protons
 Symmetry energy acts as restoring force Energy weighted sum rule largely model independent
 Inverse energy weighted sum strongly correlated to L
 Actually … JaD strongly correlated to L
 Important contribution from Pygmy resonance High quality data emerging from RCNP, GSI, HIGS
 On a variety of nuclei such as Pb, Sn, Ni, Ca, …
 and hopefully in the future along isotopic chains

SLIDE 14

Neutron-Star Radii

Compactness of Neutron Stars

Wei-Chia Chen* and J. Piekarewicz†

Department of Physics, Florida State University, Tallahassee, Florida 32306, USA (Received 27 May 2015; published 16 October 2015)

PRL 115, 161101 (2015) P H Y S I C A L R E V I E W L E T T E R S

week ending 16 OCTOBER 2015

Guillot et al., assume all neutron stars share a common radius
 Assumption in MR observable rather than on the EOS One-to-one correspondence between EOS and MR
 TOV equation + EOS Unique MR relation Lindblom’s inversion algorithm shows the inverse also true! [APJ 398, 569 (1992)]
 TOV equation + MR Unique Equation of State For a given “common” radius MR profile examine whether:
 Resulting EOS is causal or superluminal for stellar masses below 2 For a given “common” radius MR profile, to prevent causality violations
 Stellar radius of a 1.4 must exceed 10.7 km! M M

6 8 10 12 14 16 18 20

R(km)

0.5 1 1.4 2 2.5 3

M/Msun

8 9 10 11 13 R8 R9 R10 R11 AV14+UVII FSUGold FSUGold2 FSUGarnet NL3

this work L

&

P

BH

Causality

Guillot & Rutledge 2014 Updated distances

RNS = 9.4+1.9

−1.8 km

RNS = 10.3+1.9

−1.7 km

With Pile-up model

RNS = 10.8+1.8

−1.4 km

99%

SLIDE 15

"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 masses Final black hole mass is 62 solar masses; 
 3 solar masses radiated in GW!

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)

PRL 116, 061102 (2016) Selected for a Viewpoint in Physics P H Y S I C A L R E V I E W L E T T E R S

week ending 12 FEBRUARY 2016

SLIDE 16

What will we learn from
 neutron-star mergers

Tidal polarizability scales as R5 !

1 2 3 4 5 10

−23

10

−22

10

−21

f [kHz] hav(20 Mpc) 5 10 15 20 −1 1 x 10

−21

h+ at 20 Mpc t [ms] fpeak

all 1.35-1.35 simulations

M1/M2 known from inspiral

NS radius measured to better than 1km!

SLIDE 17

What else will we learn from 
 neutron-star mergers

10 11 12 13 14 15 16 0.002 0.004 0.006 0.008 0.01 0.012 Mejecta [Msun] R1.35 [km]

R1.35 proxy for mass ejecta

Bauswein,Goriely,Janka; APJ (2013)

LIGO will provide critical insights into 
 the behavior of ultra dense matter Merger rate and ejecta mass unknown
 Galactic merger rate depends on EOS: 
 4x10

• 5 (soft)

4x10

• 4 (stiff) per year to 


account for observation

Soft: Rn-Rp is small neutron star more compact merger is more violent higher abundance

The Astrophysical Journal, 773:78 (21pp), 2013 August 10 Bauswein, Goriely, & Janka x [km] y [km] 12.1235 ms −30 −20 −10 10 20 30 −30 −20 −10 10 20 30 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 x [km] y [km] 12.6867 ms −30 −20 −10 10 20 30 −30 −20 −10 10 20 30 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 x [km] y [km] 13.0056 ms −30 −20 −10 10 20 30 −30 −20 −10 10 20 30 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 x [km] y [km] 13.4824 ms −30 −20 −10 10 20 30 −30 −20 −10 10 20 30 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 x [km] y [km] 13.8024 ms −50 50 −50 −40 −30 −20 −10 10 20 30 40 50 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 x [km] y [km] 15.167 ms −50 50 −50 −40 −30 −20 −10 10 20 30 40 50 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5

How were the heavy elements from iron to uranium made?

SLIDE 18

My FSU Collaborators

Genaro Toledo-Sanchez Karim Hasnaoui Bonnie Todd-Rutel Brad Futch Jutri Taruna Farrukh Fattoyev Wei-Chia Chen Raditya Utama

My Outside Collaborators

• B. Agrawal (Saha Inst.)
• M. Centelles (U. Barcelona)
• G. Colò (U. Milano)

C.J. Horowitz (Indiana U.)

• W. Nazarewicz (MSU)
• N. Paar (U. Zagreb)

M.A. Pérez-Garcia (U. Salamanca) P .G.- Reinhard (U. Erlangen-Nürnberg)

• X. Roca-Maza (U. Milano)
• D. Vretenar (U. Zagreb)

My Collaborators