Neutron rich matter
LIGO

208Pb

Brian Alder

C. J. Horowitz, Indiana University!
Supernovae and Gamma-Ray Bursts, Yukawa Inst., Kyoto, Oct. 2013

Neutron Rich Matter• Compress almost anything to 1011+ g/cm3 andelectrons react with protons to make neutronrich matter. This material is at the heart ofmany fundamental questions in nuclear physics
and astrophysics. 	

– What are the high density phases of QCD? 	

– Where did chemical elements come from? 	

– What is the structure of many compact andenergetic objects in the heavens, and what
determines their electromagnetic, neutrino,
and gravitational-wave radiations? 	

Supernova remanentCassiopea A in X-rays• Interested in neutron rich matter over atremendous range of density and temperature
were it can be a gas, liquid, solid, plasma, liquid
crystal (nuclear pasta), superconductor (Tc=1010K!), superfluid, color superconductor...
MD simulation of Nuclear
Pasta with 100,000 nucleons

Neutron rich matter• Theory: chiral effective field theory.
• Experiment: neutron skin thickness of
208Pb, and 48Ca via parity violating
electron scattering.
• Low density nonuniform matter:–Formation of nuclear pasta.
–Neutrinosphere region in core collapse SN.

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Chiral Effective Field Theory• Expands interactions in powers ofmomentum over chiral scale.
• Predicts properties of uniform
nuclear matter at low densities.
• Many body perturbation theory
calculations now being improved
with coupled cluster calculations byG. Hagen et al.
• Note that calculations of nuclear
matter may only be applicable overa limited density range from ~1/2𝝆0
to ~𝝆0.
–At higher densities chiral expansion
may not converge.
–At lower densities matter isnonuniform.

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A. Schwenk!
• All hadronic calculations of nuclear
matter, for densities above 𝝆0, may
have large uncertainties in threeand more nucleon forces.

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!4Energy of Neutron Matter at N3LO
• Supernova EOS of
Lattimer-Swesty (LS180 orLS220) has too low
neutron matter energy atlow densities.
• H. Shen EOS based on
RMF (TM1) has E increase
too fast with density.
• Gang Shen EOS (FSU2.1)
based on extensive mean
field calculations using
FSUgold interaction
stiffened at high densities
to support 2.1Msun NS
consistent with chiralcalculations
PRC83,065808 (2011).

Kruger et al, ArXiv:1304.2212

H. ShenGang Shen

LS!5

Laboratory probe of neutron rich matter

PREX uses parity violating electron
scattering to accurately measure theneutron radius of 208Pb. 	

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208Pb
Brian Alder

This has important implications forneutron rich matter and astrophysics.	

Parity Violation Isolates Neutrons• In Standard Model Z0 boson
couples to the weak charge.	

• Proton weak charge is small:	p2=1−4sinΘW ≈ 0.05
Q!
W• Neutron weak charge is big:	

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QnW = −1

• Weak interactions, at low Q2,
probe neutrons.	

• Parity violating asymmetry Apv iscross section difference forpositive and negative helicity
electrons
dσ/dΩ+ − dσ/dΩ−
Apv =dσ/dΩ+ + dσ/dΩ−• Apv from interference of photon
and Z0 exchange. In Born
approximation	

GF Q2 FW (Q2 )√Apv =2)F(Q2πα2ch!
!
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23 sin(Qr)
FW (Q ) = d r
ρW (r)Qr!
!

• Model independently map out
distribution of weak charge in anucleus. 	

• Electroweak reaction freefrom most strong
interaction uncertainties.	

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– Donnelly, Dubach, Sick firstsuggested PV to measure neutrons.

Neutron radii from proton scattering• Tamii et al. extract the electric dipole polarizability of208
Pb using small angle proton scattering.
+0.025– Claim Rn-Rp = 0.156-0.021 fm based on a model
dependent correlation between polarizability and skin.
– Fattoyev et al show that models with a larger range of RnRp are consistent with polarizability (PRL111, 162501).

• Many model dependent extractions of neutron
densities from proton elastic scattering. For
example Terashima et al. (PRC77, 024317) modify
58
NN amplitudes until Ni has small Rn-Rp and thenuse amplitudes to extract Rn-Rp for Sn isotopes.
Note, this procedure may depend on energy andnucleus.

208Pb

PREX
Spokespersons
K. Kumar	R. Michaels	

K. Paschke	

P. Souder	

G. Urciuoli• PREX measures how much neutrons stick out past protons (neutron skin).

PREX in Hall A at JLab
Spectometers
Lead Foil
TargetPol. Source

Hall ACEBAF

MSU Seminar, Nov 2008

R. Michaels!10

First PREX result and future plans•1.05 GeV electrons elastically208
scattering at ~5 deg. fromPb.	

• APV=0.66±0.06(stat)±0.014(sym)
ppm	

+0.16

•Neutron skin: Rn-Rp=0.33 -0.18 fm	

(approved•Future plans: PREX-II
208
25 days) Run Pb again toaccumulate more statistics. Goal: Rn
to ±0.06 fm. 	

•48CREX: Approved follow on for
Ca with goal: Rn to ±0.02 fm. 	

•Lighter48

Ca allows coupled cluster
calculations to relate Rn to threeneutron forces. Important isovector
observable to bridge ab initio anddensity functional descriptions.

J. Piekarewicz

Density Dependence of EOS• Pressure of neutron matter
pushes neutrons out
against surface tension
208==> Rn-Rp of Pb
determines P at low
densities of about 2/3𝝆0(average of surface andinterior 𝝆).

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• Radius of (~1.4Msun) NS
depends on P at medium
densities of 𝝆0 and above.

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• Maximum mass of NS
depends on P at highdensities.

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• These three measurements
constrain density
dependence of EOS andpossible pressure changes
from phase transitions.
!12Low Density Nonuniform Matter• Half of heavy elements (includinggold) made in r-process.
• What makes all of the neutrons?
• Neutrinos: ratio of n/p insupernova 𝝼 driven wind set byrates of 𝝼 capture.
• Gravity: compresses matter until • r-process yield depends on:electron capture drives it n rich.
• How much material is
Tidal forces during NS mergers
ejected in a merger?
can eject n-rich material.
Better numerical relativity• Follow fluid element in tidal tail as it
simulations.
decompresses (next pages).
• What is merger rate?
• Matter ejecta so n rich that it
Advanced LIGO will soonundergoes robust r-process!
directly observe rate.
Simulation by Stephan Rosswog, University of Leicester. Visualisation by Richard West, UKAFF.

Nuclear Pasta Formation• During NS merger tidal excitation

decreases density: uniform nuclear
matter -> nuclear pasta -> nuclei + n ->r-process. Decompression pasta (mstime scale, low Yp).	

• Gravitational collapse during SN

increases density: ~ Fe nuclei -> nuclearpasta -> uniform nuclear matter ->neutron star. SN pasta (ms time scale,high Yp).	

• Cooling pasta as protoneutron starcools.	

• Accretion, slow cooks new pasta on
accretion time scales (thousands ofyears??). Accreted pasta.	

• Pasta formation involves phasetransitions between very different
shapes. Cooking pasta is not so simple!

We have started on pasta microphysics:
thermal/ electrical conductivity, shear
viscosity, neutrino opacity, dynamical
response...

(Semi)classical pasta model• Charge neutral system of n, p, and e. [e provide
screening length 𝛌 for Coulomb.] 	

• Thermal wave length of heavy clusters much shorter

MDGRAPE-2 boards in pastthan inter cluster spacing: semi-classical approx.
should be good.	

• n, p interact via 2-body pot: H = K + Σ v(r )22i<jijv(r)=a Exp[-r /𝚲]+ bij Exp[-r /2𝚲] + eiej Exp[-r/𝛌]/r	• Parameters a, b =b , b , 𝚲 fit to binding E andpp

nnpn

saturation density of nuclear matter, reasonable
symmetry E...	

Presently run on about1000 cores for ~ few weeks• Simple model allows large MD simulations with7300,000+ nucleons, long simulation times 10 + fm/c.	

•Also QMD simulations by Watanabe et al, Quantum
calculations by W. Newton ...

Porting to GPU based machines
such as IU’s new Big Red II

Simulation of pasta formation. ArXiv:1307.1678

51200
nucleons,
Yp=0.4,
T=1 MeV,
𝛌=10 fm,
ξ=2x10-8
c/fm,	

L0=80 fm
L=(1+ξt)L0Andre SchneiderSN neutrinos and r-process nucleosynthesis• Important possible site for the r-process is the neutrino driven windin core collapse supernovae.	

• Ratio of neutrons to protons in wind
set by capture rates that depend onneutrino / anti-neutrino energies.	

! νe + n → p + e

ν̄e + p → n + e+

Searching for El Dorado
with supernova neutrinos
in Superkamiokande!

• Measure ΔE, difference in averageenergy for antineutrinos andneutrinos. If ΔE is large, wind will be
neutron rich. If ΔE is small, wind will
be proton rich and likely a problem
for r-process.

Measure energy of both anti-nu(SK) and neutrinos (liquid argon?). 	

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Present SN simulations
find too few neutrons. 	

Neutrino Spectra• The stronger the neutrinointeractions, the longer aneutrino stays in thermal
equilibrium with matter tolower densities andtemperatures, and the lower
is the emitted neutrinoenergy. 	

• Electron antineutrinos

capture on protons while
neutrinos capture on
neutrons. Matter is neutronrich so neutrinos havelarger opacity. Therefore
electron neutrinos (red) areemitted with lower energy
than antineutrinos (black).

Evan O’Connor• Binding energy shift (see below) increases
antineutrino and decreases neutrinoenergies leading to a larger ΔE.

Binding Energy shift• Proton in n rich matter more bound than n because of symmetry energy.	

• Energy shift can be calculated exactly with virial expansion (with A.
Schwenk). Find it is much larger than in some mean field models becauseof cluster formation.	

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• Neutrino absorption cross section is increased by energy shift which
increases energy and phase space of outgoing electron: 𝝼e+n -> p+e	!
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• Effect opposite for anti-neutrino absorption and reduces cross section
increasing E(anti-nu). 	

• Increases ΔE and makes wind somewhat more neutron rich. Probably notenough for r-process, but still important for nucleosynthesis!

Idea due to L. Roberts, my work with G. Shen, C. Ott, E. O’Connor

Recreating Neutrinosphere on Earth• Much of the “action” in core collapse

supernovae happens near the neutrinosphereat LOW densities where the matter may benonuniform. 	

• Neutrinosphere where mean free path is size
-1of system R~10 km = (σ𝝆) --> warm, lowdensity gas (T ~ 5 MeV, density ~𝜌0/100 )	

• Properties of neutrinosphere matter (forexample composition of light clusters 4He,3He, 3H…) important for emitted neutrino
spectra and nucleosyntheis of SN.	

• Can study neutrinosphere like conditions

Composition of intermediate velocity fragments in
HI collisions: Data (blue squares) Kowalski et al,
PRC 75, 014601(2007). Our virial EOS is black.

with heavy ion collisions in lab.
TargetProjectile

In a peripheral HI collision,intermediate velocity fragmentsfrom warm low density region.

Intermediate velocity fragments

Femtonova collaboration
neutrinosphere conditions with heavy ion collisions using• Recreate
radioactive beams. 	

comparing collisions with proton rich and neutron rich systems,• By
extrapolate to very neutron rich neutrinosphere conditions.	

composition, symmetry energy, equation of state,... of• Measureneutrinosphere matter.	

more robust predictions of neutrino spectra and• Allow
nucleosynthesis for core collapse SN.	

• Workshop at ECT* in Trento, Italy, April 7-11, 2014. 	

members (HI experimentalists, astrophysicists, neutrino• New
physicists…) welcomeNeutron Rich Matter

208Pb• Can be studied in lab. with radioactive beams
and in Astrophysics with X-rays, neutrinos,
gravitational waves.	

• PREX uses parity violating electron scattering
to accurately measure the neutron radius.	

– First result: Rn-Rp(208Pb)=0.33+.16-.18 fm. 	

– Plan to get more statistics for 208Pb, also
2nd expt. on 48Ca. 	

– Many implications for astrophysics...

• Collaborators: D. Berry, M. Gorchtein, R. Michaels, J. Piekarewicz, G.
Shen... Students: C. Briggs, J. Hughto, A. Schneider.	

• Supported in part by DOE.
C. J. Horowitz, Indiana University.

Supernovae and Gamma Ray Bursts, Yukawa Inst, Kyoto, Oct. 2013