Matter under extreme conditions inneutron stars
Gordon Baym
University of Illinois
Urbana, Illinois&RIKEN iTHEMS

neutron star over Okinawa

ISCO 2023, OIST, Okinawa
28 February 2023

Inside a neutron star
Mass ~ 1-2+ Msun
Radius ~ 12-13 km
Temperature~ 106-109 K
Baryon no. ~ 1057
Magnetic fields~ 106 – 1016 G~ 106 - 1016G

Density ~ 2x1014g/cm3

Surface gravity~1011 that of Earth
Surface binding~ 1/10 mc2

Chadwick to Bohr, 24 Feb. 1932
announcing the discovery of the neutron”I enclose the proof ofa letter I have written
to Nature and which
will appear within thisweek or next.
The suggestion isthat α particles ejectfrom Be ... particles
which have a mass
almost equal to thatof the proton …"
09/05/32

NY Times
02/29/32

Baade & Zwicky propose neutron stars,
made in supernovae
APS Bulletin Dec. 1933
Cosmic Rays from Super-novae
PNAS 20, 259 (1934)
Oppenheimer & Volkoff (1939) calculate neutron star made offree neutrons (M = 0.7 M¤)...
Wheeler, 1966 (Ann. Rev. Astron. Astrophys.)A ``cool” superdense star ... is fainter than the19th magnitude and therefore hardly likely to be
seen. The rapidity of cooling makes detection
even more difficult.

Nov. 1967 First pulsar detection: 1919+21 Bell & Hewish

Jocelyn Bell1968 (Spring): Pulsars identified as rotating neutron stars by
Tommy Gold (Cornell) and Franco Pacini (Florence)Made in gravitational collapse of massive stars (supernovae)
and can be a remnant of binary neutron star mergers
Matter in neutron stars is densest in universe:
baryon density n up to ~ 5-10 n0n0 = 0.16 /fm3 <-> 3 X1014 g/cm3 = density of matter in atomic nuclei[cf. white dwarfs: r ~ 105-109 g/cm3]
1 fm = 10-13 cm
Supported against gravitational collapse by nucleon(and at higher densities quark) degeneracy pressure
Central engines in variety of compact energetic systems:
pulsars, binary X-ray sources, Soft Gamma Repeaters,magnetars, ultraluminous X-ray sources, Fast Radio Bursts (FRB),
binary neutron star (and ns-black hole) mergers
Astrophysical laboratory for study of cold high-density matter andQuantum Chromodynamics (QCD)Nuclei before neutron drip (outer crust)e-+pnn + n : makes nuclei neutron richas electron Fermi energy increases with depth_p+ e- + n : not allowed if e- state already occupied
Beta equilibrium: µn = µp + µe

Fermi seas

GB, C.J.Pethick, and
P. Sutherland, Ap.J. (1971)

Shell structure (spin-orbit forces) for very neutron rich nuclei?
Do N=50, 82 remain neutron magic numbers? Proton shell structure?
Being explored at rare isotope accelerators: RIKEN Rare Ion Beam
Facility (RIBF), and later GSI (MINOS), FRIB, RAON (KoRIA)

Neutron drip
Beyond density rdrip ~ 4.3 X 1011 g/cm3 neutron bound statesin nuclei become filled. Further neutrons must go into
continuum states. Form degenerate neutron Fermi sea.

Neutrons in neutron sea are in equilibriumwith those inside nucleus (common µn)
How do the nuclei turn into
liquid at higher densities?

Protons appear not to drip, but remain in bound states until
nuclei merge in liquid interior.

The liquid interior near nuclear matter density
Theoretical extrapolation from low energy laboratory nuclear physics
near nuclear matter density up to 2n0 or higher.
Determine the equation of state:
Pressure P(ε)
as function of energy density, ε :ε = energy density = ρc2nb = baryon density
P(r) = pressure = nb2 d(ε/nb)/dnb

1) Determine N-N potentials from scattering expts E < 300 MeV,+deuteron, 3 body nuclei (3He, 3H); solve Schrödinger eq. variationally
Two body potential alone fails!!
Fix with three body forces.

2) Chiral effective theory approach -- best now
Expansion in low energy processes, e.g., one π exch.

Construct neutron star models@P (r)=@r

E = energy density = ρc2nb = baryon density
P(r) = pressure = nb2 d(E/nb)/dnb⇢(r) + P (r)/c2G[m(r) + 4⇡r3 P (r)/c2 ]2r (r 2Gm(r)/c )<latexit sha1_base64="C91B1+PAONQlhr+ASZa0l2IX56g=">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</latexit>

TOV equation
M=<latexit sha1_base64="/aCt9I8Ls4C7HcTVDZ9GLaps9yQ=">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</latexit>

Maximum neutron star mass

Mass vs. central density

Z R4⇡r2 dr⇢(r)

0

Mass vs. radius

Akmal, Pandharipande and Ravenhall (APR) 1998 nuclear equation of stateFundamental limitations of eq. of state based on NN interactions
Accurate for n~ n0.

But for n >> n0:-sound speed becomes greater than speed of light-importance of 3 (4,5...) body forces grows with density-chiral effective theory breaks down above n ~ 1.5-2n0.
-can forces be described with static few-body potentials?
-can one even describe system in terms of well-defined “asymptotic''laboratory particles?
New degrees of freedom enter! QUARKSSqueeze:=>

Given all information on Nb+Nb atomic scattering could one predict that
Nb is a superconductor?

Atoms are made of electrons and nuclei.
Similarly neutrons, protons, and nuclei are made ofquarks and gluons
Quarks = fractionally charged spin-1/2 fermions, baryon no. = 1/3,
with internal SU(3) color degree of freedom.
Flavor Charge/|e| Mass(MeV)u

2/3~2d-1/3~5s-1/3~ 94c

2/3~1280

b-1/3~4200

t

2/3~175,000

proton = u + u + dneutron =_ u + d + dp+ = u + d, etc.

Quark matter (baryonic) in the early universe at t < 1 microsec(T > 100 MeV), and in the deep interiors of heavier neutron stars.
Can’t calculate strongly interacting matter exactly – technical problem

The Golden Age of Neutron Stars:
Wealth of new observational data, and even GoldThe Golden Age of Neutron Stars:
Wealth of new observational data, and even GoldDetections of heavy neutron stars in pulsars
Equation of state relatively stiff
Masses and radii of neutron stars
NICER measuring M, R directly for a few pulsars
Gravitational waves from ns-ns and ns-black hole mergers exploremasses, radii, and tidal deformabilities
Production of heavy elements via r-process: Au, Pt, Ag, U, Sr
LIGO/Virgo/KAGRA (Run 4 - 05/23)
Eventually Cosmic Explorer, Einstein Telescope, LISA
Glitches: probe n,p superfluidity and crust
Cooling of n-stars: search for rapid cooling from exotic states,
measuring equation of state in crustNeutron star masses
precision
GR testsÖzel & Freire, Ann Rev AA (2016)binary neutron stars

Hulse-Taylor
Hulse-Taylor

with high masscompanions

PSR J1614-2230 :Mnstar = 1.928 ± 0.017M¤
PSR J0348+0432:Mnstar = 2.01 ± 0.04M¤
PSR J0740+6620 :Mnstar = 2.08 ± 0.07 M¤

Galactic black hole masses
ns +white dwarf ns +white dwarf

optically observed
w.d companion
accreting bursters

Mass determinations of three high mass neutron stars(pulsars in binaries)
PSR J0348+0432: Mneutron star = 2.01 ± 0.04M¤
PSR J1614-2230 :
1.93 ± 0.02M¤
PSR J0740+6620 :2.08 ± 0.07M¤

2013
2016
2019

MassMass=> the equation of state is stiff
stiff e.o.s.

soft e.o.s.

Central density
Central density

Softer equation of state =>lower maximum mass andhigher central density
Binary neutron stars ~ 1.4 M¤:
consistent with soft eq. of state
Can quarks support two solar masses?

Two further massive neutron stars
PSR 1748-2021B (Arecibo, 1998)
Binary pulsar in globular cluster M5.
P = 16.7 msec.
Companion light and small. Awaiting
detection by James Webb Space TelescopeM<2.5 Msun
PSR J0952-0607(R. Romani, Ap.J. Lett. 934:L17, 2022)

Black widow pulsar, P =14.1 msec.
Mass of companion = 0.032 ± 0.002 Msun
M = 2.35 ± 0.17 Msun

S. Ransom, preliminary

Binary neutron star mergers likely siteof heavy element production (via r-process)

Periodic table of the elements with their “origins”

Gravitational radiation: new window on neutron stars
GW170817: Initial spectacular event – Multi-messenger astronomy
Neutron star – neutron star (BNS) merger observed on 17 Aug. 2017by LIGO and Virgo (gravitational radiation),
11 hours later
FERMI (gamma ray telescope) and ~ 70other electromagnetic observatories.
m1~ 1.36-1.60 M◎, m2 ~1.17-1.36 M◎
much redderradii ~ 11.9 ± 0.7 km
4 days later

Two neutron stars merging,emitting gravitational radiation
and. post-merger, forming:

Kilonova: neutron-richsite of r-process

GW190814

8 compact
objects detectedby LIGO/Virgo

GW190426
Mass gap

GW190425

8 compact objects“GW19…” objects involve neutron stars

GW170817 formed low mass(~2.7 Msun) black hole (?)

NICER = Neutron star Interior Composition ExploreR
X-ray timing (to 300 nsec)& spectroscopy (0.12-12 KeV)

Delivered to Int’lSpace Station
03 June 2017

Measure masses and radii (5%) bymonitoring X-ray pulse profiles ofnearby neutron stars (J0437, ...)
Properties of n.s. crusts via astroseismology
Periodic pulsations from transient & steady systems

Results for two neutron stars
PSR J0740+6620 : Mnstar = 2.08 ± 0.07 M¤ , Rnstar ~12-13 km
PSR J0030+0451 := 1.44 ± 0.15 M¤ ,~12-13 km

Track hot spots on neutron star. Light bending by star enables
one to see spot “behind” star. Bending depends on M and R.

Rotatingneutron starObserver= NICER

hot spot

Measure amplitudes and phases
in different frequencies, constructmodel of hot spots to interpret data
PSR J0030+0451
Mass vs Radius
Miller et al.,Ap.J. (2019)

Pulse Profile Modeling (PPM)
WeakGravity

StrongGravity

Credit: Morsink/Moir/Arzoumanian/NASA-GSFC

Messages from NICER
Would expect that adding mass
to neutron star decreases its radius.
All eqns of state based on interacting
nucleons show this behavior.
But inferred eqn of state shows radiusfrom ~1.4-2.1 Msun changing little.

APR

Points to rapid stiffening of nuclear
matter, and onset of higher momentum
degrees of freedom.
Nucleons beginning transition toquark matter. Pauli blocking of quarks
pushes quarks to become relativistic,
and start to contribute directly to thepressure, well before quark Fermi sea
develops.

Quarks in dense matter
The early universe before one microsecond
after the big bang -- hot quark gluon plasmaand created in ultrarelativistic heavy ion collisions

Quarks (and gluons) innuclei will be mapped by
future Electron-Ion Collider

Cold quark matter coresof high mass neutron stars –Strongly interacting system: cannot dolattice QCD simulations at finite density,
zero temperature, owing to fermion signproblem.

Matter under extreme conditions:baryon density/ temperature

Ultrarelativistic
heavy ion
collisions(B. Jacaktalk Friday)

1983
Building of Brookhaven Relativistic Heavy Ion
Collider (RHIC) 1983-2000, to study nuclear
matter under extreme energy density –finds hot quark gluon plasma

More modern phase diagram

Deconfined
quarks andgluons

QCD lattice gauge
theory -- for finite lightquark masses -- predicts
crossover from confinedphase at lower T todeconfined phase athigher T.
Do quarks roam freely inthe deconfined phase?
If so, they must alsoroam freely at lower T.

Quarks confined

Are there really quarks
running about freely inthe room?

T

SU(3)C x U(1)B
Asakawa-Yazaki critical pt.

SU(3)V X SU(3)AQGP
Hadronic

B

Diquark pairing
A

Possible new critical pt.

U(1)B

μB

Critical points similar to those in liquid-gas phase
diagram (H2O). Neither critical point necessary!!
Can go continuously from A to B around theupper critical point. Liquid-gas phase transition.
In lower shaded region have BCS pairing of nucleons,of quarks, and possibly other states (meson condensates, quarkyonic).
Different symmetry structure than at higher T.

T

SU(3)C x U(1)B
Asakawa-Yazaki critical pt.

Heavy ion collisions

Hadronic

SU(3)V X SU(3)AQGP
B

Diquark pairing
Possible new critical pt.

AElectron-ion collider

U(1)B

μB

Critical points similar to those in liquid-gas phase
diagram (H2O). Neither critical point necessary!!
Can go continuously from A to B around theupper critical point. Liquid-gas phase transition.
In lower shaded region have BCS pairing of nucleons,of quarks, and possibly other states (meson condensates, quarkyonic).
Different symmetry structure than at higher T.

QHC21 (quark-hadron crossover) equation of state:
QHC19 --GB, S. Furusawa, T. Hatsuda, T. Kojo & H. Togashi, Ap.J. 885:42 (2019)
QHC21 --T. Kojo, GB, &T. Hatsuda,, Ap.J. 934:46 (2022).

Have good idea of equation of state at nuclear and at high densities.

PPressure vs. baryon
chemical potential

quarks
@ 2 P/@µ2 = @nB /@µ0<latexit sha1_base64="aSlZoK5JRyQuVy/nuXrlfK6guMM=">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</latexit>

nuclearbetween ~ 1.5-8 n0 highly constrained by continuity & stability

μSimplified picture of quarks with
universal repulsive short-range qq coupling (Kunihiro)
and diquark (BCS) pairing interaction
Nuclear equation of state up to 1.5n0 (chiral effective theory)Quarks beginning to enter neutron stars
Mass vs. central density

Central density of PSR
J0740+6620 ~5n0.
Well above densities wherepure hadronic calculations arevalid. Entering transition tostrongly interacting quarkmatter.
Sound velocity

Cores of higher mass stars could
reach beyond transition.
Fully developed quark matter incores? Need fully microscopic
calculations of matter undergoingtransition from nucleonic toquark degrees of freedom.

Peak not seen innucleonic eq. of stateNuclear matter based on chiral EFT + transition to quark matterin excellent agreement with NICER inferences of radii. Rapidpressure rise!
Central density for 2.08 Msun ~ 3.6 n0
2.5

2MJ0740+6620

M/M!

3.5
1.5

10.5

1.4M!

QHC21

AχBχ
CχDχ
Drischler

2.1
1.9
1.7

1.5

1.3

0
10

10.5

1111.5
R [km]

1212.51313.5

QHC21

Sound velocity reflects stiffness of matter
Sound velocity

c2s = @P/@"
cs = sound velocity
P – pressure
ε = energy density (including rest mass)

Structure from stiffening nuclear matter
followed by superfluid quark matter
Rise for n < 2n0 characteristic of nuclear matter.
But nuclear matter eventually has
cs > c = speed of light.
Sound velocity in superfluid quark matter(BCS pairing) falls until one enters perturbativeregime ( αs <<1 <=> μ >> Λqcd ~ 300 MeV )then flattens out at cs ~ c/√3 (conformal limit).
Toru Kojo

Eventually sound velocity -> c/√3 from below!!

NICER has provided first empirical tests of theories ofneutron rich nuclear matter
1) Chiral Effective Field Theory of nuclear matter points
toward stiff neutron rich matter in nuclear regime (up to 1.5n0), adequate to allow 12-13 km neutron stars.
2) Effective equality of radii of neutron stars of 1.4 and 2.08
Msun
3) Future NICER measurements of radii of neutron stars ofintermediate masses, with improved precision,

Challenges for future:
Build consistent phenomenological picture of matter above nuclear
matter density from both gravitational radiation and NICER data.
Develop microscopic pictures of transition from hadronic to quark
degrees of freedom in the regime 1.5-8 n0.
(Not good enough to draw a curve P(ρ) that fits data. Must
understand microscopic physics at QCD level.)
What are the lightest and heaviest neutron stars, and lightest black
holes? (cf. LIGO/Virgo's eight compact objects)
Future NICER data and eventual gravitational wave data
(3rd generation detectors, to 400 Mpc => ~ 102 BNS mergers/year)
will continue to clarify physics of matter under extreme conditions.

どうもありがとう36