Properties of Neutron Stars From Radio,
X-Ray and Gravitational Radiation
J. M. Lattimer
Department of Physics & Astronomy
Stony Brook University

January 17, 2016
Neutron Star Mergers: From Gravitational Waves to Nucleosynthesis
Hirschegg, Austria
15–21 January, 2016
J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Outline
Neutron Star Masses and RadiiI Neutron Star Crusts
I Neutron Matter Theory
I Hyperons and Quarks in Neutron Stars
I Universal Relations
I Gravitational Waves from Mergers
I Alternatives to General Relativity
I New Kinds of Observations
IJ. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

vanKerkwijk 2010
Romani et al. 2012

Although simple
average mass ofw.d. companions
is 0.23 M larger,
weighted average is0.04 M smaller

Demorest et al. 2010
Fonseca et al. 2016
Antoniadis et al. 2013
Barr et al. 2016
Champion et al. 2008

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Causality + GR Limits and the Maximum Masss

qus

arkSimilarly, a precision
upper limit to R sets
an upper limit to themaximum mass.

stars

=⇒=⇒

A lower limit to theM − R curves for minimally compact EOS
maximum mass sets alower limit to theradius for a given mass.

R1.4 > 8.15 km if
Mmax ≥ 2.01M .

cs2
∂p==s
∂εc2

Mmax < 2.4M if
R < 10.3 km.
If quark matter exists in the interior, the minimum radii aresubstantially larger.
J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Radii: Observations vs. Experiment
Ozel et al., PRE zph = z:
R = 9.7 ± 0.5 km (2009-14)
PRE+QLMXB;TOV,Mmax ,crust: R = 10.8+0.5−0.4 km (2015).

@@

Suleimanov et al. (2011)

Nättilä et al. (2015), PREcooling tail R = 11.7 ± 1.1 km.

Fiducial EOS, PREs, QLMXBs w/adjusted NH

14162M (M )Guillot & Rutledge (2014),
QLMXB, common radius, NH :R = 9.4 ± 1.2 km.

2.5

Lattimer & Steiner (2013),
PRE+QLMXB; TOV, causality,crust, Mmax , zph 6= z, alt NH .
Lattimer & Lim (2013), nuclear
experiments:
R1.4 = 12.0 ± 1.4 km.
J. M. Lattimer

1.5

10.568101218R (km)Properties of Neutron Stars From Radio, X-Ray and Gravitation

Role of Systematic Uncertainties
Systematic uncertainties plague radius measurements.
I Assuming uniform surface temperatures leads tounderestimates in radii.
I Uncertainties in interstellar absorption for quiesent
sources; spectral determinations may disagree with pulsar
dispersion estimates.
I In quiescent sources, He or C atmospheres can produce
about 50% larger radii than H atmospheres.
I In PRE sources, the spherically-symmetric Eddington flux
formula underestimates radii.
I Possible reduction in FEdd redshift factor in PRE sourcesincreases radii.
I Disc shadowing in PRE sources underpredicts√
A = fc−4 (R∞ /D)2 and R∞ ∝ A.
J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Quiescent Sources and a Common Radius

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Guillot & Rutledge (2013)

NGC 6397

common Rcausality

ω Cen

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Guillot & Rutledge (2013)
ytilauscacommon R


J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

PRE Burst Models
Observations measure:GMc pGM
FEdd,∞ =1−2β,β=κD 2Rc 22R∞F∞−4A==fc4
σT∞
DDetermine parameters:
FEdd,∞ κD
α= √= β(1 − 2β)
A fc4 c 3
Afc4 c 3R∞γ==.
κFEdd,∞
αSolution:√1
1 − 8α1β= ±,α ≤ for real solutions.
448J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

PRE M − R Estimates
αmin0.164 ± 0.024
0.153 ± 0.039
0.171 ± 0.042
0.164 ± 0.037
0.167 ± 0.045
0.198 ± 0.047

causality

41/
=β

Özel & Freire (2016)
J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Theoretical Neutron Matter Calculations

EPNM [MeV]

NS crust EOS below ns /2.
Theoretical studies below 2ns
using low-energy neutron
scattering data and few-body
calculations of light nuclei.
I Auxiliary Field DiffusionQuantum Monte Carlo(Gandolfi & Carlson)
I Chiral LagrangianExpansion (Drischler,Hebeler, Schwenk;
Sammarruca et al.,Tews et al., Lynn et al.,Hagen et al., Carbone etal., Corragio et al.,...)

Lynn et al. (2016)
Tews et al. (2013)
Hebeler et al. (2010)
TT (2013)
GCR (2012)
GC (2010)
APR (1998)
FP (1981)
Unitary gas (ξ=0.37)

2520151050J. M. Lattimer

00.05

0.1

0.15

0.2

n [fm-3]

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Unitary Gas Bounds

L (MeV)The unitary gas, i.e., fermionsinteracting via a pairwise
120
NL3STOS,TM1
short-range s-wave interaction
100 Excluded
with an infinite scattering
NLρδTMA
length |akF |−1 → 0, shows aNLρ
80
universal behavior. Cold
ut=1/2
KVOR
LS220
DBHF
FSUgoldatoms experiments show thatTKHS
60
DD2,
EUG ' 0.37EFG . Neutron
KVR
DD,D3C,DD-F
IUFSU
matter has a0 = −18.9 fm,
SFHo
GCR
40−1|a0 kF 0 | = −0.03. TheHS(SLBMKVOR0 ,L0)
assumption that the neutron
20 ut=1
SFHx
Allowedmatter energy En > EUG atall densities implies strong
0bounds on the symmetry
24 26 28 30 32 34 36 38 40
energy parameters Sv and L
S0 (MeV)(Kolomeitsev et al. 2016).
J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Kolomeitsev et al. (2017)50
S0=30,32,34,36 MeV

Sym. E (MeV)

Allowed4030(SLB0 ,L0)20

SLB(u)

10
Excluded
00.2

0.4

0.6 0.8
11.2
Density u=n/n0

J. M. Lattimer

1.4

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Nuclear Experimental Constraints
The liquid droplet model is a useful frame of reference. Its
symmetry parameters Sv and Ss are related to Sv and L:
aLLKsym
Ss'1+−+ ... .
Svro Sv
6Sv
12LI

Symmetry contribution to the binding energy:−1Ss2Esym ' Sv AI 1 +.
Sv A1/3

Giant Dipole Resonance (dipole polarizability)
AR 25 Ss
αD '1+.
20Sv
3 Sv A1/3
I Neutron Skin Thicknessr−1 3 2ro I Ss
Ss
10 Ss
1+1+.
rnp '
5 3 SvSv A1/3
3 Sv A1/3
IJ. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Theoretical and Experimental Constraints
H Chiral Lagrangian
G: Quantum Monte CarloSv − L constraints fromHebeler et al. (2012)
Experimental constraints
are compatible withunitary gas bounds.

Neutron matter constraints
are compatible withexperimental constraints.
J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Piecewise Polytropes◦
n3 , p3◦n2 , p2

Crust EOS is known: n < n0 = 0.4ns .

◦n1 , p1nmRead, Lackey, Owen & Friedman (2009)
found high-density EOS can be modeledas piecewise polytropes with 3 segments.
They found universal break points(n1 ' 1.85ns , n2 ' 3.7ns ) optimized fits
to a wide family of modeled EOSs.

◦n0 , p0
13.8

14.3

14.8

15.3

15.7

For n0 < n < n1 , assume neutron matter
EOS. Arbitrarily choose n3 = 7.4ns .
For a given p1 (or Γ1 ):0 < Γ2 < Γ2c or p1 < p2 < p2c .
0 < Γ3 < Γ3c or p2 < p3 < p3c .
Minimum values of p2 , p3 set by Mmax ;maximum values set by causality.
J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

p3 <p2

Maximum Mass and Causality Constraints

Model A:J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Mass-Radius Constraints from Causality

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Other Studies↑ ↑R1.4,min = 9.25 km R1.4,min = 10.6 km
Mmax = 1.66M
Mmax = 1.97M

Hebeler, Lattimer, Pethick & Schwenk 2010
J. M. LattimerÖzel & Freire 2016Properties of Neutron Stars From Radio, X-Ray and Gravitation

Constraints From Above
Kurkela et al. (2014)

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

pQCD + Neutron Matter Constraints
Kurkela et al. (2014)

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Radius - p1 Correlation

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Piecewise-Polytrope Average Radius Distributions
Assumes P(M) from observed pulsar-timing masses

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Folding Observations with Piecewise Polytropes

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Moment of Inertia - Radius Constraints

PSR 0737-3039A

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Binding Energy - Mass Correlations

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Tidal Deformatibility - Mass

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Tidal Deformatibility

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Tidal Deformatibility

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Binary Tidal Deformability
In a neutron star merger, both stars are tidally deformed. The
most accurately measured deformability parameter isΛ̄ =
16 
λ̄1 q 4 (12q + 1) + λ̄2 (1 + 12q)
13

whereq=

M1<1M2For S/N ≈ 20 − 30, typical measurement accuracies are
expected to be (Rodriguez et al. 2014; Wade et al. 2014):∆Mchirp ∼ 0.01 − 0.02%,∆Λ̄ ∼ 20 − 25%∆(M1 + M2 ) ∼ 1 − 2%,∆q ∼ 10 − 15%

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

NS – NS Mergers

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Binary Tidal Deformatibility - Λ̄J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Binary Tidal Deformatibility

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Binary Tidal Deformatibility

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Binary Tidal Deformatibility

J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and GravitationBlack Hole–Neutron Star Mergers

Lattimer & Lim (2013)
J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation

Future Observations
Twin stars with different radii:
Evidence for phase transitions
I Neutron star seismology and r-modes from GW
observations:Iνellipticity = 2f ,νr −mode ≈ (4/3)fCompactness from νr −mode .
Temperature if r-modes dominate heating.
I Moment of inertia if r-modes dominate spindown.
I Require factor of 3–10 improvement in sensitivity overaLIGO.
I Potential sources would be very young.
III

What else?
J. M. Lattimer

Properties of Neutron Stars From Radio, X-Ray and Gravitation