From Nuclei to Neutron Stars
Madappa Prakash
Ohio University, OH
&
PALS
Andrew W. Steiner (LANL)
James M. Lattimer (Stony Brook University)
Paul. J. Ellis (Minneapolis)
June 13, 2006 @ JLab, VA
1/19
Objectives of this talk
I Why basic features such as M & R of a neutron star (NS) are
important?
I What are some key theoretical advances made in the recent past?
I How can lab experiments, particularly at JLab, help to unravel the
composition & structure of a NS?
I What key NS observations are necessary to take leaps in our
understanding?
I Why care? In one object, many fields come together to make
discoveries and provide understanding.
2/19
Some References
1. J. M. Lattimer & M. Prakash,
Phy. Rep. 333 (2000) 121.
Astrophys. Jl. 550 (2001) 426.
Science, 304 (2004) 536.
Phys. Rev. Lett., 94 (2005) 111101.
2. A. W. Steiner, M. Prakash, J. M. Lattimer & P. J. Ellis,
Phys. Rep. 411 (2005) 325.
3. S. Typel & B. A. Brown
Phys. Rev. C 64 (2001) 426.
4. C. J. Horowitz, S. J. Pollock, P. A. Souder & R. Michaels
Phys. Rev. C 63 (2001) 025501.
5. C. J. Horowitz & J. Piekarewicz
Phys. Rev. Lett., 86 (2001) 5647.
6. R. Michaels, P. A. Souder, G. M. Urciuoli
Proposal PR-00-003, Jefferson Laboratory, 2000
3/19
I M ∼ (1 − 2)M
M ' 2 × 1033 g.
I R ∼ (8 − 16) km
I ρ > 1015 g cm−3
I Bs = 109 − 1015 G.
I Tallest mountain:
E
∼ 1cm
∼ Amliq
p gs
I Atmospheric height:
RT
∼ µg
∼ 1cm
s
Lattimer & Prakash , Science 304, 536 (2004).
4/19
The Nuclear (A)Symmetry Energy
I Energy cost to create an
asymmetry (δ) between
neutrons and protons
40
E/A (MeV)
APR
NRAPR
RAPR
Esym
20
np
δ = 1−2
np + n n
= 1 − 2x
Neutron matter
0
Nuclear matter
-20
0
0.05
0.1
0.15
-3
n (fm )
0.2
1 d2 =
2n dδ 2
0.25
I Structure of nuclei &
neutron stars
determined by the
energy & pressure of
beta-stable
nucleonic matter
E(n, x) ' E(n, 0.5) + Esym (n)(1 − 2x)2
0
P (n, x) ' n2 [E 0 (n, 0.5) + Esym
(n)(1 − 2x)2 ]
5/19
Some Connections
Isospin Dependence of Strong Interactions
Nuclear Masses
Neutron Skin Thickness
Isovector Giant Dipole Resonances
Fission
Heavy Ion Flows
Multi-Fragmentation
Nuclei Far from Stability
Rare Isotope Beams
Many-Body Theory
Symmetry Energy
(Magnitude and Density Dependence)
Supernovae
Weak Interactions
Early Rise of Lν e
Bounce Dynamics
Binding Energy
Proto-Neutron Stars
ν Opacities
ν Emissivities
SN r-Process
Metastability
QPO’s
NS Cooling
Mass
Radius
Temperature
R∞ , z
Direct Urca
Superfluid Gaps
Neutron Stars
Binary Mergers
Observational
Properties
Decompression/Ejection
of Neutron-Star Matter
r-Process
X-ray Bursters
Gravity Waves
R∞ , z
Mass/Radius
dR/dM
Maximum Mass, Radius
Composition:
Hyperons, Deconfined Quarks
Kaon/Pion Condensates
Pulsars
Masses
Spin Rates
Moments of Inertia
Magnetic Fields
Glitches - Crust
6/19
Mass Radius Relationship
Lattimer & Prakash , Science 304, 536 (2004).
7/19
Measured Neutron Star Masses
I Mean & weighted
means in M
I X-ray binaries:
1.62 & 1.48
I Double NS binaries:
1.33 & 1.41
I WD & NS binaries:
1.56 & 1.34
I Lattimer & Prakash,
PRL, 94 (2005) 111101
8/19
The Skin Thickness
Schematic neutron and proton distributions in a neutron-rich nucleus
Nuclear charge radii known to better than 0.1%
Neutron-matter radii known poorly! JLab can fix this!!
9/19
The Typel-Brown Correlation
Neutron skin thickness vs pressure of subnuclear neutron-star matter
0.3
I Nucleus: 208 Pb
I Neutron skin thickness:
Potential
Field-theoretical
δR = hrn2 i1/2 − hrp2 i1/2
δ R (fm)
0.25
I Matter Pressure:
Pβ (n, x) = Pnuc (n, x)
+ Pe + Pµ
0.2
0.15
0
0.5
1
-3
1.5
3
Pβ(n=0.1 fm ) (MeV/fm )
2
I For δR = 0.2 ± 0.025
fm, Pβ = 0.9 ±
0.3 MeV/fm3
Nuclear charge radii known to better than 1%
Neutron-matter radii known poorly! JLab can fix this!!
10/19
The Lattimer-Prakash Correlation
Neutron star radius vs pressure of supranuclear neutron-star matter
8
Potential
Field-theoretical
3 n0
α=0.252
6
RP
α
2 n0
4
α=0.317
3/2 n0
2
α=0.281
0
8
10
12
R1.4 (km)
14
I Radii of 1.4 M
neutron stars from GR
structure (TOV)
equations
I Pressure from models
of neutron-star matter
I Correlation stems from
GR & matter properties as analytical studies
show
16
Pressure of neutron-star matter poorly known!
Measurement of neutron-star radii being vigorously pursued!
11/19
The Lattimer-Prakash Correlation
Neutron star radius vs pressure of supranuclear neutron-star matter
8
Potential
Field-theoretical
3 n0
α=0.249
6
RP
α
2 n0
4
α=0.292
3/2 n0
2
α=0.245
0
8
10
12
I Radii of maximum
mass neutron stars from
GR structure (TOV)
equations
I Pressure from models
of neutron-star matter
I Correlation stems from
GR & matter properties as analytical studies
show
14
Rmax (km)
Pressure of neutron-star matter poorly known!
Measurement of neutron-star radii being vigorously pursued!
12/19
The Horowitz-Piekarewicz Correlation
Neutron skin thickness vs neutron star radius
Potential
δ R (fm)
0.3
Field-theoretical
I Radii of 1.4 M
neutron stars from GR
structure (TOV)
equations
I Skin thicknesses from
models of nuclei
0.2
0.1
0
8
10
12
R1.4 (km)
14
16
For δR = 0.2 ± 0.025 fm, R1.4 = 13 ± 0.5 km
13/19
The Horowitz-Piekarewicz Correlation
Neutron skin thickness vs neutron star radius
Potential
δ R (fm)
0.3
Field-theoretical
I Radii of maximum
mass neutron stars from
GR structure (TOV)
equations
I Skin thicknesses from
models of nuclei
0.2
0.1
0
8
10
RMax (km)
12
14
For δR = 0.2 ± 0.025 fm, Rmax = 11 ± 0.5 km
Here Mmax can vary up to 2.2 M
14/19
Neutron star radius measurements
Object
Omega Cen
Chandra
Omega Cen
(XMM)
M13
(XMM)
47 Tuc X7
(Chandra)
M28
(Chandra)
EXO 0748-676
(Chandra)
R (km)
13.5 ± 2.1
D (kpc)
5.36 ± 6%
Ref
Rutledge et al. (’02)
13.6 ± 0.3
5.36 ± 6%
Gendre et al. (’02)
12.6 ± 0.4
7.80 ± 2% Gendre et al. (’02)
+1.6
14.5−1.4
(1.4 M )
+6.9
14.5−3.8
5.13 ± 4%
Rybicki et al. (’05)
5.5 ± 10%
Becker et al. (’03)
13.8 ± 1.8
9.2 ± 1.0
(2.10 ± 0.28 M )
Ozel (’06)
15/19
Moment of inertia (I) measurements
Spin precession periods:
Pp,i
2c2 aP M (1 − e2 )
=
.
GM−i (4Mi + 3M−i )
Spin-orbit coupling causes a periodic departure from the expected
time-of-arrival of pulses from pulsar A of amplitude
MB a
a IA P
δi cos i =
δtA =
sin θA cos i
2
M c
c M A a PA
P : Orbital period a: Orbital separation e: Eccentricity
M = M1 + M2 : Total mass
i: Orbital inclination angle θA : Angle between SA and L.
IA : Moment of Inertia of A
For PSR 0707-3039, δtA ' (0.17 ± 0.16)IA,80 µs ;
Needs improved technology & is being pursued.
16/19
Limits on R from M & I measurements
I 10% error bands on I in M km2
I Horizontal error bar for M = 1.34 M & I = 80 ± 8 M km2
J. M. Lattimer & B. F. Schutz, Astrophys. Jl. 629 (2005)
17/19
Ultimate Energy Density of Cold Matter
I Tolman VII:
= c (1 − (r/R)2 )
I c ∝ (M /M )2
I A measured
red-shift provides a
lower limit.
I Crucial to establish an upper
limit to Mmax .
Lattimer & Prakash, PRL, 94 (2005) 111101.
18/19
Outlook
I Growing observations of neutron stars can delineate the equation of
state (EOS) of neutron-star matter and shed light on the density
dependence of the symmetry energy (strong interactions in a
many-body context).
I Precise laboratory experiments, particularly those involving
neutron-rich nuclei, are sorely needed to pin down the subnuclear
aspects of the symmetry energy.
I All power to parity violating electron scattering experiments at
JLab to measure the neutron distributions precisely. Besides being
the first, it can also be the best!!
19/19