Dense Matter in Neutron Stars: New Insights from Theory and - - PowerPoint PPT Presentation
Dense Matter in Neutron Stars: New Insights from Theory and Observations. Sanjay Reddy INT & Univ. of Washington, Seattle EMMI workshop on Cold dense nuclear matter from short- range correlations to neutron stars, GSI, Darmstadt.
Sanjay Reddy INT & Univ. of Washington, Seattle
Dense Matter in Neutron Stars: New Insights from Theory and Observations.
EMMI workshop on “Cold dense nuclear matter from short- range correlations to neutron stars”, GSI, Darmstadt.
Massive Neutron Star
Massive Neutron Star
AP3 AP3 AP4 AP4 ENG ENG MPA1 MPA1 MS0 MS0 MS2 MS2 WFF1 WFF1 PAL1 PAL1 SQM1 SQM1 SQM3 SQM3 GS1 GS1 GM3 GM3 PAL6 PAL6 FSU FSU MS1 MS1
6 8 10 12 14 16 0.5 1.0 1.5 2.0 2.5 RNS km MNS M
Towards a measurement of neutron star radii
Thermal Relaxation in Accreting Neutron Stars
Massive Neutron Star
AP3 AP3 AP4 AP4 ENG ENG MPA1 MPA1 MS0 MS0 MS2 MS2 WFF1 WFF1 PAL1 PAL1 SQM1 SQM1 SQM3 SQM3 GS1 GS1 GM3 GM3 PAL6 PAL6 FSU FSU MS1 MS1
6 8 10 12 14 16 0.5 1.0 1.5 2.0 2.5 RNS km MNS M
Towards a measurement of neutron star radii
Thermal Relaxation in Accreting Neutron Stars
Massive Neutron Star
Multi messenger (e.g. Metzger & Ber
Kilo Nova (r-process ?)
AP3 AP3 AP4 AP4 ENG ENG MPA1 MPA1 MS0 MS0 MS2 MS2 WFF1 WFF1 PAL1 PAL1 SQM1 SQM1 SQM3 SQM3 GS1 GS1 GM3 GM3 PAL6 PAL6 FSU FSU MS1 MS1
6 8 10 12 14 16 0.5 1.0 1.5 2.0 2.5 RNS km MNS M
Towards a measurement of neutron star radii
104 4x1011 2x1014 6x1014 1015
Crust: Inner Crust: (Solid-Superfluid) nuclei, electrons, neutrons
Inner Core ?
O u t e r (solid) nuclei, electrons
~3 ~10 ~11.5 ~12
(Superfluid- Superconductor) Outer Core
neutrons, protons electrons
P=ε
neutron drip 7 11 14 15 relativistic electrons crust core nuclear matter
can calculate can speculate
P=ε
neutron drip 7 11 14 15 relativistic electrons crust core nuclear matter
can calculate can speculate
P=ε
neutron drip 7 11 14 15 relativistic electrons crust core
Maximum Mass
nuclear matter
can calculate can speculate
P=ε
neutron drip 7 11 14 15 relativistic electrons crust core
Maximum Mass Radius
nuclear matter
can calculate can speculate
P=ε
neutron drip 7 11 14 15 F i r s t O r d e r P h a s e T r a n s i t i
relativistic electrons crust core
Maximum Mass Radius
nuclear matter
can calculate can speculate
P=ε
neutron drip 7 11 14 15 F i r s t O r d e r P h a s e T r a n s i t i
relativistic electrons crust core
Maximum Mass Radius
2 M⊙ NS
nuclear matter
14 15 crust core
0.08 0.16
can calculate can speculate inner core
0.32 0.48 0.64
14 15 crust core
0.08 0.16
can calculate can speculate inner core
Q ' pF ' ΛB ΛB ' 500 MeV
0.32 0.48 0.64
14 15 crust core
0.08 0.16
Chiral EFT Systematic error estimates can calculate can speculate inner core
Q ' pF ' ΛB ΛB ' 500 MeV
0.32 0.48 0.64
14 15 crust core
0.08 0.16
Chiral EFT Systematic error estimates can calculate can speculate Chiral EFT + 𝚬 Systematic error estimates inner core
Q ' pF ' ΛB ΛB ' 500 MeV
0.32 0.48 0.64
14 15 crust core
0.08 0.16
Chiral EFT Systematic error estimates can calculate can speculate Chiral EFT + 𝚬 Systematic error estimates inner core
Q ' pF ' ΛB ΛB ' 500 MeV
0.32 0.48 0.64
Recall talks by Schwenk & Weise
14 15 crust core
0.08 0.16
Chiral EFT Systematic error estimates
Errors can only be estimated crudely can calculate can speculate Chiral EFT + 𝚬 Systematic error estimates inner core
Q ' pF ' ΛB ΛB ' 500 MeV
0.32 0.48 0.64
Recall talks by Schwenk & Weise
16
1 2
Nuclei exist here
E(ρn, ρp) MeV
Symmetric Matter
N e u t r
M a t t e r
✏ = ⇢ E(⇢) P(✏) = ⇢2 @E(⇢) @⇢
ρ0 = 2.6 × 1014 g/cm3
En(ρ ' ρ0) ' 16 MeV + S + L 3 (ρ ρ0) ρ0
16
1 2
Nuclei exist here
E(ρn, ρp) MeV
Symmetric Matter
S=32±3 MeV
N e u t r
M a t t e r
✏ = ⇢ E(⇢) P(✏) = ⇢2 @E(⇢) @⇢
ρ0 = 2.6 × 1014 g/cm3
En(ρ ' ρ0) ' 16 MeV + S + L 3 (ρ ρ0) ρ0
16
1 2
Nuclei exist here
E(ρn, ρp) MeV
Symmetric Matter
S=32±3 MeV L = 50 ± 30 MeV (Expt)
N e u t r
M a t t e r
✏ = ⇢ E(⇢) P(✏) = ⇢2 @E(⇢) @⇢
ρ0 = 2.6 × 1014 g/cm3
En(ρ ' ρ0) ' 16 MeV + S + L 3 (ρ ρ0) ρ0
16
1 2
Nuclei exist here
E(ρn, ρp) MeV
Symmetric Matter
S=32±3 MeV L = 50 ± 30 MeV (Expt)
N e u t r
M a t t e r
✏ = ⇢ E(⇢) P(✏) = ⇢2 @E(⇢) @⇢
ρ0 = 2.6 × 1014 g/cm3
En(ρ ' ρ0) ' 16 MeV + S + L 3 (ρ ρ0) ρ0
Empirical Value
Caveat: Separation between 2N and 3N contributions is resolution scale and model dependent.
Empirical Value
Caveat: Separation between 2N and 3N contributions is resolution scale and model dependent.
Empirical Value
Theory 2N
Caveat: Separation between 2N and 3N contributions is resolution scale and model dependent.
Empirical Value
Theory 2N
Theory 2N+ 3N
Caveat: Separation between 2N and 3N contributions is resolution scale and model dependent.
Implications for NS radius: R = 12 ± 2 km
0.05 0.1 0.15
n [fm-3]
5 10 15 20
E/N [MeV]
EM 500 MeV EGM 450/500 MeV EGM 450/700 MeV NLO lattice (2009) QMC (2010) APR (1998) GCR (2012)
0.1 0.2 0.3 0.4 0.5
n [fm
20 40 60 80 100
E/N [MeV]
30 32 34 36
Sv [MeV]
30 40 50 60 70
L [MeV]
35.1 33.7 32 Sv= 30.5 MeV (NN)
Prediction Extrapolation
Hebeler, Schwenk,Furnstahl, Tews, … Holt, Kaiser, Weise, … Hagen, Papenbrock, … Gandolfi, Carlson, Reddy
Gandolfi, Carlson, Reddy (2010)
S & L are correlated by the model. Experimental measurement of L & S with ~ 1 MeV error needed to test the model.
0.1 0.2 0.3 0.4 0.5
Neutron Density (fm
20 40 60 80 100
Energy per Neutron (MeV)
30 32 34 36
Esym (MeV)
30 40 50 60 70
L (MeV)
35.1 33.7 32 Esym= 30.5 MeV (NN) Fermi-gas
S (MeV)
S
Up to about twice saturation density, the 3- body contribution is smaller than the 2-body force.
This was a first attempt at estimating extrapolation errors in phenomenological models. Need to understand how to quantify uncertainties of this extrapolation by varying the short-distance behavior of both 2 and 3 body forces together.
8 9 10 11 12 13 14 15 16
R (km)
0.5 1 1.5 2 2.5 3
M (Msolar)
Causality: R>2.9 (GM/c
2
)
ρ
c e n t r a l
=2ρ ρ
central
=3ρ ρ
central
=4ρ ρcentral=5ρ0
35.1 33.7 32 Esym= 30.5 MeV (NN)
1.4 Msolar 1.97(4) Msolar
S
L=31 L=64 L=55 L=42
8 9 10 11 12 13 14 15 16
R (km)
0.5 1 1.5 2 2.5 3
M (Msolar)
Causality: R>2.9 (GM/c
2
)
ρ
c e n t r a l
=2ρ ρ
central
=3ρ ρ
central
=4ρ ρcentral=5ρ0
35.1 33.7 32 Esym= 30.5 MeV (NN)
1.4 Msolar 1.97(4) Msolar
S
L=31 L=64 L=55 L=42
8 9 10 11 12 13 14 15 16
R (km)
0.5 1 1.5 2 2.5 3
M (Msolar)
Causality: R>2.9 (GM/c
2
)
ρ
c e n t r a l
=2ρ ρ
central
=3ρ ρ
central
=4ρ ρcentral=5ρ0
35.1 33.7 32 Esym= 30.5 MeV (NN)
1.4 Msolar 1.97(4) Msolar
S
L=31 L=64 L=55 L=42
A 10% Radius Measurement
temperature is uniform; (iii) atmosphere composition is known and (iii) distance and inter-stellar absorption is measured.
Heinke et al, and Steiner & Lattimer (2014)
AP3 AP3 AP4 AP4 ENG ENG MPA1 MPA1 MS0 MS0 MS2 MS2 WFF1 WFF1 PAL1 PAL1 SQM1 SQM1 SQM3 SQM3 GS1 GS1 GM3 GM3 PAL6 PAL6 FSU FSU MS1 MS1
6 8 10 12 14 16 0.5 1.0 1.5 2.0 2.5 RNS km MNS M
Guillot et al (2014) Steiner et al, Heinke et al (2014)
Chandra XMM Hubble
Figure adapted from Guillot et al (2014)
temperature is uniform; (iii) atmosphere composition is known and (iii) distance and inter-stellar absorption is measured.
Heinke et al, and Steiner & Lattimer (2014)
AP3 AP3 AP4 AP4 ENG ENG MPA1 MPA1 MS0 MS0 MS2 MS2 WFF1 WFF1 PAL1 PAL1 SQM1 SQM1 SQM3 SQM3 GS1 GS1 GM3 GM3 PAL6 PAL6 FSU FSU MS1 MS1
6 8 10 12 14 16 0.5 1.0 1.5 2.0 2.5 RNS km MNS M
Guillot et al (2014) Steiner et al, Heinke et al (2014)
Chandra XMM Hubble
Figure adapted from Guillot et al (2014)
Ozel et al (2015)
The energy associated with converting a neutron to a proton in neutron-rich matter has important implications for astrophysics: neutron protron ∆E(p, q) = En(p) − Ep(p + q)
1500 km 3X107 km 10 km Core collapse tcollapse ~100 ms Shock wave Eshock~1051ergs 100 km
carry away ~ 3 x 1053 ergs
heat is transported in the neutron star core.
not so dense (1012-1013 g/cm3 ) neutrino-sphere.
neutrinos diffuse
newly born neutron star Quasi-static ~ 1 s
Convection: Driven by composition
depends on the pressure or neutron
neutrino diffusion convection
Heat transport : Neutrino diffusion + convection
τdiff ' R2 c λν ⇡ 3 5 s
Diffusion: Large values of L suppress convection.
Roberts, Cirigliano, Pons, Reddy, Shen, Woosley (2012)
ω2 = − g γnB (γs∇ ln(s) + γYL∇ ln(YL))
γnB = ∂ ln P ∂ ln nB
γs = ∂ ln P ∂ ln s
γYL = ∂ ln P ∂ ln YL
∂P ∂YL
≃ n4/3
B Y 1/3 e
− 4n2
BE′ sym(1 − 2Ye),
Count rate in Super-Kamiokande for galactic supernova at 10 kpc.
Count Rate (s−1) Time (s) 10 10
1
10
1
10
2
10
3
Convection MF GM3 No Convection g’=0.6 GM3 Convection g’=0.6 GM3 Convection g’=0.6 IU-FSU
0.3 0.35 0.4 0.2 0.25 0.3 0.35 Counts (0.1 s −> 1 s)/ Counts (0.1 s −> )
∞
Counts (3 s −> 10 s)/ Counts (0.1 s −> )
∞
0.45
enhanced during convection.
light curve (when convection ends).
between 3-10 s provides good discrimination.
Roberts, Cirigliano, Pons, Reddy, Shen, Woosley (2012)
w/o convection
Small L (soft)
Large L (stiff)
In extreme environments rapid neutron capture (r-process)
produce heavy elements. Properties of dense matter and neutrinos influence where and how heavy elements are synthesized.
There is general consensus that it involves either one or two neutron stars.
proto-neutron star
scenario: Neutrino driven wind in a core-collapse
scenario: Dynamical ejection of matter in binary neutron star mergers. [Robust]
neutron star mergers neutrino driven wind
High neutron to seed ratio is needed to populate the
This requires:
Hydrodynamics, Magnetic Fields, etc
Dense matter properties determine the neutrino spectra emerging from the hot neutron star.
Is set by the charged current reactions in two regions.
Neutrino-sphere at high density and moderate entropy. R ~ 10-20 km Neutrino driven wind at low- density and high entropy. R ~ 103-104 km Y NDW
e
⇡ ˙ Nνe hσνei ˙ N¯
νe hσ¯ νei + ˙
Nνe hσνei hσνei / hE2
νei
hσ¯
νei / hE2 ¯ νei
PNS
νe e− n p
Reddy, Prakash & Lattimer (1998) Roberts (2012) Martinez-Pinedo et al. (2012) Roberts & Reddy (2012) Rrapaj, Bartl, Holt, Reddy, Schwenk (2015)
Large Q crucial to overcome electron final state blocking
neutron-rich matter determines the Q value of the reaction.
change neutrons to protons and a large -Q value for changing protons to neutron.
anti-electron neutrino absorption.
Dense Medium
Q
q0 = En(p) Ep(p + q) ' pq 2m∗
n
+ (mn mp) + (Un Up)
En(p) ≈ mn + p2 2m∗
n
+ Un + i Γn Ep(p + q) ≈ mp + (p + q)2 2m∗
n
+ Up + i Γp
≈ 0
∆U = Un − Up ≈ 40 nn − np n0 MeV
' 1.3 MeV
8 12 16 <εν> (MeV) νe νe 2 4 6 8 10 Time (s) 0.4 0.45 0.5 0.55 0.6 Ye,NDW
Roberts, Reddy & Shen (2012)
w/o nuclear effects
EoS: Linear Symmetry Energy EoS: Non-Linear Symmetry Energy
with nuclear effects w/o nuclear effects neutron-rich ejecta proton-rich ejecta
The gravitational waves, EM counterparts, and nucleosynthesis are sensitive nuclear and neutrino physics.
Advanced LIGO
Inspiral: Gravitational waves, Tidal Effects & Dense Matter EoS
Merger: Disruption, NS
and r-process nucleosynthesis Post Merger: Ambient conditions power GRBs, Afterglows, and Kilo/Macro Nova
Neutron Star Merger Dynamics
(General) Relativistic (Very) Heavy-Ion Collisions at ~ 100 MeV/nucleon
Simulations: Rezzola et al (2013)
TIDAL DEFORMABILITY
10 20 30 40 50 Events 1 2 3 4 5 λ0/
95% conf MS1 95% conf H4 95% conf SQM3 True value
R=14.9 km R=13.7 km R=10.8 km
Pozzo et al. (2013)
Realistic data analysis by injecting events in a volume between 100-250 Mpc demonstrates discriminating power between EOSs. Pozzo et al. (2013) With a few tens of events the radius can be extracted to better than 10%.
ess Love numbe
2 3Gk2R5.
Love number k
Tidal deformation induces quadrupole moment.
neutron star mergers
Tidal ejecta: Early, and very neutron-rich. Robust r-process. Shocked ejecta: Processed by neutrinos, much like in a supernova. Amount and composition of the material ejected depends on the neutron star radius and neutrino interactions in dense matter.
: direct observation of r Multi messenger (e.g. Metzger & Berger 2012, Rosswog 2012, Bauswein et al. 2013)
Be T G
synthesized and ejected can power an EM signal
Metzger et al. 2010, Roberts et al. 2011, Goriely et al. 2011
to the composition of the ejecta.
Kasen 2013
Detection of a Kilonova
Tanvir et al. 2013
Observing and Interpreting Transport Phenomena in Neutron Stars
neutron star cooling.
are subject to episodic heating and subsequent cooling cycles.
Image credit: NASA/CXC/Wijnands et al.
Crust
Envelope
Brown, Bildsten Rutledge (1998) Sato (1974), Haensel & Zdunik (1990), Gupta et al (2007,2011). KS 1731-260: High accretion 1988-2000
During accretion Nuclear reactions release: ~ 1.5 MeV / nucleon
Electron capture, electron capture induced neutron emission, pycno-nuclear fusion reactions play a role
Image credit: NASA/CXC/Wijnands et al.
Crust
Envelope
Brown, Bildsten Rutledge (1998) Sato (1974), Haensel & Zdunik (1990), Gupta et al (2007,2011). KS 1731-260: High accretion 1988-2000
During accretion Nuclear reactions release: ~ 1.5 MeV / nucleon
Electron capture, electron capture induced neutron emission, pycno-nuclear fusion reactions play a role
Crust
Envelope
Core Neutrino Cooling
Watching NSs immediately after accretion ceases !
Cackett, et al. (2006) Shternin & Yakovlev (2007) Cumming & Brown (2009)
accretion the neutron star surface cools on a time scale of 100s of days.
discovered in 2001 and 6 sources have been studied to date.
detecting new sources ~ 1/year.
Figure from Rudy Wijnands (2013)
All known Quasi-persistent sources show cooling after accretion
Crust Thickness Crustal Specific Heat Thermal Conductivity
τth(ρ, T) = CV κ
The shape of the light curve is a probe of the local thermal time. In principle a collection of light curve can map the thermal and transport properties at each depth.
Negele & Vautherin (1973)
neutrons protons Outer Crust Inner Crust dripped superfluid neutrons
Baym Pethick & Sutherland (1971)
Negele & Vautherin (1973)
neutrons protons Outer Crust Inner Crust dripped superfluid neutrons
Baym Pethick & Sutherland (1971)
Negele & Vautherin (1973)
neutrons protons Outer Crust Inner Crust dripped superfluid neutrons
Baym Pethick & Sutherland (1971)
neutrons protons neutrons protons
ξi(x, y, z)
neutrons protons neutrons protons
ξi(x, y, z)
neutrons protons neutrons protons
ξi(r, t) φ(r, t) ⇥ψ↑(r)ψ↓(r)⇤ = |∆| exp (2i θ)
n ξa=1..3(r, t) → ξa=1..3(r, t) + aa=1..3
d φ(r, t) → φ(r, t) + θ
Symmetries of the underlying Hamiltonian
Only derivative terms are allowed. Lagrangian density for the phonon system with cubic symmetry:
Cirigliano, Reddy, Sharma 2011
L = f 2
φ
2 (∂0φ)2 − v2
φf 2 φ
2 (∂iφ)2 + ρ 2∂0ξa∂0ξa − 1 4µ(ξabξab) − K 2 (∂aξa)(∂bξb) − α 2
(∂aξa∂aξa) + gmixfφ √ρ ∂0φ∂aξa + · · · ,
2 2 2 ξ + 1 fep ∂0ξ ψ†
e ψe + · · ·
Low energy coefficients are related to static properties and are obtained as derivatives of the equation of state.
electrons lattice phonons superfluid phonons
k
kFe qD = ✓Z 2 ◆1/3 > 1
Flowers & Itoh (1976) Cirigliano, Reddy & Sharma (2011) Electron Bragg scatters and emits a transverse phonon.
κ = 1 3 Cv × v × λ
T = 3x10 K
7
T = 1x10 K
8
T = 1x10 K
V 3
Log C (erg/K/cm ) nSF nSF nSF nSF
N
n
N
n
N
n nSF nSF 20 19 18 17 16 15 14
0.3 0.6
i i i e e e
a = B A A B A B 1 1 1 2 3
Log (g/cm ) ρ 14 13 12 11
3
Log (g/cm ) ρ 14 13 12 11
3
Log (g/cm ) ρ 14 13 12 11
Page & Reddy (2012)
⌥
v
= 2π2 15 T 3 v3
l
+ 2 T 3 v3
t
⇥
Ce
v = 1
3µ2
e T ,
Csph
v
= 2π2 15 T 3 v3
φ
Cneutron
v
= 1 3 mn kFn T
(T ⇧ Tc)
(T > Tc)
T = 3x10 K
7
T = 1x10 K
8
T = 1x10 K
V 3
Log C (erg/K/cm ) nSF nSF nSF nSF
N
n
N
n
N
n nSF nSF 20 19 18 17 16 15 14
0.3 0.6
i i i e e e
a = B A A B A B 1 1 1 2 3
Log (g/cm ) ρ 14 13 12 11
3
Log (g/cm ) ρ 14 13 12 11
3
Log (g/cm ) ρ 14 13 12 11
Page & Reddy (2012)
properties.
superfluid state.
Shternin & Yakovlev (2007), Brown & Cumming (2009), Page & Reddy (2012,2014)
19 19 30 16 30 15 18 14 17 18 16 15 16 17 20 300 300 100 3 10 3 17 3 100 18 10 19 T
P m
T ΘD
c
T 0.1 TP ΘD
c
T
m
T
c
T ΘD 0.1 TP
m
0.1 T 10 9 10 T [K] 10 8 10
6 7 11
10
10
10
9
10
8
10 [g cm ] ρ
−3 14
10
13
10
12
10
11
10
10
10
9
10
8
10 [g cm ] ρ
−3 14
10
13
10
12 11
10
10
10
9
10
8
10 [g cm ] ρ
−3 14
10
13
10
12
10 10
V
C
κ
th
τ
for neutron stars and supernova.
to stiffen the equation of state rapidly and must persist to high density.
many-body theory has wide ranging implications for astrophysics - mergers, supernovae, and nucleosynthesis.
new insights about thermal and transport properties of the crust - revealing its phase structure
“So what does all this have to do with short- range correlations ? ”
I do not know. As a first step it would be useful to ask if electron-nucleus scattering data can constrain the two-body potential at high momentum. Disentangling the probe dependent two-body current from the two-body nucleon-nucleon potential is model and resolution scale dependent.
p p p p
2 4 3 1
p p p p p p p p p p
2
µ (2)
J
4
5
c) d) b) a)
4 1 1 2 2 1 4 3 3 3
p
NN
T
NN
ω T T
NN
T
NN
q, q,ω ω q, ω q, p
0.5 1.0 1.5 2.0 2.5
100 MeV 200 MeV 300 MeV