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.
Recent Observations Massive Neutron Star 30 20 10 0 -10 -20 -30 -40 30
Recent Observations Massive Neutron Star 30 20 10 0 -10 -20 -30 -40 30 Towards a measurement of neutron star radii MS0 MS0 MS2 MS2 2.5 MPA1 MPA1 AP3 AP3 PAL1 PAL1 ENG ENG AP4 AP4 WFF1 WFF1 2.0 M NS � M � � MS1 MS1 FSU FSU 1.5 SQM1 SQM1 GM3 GM3 GS1 GS1 1.0 SQM3 SQM3 PAL6 PAL6 0.5 6 8 10 12 14 16 R NS � km �
Recent Observations Massive Neutron Star Thermal Relaxation in Accreting Neutron Stars 30 20 10 0 -10 -20 -30 -40 30 Towards a measurement of neutron star radii MS0 MS0 MS2 MS2 2.5 MPA1 MPA1 AP3 AP3 PAL1 PAL1 ENG ENG AP4 AP4 WFF1 WFF1 2.0 M NS � M � � MS1 MS1 FSU FSU 1.5 SQM1 SQM1 GM3 GM3 GS1 GS1 1.0 SQM3 SQM3 PAL6 PAL6 0.5 6 8 10 12 14 16 R NS � km �
Recent Observations Massive Neutron Star Thermal Relaxation in Accreting Neutron Stars 30 20 10 0 -10 -20 -30 -40 30 Kilo Nova (r-process ?) Towards a measurement of neutron star radii MS0 MS0 MS2 MS2 2.5 MPA1 MPA1 AP3 AP3 PAL1 PAL1 ENG ENG AP4 AP4 WFF1 WFF1 2.0 M NS � M � � MS1 MS1 FSU FSU 1.5 SQM1 SQM1 GM3 GM3 GS1 GS1 1.0 SQM3 SQM3 PAL6 PAL6 Multi messenger (e.g. Metzger & Ber 0.5 6 8 10 12 14 16 R NS � km �
Phases of Dense Matter in Neutron nuclei, (solid) Crust: electrons r e ~12 t 10 4 u O Inner Crust: ~11.5 (Solid-Superfluid) 4x10 11 nuclei, electrons, neutrons ~10 Outer Core 2x10 14 (Superfluid- Superconductor) Density Radius neutrons, protons (g/cm 3 ) electrons (km) 6x10 14 Inner ~3 Core ? 10 15
Pressure v/s Energy Density (EoS) P= ε log P( ε ) neutron drip nuclear matter relativistic electrons crust core 7 11 14 15 log ε (g/cm 3 )
Pressure v/s Energy Density (EoS) P= ε log P( ε ) neutron drip nuclear matter relativistic electrons crust core 7 11 14 15 log ε (g/cm 3 ) can calculate can speculate
Pressure v/s Energy Density (EoS) Maximum Mass P= ε log P( ε ) neutron drip nuclear matter relativistic electrons crust core 7 11 14 15 log ε (g/cm 3 ) can calculate can speculate
Pressure v/s Energy Density (EoS) Maximum Mass P= ε log P( ε ) neutron Radius drip nuclear matter relativistic electrons crust core 7 11 14 15 log ε (g/cm 3 ) can calculate can speculate
Pressure v/s Energy Density (EoS) Maximum Mass r e d r O t s r i F n o t i i s n a r T P= ε e s a h P log P( ε ) neutron Radius drip nuclear matter relativistic electrons crust core 7 11 14 15 log ε (g/cm 3 ) can calculate can speculate
Pressure v/s Energy Density (EoS) 2 M ⊙ NS ✘ Maximum Mass r e d r O t s r i F n o t i i s n a r T P= ε e s a h P log P( ε ) neutron Radius drip nuclear matter relativistic electrons crust core 7 11 14 15 log ε (g/cm 3 ) can calculate can speculate
EFT and Phenomenological Models crust core inner core n B (fm -3 ) 0.08 0.16 0.32 0.48 0.64 15 14 log ε (g/cm 3 ) can calculate can speculate
EFT and Phenomenological Models crust core inner core n B (fm -3 ) 0.08 0.16 0.32 0.48 0.64 Q ' p F ' Λ B Λ B ' 500 MeV 15 14 log ε (g/cm 3 ) can calculate can speculate
EFT and Phenomenological Models crust core inner core n B (fm -3 ) 0.08 0.16 0.32 0.48 0.64 Q ' p F ' Λ B Λ B ' 500 MeV Chiral EFT Systematic error estimates 15 14 log ε (g/cm 3 ) can calculate can speculate
EFT and Phenomenological Models crust core inner core n B (fm -3 ) 0.08 0.16 0.32 0.48 0.64 Q ' p F ' Λ B Λ B ' 500 MeV Chiral EFT Systematic error estimates Chiral EFT + 𝚬 Systematic error estimates 15 14 log ε (g/cm 3 ) can calculate can speculate
EFT and Phenomenological Models crust core inner core n B (fm -3 ) 0.08 0.16 0.32 0.48 0.64 Q ' p F ' Λ B Λ B ' 500 MeV Chiral EFT Systematic error estimates Recall talks by Schwenk & Weise Chiral EFT + 𝚬 Systematic error estimates 15 14 log ε (g/cm 3 ) can calculate can speculate
EFT and Phenomenological Models crust core inner core n B (fm -3 ) 0.08 0.16 0.32 0.48 0.64 Q ' p F ' Λ B Λ B ' 500 MeV Chiral EFT Systematic error estimates Recall talks by Schwenk & Weise Chiral EFT + 𝚬 Systematic error estimates Phen. Potentials 2+3 body Errors can only be estimated crudely 15 14 log ε (g/cm 3 ) can calculate can speculate
S, L & Equation of State of Neutron Matter { ✏ = ⇢ E ( ⇢ ) P ( ✏ ) = ⇢ 2 @ E ( ⇢ ) r e t t a M @⇢ n E ( ρ n , ρ p ) MeV o r t u e N 16 1 2 ρ 0 = 2 . 6 × 10 14 g / cm 3 -16 Nuclei exist here Symmetric Matter ( ρ � ρ 0 ) E n ( ρ ' ρ 0 ) ' � 16 MeV + S + L 3 ρ 0
S, L & Equation of State of Neutron Matter { ✏ = ⇢ E ( ⇢ ) P ( ✏ ) = ⇢ 2 @ E ( ⇢ ) r e t t a M @⇢ n E ( ρ n , ρ p ) MeV o r t u e N 16 1 2 S=32±3 MeV ρ 0 = 2 . 6 × 10 14 g / cm 3 -16 Nuclei exist here Symmetric Matter ( ρ � ρ 0 ) E n ( ρ ' ρ 0 ) ' � 16 MeV + S + L 3 ρ 0
S, L & Equation of State of Neutron Matter { ✏ = ⇢ E ( ⇢ ) P ( ✏ ) = ⇢ 2 @ E ( ⇢ ) L = 50 ± 30 MeV (Expt) r e t t a M @⇢ n E ( ρ n , ρ p ) MeV o r t u e N 16 1 2 S=32±3 MeV ρ 0 = 2 . 6 × 10 14 g / cm 3 -16 Nuclei exist here Symmetric Matter ( ρ � ρ 0 ) E n ( ρ ' ρ 0 ) ' � 16 MeV + S + L 3 ρ 0
S, L & Equation of State of Neutron Matter { ✏ = ⇢ E ( ⇢ ) P ( ✏ ) = ⇢ 2 @ E ( ⇢ ) L = 50 ± 30 MeV (Expt) r e t t a M @⇢ n E ( ρ n , ρ p ) MeV o r t u e N 16 1 2 S=32±3 MeV ρ 0 = 2 . 6 × 10 14 g / cm 3 -16 Nuclei exist here Symmetric Matter ( ρ � ρ 0 ) E n ( ρ ' ρ 0 ) ' � 16 MeV + S + L 3 ρ 0
Neutron Matter from Ab-initio Theory (at nuclear saturation density) 35 Energy per 18 Neutron 16 (MeV) Empirical Value 14 12 Caveat: Separation between 2N and 3N contributions is resolution scale and model dependent.
Neutron Matter from Ab-initio Theory (at nuclear saturation density) Fermi Gas 35 Energy per 18 Neutron 16 (MeV) Empirical Value 14 12 Caveat: Separation between 2N and 3N contributions is resolution scale and model dependent.
Neutron Matter from Ab-initio Theory (at nuclear saturation density) Fermi Gas 35 Energy per 18 Neutron 16 (MeV) Empirical Value 14 Theory 2N 12 Caveat: Separation between 2N and 3N contributions is resolution scale and model dependent.
Neutron Matter from Ab-initio Theory (at nuclear saturation density) Fermi Gas 35 Energy per 18 Neutron Theory 2N+ 3N 16 (MeV) Empirical Value 14 Theory 2N 12 Caveat: Separation between 2N and 3N contributions is resolution scale and model dependent.
Current Status of Neutron Matter EoS Studies Prediction Extrapolation 100 70 35.1 20 EM 500 MeV EGM 450/500 MeV 60 L [MeV] EGM 450/700 MeV 80 NLO lattice (2009) 50 QMC (2010) 15 40 APR (1998) E/N [MeV] 60 GCR (2012) E/N [MeV] 30 30 32 34 36 S v [MeV] 10 40 33.7 32 5 20 S v = 30.5 MeV (NN) 0 0 0 0.1 0.2 0.3 0.4 0.5 0 0.05 0.1 0.15 -3 ] n [fm n [fm -3 ] Gandolfi, Carlson, Reddy Hebeler, Schwenk,Furnstahl, Tews, … Holt, Kaiser, Weise, … Hagen, Papenbrock, … Implications for NS radius: R = 12 ± 2 km
QMC with Phenomenological Potentials Gandolfi, Carlson, Reddy (2010) S & L are correlated by 100 the model. 70 Energy per Neutron (MeV) Experimental 60 L (MeV) 35.1 80 measurement of L & S 50 40 with ~ 1 MeV error 33.7 60 30 needed to test the 30 32 34 36 E sym (MeV) S (MeV) model. 40 Up to about twice Fermi-gas saturation density, the 3- 20 32 body contribution is S E sym = 30.5 MeV (NN) smaller than the 2-body 0 0 0.1 0.2 0.3 0.4 0.5 force. -3 ) Neutron Density (fm 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.
Neutron Star Structure 3 ρ central =5 ρ 0 2 ) Causality: R>2.9 (GM/c 2.5 =4 ρ 0 central ρ 1.97(4) M solar 2 =3 ρ M (M solar ) 0 central ρ 32 1.5 1.4 M solar =2 ρ 0 l a r t n ρ e 1 c L=55 33.7 L=64 0.5 35.1 L=31 S L=42 E sym = 30.5 MeV (NN) 0 8 9 10 11 12 13 14 15 16 R (km)
Neutron Star Structure 3 ρ central =5 ρ 0 2 ) Causality: R>2.9 (GM/c 2.5 =4 ρ 0 central ρ 1.97(4) M solar 2 =3 ρ M (M solar ) 0 central ρ 32 1.5 1.4 M solar =2 ρ 0 l a r t n ρ e 1 c L=55 33.7 L=64 0.5 35.1 L=31 S L=42 E sym = 30.5 MeV (NN) 0 8 9 10 11 12 13 14 15 16 R (km)
Neutron Star Structure 3 ρ central =5 ρ 0 2 ) Causality: R>2.9 (GM/c 2.5 =4 ρ 0 central A 10% Radius Measurement ρ 1.97(4) M solar 2 =3 ρ M (M solar ) 0 central ρ 32 1.5 1.4 M solar =2 ρ 0 l a r t n ρ e 1 c L=55 33.7 L=64 0.5 35.1 L=31 S L=42 E sym = 30.5 MeV (NN) 0 8 9 10 11 12 13 14 15 16 R (km)
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