Exotic Nuclei, Neutron Stars and Supernovae Jürgen Schaffner-Bielich Institut für Theoretische Physik ECT*-APCTP Joint Workshop: From Rare Isotopes to Neutron Stars ECT*, Trento, September 14-18, 2015 HGS-HIRe Helmholtz Graduate School for Hadron and Ion Research
Nuclear Chart
Content 1 Introduction: Neutron Stars 2 Modelling the Outer Crust of Neutron Stars 3 Nuclear Composition in Core-Collapse Supernovae 4 Summary
Content 1 Introduction: Neutron Stars 2 Modelling the Outer Crust of Neutron Stars 3 Nuclear Composition in Core-Collapse Supernovae 4 Summary
Stellar Evolution (Credit: NASA/CXC/M.Weiss)
Supernova Explosions (Janka, (MPIA, Munich)) stars with a mass of more than 8 solar masses end in a (core collapse) supernova Supernova of AD 1054 was visible for three weeks during daytime (crab nebula)! supernovae are several thousand times brighter than a whole galaxy! last supernova explosion for the last 400 years in our local group: SN1987A most prominent candidate in the universe for producing the heavy elements (r-process)
Neutron Stars produced in core collapse supernova explosions compact, massive objects: radius 10 km, mass 1 2M extreme densities, several times nuclear density: n n 0 = 2.5 10 14 g/cm 3 in the middle of the crab nebula: a pulsar, a rotating neutron star!
The Double Pulsar PSR J0737-3039 sensational discovery of two pulsars orbiting each other (Lyne et al. 2004) measured five post-keplerian parameters: Shapiro delay r and s, redshift γ, periastron advance ω, decrease in orbital period Ṗb (Kramer et al. 2006) all in agreement with the prediction of GR to within 0.05%! fundamental tests of General Relativity in STRONG fields animation (credit: Michael Kramer)
Masses of Pulsars more than 2000 pulsars known with 140 binary pulsars best determined mass: M = 1.4414±0.0002M Hulse-Taylor pulsar PSR 1748-2021B: M = 2.74±0.21M (stat. analysis in inclination) (Freire et al. 2007) black-widow pulsar PSR B1957+20: M = 2.40±0.12M (pulsar consumes its star) (van Kerkwijk et al. 2010) black widow pulsar PSR J1311-3430: M > 2.1M (Romani et al. 2012) (Lattimer 2012)
89.24 89.22 89.2 89.18 89.16 89.14 89.12 89.1 30 20 10 0-10 -20-30 -40 30 20 10 0-10 -20-30 -40 30 20 10 0-10 -20-30 -40 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Orbital Phase (turns) 0.48 0.49 0.5 0.51 0.52 Companion Mass (solar) 1.8 1.85 1.9 1.95 2 2.05 2.1 2.15 Pulsar Mass (solar) Mass of pulsar PSR J1614-2230 (Demorest et al. 2010) Inclination Angle (deg) Timing residual (µs) Probability Density extremely strong signal for Shapiro delay Shapiro delay parameters r and s alone give M = (1.97±0.04)M very high mass! high pulsar masses confirmed with PSR J0348+0342: M = (2.01±0.04)M (Antoniadis et al. 2013) considerable constraints on neutron star matter properties!
Constraints on the Mass Radius Relation (Lattimer and Prakash 2004) Mass (solar) 2.5 2.0 1.5 1.0 GR P < causality MPA1 AP3 ENG AP4 J1614-2230 SQM3 MS1 J1903+0327 FSU SQM1 PAL6 GM3 J1909-3744 GS1 Double NS Systems PAL1 MS2 MS0 0.5 rotation Nucleons Nucleons+ExoticStrange Quark Matter 0.0 7 8 9 10 11 12 13 14 15 Radius (km) spin rate from PSR B1937+21 of 641 Hz: R < 15.5 km for M = 1.4M Schwarzschild limit (GR): R > 2GM = R s causality limit for EoS: R > 3GM mass limit from PSR J1614-2230 (red band): M = (1.97±0.04)M
X-Ray burster binary systems of a neutron star with an ordinary star accreting material on the neutron star ignites nuclear burning explosion on the surface of the neutron star: x-ray burst red shifted spectral lines measured! (z = 0.35 M/M = 1.5 (R/10 km)) (Cottam, Paerels, Mendez (2002))
Future: Square Kilometer Array (SKA) receiving surface of 1 million square kilometers 1 billion dollar international project potential to discover: 10,000 to 20,000 new pulsars more than 1,000 millisecond pulsars at least 100 compact relativistic binaries! probing the equation of state at extreme limits! cosmic gravitational wave detector by using pulsars as clocks! to be built in Australia and South Africa
Content 1 Introduction: Neutron Stars 2 Modelling the Outer Crust of Neutron Stars 3 Nuclear Composition in Core-Collapse Supernovae 4 Summary
Hydrostatic Equilibrium in General Relativity General Relativity: three relativistic correction factors dp dr = G M ( rǫ r 2 1+ P )( 1+ 4πr 3 )( P 1 2GM ) 1 r (1) ǫ M r r with the mass conservation equation dm dr = 4πr 2 ǫ (2) these are called the Tolman Oppenheimer Volkoff equations (Tolman (1934), Oppenheimer and Volkoff (1939)). The Schwarzschild radius is defined as R s = 2GM: for the sun R s = 3 km and for earth R s = 9 mm. Note: the mass density ρ is replaced by the energy density ǫ!
Structure of Neutron Stars the Crust (Dany Page) n 10 4 g/cm 3 : atmosphere (atoms) n = 10 4 4 10 11 g/cm 3 : outer crust or envelope (free e, lattice of nuclei) n = 4 10 11 10 14 g/cm 3 : Inner crust (lattice of nuclei with free neutrons and e )
Composition of the crust of a neutron star lattice of nuclei surrounded by free electrons Wigner Seitz cell, lattice structure is bcc minimize E = E nuclei + E lattice + E electrons loop over all particle stable nuclei (up to 14.000) use atomic mass evaluation of 2003/2012 extrapolate to the drip line with various models = sequence of nuclei A Z as a function of density
Nuclear Models Nonrelativistic nuclear models: Skyrme Hartree-Fock plus BCS pairing (MSk7) Skyrme Hartree-Fock-Bogoliubov (SLy4, SkP, SkM*, BSk8) Extended Thomas-Fermi models plus BCS pairing (SkSC4, SkSC18) Relativistic nuclear models: Relativistic Mean Field (NL3, NL-Z2) Relativistic Point Coupling (PCF1) Chiral Effective Lagrangian (Chiral) nuclear data tables taken from homepages of BRUSLIB (Brussels) and Jacek Dobaczewski (Warsaw) or generated by Stefan Schramm (Frankfurt)
Sequence to the Dripline (Rüster, Hempel, JSB 2005) P in dyne/cm 2 10 30 10 29 10 28 10 27 10 26 10 25 10 24 62 Ni 10 23 BPS NL3p 10 22 56 Fe PCF1np 10 21 BSk8 SLy4 10 20 NL3def TMA 10 19 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 12 in g/cm 3 66 Ni 64 Ni 86 Kr 84 Se outer crust starts with iron ( 56 Fe) up to ρ 10 7 g/cm 3 continues along nickel isotopes (Z = 28), then Kr, Se (N = 50) initial sequence at low densities known (data)! equation of state (nearly) independent of parameter set!
Sequence to the Dripline II (Rüster, Hempel, JSB 2005) 48 44 40 Z 36 32 84 Se 82 Ge 80 Zn 28 SLy4 BSk8 24 NL3def TMA FRDM 20 10 10 2 5 10 11 2 5 10 12 in g/cm 3 selection of state-of-the-art mass tables (deformed calculations) initial sequence of nuclei: Se, Ge, Zn (data) overall narrow range in Z neutron drip around 5 10 11 g/cm 3
Nuclei in the crust (Rüster, Hempel, JSB 2005) sequence of nuclei: along N = 50 then along N = 82 with Z = 46 34 common endpoint around N = 82 and Z = 36 (!) common location of the dripline at N= 82 (!) updates classic work of Baym, Pethick, Sutherland from 1971!
Mass and Radius of the Outer Crust M [10-4 M ] 6 5 4 3 2 1 M 0 =1.0 M M 0 =1.2 M M 0 =1.4 M M 0 =1.6 M M 0 =1.8 M M 0 =2.0 M 0 10 12 14 16 18 R 0 [km] 2.5 2.0 1.5 1.0 0.5 0.0 10 12 14 16 18 20 R 0 [km] R [km] (Hempel and JSB 2008) total mass and radius of the outer crust depends on mass and radius of the core typical values: M 10 4 M, R 500 km
Composition of the Crust N(A)/N tot N(A)/N tot 0.4 0.3 0.2 0.1 0.0 0.3 0.2 0.1 0.0 FRDM NL3 M 0=1.4 M, R 0=10 km M 0=1.0 M, R 0=20 km FRDM NL3 0.4 0.3 0.2 0.1 0.0 0.3 0.2 0.1 0.0 N(Z)/N tot N(Z)/N tot N(A)/N tot 0.3 0.2 0.1 0.0 Chiral 60 80 100 120 140 160 A Chiral (Hempel and JSB 2008) 24 28 32 36 40 44 48 Z overall composition of the crust in β-equilibrium around Z = 28 to 40, peaks at A 80 and 126 0.3 0.2 0.1 0.0 N(Z)/N tot
New nuclear mass tables from BRUSLIB (Goriely, Chamel, Janka, Pearson 2011) new mass tables for Skyrme force (HFB19 and HFB21) and Gogny force (D1M) very similar sequence of nuclei
Plumbing Neutron Stars to New Depths... with the binding energy of the exotic nuclide 82 Zn new mass measurement by ISOLTRAP implies that 82 Zn does not appear in the neutron star crust (Wolf et al. (ISOLTRAP) 2013)
Determining neutron star composition to new densities [g/cm 3 ] 4 10 11 3 10 11 2 10 11 1 10 11 0 HFB8 MSk7 FRDM HFB19 HFB20 HFB21 (Kreim, Hempel, Lunney, JSB 2013) IC 118Kr 126 Sr 124 Sr 122 Sr 120 Sr 121 Y 124 Zr 122 Zr 126 Mo 124 Mo 126 Ru 128 Pd 80 Ni 78 Ni 79 Cu 82 Zn 80 Zn trans. c.s. comparison of sequence of nuclei without (left columns) and with (right columns) for different nuclear models use new mass table AME2012 and ISOLTRAP measurement 82 Zn is not present anymore!
Content 1 Introduction: Neutron Stars 2 Modelling the Outer Crust of Neutron Stars 3 Nuclear Composition in Core-Collapse Supernovae 4 Summary
Composition of hot nuclear matter Z 50 1E-10 seq. T=0 1E-9 drip line 1E-8 40 1E-7 1E-6 1E-5 1E-4 30 1E-3 0,01 0,1 20 10 T=0.1 MeV 0 n B =10-6 1/fm³ 0 10 20 30 40 50 60 70 80 N X i 1 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 T=0.1 MeV n B =10-6 1/fm 3 10-10 0 20 40 60 80 100 120 140 A (Matthias Hempel) gas of nucleons, nuclei and electrons (plus Coulomb-lattice) thermodynamic consistent by construction for T = 0.1 MeV, n = 10 6 fm 3 : smeared out transition between 66 Ni and 86 Kr, two peaks!
Composition of hot nuclear matter II Z 50 1E-10 seq. T=0 1E-9 drip line 1E-8 40 1E-7 1E-6 1E-5 1E-4 30 1E-3 0,01 0,1 20 10 T=0.1 MeV 0 n B =10-4 1/fm³ 0 10 20 30 40 50 60 70 80 N X i 1 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 T=0.1 MeV n B =10-4 1/fm 3 10-10 0 20 40 60 80 100 120 140 A (Matthias Hempel) solid line and squares: sequence of nuclei for T = 0 for T = 0.1 MeV, n = 10 4 fm 3 small temperature effects, pronounced peak at N = 82, A 120
Composition of hot nuclear matter III Z 50 1E-10 seq. T=0 1E-9 drip line 1E-8 40 1E-7 1E-6 1E-5 1E-4 30 1E-3 0,01 0,1 20 10 T=0.5 MeV 0 n B =10-6 1/fm³ 0 10 20 30 40 50 60 70 80 90 100 N X i 1 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 T=0.5 MeV n B =10-6 1/fm 3 10-10 0 20 40 60 80 100 120 140 A (Matthias Hempel) increase temperature to T = 0.5 MeV and fix n = 10 6 fm 3 sizable temperature effects broad distribution around cold nuclear sequence
Composition of hot nuclear matter IV Z 50 1E-10 seq. T=0 1E-9 drip line 1E-8 40 1E-7 1E-6 1E-5 1E-4 30 1E-3 0,01 0,1 20 10 T=0.5 MeV 0 n B =10-4 1/fm³ 0 10 20 30 40 50 60 70 80 90 100 N X i 1 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 T=0.5 MeV n B =10-4 1/fm 3 10-10 0 20 40 60 80 100 120 140 A (Matthias Hempel) increase density to n = 10 4 fm 3 and keep T = 0.5 MeV pronounced shell effects, triple peak structure
Composition of Supernova Matter Z 110 1E-10 seq. T=0 100 1E-9 drip line 90 1E-8 1E-7 80 1E-6 1E-5 70 1E-4 1E-3 60 0,01 50 0,1 40 30 20 10 0 Y p =0.4 T=5 MeV n B =10-2 1/fm³ 0 20 40 60 80 100 120 140 160 180 200 N X i 1 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 Y p =0.4 T=5 MeV n B =10-2 1/fm 3 10-10 0 50 100 150 200 250 300 A (Matthias Hempel) supernovae matter for Y p = 0.4 and T = 5 MeV broad distribution along valley of stability small peaks in mass number distribution due to shell effects
Content 1 Introduction: Neutron Stars 2 Modelling the Outer Crust of Neutron Stars 3 Nuclear Composition in Core-Collapse Supernovae 4 Summary
Summary sequence of nuclei in the outer crust of neutron stars determined by nuclear mass only (in β-equilibrium) models predict sequences along magic neutron numbers N = 50 and 82 nuclei up to the neutron-dripline appear nuclei in supernova matter: large regions of the nuclear chart up to the driplines covered