Constraints on neutron stars from nuclear forces

Transcription

1 Constraints on neutron stars from nuclear forces Achim Schwenk Workshop on the formation and evolution of neutron stars Bonn, Feb. 27, 2012

2 Main points Advances in nuclear forces and nuclear matter theory Impact on neutron stars: provides strong constraints for the equation of state neutron star radius km for M=1.4 M sun (±15%) K. Hebeler, J.M. Lattimer, C.J. Pethick, AS, PRL 105, (2010) and in preparation.

3 Chiral Effective Field Theory for nuclear forces Separation of scales: low momenta breakdown scale ~500 MeV NN 3N 4N limited resolution at low energies, can expand in powers (Q/Λ b ) n (compare to multipole expansion) LO, n=0 - leading order, NLO, n=2 - next-to-leading order, expansion parameter ~ 1/3 include long-range pion physics few short-range couplings, fit to experiment once systematic: can work to desired accuracy and obtain error estimates Weinberg, van Kolck, Kaplan, Savage, Wise, Epelbaum, Kaiser, Machleidt, Meissner,

4 Chiral Effective Field Theory and many-body forces Separation of scales: low momenta breakdown scale ~500 MeV NN 3N 4N consistent NN-3N interactions 3N,4N: only 2 new couplings to N 3 LO long-range 3N: c i from πn and NN 3- and 4-neutron forces are predicted to N 3 LO (c D,E don t contribute) Hebeler, AS (2010) Weinberg, van Kolck, Kaplan, Savage, Wise, Epelbaum, Kaiser, Machleidt, Meissner,

5 Advances in nuclear matter theory Nuclear matter seems perturbative with chiral EFT and RG evolution empirical range of curves estimates theoretical uncertainty exciting: empirical saturation within uncertainties Hebeler et al. (2009, 2010) input to develop a universal energy density functional for all nuclei

6 Impact of 3N forces on neutron matter Hebeler, AS (2010); Tolos, Friman, AS (2007) only long-range parts of 3N forces contribute to neutron matter (c 1 and c 3 ) neutron matter: many-body forces are predicted to N 3 LO! 3N uncertainties dominated by c 3 coupling

7 Chiral Effective Field Theory and many-body forces Separation of scales: low momenta breakdown scale ~500 MeV NN 3N 4N consistent NN-3N interactions 3N,4N: only 2 new couplings to N 3 LO long-range 3N: c i from πn and NN 3- and 4-neutron forces are predicted to N 3 LO (c D,E don t contribute) Hebeler, AS (2010) Weinberg, van Kolck, Kaplan, Savage, Wise, Epelbaum, Kaiser, Machleidt, Meissner,

8 Impact of 3N forces on neutron matter Hebeler, AS (2010); Tolos, Friman, AS (2007) only long-range parts of 3N forces contribute to neutron matter (c 1 and c 3 ) neutron matter: many-body forces are predicted to N 3 LO! 3N uncertainties dominated by c 3 coupling other microscopic calculations within band (but without uncertainties) cold atoms/qmc Gezerlis, Carlson (2009)

9 Impact of neutron matter on neutron stars Equation of state/pressure for neutron-star matter (includes small Y e,p ) log 10 P [dyne / cm 2 ] crust EOS (BPS) neutron star matter with c i uncertainties crust log 10 [g / cm 3 ] pressure below nuclear densities agrees with standard crust equation of state only after 3N forces are included extend uncertainty band to higher densities using piecewise polytropes allow for soft regions 1

10 Pressure of neutron star matter constrain polytropes by causality and require to support 1.97 M sun star log 10 P [dyne / cm 2 ] WFF1 WFF2 WFF3 AP4 AP3 MS1 MS3 GM3 ENG PAL GS1 GS2 PCL2 SQM1 SQM2 SQM3 PS log 10 [g / cm 3 ] low-density pressure sets scale, chiral EFT interactions provide strong constraints, ruling out many model equations of state 33

11 Pressure of neutron star matter constrain polytropes by causality and require to support 1.97 M sun star log 10 P [dyne / cm 2 ] WFF1 WFF2 WFF3 AP4 AP3 MS1 MS3 GM3 ENG PAL GS1 GS2 PCL2 SQM1 SQM2 SQM3 PS low-density pressure sets scale, chiral EFT interactions provide strong constraints, ruling out many model equations of state darker blue band for 2.4 M sun star log 10 [g / cm 3 ]

12 Neutron star radius constraints uncertainty from many-body forces and general extrapolation 3 Mass [M sun ] causality Radius [km] constrains neutron star radius: km for M=1.4 M sun (±15%!) consistent with extraction from X-ray burst sources Steiner et al., ApJ (2010) provides important constraints for EOS for core-collapse supernovae

13 Neutron star radius constraints uncertainty from many-body forces and general extrapolation 3 Mass [M sun ] causality 0.5 for 2.4 M sun star Radius [km] constrains neutron star radius: km for M=1.4 M sun (±15%!) consistent with extraction from X-ray burst sources Steiner et al., ApJ (2010) provides important constraints for EOS for core-collapse supernovae

14 Symmetry energy neutron matter band predicts symmetry energy S v and its density dependence L and neutron skin of 208 Pb: 0.17±0.03 fm compare to ±0.05 fm future PREX goal, first result: fm neutron matter from complete E1 response fm Tamii et al., PRL (2011).

15 Main points and summary Chiral EFT interactions provide strong constraints for EOS, 3N forces are a frontier for neutron-rich nuclei/matter dominant uncertainty of neutron (star) matter below nuclear densities also key to explain neutron-rich nuclei neutron star radius km for M=1.4 M sun (±15%) exciting interactions with experiments and observations