Constraining the Radius of Neutron Stars Through the Moment of Inertia

Transcription

1 Constraining the Radius of Neutron Stars Through the Moment of Inertia Neutron star mergers: From gravitational waves to nucleosynthesis International Workshop XLV on Gross Properties of Nuclei and Nuclear Excitations Hirschegg, Kleinwalsertal, Austria, January 15-21, 2017 January 19, 2017 Institut für Kernphysik Svenja Kim Greif 1

2 Observation Theoretical description of neutron stars Equation of state and neutron star structure Constraining the radius of neutron stars Summary January 19, 2017 Institut für Kernphysik Svenja Kim Greif 2

3 Observation knowledge of EOS is restricted relationship between EOS and MR relation precise mass measurements are possible radius determination influenced by systematic uncertainties moment of inertia measurement seems feasible in the future PSR J A, M = 1.337(5) M Burgay et al., Nature (2003); Lyne et al., Science (2004) goal: constraining radius/eos by moment of inertia January 19, 2017 Institut für Kernphysik Svenja Kim Greif 3 Courtesy of J. M. Lattimer

4 Observation Mass measurement pulsar observation determine post Keplerian parameters Stairs, Living Rev. Relativity (2003) post Keplerian parameters as functions of the masses Damour and Deruelle, Ann. Inst. Henri Poincare (1986) intersection area yields masses for binary system see also talk of Paulo Freire Kramer et al., Science (2006) January 19, 2017 Institut für Kernphysik Svenja Kim Greif 4

5 Observation Moment of inertia measurement relativistic spin-orbit (SO) coupling causes an additional contribution to advance of the periastron spin of PSR J B is negligible contributions to advance of periastron (pn: post-newtonian) ω = ω 1pN + ω 2pN + ω SO Kramer & Wex, Class. Quant. Grav. (2009) January 19, 2017 Institut für Kernphysik Svenja Kim Greif 5

6 Observation Moment of inertia measurement relativistic spin-orbit (SO) coupling causes an additional contribution to advance of the periastron spin of PSR J B is negligible contributions to advance of periastron (pn: post-newtonian) ω = ω 1pN + ω 2pN + ω SO Kramer & Wex, Class. Quant. Grav. (2009) candidate for future measurement: PSR J A highly relativistic binary Kramer & Wex, Class. Quantum Grav. (2009) January 19, 2017 Institut für Kernphysik Svenja Kim Greif 5

7 Theoretical description of neutron stars Non-rotating neutron stars hydrostatic equilibrium Schwarzschild metric TOV equations ds 2 = e ν dt 2 + e λ dr 2 + r 2 dθ 2 + r 2 sin 2 θdφ 2 dp = 1 dr r (ɛ + P) ( m + 4πr 3 P ) ( 1 2m 2 r dm = 4πɛr 2 dr dν dr = 2 ( m + 4πr 3 P ) ( 1 2m ) 1 r 2 r ) 1 January 19, 2017 Institut für Kernphysik Svenja Kim Greif 6

8 Theoretical description of neutron stars Slowly rotating neutron stars hydrostatic equilibrium Schwarzschild metric Hartle-Thorne metric Hartle, APJ (1967); Hartle & Thorne, APJ (1968) ds 2 = e ν dt 2 + e λ dr 2 + r 2 dθ 2 + r 2 sin 2 θ ( dφ ( ω + O ( Ω 3)) dt ) 2 TOV equations remain dp = 1 dr r (ɛ + P) ( m + 4πr 3 P ) ( 1 2m 2 r dm = 4πɛr 2 dr dν dr = 2 ( m + 4πr 3 P ) ( 1 2m ) 1 r 2 r ) 1 January 19, 2017 Institut für Kernphysik Svenja Kim Greif 6

9 Theoretical description of neutron stars Moment of inertia Hartle, APJ (1967), Hartle & Thorne, APJ (1968) auxiliary function j = e 1 2 ν ( 1 2m r ) 1 2 in addition to TOV eqns. ( ω = Ω ω) ( d r 4 j d ω ) = 4r 3 dj dr dr dr ω moment of inertia I = 8π 3 R 0 dr r 4 (ɛ + P) j ( 1 2m r ) 1 ω Ω January 19, 2017 Institut für Kernphysik Svenja Kim Greif 7

10 Equation of state and neutron star structure Piecewise polytropes Hebeler, Lattimer, Pethick, Schwenk, Phys. Rev. Lett. (2010); Hebeler, Lattimer, Pethick, Schwenk, APJ (2013) see also talk of Kai Hebeler low density regime: knowledge of nuclear physics BPS crust up to ρ sat/2 chiral EFT expansion up to ρ sat high density regime: requirement of causality and constraints from 2.01 M neutron stars polytropic expansion Read, Lackey, Owen, Friedman, Phys. Rev. D (2009) P(ρ) = K ρ Γ log 10 P [dyne cm 2 ] 37 crust EOS (BPS) neutron star matter 36 with c i uncertainties 2 35 crust log 10 [g cm 3 ] Hebeler, Lattimer, Pethick, Schwenk, APJ (2013) 3 January 19, 2017 Institut für Kernphysik Svenja Kim Greif 8

11 Equation of state and neutron star structure Piecewise polytropes Hebeler, Lattimer, Pethick, Schwenk, Phys. Rev. Lett. (2010); Hebeler, Lattimer, Pethick, Schwenk, APJ (2013) see also talk of Kai Hebeler low density regime: knowledge of nuclear physics BPS crust up to ρ sat/2 chiral EFT expansion up to ρ sat high density regime: requirement of causality and constraints from 2.01 M neutron stars polytropic expansion Read, Lackey, Owen, Friedman, Phys. Rev. D (2009) log 10 P [dyne cm 2 ] P(ρ) = K ρ Γ cm =1.97 M log 10 [g cm 3 ] Hebeler, Lattimer, Pethick, Schwenk, APJ (2013) January 19, 2017 Institut für Kernphysik Svenja Kim Greif 8

12 Equation of state and neutron star structure MR relation Hebeler, Lattimer, Pethick, Schwenk, Phys. Rev. Lett. (2010); Hebeler, Lattimer, Pethick, Schwenk, APJ (2013) see also talk of Kai Hebeler low density regime: knowledge of nuclear physics BPS crust up to ρ sat/2 chiral EFT expansion up to ρ sat high density regime: requirement of causality and constraints from 2.01 M neutron stars polytropic expansion Read, Lackey, Owen, Friedman, Phys. Rev. D (2009) Mass [M ] causality P(ρ) = K ρ Γ radius prediction for PSR J A: R ( ) km Radius [km] Hebeler, Lattimer, Pethick, Schwenk, APJ (2013) January 19, 2017 Institut für Kernphysik Svenja Kim Greif 8

13 Constraining the radius of neutron stars Universal relation I/MR soft intermediate stiff Lattimer and Schutz, APJ (2005) several studies have investigated I ( MR 1) Bejger & Haensel, A&A (2002); Lattimer & Schutz, APJ (2005); Breu & Rezzolla, MNRAS (2016);... dimensionless moment of inertia is not sensitive to EOS find fit and determine radius constraints M/R [M /km] grey band holds for 0.07 M km 1 MR 1 January 19, 2017 Institut für Kernphysik Svenja Kim Greif 9

14 Constraining the radius of neutron stars Universal relation I/MR soft intermediate stiff Lattimer and Schutz, APJ (2005) M/R [M /km] grey band holds for 0.07 M km 1 MR 1 several studies have investigated I ( MR 1) Bejger & Haensel, A&A (2002); Lattimer & Schutz, APJ (2005); Breu & Rezzolla, MNRAS (2016);... dimensionless moment of inertia is not sensitive to EOS find fit and determine radius constraints our approach: use the whole EOS uncertainty band created by polytropic expansion January 19, 2017 Institut für Kernphysik Svenja Kim Greif 9

15 Constraining the radius of neutron stars use all EOS from uncertainty band consider different masses use I(M) band in order to find reasonable moment of inertia values soft intermediate stiff 200 I [M km 2 ] M [M ] January 19, 2017 Institut für Kernphysik Svenja Kim Greif 10

16 Constraining the radius of neutron stars use all EOS from uncertainty band consider different masses use I(M) band in order to find reasonable moment of inertia values combine mass, moment of inertia and I I [M km 2 ] soft intermediate stiff 10 % 20 % all M = M M = M M = M R [km] January 19, 2017 Institut für Kernphysik Svenja Kim Greif 10

17 Constraining the radius of neutron stars use all EOS from uncertainty band consider different masses use I(M) band in order to find reasonable moment of inertia values combine mass, moment of inertia and I assumption for PSR J A: I = (70 ± 7) M km 2 I [M km 2 ] soft intermediate stiff 10 % 20 % all M = M M = M R ( ) km 50 M = M R [km] January 19, 2017 Institut für Kernphysik Svenja Kim Greif 10

18 Constraining the radius of neutron stars use all EOS from uncertainty band consider different masses use I(M) band in order to find reasonable moment of inertia values combine mass, moment of inertia and I assumption for PSR J A: I = (70 ± 7) M km 2 I [M km 2 ] soft intermediate stiff 10 % 20 % all M = M M = M R ( ) km R ( ) km 50 M = M R [km] January 19, 2017 Institut für Kernphysik Svenja Kim Greif 10

19 Summary derived constraints for the EOS over wide range of densities and resulting NS radii using BPS crust EOS up to ρ sat/2 results based on chiral EFT interactions up to ρ sat causality at all densities M max > 2.01 M + assumed fixed measured values for moment of inertia (including uncertainties) developed a framework to perform an extensive large scale sampling of all possible high-density extensions for EOS compatible with constraints find a reduction of radius uncertainty from moment of inertia measurements by about 50 % ( I = ±10 %) In collaboration with K. Hebeler and A. Schwenk. I [M km 2 ] 250 soft intermediate stiff % 20 % M = M all 150 M = M 100 M = M R [km] January 19, 2017 Institut für Kernphysik Svenja Kim Greif 11

20 Summary derived constraints for the EOS over wide range of densities and resulting NS radii using BPS crust EOS up to ρ sat/2 results based on chiral EFT interactions up to ρ sat causality at all densities M max > 2.01 M + assumed fixed measured values for moment of inertia (including uncertainties) developed a framework to perform an extensive large scale sampling of all possible high-density extensions for EOS compatible with constraints find a reduction of radius uncertainty from moment of inertia measurements by about 50 % ( I = ±10 %) In collaboration with K. Hebeler and A. Schwenk. Thanks for your attention! January 19, 2017 Institut für Kernphysik Svenja Kim Greif 11 I [M km 2 ] soft intermediate stiff 10 % 20 % all M = M M = M M = M R [km]