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Constraining Gravity with the Equation of State in Neutron Stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Constraining gravity with the equation of state in neutron stars Felipe J. Llanes-Estrada Universidad Complutense de Madrid Departamento de F´ısica Te´orica I Institute of Nuclear Theory Seminar September 16th 2015, U. of Washington at Seattle In collaboration with M. Aparicio, A. de la Cruz Dombriz, V. Zapatero (work in progress) and A. Dobado, A. Oller Phys.Rev. C85 (2012) 012801 F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Constraining gravity with the equation of state in N stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Outline Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Often emphasized: Neutron stars test structure of matter Metallic crust Various phases of hadron matter Possibly a quark core 10 km 1.2 sM # include INT TALENT 2015: Nuclear Physics of Neutron Stars and Supernovae F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Only window to a part of the QCD phase diagram (hep-ph/0503184) F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary But consider... Inside the star ◮ ρ < 3 4ρ − 0 ◮ g = O(1012)m/s2 vs. O(300)m/s2 outside (where GR tests with pulsars are performed) or O(106)m/s2 at white dwarves. i.e. we extrapolate General Relativity 6 orders of magnitude to learn nuclear physics only a factor 3-4 away !!?? F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Rube Goldberg contraption F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Turn it around Can nuclear physics constrain General Relativity inside a neutron star? F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Motivations to keep testing gravity Dark matter is obscure. Who missed something? D. Clowe et al. Astrophys. J. Lett. 648 L109 (2006) F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Motivations to keep testing gravity What about accelerated expansion, e.g. primordial inflation? Add incompatibility of GR with quantum theory, and prediction of spacetime singularities F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Motivations to keep testing gravity What about accelerated expansion, e.g. primordial inflation? Add incompatibility of GR with quantum theory, and prediction of spacetime singularities F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Binary neutron star systems used to constrain gravity F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Constraints “external” to star, e.g. Tensor+Scalar theories ◮ Two-solar mass pulsar J0348+0432 with white dwarf companion ◮ Grav. wave emission constrained from dT /dt ◮ Constraint on αPSR (scalar/tensor coupling ratio), Science 340 1233232 (2010) F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Neutron star interior great for Gen. Rel. tests Large fractional binding energy J.Antoniadis et al., Science 340, 1233232 (2013) F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Future: perhaps gravity waves Left: binary merger simulation by Alan Calder (not equilibrium either). Right: theory prediction of quadrupole moment Q/J2 for three equations of state (arXiv:1503.05405) F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Only probes of interior that might get to us are neutrinos (arXiv:0702613) 5 4 ] 32 Combined 3 ) [ 10 IMB + 2 N ( E 1 Kam-II 0 1 0.8 Kam-II ) + 0.6 IMB f ( E 0.4 0.2 0 12 10 8 6 t [ s ] 4 2 0 0 10 20 30 40 50 60 E+ [ MeV ] Analysis of SN87A; not a neutron star in equilibrium Resort to indirect means, such as bulk properties (M, R, T , I , τcooling . ) (very much like nuclear physics) F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary So let’s do something about it F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Outline Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Gravity acceleration in General Relativity (G = c = 1) dΦ M(r) g = = dr r 2 M(r) + 4πr 3P(r) g = . r(r 2M(r)) − g O(1012)m/s2 ≃ F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Gravity acceleration in General Relativity (G = c = 1) dΦ M(r) g = = dr r 2 M(r) + 4πr 3P(r) g = . r(r 2M(r)) − g O(1012)m/s2 ≃ F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Measured pulsar masses before 2010 PRC77 065803 (2008) F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Maximum mass for a given eq. of state ◮ Hydrostatic equilibrium: pressure compensates weight of upper layers ◮ Causality limits the achievable pressure, c2 c2 = dP ≥ s dρ ◮ But nothing limits the amount of matter falling on the star ◮ Only solution: increase density ◮ When R∗ < RSchwarzschild = 2M∗, Gen. Rel. predicts collapse ◮ Finding heavier N-stars tests General Relativity F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Maximum mass for a given eq. of state ◮ Hydrostatic equilibrium: pressure compensates weight of upper layers ◮ Causality limits the achievable pressure, c2 c2 = dP ≥ s dρ ◮ But nothing limits the amount of matter falling on the star ◮ Only solution: increase density ◮ When R∗ < RSchwarzschild = 2M∗, Gen. Rel. predicts collapse ◮ Finding heavier N-stars tests General Relativity F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Maximum mass for a given eq. of state ◮ Hydrostatic equilibrium: pressure compensates weight of upper layers ◮ Causality limits the achievable pressure, c2 c2 = dP ≥ s dρ ◮ But nothing limits the amount of matter falling on the star ◮ Only solution: increase density ◮ When R∗ < RSchwarzschild = 2M∗, Gen. Rel. predicts collapse ◮ Finding heavier N-stars tests General Relativity F. J. Llanes-Estrada Constraining gravity with the equation of state in neutron stars Motivation Static neutron stars Constraining Cavendish’s constant with heavy stars Modified gravity Summary Maximum mass for a given eq. of state ◮ Hydrostatic equilibrium: pressure compensates weight of upper layers ◮ Causality limits the achievable pressure, c2 c2 = dP ≥ s dρ ◮ But nothing limits the amount of matter falling on the star ◮ Only solution: increase density ◮ When R∗ < RSchwarzschild = 2M∗, Gen. Rel. predicts collapse ◮ Finding heavier N-stars tests General Relativity F. J. Llanes-Estrada Constraining gravity with the
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