, G RAVITATIONAL-WAVE. Kent Yagi. with N. Yunes. Montana State University. YKIS2013, Kyoto

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1 UNIVERSAL I-LOVE OVE-Q Q RELATIONSR IN Q R NEUTRON STARS AND THEIR APPLICATIONS TO ASTROPHYSICS STROPHYSICS,, GRAVITATIONAL G RAVITATIONAL-WAVE AVE, G AND FUNDAMENTAL PHYSICS Kent Yagi with N. Yunes Montana State University YKIS2013, Kyoto arxiv: (submitted to Science) (submitted to PRD)

2 Contents 1 Introduction 2 I, Love, Q 3 Universal Relations 4 Application (I): GW physics 5 Application (II): Fundamental Physics 6 Summary

3 Contents 1 Introduction 2 I, Love, Q 3 Universal Relations 4 Application (I): GW physics 5 Application (II): Fundamental Physics 6 Summary

4 Testing GR Solar System (I) Weak field regime: (II) Strong field regime: Neutron Stars Binary Pulsars Black Holes Gravitational Waves

5 Big Uncertainties in the Equation of State Lattimer & Prakash (2001)

6 Big Uncertainties in the Equation of State Degeneracy between the EoS and non-gr effect Lattimer & Prakash (2001)

7 Big Uncertainties in the Equation of State Lattimer & Prakash (2001)

8 Mass-Radius Relation Lattimer & Prakash (2007) Difficult to test GR with the MR relation.

9 Q: Can we find relations between NS observables that depend on the EoSs only very weakly? A: YES!! Universal I-Love-Q Relations Love I: Moment of Inertia Love: (tidal) Love Numbers Q: Quadrupole moment

10 Contents 1 Introduction 2 I, Love, Q 3 Universal Relations 4 Application (I): GW physics 5 Application (II): Fundamental Physics 6 Summary

11 Moment of Inertia Spin angular momentum Angular frequency How fast one can spin given a spin angular momentum. Mao Asada

12 Quadrupole Moment Quadrupolar deformation away from sphere. Potential: non-rotating

13 Love Numbers (Apsidal Constants) Love number Disturbing potential Tidal Love Number (Tidally induced) Quadrupole Moment Tidal Potential Rotational Love Number (Spin induced) Quadrupole Moment Centrifugal Potential

14 Contents 1 Introduction 2 I, Love, Q 3 Universal Relations 4 Application (I): GW physics 5 Application (II): Fundamental Physics 6 Summary

15 Dimensionless Quantities Assumptions -uniform & slow rotation -small & stationary deformation -isotropic pressure

16 Love-Love Relation Newtonian limit

17 I-Love Relation Newtonian limit

18 Q-Love Relation Newtonian limit

19 Analytic I-Love-Q in the Newtonian limit etc. n=0 and 1 polytropic EoSs

20 Why I-Love-Q? (I) Increasing the NS compactness Approaches the BH limit where the no-hair theorem holds

21 Why I-Love-Q? (II) (Newtonian) I-Love-Q depend most sensitively on the NS outer layer

22 Neutron Stars (NSs) vs Quark Stars (QSs) quark star neutron star I-Love-Q relations One can distinguish NSs and QSs

23 dynamical deformation I-Love-Q Forever Maselli et al. (2013) NS/NS binary inspiral

24 I-Love-Q with different f in 1 plot KY & Yunes Maselli et al Maselli et al. (2013)

25 Contents 1 Introduction 2 I, Love, Q 3 Universal Relations 4 Application (I): GW physics 5 Application (II): Fundamental Physics 6 Summary

26 Measurement Accuracies of I Love Q Advance rate of periastron of double binary pulsar [Lattimer & Schutz (2004)] GWs from compact binary inspiral GW phase (equal-mass NS/NS):

27 difficult to measure are measureable

28 Spin Accuracy Without Q-Love relation With Q-Love relation The averaged spin can be measured within O(0.01).

29 Contents 1 Introduction 2 I, Love, Q 3 Universal Relations 4 Application (I): GW physics 5 Application (II): Fundamental Physics 6 Summary

30 I-Love Relation for different mass systems Universal relations still hold for systems with different masses.

31 Testing GR 10 6 times stronger than the current solar system bound.

32 Love-C Relation This might be more practical.

33 Contents 1 Introduction 2 I, Love, Q 3 Universal Relations 4 Application (I): GW physics 5 Application (II): Fundamental Physics 6 Summary

34 -We found universal relations between the NS moment of inertia, tidal Love number and quadrupole moment that do not depend on the EoS. Applications: (I) Astrophysics: (II) GW physics: -One can distinguish NSs and QSs -Any 1 measurement of the I-Love-Q trio would automatically gives the other 2 quantities. -The NS spin can be measured to O(0.01). (III) Fundamental physics: -Theory-independent & EoS-independent test of GR

35 Future Work: -Rapidly or differentially rotating NS -Why such universal relations hold? NS no-hair conjecture? -Extending Fisher to Bayesian analysis -Model-independent & EoS-independent test of GR with NS oscillations

36 Future Work: -Rapidly or differentially rotating NS -Why such universal relations hold? NS no-hair conjecture? -Extending Fisher to Bayesian analysis -Model-independent & EoS-independent test of GR with NS oscillations