1. Renxin Xu ( 徐仁新 ) School of Physics, Peking University ( ) “2015 China-New Zealand Joint SKA Summer School” Aug. 19, 2015; Kunming, China Pulsars as probes for EoS of Dense Matter PSR-EoS http:// www.phy.pku.edu.cn/~xurenxin/ R. X. Xu

2. Beautiful Dianchi, we are here for PSR! 滇池

3. Let’s begin with a thought experiment: Dianchi: 330km 2 x (5~8)m, Water (H 2 O) What if compressed until nuclei contact? 滇池

4. H 2 O  Atom  Nucleus  Quark  ~10 -8 cm~10 -13 cm.... {uud}{uud}{udd}{udd} Baryon (a quark) = 1/3 Only 3 (u,d;e) of 12 !

5. Let’s do OoM calculations… Total mass: ~100km 2 x 10m x 1g/cm 3 ~ 10 15 g Total baryon number: ~ 10 15 g/10 -24 g ~ 10 39 Note: M sun /10 -24 g ~ 10 57 Volume if forming a “macro-nucleus”: ~10 15 g/10 14 g cm -3 ~ 10 cm 3  scale ~ 1 cm! No change even so compressed? Neutronization ? e - + p  n + e ? Strangenization ? a 3-f nucleus? …neutron matter vs strange matter R >> c ~10 -10 cm

6. Similar compression in astrophysics Core mass:M sun ~10 33 g Baryon number: ~ M sun /10 -24 g ~ 10 57 Scale~10 33 g/10 14 g cm -3 ~ 10 19 cm 3  ~ 10 6 cm! compressed by gravity Supernova: death of evolved massive stars ( >~8M sun ) Big Question: Neutron Star vs Strange Star?

7. SKA provides opportunity to know

8. Outline EoS-dependent pulsar inner structure Observables to constrain EoS  NS mass measurements (M)  NS moment of inertia measurements (I)  Discovering fastest spinning pulsars (P)  Magnetospheric activity (pulse-profile) Conclusions PSR-EoS http:// www.phy.pku.edu.cn/~xurenxin/ R. X. Xu

9. Outline EoS-dependent pulsar inner structure Observables to constrain EoS  NS mass measurements (M)  NS moment of inertia measurements (I)  Discovering fastest spinning pulsars (P)  Magnetospheric activity (pulse-profile) Conclusions PSR-EoS http:// www.phy.pku.edu.cn/~xurenxin/ R. X. Xu

10. Stars in static equilibrium: Newtonian Gravity Assuming spherical symmetry  Q = Q(r)  1D problem Gravity ： Gm(r)  M/r 2 （ mass  M =  Adr ） Pressure ：  A [P-(P+dP)] = -  A  dP gravity = pressure against Newtonian gravity Two unknown ： P(r) 、  (r) ； 1 eq more: P(  ) (EoS) ！ EoS-dependent PSR inner structure PSR-EoS http:// www.phy.pku.edu.cn/~xurenxin/ R. X. Xu

11.  Perfect fluid TOV Eq. ：  Solid ： where Conclusion: EoS is also necessary to know  (r) ！ EoS-dependent PSR inner structure Stars in static equilibrium: Einstein Gravity (g)(g) (P,  ; g  ) PSR-EoS http:// www.phy.pku.edu.cn/~xurenxin/ R. X. Xu

12. EoS-dependent PSR inner structure We have a “machine” to calculate M-R curve To calculate step-by-step PSR-EoS http:// www.phy.pku.edu.cn/~xurenxin/ R. X. Xu

13. EoS generates unique mass-radius relation some of EOSs some of M-R curves TOV Measuring M and R uniquely determines the EoS EoS-dependent PSR inner structure

14. Different models/EoSs of pulsar in the market conventional Neutron Star light flavour symmetry: Strange Star EoS-dependent PSR inner structure PSR-EoS http:// www.phy.pku.edu.cn/~xurenxin/ R. X. Xu

15. Outline EoS-dependent pulsar inner structure Observables to constrain EoS  NS mass measurements (M)  NS moment of inertia measurements (I)  Discovering fastest spinning pulsars (P)  Magnetospheric activity (pulse-profile) Conclusions PSR-EoS http:// www.phy.pku.edu.cn/~xurenxin/ R. X. Xu

16. Watts et al. (2015) Hyperon puzzle? Quark-confinement? in this quark-cluster star model How to find with FAST?_ M ~1.4 M sun

17. How to find with FAST?_ M Maximum mass Maximum mass detected  0. 6 1.4 ~ ? (~3.3!) What’s the real PSR mass spectrum? deep massive Limoges et al. arXiv:1505.02297 For WD, Maximum mass (<20pc) = 1.13 M ⊙ Maximum mass (<40pc) = 1.26 M ⊙ PSR-EoS http:// www.phy.pku.edu.cn/~xurenxin/ R. X. Xu

18. Message from PRE X-ray bursts: low-mass? Photospheric radius expansion in 4U 1746-37 Constraints by PRE bursts of 4U 1746-37, on the assumption that the touchdown flux corresponded to L Edd, and the obscure effect is included. Li et al. (ApJ, 2015) How to find with FAST?_ M PSR-EoS http:// www.phy.pku.edu.cn/~xurenxin/ R. X. Xu

19. R, but to measure I via spin-orbit coupling… + J S L S2S2 S1S1 2-body in Newtonian gravity2-body in Einstein gravity The two-body problem in GR:  Analytical approach (post-Minkowskian, post-Newtonian, matching of asymptotic expansions)  Numerical Relativity Three routes to measure I by pulsar timing (Kramer & Wex, 2009): for highly relativistic binaries …  Correction to the advance of periastron,   Non-linear time evolution of the longitude of periastron if the spin is inclined with respect to J  Two derivatives, x, once again leading to an estimate of I sin ..  How to find with FAST?_ I J = S+L S = I 

20. P is limited by mass shedding & r-mode inst… Spin figure: Alessandro Patruno Spin of self-bound on surface may not limited by mass shedding: NS  sub-Keplerian SS  super-Keplerian? The GW-induced rotation- mode instability depends on the viscosity of matter, thus the EoS. Higher sensitivity of FAST will give the first opportunity to undertake a deep survey for fast pulsars, for even sub-ms pulsars! How to find with FAST?_ P PSR-EoS http:// www.phy.pku.edu.cn/~xurenxin/ R. X. Xu

21. How to find with FAST?_ pulse Magnetospheric activity depends on surface… PSR-EoS http:// www.phy.pku.edu.cn/~xurenxin/ R. X. Xu RS’75

22. Conclusions Besides testing gravity and detecting GW waves, pulsars provide a unique test-ground for the fundamental strong interaction (QCD). We are expecting advances facilities (FAST, SKA) to improve our knowledge about M and I, the lower-ends of P and drifting subpulses. These observations are surely related to the EoS of cold dense matter, and may finally solve problem of EoS of dense matter. THANKS! PSR-EoS http:// www.phy.pku.edu.cn/~xurenxin/ R. X. Xu