1. GENERAL RELATIVITY AND PRECISE MEASUREMENTS GENERAL RELATIVITY AND PRECISE MEASUREMENTS OF PULSAR MASSES D.G. Yakovlev Ioffe Physical Technical Institute, St.-Petersburg, Russia Introduction X-ray binaries Double neutron star binaries Pulsar – white dwarf binaries Summary FFC, Pulkovo Observatory, October 10, 2013

2. INTRODUCION Galaxy, stars and the Sun Galaxy: more than 10 11 stars Luminosity: L~10 46 erg/s Sun: M=2x10 33 g, R=700,000 km, L=3.83x10 33 erg/s, mean density of matter = 1.4 g/cm 3, surface temperature ~6,000 К, internal temperature 15.7 MК. Composition: rarefied plasma, pressure P=nkT ~10 17 dyn/cm 2. Supported by thermonuclear reactions in central region

3. Giant star WD NS BH NS BH Normal star M<8 M SUN Quiet removal of outer shell, birth of white dwarf (WD) M>25 M SUN collapse into black hole (BH) SCHEME! M=(8—25 ) M SUN Core-collapsed supernova (SN II) birth of neutron star SN Ia i, b b b WD, NS, BH = graveyard i=isolated b=binary

4. Extreme Physics Problem: EOS, High B, High Tc Main mystery: EOS of super-dense core – longstanding fundamental problem of physics and astrophysics complicated by high B and T c Main practical problem: How to relate EOS to observables

5. MOTIVES TO ACCURATELY MEASURE NS MASSES Мass – most important parameter of any star To find critical mass which separates NSs and BHs To constrain EOS of superdense matter in NS core Most massive NSs are most important!

6. X-ray binaries NS Companion in binary system Riccardo Giacconi Nobel Prize: 2002

7. Kepler Orbits Integrals of motion: Orbital period: Measuring radial velocities of companion 1: Measuring radial velocities of companion 2: Need more parameters: 2 1

8. Vela X-1 Vela X-1 (=4U 0900--40) GP Vel (=HD 77581, B0.5 Ib supergiant) P spin =283 s, P b =8.96 d, e=0.09 a=50 R sun, i>70 o, R 2 =30 R sun Discovery: Chodil et al. (1967) GP Vel: Brucato & Kristian (1972), Hiltner et al. (1972) K 2 for GP Vel: Hiltner et al. (1972) Quaintrell et al. (2003): K 1 for Vela X-1: Rappaport et al. (1976) P for Vela X-1: McClintock et al. (1976)

9. Masses of Neutron Stars in X-ray Binaries

10. SUMMARY: NEUTRON STAR MASSES IN X-RAY BINARIES (1) There is a wide spectrum of neutron star masses in XRBs (2) XRBs almost certainly contain massive neutron stars (3) The best candidates are Vela X-1 (M>1.62 M SUN ) Cyg X-2 4U 1700—37 (4) The prospects to accurately measure M are poor

11. Radio Pulsars in Compact Binaries Spin axis Magnetic axis L

12. Relativistic Objects: Radio Pulsar – Compact Companion Energy and orbital momentum: Peters & Mathews (1963), Peters (1963) Evolution of orbital parameters: Advantages: (1) Very precise timing P(t) (2) Point-like masses (3) GR effects

13. Example: Timing of pulsars and NS mass measurements Stage 1: Measurements of Keplerian parameters Stage 2: Measurements of relativistic parameters : 2 extra equations are required (a) Pereastron advance: (b) Transverse Doppler effect + gravitational dilation of signals by М 2: (c) Shapiro parameters: (d) Orbital decay: Up to 5 extra equations can be obtained !.

14. Russel Hulse and Joseph Taylor The Arecibo 305-m radio telescope (NAIC-Arecibo Observatory, NSF)

15. The Hulse-Taylor Pulsar (PSR B1913+16) Discovery: 2 June 1974 (ApJ Lett, January 15, 1975) 5083 observations from 1981 to 2001 Orbit: Relativistic effects (Weisberg & Taylor, 2010) : (a)(a) Rotation by 125 о in 30 years (Mercury: 43’’ in 100 yrs) (b)(b) (c)(c) Observations: Theoretical prediction: Nobel Prize: 1993

16. MASSES OF PSR B1913+16 & COMPANION (Weisberg, Nice, Taylor, 2010) The mass of the Hulse-Taylor Pulsar (PSR B1913+16)

17. Evolution of the Hulse-Taylor pulsar At birth: Now: In 200 Myr:

18. The last 10 Years of the Hulse-Taylor Pulsar 10 years before death: 1 ms before death : M31 Time to merging = 300 Myr

19. Geodetic precession of the Hulse-Taylor pulsar Barker & O’Connell (1975):

20. Ideal Wolszczan Pulsar (PSR B1534+12) Discovery: Wolszczan (1991) All 5 GR parameters measured: Neutron star masses (Stairs et al. 2003):

21. J0737-3039 A and B: Double Pulsar Binary PulsarА Burgay et al. (2003) Observation: 4.5 min in August 2001 + systematic observations since 2003 (5 months) Pulsar B Lyne et al. (2004) Systematic observations since May 2003 (7 months) Results: Fifth binary with short lifetime Radio eclipses

22. Double Neutron Star Binaries

23. MASSES OF DOUBLE NEUTRON STAR BINARIES 5 DNSB = 10 neutron star masses accurately measured All masses are in narrow range HT pulsar is most massive among them No recent progress with these objects

24. RADIO PULSARS AND WHITE DWARFS (or other compact companions) Advantages: Compact stars – point-like masses Often – recycled millisecond pulsars: pulsars can be massive, short periods – good timing, weak magnetic fields – no glitches or pulsar noise Disadvantages: Underwent active accretion phase – as a rule, almost circular orbits = difficult to measure periastron advance and gamma-parameter Low-mass companions – difficult to measure Shapiro effect and dP b /dt Specific feature: Often observed in globular clusters

25. Neutron Stars and White Dwarfs White dwarfs: M 2 —P b

26. Neutron Stars and White Dwarfs

27. Ideal System Radio Pulsar—White Dwarf (PSR J1141—6545) Discovery: Kaspi et al. (2000) Three GR parameters measured: Masses (Bailes et al. 2003):

28. Ideal Binary Radio Pulsar—White Dwarf (PSR J1909—3744) Discovery: Jacoby et al. (2003) Two relativistic parameters measures: s, r Masses of stars (Jacoby et al. 2005):

29. Fallen Down Angel Radio Pulsar—White Dwarf (PSR J0751+1807) Discovery: Lundgren et al. (1995) One relativistic parameter measured: dP b /dt Shapiro effect is poorly pronounced: i~65-85 0 Masses of companions (Nice, Splaver, Stairs 2004, 2005): After 2007 (Nice, Stairs, Kasian 2008):

30. Radio Pulsar—White Dwarf (PSR J1911—5958A) Discovery: D’Amico et al. (2001) No relativistic parameters measured Bassa et al. (2006), Cocozza et al. (2006) – radial velocity curve and mass of white dwarf are measured in optical observations

31. PSR J1903+0327 (2009) Discovery: Cordes et al. (2006) The first eccentric binary MCP in the galactic disk Companion: MS star, M~1 M SUN Evolutionary scenario: unclear Measured: periastron advance + s, r Problem: large size of companion can affect periastron advance Perspective: timing, refined measurements of periastron advance, s, r

32. Most Massive Known Neutron Star PSR J1614-2230 + WD Measured: Shapiro effect, s, r Most massive neutron star currently known 28 0ct. 2010, Nature 467, 1081 Discovery: 2002 (Hessels et al. 2005)

33. Most Massive Known Neutron Star Shapiro delay in PSR J1614-2230 + WD 00.5 1.0 Orbital phase Time residual, microseconds Demorest et al. (2010)

34. THE SECOND MOST MASSIVE NEUTRON STAR PSR J0348+0432 + WD Radio observations: Green Bank (USA) 2007 Publication: Lynch et al. (2013) Science, 26 April 2013, Vol. 340, Issue 6131, 448 Pulsar: moderately spun up by accretion WD: low-massive, He core Age of the system: about 3 Gyrs Measured: radial velocities of PSR and WD and spectroscopic WD mass

35. Checked by orbital decay: Theory Observations Time to merging: 400 Myr Ideal binary for checking GR! Measured without GR effects THE SECOND MOST MASSIVE NEUTRON STAR PSR J0348+0432 + WD

36. Summary of NS-WD and NS-NS binaries Kiziltan et al. (2013)

37. MOST MASSIVE NEUTRON STAR VERSUS TIME PSR B1913+16 PSR J0751+1807 PSR J1903+0327 PSR J1614—2230 PSR J0348+0432

38. HT pulsar PSR J1614-2230 PSR J0348+0432 General Relativity Causality Mass—Radius Diagram for Exploring EOS of Superdense

39. RESULTS General Relativity Theory was tested Gravitational radiation discovered Geodetic precession discovered Double neutron star mergers were discovered Gravitational observatories of new generation are built General Relativity has become useful tool Masses of some neutron stars accurately measured Currently: M max >2 M SUN => soft and moderate EOSs are ruled out => EOS is stiff => little room for exotic matter Unsolved Problems M MAX = ? Stiff EOS = just stiff or superstiff? Main feature at present: Rapid progress!