Constraints on pulsar masses from the maximum observed glitch

Abstract

Neutron stars are unique cosmic laboratories in which fundamental physics can be probed in extreme conditions not accessible to terrestrial experiments. In particular, the precise timing of rotating magnetized neutron stars (pulsars) reveals sudden jumps in rotational frequency in these otherwise steadily spinning-down objects. These ‘glitches’ are thought to be due to the presence of a superfluid component in the star, and offer a unique glimpse into the interior physics of neutron stars. In this paper we propose an innovative method to constrain the mass of glitching pulsars, using observations of the maximum glitch observed in a star, together with state-of-the-art microphysical models of the pinning interaction between superfluid vortices and ions in the crust. We study the properties of a physically consistent angular momentum reservoir of pinned vorticity, and we find a general inverse relation between the size of the maximum glitch and the pulsar mass. We are then able to estimate the mass of all the observed glitchers that have displayed at least two large events. Our procedure will allow current and future observations of glitching pulsars to constrain not only the physics of glitch models but also the superfluid properties of dense hadronic matter in neutron star interiors.

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Figure 1: Critical lag profile as a function of the cylindrical radiusx.
Figure 2: Upper limit to the mass for a selection of pulsars.
Figure 3: Glitch amplitude as a function of the nominal lag since corotation.
Figure 4: Mass estimates for 17 large glitchers with the Bsk21 equation of state.
Figure 5: Estimates of pulsar masses with different equations of state.

References

  1. 1

    Haskell, B. et al. Detecting gravitational waves from mountains on neutron stars in the advanced detector era. Mon. Not. R. Astron. Soc. 450, 2393–2403 (2015).

    ADS  Article  Google Scholar 

  2. 2

    Abbott, B. P. et al. Comprehensive all-sky search for periodic gravitational waves in the sixth science run LIGO data. Phys. Rev. D 94, 042002 (2016).

    ADS  Article  Google Scholar 

  3. 3

    Manchester, R. N. Pulsars and gravity. Int. J. Mod. Phys. D 24, 1530018 (2015).

    ADS  Article  Google Scholar 

  4. 4

    Hobbs, G. et al. Development of a pulsar-based timescale. Mon. Not. R. Astron. Soc. 427, 2780–2787 (2012).

    ADS  Article  Google Scholar 

  5. 5

    Sauls, J. A. in Timing Neutron Stars (eds Ogelman, H. & van den Heuvel, E. P. J. ) NATO ASI Series C, Vol. 262, 457–490 (Kluwer Academic, 1989).

    Google Scholar 

  6. 6

    Anderson, P. W. & Itoh, N. Pulsar glitches and restlessness as a hard superfluidity phenomenon. Nature 256, 25–27 (1975).

    ADS  Article  Google Scholar 

  7. 7

    Chamel, N. & Haensel, P. Physics of neutron star crusts. Living Rev. Relat. 11, 10–191 (2008).

    ADS  Article  Google Scholar 

  8. 8

    Haskell, B. & Melatos, A. Models of pulsar glitches. Int. J. Mod. Phys. D 24, 1530008 (2015).

    ADS  MathSciNet  Article  Google Scholar 

  9. 9

    Hall, H. E. & Vinen, W. F. The rotation of liquid helium II. II. The theory of mutual friction in uniformly rotating helium II. Proc. R. Soc. A 238, 215–234 (1956).

    ADS  MATH  Google Scholar 

  10. 10

    Mendell, G. Superfluid hydrodynamics in rotating neutron stars. I. Nondissipative equations. II. Dissipative effects. Astrophys. J. 380, 515–540 (1991)

    ADS  MathSciNet  Article  Google Scholar 

  11. 11

    Carter, B. & Langlois, D. Relativistic models for superconducting superfluid mixtures. Nucl. Phys. B 531, 478–504 (1998).

    ADS  MathSciNet  Article  Google Scholar 

  12. 12

    Prix, R., Comer, G. L. & Andersson, N. Slowly rotating superfluid Newtonian neutron star model with entrainment. Astron. Astrophys. 381, 178–196 (2002).

    ADS  Article  Google Scholar 

  13. 13

    Andersson, N. & Comer, G. L. A flux-conservative formalism for convective and dissipative multi-fluid systems, with application to Newtonian superfluid neutron stars. Class. Quant. Grav. 23, 5505–5529 (2006).

    ADS  MathSciNet  Article  Google Scholar 

  14. 14

    Andersson, N. & Comer, G. L. Relativistic fluid dynamics: physics for many different scales. Living Rev. Relat. 10, 1–83 (2007).

    Article  Google Scholar 

  15. 15

    Haskell, B., Pizzochero, P. M. & Sidery, T. Modelling pulsar glitches with realistic pinning forces: a hydrodynamical approach. Mon. Not. R. Astron. Soc. 420, 658–671 (2012).

    ADS  Article  Google Scholar 

  16. 16

    Howitt, G., Haskell, B. & Melatos, A. Hydrodynamic simulations of pulsar glitch recovery, Mon. Not. R. Astron. Soc. 460, 1201–1213 (2016).

    ADS  Article  Google Scholar 

  17. 17

    Sourie, A., Chamel, N., Novak, J. & Oertel, M. Global numerical simulations of the rise of vortex-mediated pulsar glitches in full general relativity. Mon. Not. R. Astron. Soc. 464, 4641–4657 (2016).

    ADS  Article  Google Scholar 

  18. 18

    Link, B., Epstein, R. I. & Lattimer, J. M. Pulsar constraints on neutron star structure and equation of state. Phys. Rev. Lett. 83, 3362–3365 (1999).

    ADS  Article  Google Scholar 

  19. 19

    Andersson, N., Glampedakis, K., Ho, W. C. G. & Espinoza, C. M. Pulsar glitches: the crust is not enough. Phys. Rev. Lett. 109, 241103 (2012).

    ADS  Article  Google Scholar 

  20. 20

    Chamel, N. Crustal entrainment and pulsar glitches. Phys. Rev. Lett. 110, 011101 (2013).

    ADS  Article  Google Scholar 

  21. 21

    Ho, W. C. G., Espinoza, C. M., Antonopoulou, D. & Andersson, N. Pinning down the superfluid and measuring masses using pulsar glitches. Science Adv. 1, e1500578 (2015).

    ADS  Article  Google Scholar 

  22. 22

    Newton, W. G., Berger, S. & Haskell, B. Observational constraints on neutron star crust–core coupling during glitches. Mon. Not. R. Astron. Soc. 454, 4400–4410 (2015).

    ADS  Article  Google Scholar 

  23. 23

    Delsate, T. et al. Giant pulsar glitches and the inertia of neutron-star crusts. Phys. Rev. D 94, 023008 (2016).

    ADS  Article  Google Scholar 

  24. 24

    Seveso, S., Pizzochero, P. M., Grill, F. & Haskell, B. Mesoscopic pinning forces in neutron star crusts, Mon. Not. R. Astron. Soc. 455, 3952–3967 (2016).

    ADS  Article  Google Scholar 

  25. 25

    Antonelli, M. & Pizzochero, P. M. Axially symmetric equations for differential pulsar rotation with superfluid entrainment. Mon. Not. R. Astron. Soc. 464, 721–733 (2017).

    ADS  Article  Google Scholar 

  26. 26

    Alpar, M. A., Anderson, P. W., Pines, D. & Shaham, J. Giant glitches and pinned vorticity in the VELA and other pulsars. Astrophys. J. Lett. 249, L29–L33 (1981).

    ADS  Article  Google Scholar 

  27. 27

    Andreev, A. F. & Bashkin, E. P. Three velocity hydrodynamics of superfluid solutions. Sov. Phys. JETP 42, 164–167 (1976).

    ADS  Google Scholar 

  28. 28

    Chamel, N. Neutron conduction in the inner crust of a neutron star in the framework of the band theory of solids. Phys. Rev. C 85, 035801 (2012).

    ADS  Article  Google Scholar 

  29. 29

    Chamel, N. & Haensel, P. Entrainment parameters in a cold superfluid neutron star core. Phys. Rev. C 73, 045802 (2006).

    ADS  Article  Google Scholar 

  30. 30

    Andersson, N., Sidery, T. & Comer, G. L. Superfluid neutron star turbulence. Mon. Not. R. Astron. Soc. 381, 747–756 (2007).

    ADS  Article  Google Scholar 

  31. 31

    Douchin, F. & Haensel, P. A unified equation of state of dense matter and neutron star structure. Astron. Astrophys. 380, 151–167 (2001).

    ADS  Article  Google Scholar 

  32. 32

    Goriely, S., Chamel, N. & Pearson, J. M. Further explorations of Skyrme–Hartree–Fock–Bogoliubov mass formulas. XII. Stiffness and stability of neutron-star matter. Phys. Rev. C 82, 035804 (2010).

    ADS  Article  Google Scholar 

  33. 33

    Dodson, R. G., Lewis, D. & McCulloch, P. Two decades of pulsar timing of Vela. Astrophys. Space Sci. 308, 585–589 (2007).

    ADS  Article  Google Scholar 

  34. 34

    Melatos, A., Peralta, C. & Wyithe, J. S. B. Avalanche dynamics of radio pulsar glitches. Astrophys. J. 672, 1103–1118 (2008).

    ADS  Article  Google Scholar 

  35. 35

    Espinoza, C. M., Lyne, A. G., Stappers, B. W. & Kramer, M. A study of 315 glitches in the rotation of 102 pulsars. Mon. Not. R. Astron. Soc. 4, 1679–1704 (2011).

    ADS  Article  Google Scholar 

  36. 36

    Haskell, B. Effect of superfluidity on pulsar glitch statistics. Mon. Not. R. Astron. Soc. Lett. 461, L77–L81 (2016).

    ADS  Article  Google Scholar 

  37. 37

    Ozel, F. & Freire, P. Masses, radii, and the equation of state of neutron stars. Annu. Rev. Astron. Astrophys. 54, 401–440 (2016).

    ADS  Article  Google Scholar 

  38. 38

    Lyne, A.G. The binary nature of PSR J2032+4127. Mon. Not. R. Astron. Soc. 451, 581–587 (2015).

    ADS  Article  Google Scholar 

  39. 39

    Demorest, P. B., Pennucci, T., Ransom, S. M., Roberts, M. S. E. & Hessels, J. W. T. A two-solar-mass neutron star measured using Shapiro delay. Nature 476, 1081–1083 (2010).

    ADS  Article  Google Scholar 

  40. 40

    Lattimer, J. M. & Steiner, A. W. Neutron star masses and radii from quiescent low-mass X-ray binaries. Astrophys. J. 784, 123–137 (2014).

    ADS  Article  Google Scholar 

  41. 41

    Easson, I. Postglitch behavior of the plasma inside neutron stars. Astrophys. J. 228, 257–267 (1979).

    ADS  Article  Google Scholar 

  42. 42

    Epstein, R. I. & Baym, G. Vortex pinning in neutron stars. Astrophys. J. 328, 680–690 (1988).

    ADS  Article  Google Scholar 

  43. 43

    Donati, P. & Pizzochero, P. M. Realistic energies for vortex pinning in intermediate-density neutron star matter. Phys. Lett. B 640, 74–81 (2006).

    ADS  Article  Google Scholar 

  44. 44

    Wlazłowski, G., Sekizawa, K., Magierski, P., Bulgac, A. & Forbes, M. Vortex pinning and dynamics in the neutron star crust. Phys. Rev. Lett. 117, 232701 (2016).

    ADS  Article  Google Scholar 

  45. 45

    Taranto, G., Burgio, G. F. & Schulze, H.-J. Cassiopeia A and direct URCA cooling. Mon. Not. R. Astron. Soc. 456, 1451–1458 (2015).

    ADS  Article  Google Scholar 

  46. 46

    Heinke, C. O. & Ho, W. C. G. Direct observation of the cooling of the Cassiopeia A neutron star. Astrophys. J. Lett. 719, L167–L171 (2010).

    ADS  Article  Google Scholar 

  47. 47

    Elshamouty, K. J. et al. Measuring the cooling of the neutron star in Cassiopeia A with all Chandra X-ray Observatory detectors. Astrophys. J. 777, 22 (2013).

    ADS  Article  Google Scholar 

  48. 48

    Posselt, B., Pavlov, G. G., Suleimanov, V. & Kargaltsev, O. New constraints on the cooling of the central compact object in Cas A. Astrophys. J. 779, 186–203 (2013).

    ADS  Article  Google Scholar 

  49. 49

    Ruderman, M. Crust-breaking by neutron superfluids and the Vela pulsar glitches. Astrophys. J. 203, 213–222 (1976).

    ADS  Article  Google Scholar 

  50. 50

    Pizzochero, P. M. Angular momentum transfer in Vela-like pulsar glitches. Astrophys. J. Lett. 743, L20–L25 (2011).

    ADS  Article  Google Scholar 

  51. 51

    Gugercinoglu, E. & Alpar, M. A. Vortex creep against toroidal flux lines, crustal entrainment, and pulsar glitches. Astrophys. J. Lett. 788, L11–L15 (2014).

    ADS  Article  Google Scholar 

  52. 52

    Link, B. Instability of superfluid flow in the neutron star core. Mon. Not. R. Astron. Soc. 421, 2682–2691 (2012).

    ADS  Article  Google Scholar 

  53. 53

    Haskell, B., Pizzochero, P. M. & Seveso, S. Investigating superconductivity in neutron star interiors with glitch models. Astrophys. J. Lett. 764, L25–L29 (2013).

    ADS  Article  Google Scholar 

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Acknowledgements

Partial support comes from NewCompStar, COST ActionMP1304. B.H. is supported by a Marie Curie Individual Fellowship, project 702713 Super-DENSE and NCN grant 2015/18/E/ST9/00577.

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P.M.P. led the research, contributed to developing the model and wrote the final manuscript. M.A. contributed to developing the model, selected the observational data, performed the calculations and contributed to the initial manuscript. B.H. contributed to the model and to the initial manuscript. S.S. contributed to the model and selected the observational data.

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Correspondence to P. M. Pizzochero.

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The authors declare no competing financial interests.

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Pizzochero, P., Antonelli, M., Haskell, B. et al. Constraints on pulsar masses from the maximum observed glitch. Nat Astron 1, 0134 (2017). https://doi.org/10.1038/s41550-017-0134

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