Skip to main content

Advertisement

Log in

The effect of the energy functional on the pasta-phase properties of catalysed neutron stars

  • Regular Article
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

Abstract

Nuclear pasta, that is an inhomogeneous distribution of nuclear matter characterised by non-spherical clustered structures, is expected to occur in a narrow spatial region at the bottom of the inner crust of neutron stars, but the width of the pasta layer is strongly model dependent. In the framework of a compressible liquid-drop model, we use Bayesian inference to analyse the constraints on the sub-saturation energy functional and surface tension imposed by both ab-initio chiral perturbation theory calculations and experimental measurements of nuclear masses. The posterior models are used to obtain general predictions for the crust-pasta and pasta-core transition with controlled uncertainties. A correlation study allows us to extract the most influential parameters for the calculation of the pasta phases. The important role of high-order empirical parameters and of the surface tension is underlined.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Data generated during this study are contained in this published article.]

Notes

  1. In this section and the following ones, the surface parameter p is systematically included in the \(\mathbf {X}\) parameter set as an additional independent parameter, with a flat prior distribution as given in Table 1.

References

  1. D. Blaschke, N. Chamel, in The Physics and Astrophysics of Neutron Stars, vol. 457, ed. by L. Rezzolla, P. Pizzochero, D.I. Jones, N. Rea, I. Vidaña (Astrophysics and Space Science Library, Springer, Cham, 2018), pp. 337–400

  2. P. Haensel, A.Y. Potekhin, D.G. Yakovlev, Neutron Stars 1. Equation of State and Structure (Springer, New York, 2007)

    Google Scholar 

  3. J.A. Pons, D. Viganò, N. Rea, Nat. Phys. 9, 431 (2013)

    Article  Google Scholar 

  4. D. Viganò, N. Rea, J.A. Pons, R. Perna, D.N. Aguilera, J.A. Miralles, Mon. Not. R. Astron. Soc. 434, 123 (2013)

    Article  ADS  Google Scholar 

  5. C.J. Horowitz, D.K. Berry, C.M. Briggs, M.E. Caplan, A. Cumming, A.S. Schneider, Phys. Rev. Lett. 114, 031102 (2015)

    Article  ADS  Google Scholar 

  6. Z. Lin, M.E. Caplan, C.J. Horowitz, C. Lunardini, Phys. Rev. C 102, 045801 (2020)

    Article  ADS  Google Scholar 

  7. W.G. Newton, K. Murphy, J. Hooker, B. An Li, Astrophys. J. Lett. 779, L4 (2013)

    Article  ADS  Google Scholar 

  8. A. Schmitt, P. Shternin, in The Physics and Astrophysics of Neutron Stars, vol. 457, ed. by L. Rezzolla, P. Pizzochero, D.I. Jones, N. Rea, I. Vidaña (Astrophysics and Space Science Library, Springer, Cham, 2018), pp. 455–574

  9. M. Gearheart, W.G. Newton, J. Hooker, B. An Li, Mon. Not. R. Astron. Soc. 418, 2343 (2011)

    Article  ADS  Google Scholar 

  10. H. Sotani, K. Nakazato, K. Iida, K. Oyamatsu, Phys. Rev. Lett. 108, 201101 (2012)

    Article  ADS  Google Scholar 

  11. M. Hashimoto, H. Seki, M. Yamada, Prog. Theor. Phys. 71, 320 (1984)

    Article  ADS  Google Scholar 

  12. K. Oyamatsu, M. Hashimoto, M. Yamada, Prog. Theor. Phys. 72, 373 (1984)

    Article  ADS  Google Scholar 

  13. D.G. Ravenhall, C.J. Pethick, J.M. Lattimer, Nucl. Phys. A 407, 571 (1983)

    Article  ADS  Google Scholar 

  14. C.P. Lorenz, D.G. Ravenhall, C.J. Pethick, Phys. Rev. Lett. 70, 379 (1993)

    Article  ADS  Google Scholar 

  15. W.G. Newton, M. Gearheart, B.A. Li, Astrophys. J. Suppl. Ser. 204, 9 (2013)

    Article  ADS  Google Scholar 

  16. H. Pais, D.P. Menezes, C. Providência, Phys. Rev. C 93, 065805 (2016)

    Article  ADS  Google Scholar 

  17. X. Viñas, C. Gonzalez-Boquera, B.K. Sharma, M. Centelles, Acta Physica Polonica B Proc. Suppl. 10, 259 (2017)

    Article  ADS  Google Scholar 

  18. Y. Lim, J.W. Holt, Phys. Rev. C 95, 065805 (2017)

    Article  ADS  Google Scholar 

  19. L.E. Balliet, W.G. Newton, S. Cantu, S. Budimir, Astrophys. J. 918, 79 (2021)

    Article  ADS  Google Scholar 

  20. N. Martin, M. Urban, Phys. Rev. C 92, 015803 (2015)

    Article  ADS  Google Scholar 

  21. B.K. Sharma, M. Centelles, X. Viñas, M. Baldo, G.F. Burgio, Astron. Astrophys. 584, A103 (2015)

    Article  ADS  Google Scholar 

  22. J.M. Pearson, N. Chamel, A.Y. Potekhin, Phys. Rev. C 101, 015802 (2020)

    Article  ADS  Google Scholar 

  23. I. Sengo, H. Pais, B. Franzon, C. Providência, Phys. Rev. D 102, 063013 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  24. F. Ji, J. Hu, H. Shen, Phys. Rev. C 103, 055802 (2021)

    Article  ADS  Google Scholar 

  25. B. Schuetrumpf, W. Nazarewicz, Phys. Rev. C 92, 045806 (2015)

    Article  ADS  Google Scholar 

  26. I. Sagert, G.I. Fann, F.J. Fattoyev, S. Postnikov, C.J. Horowitz, Phys. Rev. C 93, 055801 (2016)

    Article  ADS  Google Scholar 

  27. F.J. Fattoyev, C.J. Horowitz, B. Schuetrumpf, Phys. Rev. C 95, 055804 (2017)

    Article  ADS  Google Scholar 

  28. A.S. Schneider, D.K. Berry, M.E. Caplan, C.J. Horowitz, Z. Lin, Phys. Rev. C 93, 065806 (2016)

    Article  ADS  Google Scholar 

  29. D.K. Berry, M.E. Caplan, C.J. Horowitz, G. Huber, A.S. Schneider, Phys. Rev. C 94, 055801 (2016)

    Article  ADS  Google Scholar 

  30. C.J. Pethick, D.G. Ravenhall, Annu. Rev. Nucl. Part. Sci. 45, 429 (1995)

    Article  ADS  Google Scholar 

  31. N. Chamel, P. Haensel, Living Rev. Relat. 11, 10 (2008)

    Article  ADS  Google Scholar 

  32. G. Watanabe, T. Maruyama, in Neutron Star Crust. ed. by C. Bertulani, J. Piekarewicz (Nova Science Publishers, New York, 2012), p. 23

  33. T. Maruyama, G. Watanabe, S. Chiba, Prog. Theor. Exp. Phys. 2012, 01A201 (2012)

    Article  Google Scholar 

  34. T. Carreau, F. Gulminelli, J. Margueron, Eur. Phys. J. A 55, 188 (2019)

    Article  ADS  Google Scholar 

  35. T. Carreau, F. Gulminelli, N. Chamel, A.F. Fantina, J.M. Pearson, Astron. Astrophys. 635, A84 (2020)

    Article  ADS  Google Scholar 

  36. H. Dinh Thi, T. Carreau, A.F. Fantina, F. Gulminelli, Accepted in Astron. Astrophys. 654, A114 (2021)

  37. G. Baym, H.A. Bethe, C.J. Pethick, Nucl. Phys. A 175, 225 (1971)

    Article  ADS  Google Scholar 

  38. F. Douchin, P. Haensel, Astron. Astrophys. 380, 151 (2001)

    Article  ADS  Google Scholar 

  39. J. Margueron, R. Hoffmann Casali, F. Gulminelli, Phys. Rev. C 97, 025805 (2018)

    Article  ADS  Google Scholar 

  40. J. Margueron, R. Hoffmann Casali, F. Gulminelli, Phys. Rev. C 97, 025806 (2018)

    Article  ADS  Google Scholar 

  41. J. Piekarewicz, M. Centelles, Phys. Rev. C 79, 054311 (2009)

    Article  ADS  Google Scholar 

  42. T. Maruyama, T. Tatsumi, D.N. Voskresensky, T. Tanigawa, S. Chiba, Phys. Rev. C 72, 015802 (2005)

    Article  ADS  Google Scholar 

  43. J.M. Lattimer, F.D. Swesty, Nucl. Phys. A 535, 331 (1991)

    Article  ADS  Google Scholar 

  44. Y. Lim, J.W. Holt, R.J. Stahulak, Phys. Rev. C 100, 035802 (2019)

    Article  ADS  Google Scholar 

  45. Y. Lim, J.W. Holt, Eur. Phys. J. A 55, 209 (2019)

    Article  ADS  Google Scholar 

  46. M. Wang, G. Audi, F.G. Kondev, W.J. Huang, S. Naimi, X. Xu, Chin. Phys. C 41, 030003 (2017) and Atomic Mass Data Center. http://amdc.in2p3.fr/web/masseval.html

  47. S. Goriely, N. Chamel, J.M. Pearson, Phys. Rev. C 88, 024308 (2013)

    Article  ADS  Google Scholar 

  48. E. Chabanat, P. Bonche, P. Haensel, J. Meyer, R. Schaeffer, Nucl. Phys. A 635, 231 (1997)

    Article  ADS  Google Scholar 

  49. M. Rayet, M. Arnould, F. Tondeur, G. Paulus, Astron. Astrophys. 116, 183 (1982)

    ADS  Google Scholar 

  50. G.A. Lalazissis, T. Nikšić, D. Vretenar, P. Ring, Phys. Rev. C 71, 024312 (2005)

    Article  ADS  Google Scholar 

  51. X. Roca-Maza, X. Viñas, M. Centelles, P. Ring, P. Schuck, Phys. Rev. C 84, 054309 (2011)

    Article  ADS  Google Scholar 

  52. G.A. Lalazissis, J. König, P. Ring, Phys. Rev. C 55, 540 (1997)

    Article  ADS  Google Scholar 

  53. W. Long, J. Meng, N. Van Giai, S.G. Zhou, Phys. Rev. C 69, 034319 (2004)

    Article  ADS  Google Scholar 

  54. S. Typel, H.H. Wolter, Nucl. Phys. A 656, 331 (1999)

    Article  ADS  Google Scholar 

  55. F. Grill, C. Providência, S.S. Avancini, Phys. Rev. C 85, 055808 (2012)

    Article  ADS  Google Scholar 

  56. C. Drischler, K. Hebeler, A. Schwenk, Phys. Rev. C 93, 054314 (2016)

    Article  ADS  Google Scholar 

  57. B.P. Abbott et al., Phys. Rev. Lett. 121, 161101 (2018)

    Article  ADS  Google Scholar 

  58. T. Carreau, F. Gulminelli, J. Margueron, Phys. Rev. C 100, 055803 (2019)

  59. T. Carreau, PhD dissertation. https://tel.archives-ouvertes.fr/tel-03019954 (2020)

  60. M. Shelley, A. Pastore, Phys. Rev. C 103, 035807 (2021)

    Article  ADS  Google Scholar 

  61. C. Providência, S.S. Avancini, R. Cavagnoli, S. Chiacchiera, C. Ducoin, F. Grill, J. Margueron, D.P. Menezes, A. Rabhi, I. Vidaña, Eur. Phys. J. A 50, 44 (2014)

    Article  ADS  Google Scholar 

  62. C. Ducoin, J. Margueron, C. Providência, I. Vidaña, Phys. Rev. C 83, 045810 (2011)

    Article  ADS  Google Scholar 

  63. M. Grasso, D. Lacroix, C.J. Yang, Phys. Rev. C 95, 054327 (2017)

    Article  ADS  Google Scholar 

  64. C.J. Yang, M. Grasso, D. Lacroix, Phys. Rev. C 94, 031301(R) (2016)

    Article  ADS  Google Scholar 

  65. U.J. Furtado, F. Gulminelli, J. Phys. G 48, 015102 (2020)

    Article  ADS  Google Scholar 

  66. F. Douchin, P. Haesel, J. Meyer, Nucl. Phys. A 665, 419 (2000)

    Article  ADS  Google Scholar 

  67. M. Oertel, M. Hempel, T. Klähn, S. Typel, Rev. Mod. Phys. 89, 015007 (2017)

    Article  ADS  Google Scholar 

  68. G.F. Burgio, A.F. Fantina, in The Physics and Astrophysics of Neutron Stars, vol. 457, ed. by L. Rezzolla, P. Pizzochero, D.I. Jones, N. Rea, I. Vidaña (Astrophysics and Space Science Library, Springer, Cham, 2018), pp. 255–335

  69. F. Gulminelli, A.F. Fantina, Nucl. Phys. News 31, 2 (2021)

    Article  Google Scholar 

  70. H. Dinh Thi, C. Mondal, F. Gulminelli, Universe 7, 373 (2021)

  71. https://compose.obspm.fr

Download references

Acknowledgements

This work has been partially supported by the IN2P3 Master Project NewMAC and the CNRS International Research Project (IRP) “Origine des éléments lourds dans l’univers: Astres Compacts et Nucléosynthèse (ACNu)”.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. F. Fantina.

Additional information

Communicated by Laura Tolos.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dinh Thi, H., Fantina, A.F. & Gulminelli, F. The effect of the energy functional on the pasta-phase properties of catalysed neutron stars. Eur. Phys. J. A 57, 296 (2021). https://doi.org/10.1140/epja/s10050-021-00605-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epja/s10050-021-00605-6

Navigation