Abstract
Formed in the aftermath of gravitational core-collapse supernova explosions, neutron stars are unique cosmic laboratories for probing the properties of matter under extreme conditions that cannot be reproduced in terrestrial laboratories. The interior of a neutron star, endowed with the highest magnetic fields known and with densities spanning about ten orders of magnitude from the surface to the centre, is predicted to exhibit various phases of dense strongly interacting matter, whose physics is reviewed in this chapter. The outer layers of a neutron star consist of a solid nuclear crust, permeated by a neutron ocean in its densest region, possibly on top of a nuclear “pasta” mantle. The properties of these layers and of the homogeneous isospin asymmetric nuclear matter beneath constituting the outer core may still be constrained by terrestrial experiments. The inner core of highly degenerate, strongly interacting matter poses a few puzzles and questions which are reviewed here together with perspectives for their resolution. Consequences of the dense-matter phases for observables such as the neutron-star mass-radius relationship and the prospects to uncover their structure with modern observational programmes are touched upon.
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Notes
- 1.
The depth z 0 below the surface of a cold and fully catalysed neutron star at a pressure P 0 was estimated as \(\displaystyle z_0\approx \int _{0}^{P_0} \frac {dP}{\rho g_s}\), with \(\displaystyle g_s=\frac {G\mathcal {M}}{R^2} \left (1-\frac {2 G\mathcal {M}}{R c^2}\right )^{-1/2}\), see, e.g., Chamel and Haensel (2008), and we have made use of an interpolation of the “QEOS” equation of state from More et al. (1988), as tabulated in Lai et al. (1991).
- 2.
- 3.
- 4.
Because the electron chemical potential scales as \(\mu _e\sim 2 pi^2 m_e c^2 \lambda _e^3 n_e B_{\mathrm{rel}}/B\) with B rel ≃ 4.4 × 1013 G in strongly quantising magnetic fields, the expansion of g to first order in α eventually breaks down in high enough magnetic fields. See also Sect. 7.4.2.
- 5.
This assumption may be violated in the presence of a very high magnetic field, as discussed in Sect. 7.3.1.
- 6.
- 7.
- 8.
- 9.
If one would not pay attention and apply a Maxwell construction to this example one would have to let the physical pressure go along the larger pressure, which would mean to join the two not trustable parts of the model EoS. A recent example for matching unphysical EoS is Annala et al. (2017), where the authors in such grounds suggest a new type of holographic hybrid stars, with nuclear matter core surrounded by a quark matter shell.
- 10.
- 11.
Note that the transition from a configuration at the endpoint of the neutron star branch in the M − R diagram to the third family branch of hybrid stars (triggered, e.g., by mass accretion or spin-down) occurs under simultaneous conservation of baryon mass and angular momentum, as has been demonstrated in Bejger et al. (2017) for the case of the high-mass twin EoS (Benic et al. 2015b). It could therefore occur at the free-fall timescale, accompanied by a burst-type phenomenon (Alvarez-Castillo et al. 2015) (such as a fast radio burst (Falcke and Rezzolla 2014)) unlike the case discussed earlier in Glendenning et al. (1997) where an angular momentum mismatch had to be compensated by, e.g., dipole radiation an estimated timescale for the transition period of 105 years.
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Acknowledgements
The work of N.C. was supported by Fonds de la Recherche Scientifique - FNRS (Belgium) under grants n∘ CDR-J.0187.16 and CDR-J.0115.18. D.B. received support from Narodowe Centrum Nauki - NCN (Poland) under contract No. UMO-2014/13/B/ST9/02621 (Opus7) and by the MEPhI Academic Excellence programme under contract no. 02.a03.21.0005. This work was also partially supported by the European Cooperation in Science and Technology (COST) Action MP1304 NewCompStar.
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Blaschke, D., Chamel, N. (2018). Phases of Dense Matter in Compact Stars. In: Rezzolla, L., Pizzochero, P., Jones, D., Rea, N., Vidaña, I. (eds) The Physics and Astrophysics of Neutron Stars. Astrophysics and Space Science Library, vol 457. Springer, Cham. https://doi.org/10.1007/978-3-319-97616-7_7
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