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The Equation of State of Neutron Star Matter

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Millisecond Pulsars

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 465))

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Abstract

Neutron stars are remarkable natural laboratories that allow us to investigate the fundamental constituents of matter and their interactions under extreme conditions that cannot be reproduced in terrestrial laboratories. This chapter gives a brief pedagogical introduction to the physics of matter at very high densities (i.e. up to several times the density of atomic nuclei) that hopefully could be useful to researchers in pulsars’ astrophysics and related areas.

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Notes

  1. 1.

    Stellar masses will be given in unit of the mass of the Sun, M ⊙ = 1.988  × 1033g.

  2. 2.

    The star may also contain species of identical bosons as in the case of negative pions (π −) or negative kaons (K −) condensation.

  3. 3.

    The Coulomb interaction, together with finite size effects (mainly surface effects), is responsible for the formation of the so called nuclear pasta phases in the neutron star crust [13]. For the same physical reasons, similar quark matter pasta phases could appear inside hybrid stars [14].

  4. 4.

    k B T = 1 MeV corresponds to T ≃ 1.134 × 1010 K.

  5. 5.

    i.e. imagine for a moment to “switch off” the weak interaction.

  6. 6.

    This is possible if the electron Fermi momentum satisfies , thus for densities .

  7. 7.

    Neutrino are trapped in neutron star interior for a few tens of second after their birth [15].

  8. 8.

    Including those considered in the present chapter.

  9. 9.

    Notice that the presence of tiny charge-symmetry breaking (CSB) and charge-independence breaking (CIB) terms in the nuclear interaction (for a review, see e.g. [29]) could invalidate Eq. (9.23). For example a CSB component in the NN interaction produces a linear (and more generally odd-power) β-term in Eq. (9.23) [30]. However, it has been numerically demonstrated by various authors (e.g. [30] and [31]) that the effects on \({\widetilde E}(n, \beta )\) and on the nuclear symmetry energy of CSB and CIB terms in the nucleon-nucleon interaction are essentially negligible.

  10. 10.

    Hadrons, i.e. particles subject to the strong interaction, can be classified in two groups: baryons if they have spin J = 1∕2, 3∕2, 5∕2, …, or mesons if they have spin J = 0, 1, 2, … . According to the hadrons’ quark model, baryons are colorless bound states of three quarks (q 1 q 2 q 3), and mesons are colorless quark–anti-quark \((q_1 \bar {q}_2\)) bound states.

  11. 11.

    The strong interaction between quarks can be neglected due to the asymptotic freedom of QCD which, for the purpose of the present estimate, is a reasonable approximation at the high densities found in neutron stars cores.

  12. 12.

    The actual mean-life time of the HS will depend on the mass accretion or on the spin-down rate which modifies the nucleation time τ via an explicit time dependence of the stellar central pressure.

  13. 13.

    Since the nucleation time is extremely sensitive to the value of the stellar central pressure P c and thus to its corresponding gravitational mass M HS(P c) (see Fig. 4 and 5 in Ref. [106]), the critical mass value is not influenced by the particular choice τ = 1 yr.

  14. 14.

    The SQM EoS used to calculate the QS configurations reported in Fig. 9.9 satisfies the strange matter hypothesis.

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Acknowledgements

I thank the editors of the present book, Sudip Bhattacharyya, Alessandro Papitto, and Dipankar Bhattacharya, for inviting me to write this chapter. I dedicate this work to my beloved son, Paride.

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  1. Dipartimento di Fisica “Enrico Fermi”, Università di Pisa, INFN Sezione di Pisa, Pisa, Italy

    Ignazio Bombaci

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  1. Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Mumbai, Maharashtra, India

    Sudip Bhattacharyya

  2. INAF Osservatorio Astronomico di Roma, Monte Porzio Catone, Roma, Italy

    Alessandro Papitto

  3. Inter-University Centre for Astronomy and Astrophysics, Pune, India

    Dipankar Bhattacharya

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Bombaci, I. (2022). The Equation of State of Neutron Star Matter. In: Bhattacharyya, S., Papitto, A., Bhattacharya, D. (eds) Millisecond Pulsars. Astrophysics and Space Science Library, vol 465. Springer, Cham. https://doi.org/10.1007/978-3-030-85198-9_9

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