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Radial and nonradial oscillations of inverted hybrid stars

Chen Zhang, Yudong Luo, Hong-Bo Li, Lijing Shao, and Renxin Xu
Phys. Rev. D 109, 063020 – Published 15 March 2024
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  • INTRODUCTION
  • A RECAP ON THE EOS AND MASS-RADIUS…
  • RADIAL OSCILLATIONS
  • NONRADIAL OSCILLATIONS
  • SUMMARY
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We study the radial and nonradial oscillations of Cross stars (CrSs), i.e., stars with a quark matter crust and a hadronic matter core in an inverted order compared to conventional hybrid stars. We draw comparisons of their oscillation modes with those of neutron stars, quark stars, and conventional hybrid stars. We find that the stellar stability analysis from the fundamental mode of radial oscillations, and the g, f modes of nonradial oscillations are quite similar to those of conventional hybrid stars. However, due to the inverted stellar structure, the first nonradial p-mode of CrSs behaves in an inverted way and sits in a higher-frequency domain compared to that of conventional hybrid stars. These results provide a direct way to discriminate CrSs from other types of compact stars via gravitational wave (GW) probes. Specifically, compact stars emitting g-mode GWs within the 0.5–1 kHz range should be CrSs or conventional hybrid stars rather than neutron stars or pure quark stars, and a further GW detection of the first p-mode above 8 kHz or an identification of a decreasing trend of frequencies versus star masses associated with it will help identify the compact object to be a CrS rather than a conventional hybrid star.

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    • Received 20 June 2023
    • Accepted 6 February 2024

    DOI:https://doi.org/10.1103/PhysRevD.109.063020

    © 2024 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Gravitational wave sourcesGravitational wavesNuclear matter in neutron starsQuark matter
    1. Physical Systems
    Neutron stars & pulsars
    Gravitation, Cosmology & Astrophysics

    Authors & Affiliations

    Chen Zhang1,*, Yudong Luo2,3,†, Hong-Bo Li2,3,‡, Lijing Shao3,4,§, and Renxin Xu2,3,∥

    • 1The HKUST Jockey Club Institute for Advanced Study, The Hong Kong University of Science and Technology, Hong Kong, People’s Republic of China
    • 2School of Physics, Peking University, Beijing 100871, China
    • 3Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China
    • 4National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China

    • *Corresponding author: iasczhang@ust.hk
    • †yudong.luo@pku.edu.cn
    • ‡lihb2020@stu.pku.edu.cn
    • §lshao@pku.edu.cn
    • ∥r.x.xu@pku.edu.cn

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    Issue

    Vol. 109, Iss. 6 — 15 March 2024

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    Images

    • Figure 1
      Figure 1

      Masses versus center pressure Pc for CrSs of APR HM EOS with udQM (left) and SQM (right) of B=20 (black), 35 (blue), 50 (red) MeV/fm3, and a4=a4,min, (a4,min+a4,max)/2, a4,max from the darker to lighter color. APR EOS is applied for the hadronic composition, with the green dot-dashed curve denoting NSs with APR EOS. Dashed lines denote pure QSs.

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    • Figure 2
      Figure 2

      Radial-oscillation frequency squares for (top) slow conversion and (bottom) rapid conversion of CrSs with udQM (left) and SQM (right) as a function of center pressure. The line-color convention follows that of Fig. 1. In addition, we use hollow circles to mark the transition points and filled one to mark the maximum mass points. Those with nearly vertical lines are nontwin branches, where the eigenfrequencies drop more continuously after the transition point. Those without nearly vertical lines (i.e., twin branches) signal more abrupt change in frequencies at the transition point.

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    • Figure 3
      Figure 3

      Nonradial oscillation frequencies of (top) f-modes (solid lines) and g-modes (dotted lines), and (bottom) p1-modes (solid lines) for CrSs with udQM (left) and SQM (right) as a function of star mass. The line-color convention follows that of Fig. 1.

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    • Figure 4
      Figure 4

      Δρ/ρtrans vs g-mode frequencies for different (B,a4) sets. Filled and empty circles denote the maximum g-mode frequencies of CrSs with udQM and SQM, respectively, with the color convention being same as Fig. 1, and the vertical bars denote the frequencies ranges. The dashed purple line represents the fit for conventional hybrid stars adapted from Ref. [109], while the solid purple line denotes our fit for CrSs.

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    • Figure 5
      Figure 5

      Eigenfunctions of f-mode (top) and g-mode (bottom) for the twin branch with a frequency jump at the transition point. The CrS has center pressure 15.68  MeV fm3 (star mass 1.60M⊙), above and close to the transition pressure, consisting of a small hadronic core. The set of parameters is chosen as the lightest black lines in the left top panel of Fig. 3 in the paper (B=20  MeV/fm3, a4=a4,max).

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    • Figure 6
      Figure 6

      Top: Chemical potentials μ(P) of the hyperonic EOSs with SQM (black dashed) of B=20  MeV/fm3, a4=a4,min, and the hadronic EOSs are DD2YDelta1.1 (green) [129], DD2YDelta1.3 (blue) [130], DS(CMF)-7 (purple) [131], DS(CMF)-8 (red) [132], as the top legends shows. Bottom: The mass-radius curves of the resulting CrSs (solid colored lines), with the same color convention as the top panel. The shaded regions are the constraints with 90% credibility from the NICER mission PSR J0030+0451 (green colored) [133, 134], PSR J0740+6620 (cyan colored) [135, 136].

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    • Figure 7
      Figure 7

      Top: Frequencies of f-modes (solid lines) and g modes (dotted lines). Bottom: p1-modes (solid lines) for CrSs with the same parameter choices and color style conventions as Fig. 6.

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