Large sound speed in dense matter and the deformability of neutron stars

The historic first detection of the binary neutron star merger GW170817 by the LIGO-Virgo collaboration has set a limit on the gravitational deformability of neutron stars. In contrast, radio observations of PSR $\mathrm{J}0740+6620$ find a very massive neutron star. Tension between the small deformability and the large maximum mass may suggest that the pressure rises rapidly with density and thus the speed of sound in dense matter is likely a large fraction of the speed of light. We use these observations and simple constant sound-speed model equations of state to set a lower bound on the maximum speed of sound in neutron stars. If the tidal deformability of a $1.4M_{\odot }$ neutron star is less than 600, as is suggested by subsequent analyses of GW170817, then we find that the sound speed in the cores of neutron stars is likely larger than the conformal limit of $c/\sqrt{3}$. Implications of this for our understanding of both hadronic and quark-gluon descriptions of dense matter are discussed.

Figure 1

Equation of state—pressure $p$ versus energy density $\rho$. A model EOS, in this case the IUFSU relativistic mean field EOS, is shown as the solid black line while the dotted red line shows Eq. (2) with ${\rho }_2=240\mathrm{MeV}/{\mathrm{fm}}^3$ and $C_s^2=0.365$. Finally, the dashed blue line shows Eq. (2) with ${\rho }_2=572\mathrm{MeV}/{\mathrm{fm}}^3$ and $C_s^2=1$.

Figure 2

Square of the speed of sound $C_s^2$ versus deformability ${\mathrm{\Lambda }}_{1.4}$ of a 1.4 $M_{\odot }$ neutron star. The shaded region represents the range of sound speeds from the EOSs shown in Table 1. The red and blue curves correspond to the ${\mathrm{\Lambda }}_{1.4}-C_s^2$ relations with ${\rho }_1=225\mathrm{MeV}/{\mathrm{fm}}^3$ (dashed) and with ${\rho }_1=300\mathrm{MeV}/{\mathrm{fm}}^3$ (dash-dot). The choice of using the EOSs GNH3 and WFF2 here is to represent the upper and lower-most bounds on sound speed. Also shown by the vertical dotted lines are the LIGO observation ${\mathrm{\Lambda }}_{1.4}={190}_{-120}^{+390}$ from GW170817 [23]. The solid horizontal line represents where $C_s^2=1/3$.

Figure 3

Square of the speed of sound $C_s^2$, in units of $c^2$, versus radius $R_{1.4}$ of a 1.4 $M_{\odot }$ neutron star. Like in Fig. 2, the shaded region represents the full extent of our EOSs. The dashed and dot-dash lines indicate EOSs where ${\rho }_1=225\mathrm{MeV}/{\mathrm{fm}}^3$ and ${\rho }_1=300\mathrm{MeV}/{\mathrm{fm}}^3$, respectively.