Magnetic-type Love number differentiating quark stars from neutron stars

TL;DR

This study proposes the magnetic-type quadrupolar Love number $k^{\mathrm{mag}}_2$ as a robust observable to distinguish quark stars (QSs) from neutron stars (NSs), even when they share similar masses and radii. By constructing a broad set of QS equations of state (EoSs) that interpolate between a surface density $\varepsilon_0$ and a high-density pQCD regime, and contrasting them with NS EoSs, the authors show that the $M$–$k^{\mathrm{mag}}_2$ relation separates QSs and NSs while the conventional $M$–$R$ and $M$–$k^{\mathrm{el}}_2$ relations do not. They demonstrate that NSs satisfy $|k^{\mathrm{mag}}_2| \lesssim 0.0033$ in the high-mass range, whereas QSs can attain $|k^{\mathrm{mag}}_2|$ around $0.004$, making gravitational-wave measurements of $k^{\mathrm{mag}}_2$ a promising path to identifying QS candidates. The analysis also discusses practical SNR thresholds for distinguishing QS–QS mergers from NS–NS mergers with third-generation detectors, highlighting the potential of a single GW signal to encode both electric and magnetic tidal information without requiring simultaneous electromagnetic observations.

Abstract

The quark star (QS) is a hypothetical and yet undiscovered stellar object, and its existence would mark a paradigm shift in research on nuclear and quark matter. Although compactness is a well-known signature for distinguishing between two branches of QSs and neutron stars (NSs), some QSs can overlap with NSs in the radius-mass plane. To manifest their evident differences, we investigate the tidal properties of QSs and NSs. We then find that the magnetic-type Love number is a robust indicator for differentiating between QSs and NSs, whereas the electric-type one is insufficient when QSs and NSs have similar masses and radii. Finally, we show that gravitational waves from binary star mergers can be sensitive to differences between QSs and NSs to the detectable level.

Figures (4)

• Figure 1: Parametrization of the SQM EoS with $\varepsilon_0$ and $\varepsilon_1$. The red curve represents the resulting SQM EoS for given $\varepsilon_0$ and $\varepsilon_1$. The slope is adjusted so that the polytropic EoS is smoothly connected to the pQCD EoS at $\varepsilon=\varepsilon_1$.
• Figure 2: $M$-$R$ curves for NSs (solid) and QSs (dotted). The gray band indicates the mass region favored by current NS observations. At $M=1.7\,M_\odot$, the red (QS) and the purple (NS) bars represent the $1\sigma$ width in $R$ estimated from EoS samples.
• Figure 3: $M$-$k^\mathrm{el}_2$ curves for NSs (solid) and QSs (dotted). At $M=1.7\,M_\odot$, the red (QS) and the purple (NS) bars represent the $1\sigma$ width in $k^\mathrm{el}_2$ in the same way as Fig. \ref{['fig:mr']}.
• Figure 4: $M$-$k^\mathrm{mag}_2$ curves for NSs (solid) and QSs (dotted). The horizontal axis shows (irrotational) $-k^\mathrm{mag}_2$. At $M=1.7\,M_\odot$, the red (QS) and the purple (NS) bars represent the $1\sigma$ width in $-k^\mathrm{mag}_2$ in the same way as Figs. \ref{['fig:mr']} and \ref{['fig:mkel']}.