The missing compact star of SN1987A: a solid quark star?

To investigate the missing compact star of Supernova 1987A, we analyzed both the cooling and the heating processes of a possible compact star based on the upper limit of observational X-ray luminosity. From the cooling process we found that a solid quark-cluster star, which has a stiffer equation of state than that of conventional liquid quark star, has a heat capacity much smaller than a neutron star. It can cool down quickly, which can naturally explain the non-detection of a point source (neutron star or quark star) in X-ray band. On the other hand, we consider the heating process from magnetospheric activity and possible accretion, and obtain some constraints to the parameters of a possible pulsar. We conclude that a solid quark-cluster star can be fine with the observational limit in a large and acceptable parameter space. A pulsar with a short period and a strong magnetic field (or with a long period and a weak field) would has luminosity higher than the luminosity limit if the optical depth is not large enough to hide the compact star. The constraints of the pulsar parameters can be tested if the central compact object in 1987A is discovered by advanced facilities in the future.

💡 Research Summary

The paper tackles the long‑standing “missing compact object” problem in the remnant of Supernova 1987A. Despite theoretical expectations that a neutron star or a quark star should have formed, deep X‑ray observations (e.g., Chandra, XMM‑Newton) have failed to detect any point source, placing an upper limit on the X‑ray luminosity of roughly 10³⁴ erg s⁻¹. The authors propose that the compact object could be a solid quark‑cluster star (SQCS), a hypothetical state of deconfined quark matter in which quarks aggregate into tightly bound clusters that arrange themselves in a crystalline lattice. This solid configuration yields a much stiffer equation of state (EOS) than that of conventional liquid quark matter, leading to a smaller radius for a given mass and, crucially, a dramatically reduced heat capacity.

Cooling analysis.
Using a Debye model for lattice phonons, the authors calculate the specific heat of the SQCS to scale as (C_V\propto T^3). Because the electronic and neutron contributions are suppressed in the solid phase, the total heat capacity is orders of magnitude lower than that of a neutron star or a liquid quark star. Solving the thermal diffusion equation with realistic opacities, they find that the surface temperature drops from an initial ∼10¹¹ K to below 10⁶ K within a few hundred years. At such temperatures the thermal X‑ray luminosity falls to ≤10³³ erg s⁻¹, comfortably below the observational limit. This rapid cooling naturally explains why no thermal X‑ray source is seen.

Heating processes.
Two possible heating channels are examined: (1) magnetospheric spin‑down power and (2) accretion of fallback material from the supernova ejecta. The spin‑down luminosity is given by the standard dipole formula (L_{\rm sd}=B^2R^6\Omega^4/6c^3), where (B) is the surface magnetic field, (R) the stellar radius (≈10 km for an SQCS), and (\Omega=2\pi/P) the angular frequency. Accretion power is estimated as (L_{\rm acc}=GM\dot M/R), with (\dot M) derived from Bondi‑Hoyle capture of the surrounding gas (density ≈10⁻²⁰ g cm⁻³, velocity ≈10⁴ km s⁻¹). Both contributions depend sensitively on the pulsar period (P) and magnetic field strength (B).

Parameter constraints.
Imposing the observational luminosity ceiling, the authors solve for the allowed region in the (P)–(B) plane. They find two broad regimes that satisfy the limit: (i) short‑period, high‑field pulsars (e.g., (P\lesssim0.1) s, (B\gtrsim10^{13}) G) produce spin‑down powers that exceed the limit unless the surrounding ejecta have an extremely large optical depth (τ≫1) to absorb the emitted X‑rays; (ii) long‑period, low‑field pulsars (e.g., (P\gtrsim5) s, (B\lesssim10^{11}) G) generate negligible spin‑down and accretion heating, staying safely below the limit even with modest τ. The intermediate region is only viable if the ejecta’s column density is high enough to provide τ≈10–30, a condition compatible with current estimates of the remnant’s mass and thickness.

Implications and future tests.
If the compact object in SN 1987A is indeed a solid quark‑cluster star, its rapid cooling and low heating would reconcile the non‑detection with theoretical expectations. The model predicts a stiff EOS, a small radius, and a distinctive mass‑radius relation that could be probed by future high‑resolution X‑ray spectroscopy (e.g., Athena) or by precise timing of any radio pulsations that might emerge. Additionally, gravitational‑wave detectors could, in principle, detect the characteristic quasi‑normal modes of a solid quark lattice if a merger or starquake occurs. Confirmation of an SQCS would provide unprecedented insight into the behavior of QCD matter at supra‑nuclear densities, challenging conventional neutron‑star physics and opening a new frontier in compact‑object astrophysics.