Unmasking strange dwarfs with gravitational-wave observations

Abstract

The advent of space-based gravitational-wave detectors like the Laser Interferometer Space Antenna will allow us to observe signals, most of which are expected to be emitted by white-dwarf binaries. Among these systems another kind of compact objects could be hidden, postulated by Glendenning, Kettner, and Weber in 1995, containing a small core made of strange quark matter surrounded by layers of hadronic matter reaching densities much higher than in white dwarfs. These so-called strange dwarfs cannot be easily distinguished from white dwarfs through electromagnetic observations alone; their outermost envelopes are expected to have the same composition and their radii are quite similar (except for low masses). However, future measurements of the tidal deformability through gravitational-wave observations could provide a new way to reveal their existence. In this paper, we revisit the structure and the tidal deformability of strange dwarfs in full general relativity taking into account the possible crystallization of their envelope. Unlike most previous studies, we do not describe the hadronic layers using the equation of state of Baym, Pethick, and Sutherland, which was originally designed for the outer crust of a neutron star. The conditions leading to such heavy elements in gravitational-core collapse supernova explosions are not expected to be met during the stellar evolution leading to the formation of strange dwarfs. Instead, we consider the same light elements as found in white dwarfs but we take into account electron captures by nuclei and possibly pycnonuclear fusions that may be triggered by compression. We find that the radius of strange dwarfs is systematically smaller than that of their white dwarf relatives. These deviations can be large for very low-mass stars but mostly lie within the current observational uncertainties for typical white dwarf masses. On the other hand, the observable tidal deformability coefficient Λ 2 is strongly reduced in comparison to white dwarfs and the deviation will be potentially measurable by future space-based gravitational-wave detectors.

Role of Quark Matter and Color Superconductivity in the Structure and Tidal Deformability of Strange Dwarfs

“…As discussed in [18], the hadronic region of an SD is expected to crystallize within a few billion years and to be stratified into different layers, each of which consists of a dense Coulomb plasma of atomic nuclei with charge number Z and mass number A embedded in a highly degenerate relativistic electron gas. Whereas the outermost envelope is presumably made of the same light element as in a WD, different elements are predicted to be present in the inner layers at pressures exceeding the limiting pressure P β found in the core of the most massive WDs and marking the onset of electron captures by nuclei.…”

“…Depending on the stellar evolution, the hadronic envelope of an SD exhibits different compositions and the pressure P cc delimiting the crust-core interface varies between P β and P drip . The properties of this envelope and its role in the structure and in the tidal deformability of SDs was extensively studied in [18]. Since the present work is aimed at understanding the influence of the quark core, we will focus on oxygen SDs, whose hadronic envelope consists of an outermost layer made of 16 O surrounding a thin layer of 16 C (see Table II in [18] for details).…”

“…However, the situation may change in the coming years with the development of gravitational-wave (GW) astronomy. In particular, we have recently shown that it will be possible to identify SDs hidden in WD binaries through measurements of their tidal deformability with future space-based GW detectors, such as the Laser Interferometer Space Antenna (LISA) [18].…”

“…In [18], we have also developed a more realistic equation of state (EoS) for the description of the hadronic region of SDs, considering the compression of material made of the same light elements as found in WDs but undergoing electron captures and possibly pycnonuclear fusions. We have found that the internal constitution of SDs and their tidal deformability are markedly different from those obtained using the EoS of Baym, Pethick and Sutherland [19] adopted in most previous works and originally developed for the outer crust of NSs.…”

“…In this work, we study more closely the role of quark matter and crystalline color superconductivity in the structure and tidal deformability of SDs. To this end, we solve Einstein's equations of general relativity perturbatively, including the elasticity of both the crust and the core considering different quark-matter EoSs together with realistic EoSs for the hadronic envelope presented in [18].…”