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Searching for Strange Quark Matter Objects Among White Dwarfs Prepared for submission to JCAP Searching for Strange Quark Matter Objects Among White Dwarfs Abudushataer Kuerban,a;b Yong-Feng Huang,a;b;1 Jin-Jun Genga;b and Hong-Shi Zongc;d;e;f aSchool of Astronomy and Space Science, Nanjing University, Nanjing 210023, People’s Republic of China bKey Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210023, People’s Republic of China cDepartment of Physics, Nanjing University, Nanjing 210093, People’s Republic of China dJoint Center for Particle, Nuclear Physics and Cosmology, Nanjing 210093, People’s Republic of China eNanjing Institute of Proton Source Technology, Nanjing 210046, People’s Republic of China f Department of Physics, Anhui Normal University, Wuhu, Anhui 241000, People’s Republic of China E-mail: [email protected] Abstract. It has long been argued that the ground state of matter may be strange quark matter (SQM), not hadronic matter. A whole sequence of SQM objects, ranging from strange quark stars and strange quark dwarfs to strange quark planets, can stably exist according to this SQM hypothesis. A strange dwarf has a mass similar to that of a normal white dwarf, but could harbor an extremely dense SQM core (with the density as large as ∼ 4 × 1014 g cm−3) at the center so that its radius can be correspondingly smaller. In this study, we try to search for strange dwarfs among the observed “white dwarfs” by considering their difference in the mass-radius relation. Eight strange dwarf candidates are identified in this way, whose masses are in the range of ∼ 0:02M – 0:12M , with the radii narrowly distributed in ∼ 9,000 km – 15,000 km. The eight objects are SDSS J165143.45+364647.6, LSPM J0815+1633, LP 240-30, BD+20 5125B, LP 462-12, WD J1257+5428, 2MASS J13453297+4200437, and SDSS J085557.46+053524.5. Comparing with white dwarfs of similar mass, these candidates are arXiv:2012.05748v1 [astro-ph.SR] 10 Dec 2020 obviously smaller in radius. Further observations with large radio/IR/optical telescopes on these interesting candidates are solicited. Keywords: stars, neutron stars, white dwarfs 1Corresponding author. Contents 1 Introduction1 2 Structure of strange dwarf2 3 Data Collection3 4 Identifying strange dwarf candidates4 4.1 Mass-Radius Relation4 4.2 Comparison with Observations5 5 Comparison with previous studies7 6 Discussion and Conclusions7 1 Introduction It has long been argued that the ground state of matter may be quark matter [1,2] rather than hadronic form, because its energy per baryon could be less than that of the most stable atomic nucleus (56Fe). The existence of more exotic states such as strange quark matter (SQM – an approximately equal mixture of u, d, s quarks) in the core of compact stars was also speculated [1–4]. According to this SQM hypothesis, there could exist a whole sequence of SQM objects, ranging from strange stars (SSs, with masses similar to those of neutron stars) [3–5], to strange dwarfs (SDs) – stellar objects composed of a small SQM core and a thick normal matter crust which could be regarded as the counterpart of normal white dwarfs [6–8], and even to strange quark planets [6,7,9–12]. According to previous studies [5–7], SQM stars may be bare SQM objects, but they also may be covered by a crust of normal hadronic matter. From this point of view, crusted SQM objects share many common features with ordinary compact objects. The similarity between SQM stars and normal neutron stars makes it difficult to discriminate these two internally different compact stars observationally [5]. Anyway, a great effort has been made to try to reveal the difference between them. For example, they may have different mass-radius (M − R) relations, cooling rates, maximum masses, gravitational wave patterns, etc. It was even suggested that strange stars can host very close-in planets so that pulsar planets with an orbit period less than ∼ 6100 s can be safely regarded as an indication of the existence of SQM planetary systems [12, 13]. Recent discovery of several 2 M pulsars [14–16] greatly stimulated the study of the internal composition of these enigmatic compact stars. Especially, an interesting compact object of 2:6 M was reported to be associated with the gravitational wave event GW190814 [17]. If it was a “neutron star” instead of a black hole, then the equation of state (EOS) of hadronic matter will be significantly constrained so that it will greatly benefit the study of dense matter. More interestingly, a recent study by [18] suggested some evidence for the existence of quark-matter cores in massive neutron stars. It further arizes researchers’ interests of trying to find SQM in compact stars. Here we will mainly focus our attention on strange dwarfs (SDs). The normal matter crust of strange dwarfs makes them similar to normal white dwarfs (WDs), but they still – 1 – have different features in the M − R relation. As mentioned above, [6,7] and many other authors have investigated the properties of strange dwarfs and tried to differentiate them from white dwarfs in both theoretical [19–28] and observational aspects [29–33]. Especially, [24, 30] identified eight objects as candidates of strange dwarfs because their measured masses and radii are consistent with the expected mass-radius relation of strange quark dwarfs with a carbon crust. The progress in observational technology leads to a drastic increase in the number of white dwarfs being detected in the past decades. These vast amounts of data inspire us to re-examine all of them to identify more strange dwarf candidates. In this study, we will study the structural parameters of the dwarf objects systematically and try to identify possible strange dwarfs by comparing the observational data with theoretical modeling. Our paper is organized as follows. In Section2, the theoretical background relevant to strange dwarf is briefly introduced. In Section3, we describe the data source of our sample. In Section4, strange dwarf candidates are selected according to the theoretical modeling in Section2. In Section5, we compare our strange dwarf candidates with previously published samples and determine the SQM fraction. Finally, Section6 presents our conclusions and discussion. 2 Structure of strange dwarf The internal structure of compact objects can be inferred from the general relativistic form of Tolman-Oppenheimer-Volkoff (TOV) equation [34], dp(r) −G[ρ(r) + p(r)=c2][m(r) + 4πr3p(r)=c2] = ; (2.1) dr r2[1 − 2Gm(r)=rc2] dm(r) = 4πr2ρ(r); (2.2) dr where m(r), ρ(r), and p(r) are mass, mass density, and pressure at radial coordinate r, respectively; G is the gravitational constant, and c is the speed of light. The relation between p(r) and ρ(r) is determined by the EOS which itself depends on the internal composition of the compact object. As described in [6,7], a strange dwarf can be composed of SQM in the core and normal matter in the crust. Consequently, the property of the strange dwarf is determined by two parameters, the central density and the crust bottom density (ρcb). The central density at the exact center of the whole star can be as high as ∼ 4:0 × 1014 g cm−3. It determines the mass (Mcore) and radius of the SQM core. For the normal matter at the bottom of the crust, the maximum density should definitely be less than the so called neutron drip density 11 −3 (ρdrip = 4:3 × 10 g cm ). If ρcb & ρdrip, neutrons will drop out of the nuclei and form a neutron reach crust. These free neutrons cannot be supported by the outwardly directed electric field near the SQM surface. They will fall onto the SQM core and finally be converted into strange quark matter. Note that a further study by [35, 36] indicates that the maximum density at the crust bottom actually should be significantly smaller, i.e. no larger than 10 −3 ∼ ρdrip=5 ≈ 8:3 × 10 g cm . The SQM core and the normal matter crust are two distinct regions. Each region requires a different EOS. For SQM in the core, we employe the EOS derived from the simple MIT bag model [4,5], 1 p(r) = (ρ(r)c2 − 4B); (2.3) 3 – 2 – 101 10 3 ) M ( e r o c 10 7 M 10 11 14.60 14.65 14.70 14.75 14.80 3 log core (g cm ) Figure 1. Mean-density vs. the total mass for pue SQM cores. where B is the so called bag constant. In our study, we take a typical value of B = −3 57 MeV fm . For normal matter in the crust, we employe the EOS (BPS, with ρ < ρdrip) of [37]. Figure1 illustrates the mean-density vs. the total mass for pure SQM cores. From the figure, we see that the mean-density almost remains constant when the SQM core is less −2 massive than 10 M . For strange dwarfs, the SQM core is usually not massive so that the mean core density is almost fixed as ∼ 4 × 1014 g cm−3. On the other hand, the pressure versus density in the crust are plotted in figure2, with various ρcb being assumed. Having specified the EOS, we can solve the TOV equation by using the Runge-Kutta method to derive the properties of SQM objects with a normal matter crust. Our calculations will be carried out by assuming different initial values for ρcb to investigate the effect of crusts 11 −3 10 −3 9 −3 8 −3 with various thicknesses (ρcb = 4:3 × 10 g cm , 8:3 × 10 g cm , 10 g cm , 10 g cm , −12 etc).
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