Following Wolszczan's landmark discovery of planets in orbit around pulsar PSR B1257+12 in 1991, over 300 planets in more than 200 planetary systems have been found. Therefore, the meaning of Wolszczan's discovery cannot be overestimated. In this paper we aim to convince the reader that the objects accompanying pulsar PSR B1257+12 are more exotic than thought so far. They might not be ordinary planets but dwarf strange quark stars, whereas the pulsar might be a quark star with standard mass, not a neutron star. If this was the case, it would indicate that strange quark matter is the ground state of matter.
Deep Dive into SQM stars around pulsar PSR B1257+12.
Following Wolszczan’s landmark discovery of planets in orbit around pulsar PSR B1257+12 in 1991, over 300 planets in more than 200 planetary systems have been found. Therefore, the meaning of Wolszczan’s discovery cannot be overestimated. In this paper we aim to convince the reader that the objects accompanying pulsar PSR B1257+12 are more exotic than thought so far. They might not be ordinary planets but dwarf strange quark stars, whereas the pulsar might be a quark star with standard mass, not a neutron star. If this was the case, it would indicate that strange quark matter is the ground state of matter.
The millisecond pulsar PSR B1257+12 with the estimated age of 800 millions years, is located at a distance of 300 parsecs from the Earth. The tiny pulsar is being orbited by three bodies with masses 0.025, 3.9, and 4.3 of the Earth mass, typical of ordinary planets, and the respective radii of 0.19, 0.36 and 0.46 AU [1], [2]. For that reason, the bodies are considered to be planets. It was clear from the start, that the planetary system around PSR B1257+12 was unusual. Before Wolszczan's discovery, the existence of planets around neutron stars had not been considered seriously. If the planets were to be remnants of a planetary system existing around the progenitor star of PSR B1257+12, then it would be highly improbable for these planets to have survived the supernova explosion accompanying the neutron star's birth, since then compact bodies acquire velocities high enough to escape from the binding potential of the gravitational well of the surrounding matter. These planets might also had been formed already after the supernova explosion and the neutron star's formation. In particular, models of planetary system formation around pulsar accreting matter from its companion have been suggested [3]. However, this scenario seems also improbable because of strong radiation in the pulsar's vicinity [4]. Therefore, another hypothesis seems worth considering. The objects in orbit around PSR B1257+12 may be just miniature quark stars.
A quark star is a hypothetical object consisting of strange quark matter (SQM). SQM is a mixture of quasifree quarks u, d, s and electrons, all of which form relativistic fermi gas. If SQM is the ground state of strong interactions, then one could expect strange stars to form in space. For SQM to be the ground state, one needs the minimum of energy per baryon to be not greater than the energy per baryon for the strongest bound nucleus in nature -the nucleus of iron-56. Hence, (ρ E /n B ) SQM ≤ E(Fe 56 )/56 = 930.4MeV at zero pressure, where ρ E is the energy density and n B the baryon density. The possibility of existence of such objects was put forward first in [5]. The easiest way to obtain a phenomenological equation of state for SQM, is to consider the following simplified model [6]. Suppose that quarks form ultra-relativistic and electrically neutral quantum gas of non-interacting fermions in the β-equilibrium at temperature T = 0[K]. In this case, the pressure p and the total energy density ρ E are
where n B is the baryon density and B is the bag constant, B = 50÷200 [MeV/fm 3 ]. These equations are valid when the Fermi energy is much higher than the rest energy of the heaviest quark (in our numerical calculations we included also the strange quark mass, but the full form of the resulting equations is not important here).
The maximal mass and the corresponding size of a quark star are close to those for a neutron star. With the assumed example values B = 70 [MeV/fm 3 ] and the strange quark mass m s = 150 [MeV/c 2 ], SQM would be the ground state for strong interactions. Then, the maximal mass of a quark star made of SQM would be ≈ 1.68 M ⊙ with the corresponding areal radius of about 9.3 [km][? ], whereas a neutron star with the UV14+TNI equation of state [7] attains M max = 1.83 M ⊙ at R = 9.5 [km], see figure 1. Here, the similarities end. Only for sufficiently massive neutron stars, their gravitational field could prevent neutron matter from disintegration. Thus, there is the lower bound for masses of neutron stars. For realistic equations of state the minimum is approximately 0.1M ⊙ [8]. Unlike for neutron stars, there be no such a limit for SQM stars bound mainly by quark forces. Consequently, there are possible SQM stars of arbitrary low mass and radius. The mass-radius diagram for SQM stars is also different, see figure 1(b). Low mass quark stars have small radii, while the radii of neutron stars grow with decreasing mass. Confirmation of the presence of quark stars in space would indicate that SQM is the ground state for strong interactions. It is thus natural that astrophysicists have been intensively searching for such objects [9], [10]. Unfortunately, this endeavor is difficult, since quark and neutron stars are hardly distinguishable from each other in the range of masses close to 1.4 M ⊙ , typical of pulsars, in which range the mass-radius relations are similar for both kinds of stars. On the other hand, it may turn out that quark stars have been already found.
The pulsar PSR B1257+12 is being orbited by three bodies of masses 0.025, 3.9 and 4.3 in units of Earth mass. Owing to small masses, the objects are regarded as planets. The possibility the planets might be miniature compact stars has been already suggested in [11] in the context of pulsar PSR B1828-11 precession torqued by a quark planet. Masses of these objects are too small for them to be neutron stars. If they were to be compact objects, their building material would have to be made of SQM. If this rea
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