The extremely long period X-ray source in RCW 103: ˙ a descendant of Thorne-Zytkow Object? 1 X. W. Liu , R. X. Xu and G. J. Qiao 2 1 School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking 0 2 University, Beijing 100871, China l u J J. L. Han 9 1 National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China ] E H Z. W. Han . h Yunnan Astronomical Observatory, Chinese Academy of Sciences, Kunming 650011, China p - o r and t s a [ X. D. Li 1 v Department of Astronomy, Nanjing University, Nanjing 210093, China 7 8 6 4 Received ; accepted . 7 0 2 1 : v i X r a 1 [email protected] – 2 – ABSTRACT The spin evolution of the compact neutron core in a Thorne-Z˙ytkow Object ˙ (TZO) is investigated to explore the originof extremely long periodX-ray source. It is found that the outflow would effectively take away angular momentum from the core when radiation pressure dominates the accretion process. Thus the compact core could quickly spin-down to the co-rotation period (e.g. several hours) within the massive envelope, in about 103−104 years. The compact core could become an extremely long period compact star if the envelope is disrupted bysomepowerfulburstsorexhaustedviathestellarwind. The6.67-hourperiodic modulationofthecentral compact object(CCO) insupernovaremnant RCW103 ˙ could be naturally understood as the descendant of a TZO. Subject headings: ISM: supernova remnants – stars: evolution – stars: individual (1E161348-5055) – stars: neutron – 3 – 1. Introduction The central compact object (CCO) in supernova remnant RCW 103, 1E161348-5055 (hereafter 1E1613), is a very strange X-ray point source. It has a X-ray luminosity in the range of ∼ 1033 −1035 erg/s, and has no identified radio, infrared or optical counterpart. In 2005, a periodic modulation of 6.67 hours was detected by the EPIC MOS cameras onboard XMM-Newton (De Luca et al. 2006), and any other periodicities with P ≥ 12 ms are excluded with high confidence. However, RCW 103 is a supernova remnant of only about 2000 years old (Nugent et al. 1984; Carter et al. 1997)), which means that the CCO 1E1613 is very young. These features make 1E1613 a unique source among all the CCOs (De Luca 2008). The 6.67-hour periodicity is normal if it is the orbital period of a binary. But it is difficult to explain how the companion survive from the supernova explosion and escape from the multi-wavelength observations, and why the spin period of 1E1613 has not been detected if 6.67 hour is the orbital period. If 6.67 hour is the spin period of 1E1613, it would be the longest one of all isolated pulsars. How could an isolated pulsar spin-down to such a long period in 2000 years? De Luca et al. (2006) proposed a scheme that a magnetar with an initial period of 0.3 s and a surface magnetic field of 5×1015 G surrounded by a disk of 3×10−5M may spin down to a period of 6.67 hour in 2000 years, owning to the ⊙ extremely large propeller torque. This initial period is too large according to the magnetar theory (Duncan & Thompson 1992), and its current period is very different from the range of 2-12 s for the other magnetars detected as anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs). The AXP 0142+61 (Wang et al. 2006) has a period of only 8.7 s. We noticed that even in binaries, extremely long periods have been detected from X-ray sources in binaries, such as the ∼ 2.7 hour period X-ray source in 2S 0114+65 (Finley, Belloni, & Cassinelli 1992; Li & van den Heuvel 1999) and the ∼ 1.5 hour period – 4 – X-ray source in 4U 2206+54 (Wang 2009). On the other hand, the predicted stars with compact neutron cores remain mystery which was first proposed by Gamow (1937) and Landau (1938) to solve the stellar energy problem. The idea was abandoned when the stellar energy is realized to be generated from thermonuclear reactions (Bethe 1939). Thorne & Z˙ytkow (1975, 1977) discussed the possible equilibrium states of a massive star with a degenerate neutron core, which was called Thorne-Z˙ytkow Object (TZ˙O). A TZ˙O could be produced in at least three ways: 1) The expansion of the normal star in a binary drags the companion neutron star (NS) and gradually merges (Taam et al. 1978); 2) A collision of a NS with a massive main-sequence star (MS star) (Benz & Hills 1992); and 3) A supernova (SN) explosion gives the young NS an appropriate kick velocity and a direction which make it embed in its binary companion (Leonard et al. 1994). Podsiadlowski et al. (1995) estimated a total number of 20-200 TZ˙Os existing in the Galaxy given the characteristic lifetime of TZ˙O as being 105 −106 yr. The TZ˙Os usually manifest as red supergiants or red giants (Thorne & Z˙ytkow 1977; Eich et al 1989). But they can be distinguished from the ordinary ones since they have extraordinary high abundances of lithium and rapid proton process elements ˙ ˙ (Thorne & Zytkow 1977). The final fates of TZOs are not entirely clear. It is generally believed that a neutron core accreted enough material and finally transform to a black hole (BH), and that the massive envelope may be dissipated and form a disk. Here we discuss another possibility. If a powerful burst occurs before the neutron core transform to a BH, the burst can disrupts the envelope, the neutron core may looks like a CCO, and the envelope may mix with the original SNR which produced the neutron core or form a new SNR. Usually, the spin energy of the neutron core is much smaller than its kinetic energy and the accretion energy, thus has little influence to the evolution of a TZ˙O. However, if the core could be observable after the envelope is disrupted, the spin behavior of the core could – 5 – be very important. We proposed that 1E1613 and RCW 103 are the TZ˙O descendant. We will deliberate how the compact core in a TZ˙O spin down to a long period, and analyze different fates of the compact cores in TZ˙Os. There may be two possible approaches for a TZ˙O transforming to 1E1613 and RCW 103. Case A. About 2000 years ago, the more massive star of a binary experienced a supernova explosion, which produced RCW 103 and a compact star. By some possibility the compact star got an appropriate kick velocity and direction to be embedded in the companion MS star and formed a TZ˙O (Leonard et al. 1994). The TZ˙O would manifest as a red giant or red supergiant afterwards (Eich et al 1989), which has angular frequency much smaller than its compact core. Thus, the core is then spun down to the co-rotational period (6.67 hour) by the envelop efficiently, as discussed below. And then a powerful burst occurred and destroyed the envelope (e.g., due to a phase transition of its crust (Cheng et al. 1998), or other processes such as thermal nuclear explosion). As a result, the envelope mixed together with the original SNR RCW 103, and the core became observable as a central compact object, i.e. 1E1613. The accretion from the residual envelope or a fall-back disk reproduces the observational X-ray emission. Case B. More than 2000 years ago, a neutron star in a binary was embedded in its companion star or was swallowed by it (Benz & Hills 1992) and formed a TZ˙O. The core spin down quickly to the co-rotational period, 6.67 hours. About 2000 years ago, a global thermal nuclear explosion took place or the whole neutron star occurred a phase transition as a quark-nova (Ouyed et al. 2002). The powerful energy emission destroyed the TZ˙O envelope and formed an analogous supernova remnant, i.e. RCW 103. The central compact object 1E1613 accretes from the residual envelope or a fall-back disk and emits the observational X-ray. In both cases above, the central compact object would has very small proper motion – 6 – velocity, which is consistent with the observation of 1E1613. 2. Spin evolution of the neutron core in a TZ˙O Podsiadlowski et al. (1995) estimated the spin evolution of a neutron core in a TZ˙O via the total angular momentum carried by the accretion material. They found a slowly spin-down process during the steady-burning phase where the accretion has an Eddington rate, and a quickly spin-up process in the neutrino runaway case where the accretion is not Eddington-limited which could spin-up the core to a typical period of ∼ 10 ms. Nevertheless, they did not consider the interaction between the neutron core magnetosphere and the TZ˙O envelope, and also ignored the outflow of the convection envelope. The convection passes through the whole envelope out to the photosphere (Thorne & Z˙ytkow 1977). The outflow carries away the heat energy as well as the angular momentum, which would make the neutron core spin-down effectively. We now deliberate the spin evolution of the neutron core by considering both the interaction and the outflow. 2.1. The model During the steady-burning phase of a TZ˙O, some of the envelope material is accreted to the neutron core surface. The radiation pressure opposes the gravitational force and forms an equilibrium. The difference between the inflow rate (M˙in) and outflow rate (M˙out) ˙ determines the rest accretion rate (Macc), i.e. M˙acc = M˙in −M˙out. (1) In a spherical symmetry accretion case, M˙acc approximates the Eddington rate, i.e. M˙acc ≈ 1018R6g/s, (2) – 7 – 6 where R6 = R∗/10 cm, where R∗ is the compact star radius. To estimate the inflow rate we consider the accretion in the steady medium, whose accretion rate is ∼ πRa2csρ, where Ra is the accretion radius, cs and ρ are the sound velocity and density at Ra. The sum of the gravitational potential energy and the kinetic energy of a particle at Ra is zero. When r < Ra, the kinetic energy of the particle cannot overcome the gravitation, thus the particle is captured by the core. For a neutron core surrounded by a envelope with a structure gave in Thorne & Z˙ytkow (1977), the accretion rate in a 21 steady medium is about 10 g/s, much larger than the rest accretion rate. The inflow rate should be equal the accretion rate in a steady medium at Ra, if the radiation pressure is insignificant. When considering radiation pressure, we take M˙in(Ra) = ηπRa2csρ, (3) where 0 < η < 1. If we set M˙in(R∗) = M˙acc, (4) we get M˙out(R∗) = 0 and M˙out(Ra) = M˙in(Ra)−M˙acc. In the range of R∗ ≤ r ≤ Ra, the outflow can be different for different TZ˙Os, we take an exponential form of: r −R M˙out(r) = ( ∗ )α(M˙in(Ra)−M˙acc), (5) Ra −R∗ where the parameter α ∼ 1. The above equations provide the distribution of the inflow and outflow inside Ra. Their radial velocities are determined by the gravitational force, radiation pressure and the distribution. Their rotational velocities, which are related to the angular momentum, – 8 – should be determined by the interaction between them and the magnetosphere of the neutron core. The accretion in a TZ˙O is different from the traditional accretion of a NS. The envelope has extremely slow rotation (Podsiadlowski et al. 1995) thus a disk could not form around the neutron core. The interaction between the magnetosphere and accretion flow would not confined by the Alfv´en radius (Lamb et al. 1973) since the structure of the accretion region is radiation-pressure dominant. The magnetosphere of the neutron core is insignificant in the radial direction since the convection flows are radiation-pressure dominated. Nevertheless, it would dominate the rotational movement of the flows because the gravitational force and radiation pressure do not work in this direction. If the flows rotate so fast, that the centrifugal force can compete with the gravitational force, the structure of accretion region would be affected. If the centrifugal force is much smaller than the gravitational force, the rotational movement and radial movement should be relatively independent. Therefore, we can seperatedly study the rotational interaction between the magnetosphere and the flows while their distributions are determined by the radial direction forces. The rotational velocities of the flows are shown in Figure 1. The flows have a potential to co-rotate with the magnetosphere with a co-rotational velocity vco = rΩ (6) because of the magnetic freezing effect, where Ω is the angular velocity of the compact core. But the magnetic field can draw the flows to a velocity at most with kinetic energy density equal to the magnetic energy density, i.e. vdr = βB(4πρ)−1/2, (7) here 0 < β ≤ 1, and B is the magnetic field strength. Thus the real rotational velocity v φ – 9 – should be the smaller one of vco and vdr, i.e. vφ = min(vco,vdr). (8) As shown in figure 1, the flows would be drawn by the magnetosphere with vdr when they are far from the core, and they would co-rotate with the magnetosphere when they are near to the core. At a radius Re, vco(Re) = vdr(Re), we obtain Re = βB(4πρ)−1/2Ω−1. (9) Note that B and ρ are the functions of radius r. When a particle accesses the accretion radius Ra, it will be drawn by the magnetosphere and rotate around the core with velocity vdr. If it passes through the equal velocity radius Re, it would co-rotate with the core. Therefore, the particle should be accelerated in the magnetosphere and get angular momentum from the core. If a particle finally hits to the core surface it would return the angular momentum to the core, as well as the initial angular momentum when it was in the envelope. But if it goes out it takes away angular momentum from the core, and helps the core to spin down. If a particle goes out from Re ≤ r < Ra, the angular momentum it takes away from the core is j = mrvdr, (10) where m is the particle mass. If a particle goes out from R∗ < r < Re, it would take away an angular momentum of j = mRevco(Re). (11) Note this value is calculated at Re not at r, because the particle would co-rotate with the core when going out from r to Re. When the particles are going out from Re ≤ r < Ra to – 10 – Ra, they could also get a bit more angular momentum from the core because the field lines are sweeping them. We ignore this additional amount of the angular momentum, because it is the same order as the initial value and can be degenerated with the model parameters (e.g. B and β). If we assume the envelope spins with a angular velocity of Ωa at Ra, we get the angular momentum change rate of the neutron core as IΩ˙ = J˙ = J˙in −J˙out, (12) where ˙ ˙ 2 Jin = Min(Ra)ΩaRa (13) is the angular momentum change rate from inflow and J˙out the angular momentum change rate from outflow. From equations (10) and (11) we know that the angular momentums took away by the particles go out from the range of r < Re and r > Re are different, thus J˙out should be the sum of the contributions in the two ranges, i.e. J˙out = J˙r<Re +J˙r>Re, (14) where J˙r<Re = ZRR∗e∇M˙outvco(Re)Redr = ZRR∗e α(RRe2aM−˙ouRt(∗R)αa)(r−R∗)α−1Ωdr, (15) and J˙r>Re = ZRRea ∇M˙outvdrrdr = ZRRea (αRMa˙o−utR(R∗a))α(r −R∗)α−1βB(4πρ)−1/2rdr. (16) In the above equations, B is defined by the structure of the magnetosphere, ρ defined by the structure of the envelope. Therefore, the spin evolution of the compact core in a TZ˙O could be numerically obtained from equations (2), (3), (5), (9), and (12)-(16), with a set of given parameters.