Ejecting the envelope of red supergiant stars with jets launched by an inspiralling neutron star

Abstract

We study the properties of jets launched by a neutron star (NS) spiralling inside the envelope and core of a red supergiant (RSG). We propose that Thorne–Żytkow objects (TZO) are unlikely to be formed via common envelope (CE) evolution if accretion on to the NS can exceed the Eddington rate with much of the accretion energy directed into jets that subsequently dissipate within the giant envelope. We use the jet-feedback mechanism, where energy deposited by the jets drives the ejection of the entire envelope and part of the core, and find a very strong interaction of the jets with the core material at late phases of the CE evolution. Following our results, we speculate on two rare processes that might take place in the evolution of massive stars. (1) Recent studies have claimed that the peculiar abundances of the HV2112 RSG star can be explained if this star is a TZO. We instead speculate that the rich-calcium envelope comes from a supernova (SN) explosion of a stellar companion that was only slightly more massive than HV2112, such that during its explosion HV2112 was already a giant that intercepted a relatively large fraction of the SN ejecta. (2) We raise the possibility that strong r-process nucleosynthesis, where elements with high atomic weight of A ≳ 130 are formed, occurs inside the jets that are launched by the NS inside the core of the RSG star.

stars: AGB and post-AGB, binaries: close, stars: neutron

1 INTRODUCTION

Massive stars, in particular those in interacting binary systems, hold many secretes in their evolution. Some of these puzzles are related to the synthesis of different isotopes. Our study is related to the peculiar abundances of some isotopes in the red supergiant (RSG) star HV2112 in the Small Magellanic Cloud, and to the site of the strong r-process. The paper is centred around jets that are assumed to be launched by the neutron star (NS) as it accretes material from the common envelope (CE) with an RSG star.

Contrary to recent claims that HV2112 is a Thorne–Żytkow object (TZO; Levesque et al. 2014; Tout et al. 2014), we show that a TZO is unlikely to be formed through the evolution of an NS inside the envelope of an RSG star. The reason is that the jets launched by the NS expel the entire envelope and most of the core.

Another major problem in astrophysics is the exact sites where the r-process nucleosynthesis takes place. For the site(s) of the ‘strong r-process’, where elements of atomic weight A ≳ 130 are formed, there have been two main contenders in recent years (e.g. Thielemann et al. 2011): the merge of two NSs (e.g. Qian 2012; Rosswog et al. 2014, and references therein), and jets from a rapidly rotating newly born single NS (Winteler et al. 2012).

Previous studies of r-process nucleosynthesis in jets include Cameron (2001) who suggested the possibility of creating r-process elements inside the jets launched at a velocity of |$\frac{1}{2} c$| from an accretion disc around a rapidly rotating proto-NS. Nishimura et al. (2006) simulated the r-process nucleosynthesis during a jet-powered explosion. In their simulation, a rotating star with a magnetic field induced a jet-like outflow during the collapse which explodes the star. Neutrinos played no role in their simulation. Papish & Soker (2012) calculated the nucleosynthesis inside the hot bubble formed in the jittering-jets model for core-collapse supernova explosions (CCSN), and found that substantial amount of r-process material can be formed. Papish & Soker (2012) assumed that in the jittering-jets explosion model the jets are launched close to the NS where the gas is neutron-rich (e.g. Kohri, Narayan & Piran 2005).

Some r-process elements are believed to be found in all low-metallicity stars, and thus r-process nucleosynthesis must take place continuously from very early times in the Galactic evolution (Sneden, Cowan & Gallino 2008). Since the jittering-jets model was constructed to account for the explosion of all CCSNe, the r-process induced by the jittering jets can account for the continuous formation of r-process elements. However, the abundance of heavy r-process elements has much larger variations among different stars, implying that part of the heavy r-process, termed strong r-process, is formed in rare events (Qian 2000; Argast et al. 2004).

Here, we propose a new speculative site for strong r-process nucleosynthesis in which it is formed by jets launched by an NS spiralling-in inside the core of a giant star. These jets will also explode the star. This is a rare evolutionary route and hence complies with the finding of large variations in the abundances of these elements. In this first study, we limit ourselves to present the scenario and show its viability. Most ingredients of our newly proposed scenario were studied in the past but were never put together into a coherent picture to yield a new possible site for the strong r-process. Previously studied ingredients of our proposed scenario include the CE of an NS and a giant (Thorne & Zytkow 1975; Armitage & Livio 2000; Chevalier 2012), the launching of neutron-rich gas from accretion discs around compact objects (e.g. Surman & McLaughlin 2004; Kohri et al. 2005), the launching of jets by NS accreting at a high rate (Fryer, Benz & Herant 1996) and the formation of r-process elements in jets from NS (Fryer et al. 2006). The idea that jets can explode stars under specific conditions was also studied in the past, e.g. in a CE evolution (Chevalier 2012). Another specific class of models are based on magnetic amplification by a rapidly rotating stellar core (e.g. LeBlanc & Wilson 1970; Bisnovatyi-Kogan, Popov & Samokhin 1976; Meier et al. 1976; Khokhlov et al. 1999; MacFadyen, Woosley & Heger 2001; Woosley & Janka 2005; Couch, Wheeler & Milosavljević 2009). This magnetorotational mechanism creates bipolar outflows (jets) around the newly born NS that are able to explode the star. However, the required core's rotation rate is much larger than what stellar evolution models give, hence making most of these models applicable for only special cases. We, on the other hand, claim that all CCSNe are exploded by jets, the jittering-jets model, that also synthesize r-process elements (but not the strong r-process), and hence our newly proposed scenario is part of a unified picture we try to construct for exploding all massive stars and the synthesis of r-process elements. In the jittering-jets model, the explosion of CCSNe is powered by jittering jets launched by an intermittent accretion disc around the newly born NS (Papish & Soker 2014a,b). The intermittent accretion disc is formed by gas accreted from the convective core regions that have a stochastic angular momentum (Gilkis & Soker 2014; Papish & Soker 2014a).

Taam, Bodenheimer & Ostriker (1978) already studied the spiralling-in of an NS inside an RSG envelope and considered two outcomes, that of envelope ejection, and that of core-NS merger. However, they did not consider jets. The removal of the envelope during a CE evolution by jets launched by an NS or a white dwarf (WD) companion was discussed by Armitage & Livio (2000) and Soker (2004). Chevalier (2012) explored the possibility that the mass-loss prior to an explosion of a core-NS merger process is driven by a CE evolution of an NS (or a BH, black hole) in the envelope of a massive star. As already discussed by Armitage & Livio (2000), jets launched by an accretion disc around the NS companion deposit energy to the envelope and help in removing the envelope. WDs can do the same (Soker 2004). However, for an NS the accretion process to form an accretion disc is much more efficient due to neutrino cooling (Houck & Chevalier 1991; Chevalier 1993, 2012). This allows the NS to accrete at a very high rate, much above the classical Eddington limit, hence leading to an explosive deposition of energy to the envelope (Chevalier 2012). The process by which jets launched by an inspiralling NS expel the envelope (Armitage & Livio 2000; Soker 2004) and then the core in an explosive manner (Chevalier 2012) implies that no TZO (Thorne & Zytkow 1975; a red giant with an NS in its core) can be formed via a CE evolutionary route. We strengthen this conclusion in Section 2.

In Section 2, we study the CE evolution towards the explosion and estimate the typical accretion rate and time-scale. A new ingredient in our CE calculation is the assumption that mainly jets launched by the inspiralling NS drive the envelope ejection via the jet-feedback mechanism (Soker 2004, 2014; Soker et al. 2013). It is possible that the NS is able to expel the entire envelope by the jets (Soker 2004), and as a consequence cannot enter inside the core. However, it seems that a merger at the end of the CE phase can be quite common (Soker 2013), and we study such cases. In Section 3, we list two, somewhat speculative, processes that are motivated by our results. Our summary is in Section 4.

2 JETS INSIDE A CE

2.1 General derivation

The Bondi–Hoyle–Lyttleton (BHL) mass accretion rate (Hoyle & Lyttleton 1939; Bondi & Hoyle 1944) inside the envelope is (e.g. Armitage & Livio 2000; for a general overview of CE see Ivanova et al. 2013)

\begin{equation} \dot{M}_{\rm BHL}=\pi \left(\frac{2GM_{{\rm NS}}}{v_{{\rm r}}^2+c_{{\rm s}}^2}\right)^2 \rho _{{\rm e}} \sqrt{v_{{\rm r}}^2+c_{{\rm s}}^2 }, \end{equation}

(1)

where M_NS is the NS mass, v_r its velocity relative to the giant's envelope, c_s is the sound speed inside the envelope and ρ_e is the envelope density at the NS location. The NS moves mildly supersonically and we can use the approximation |$\sqrt{v_{{\rm r}}^2+c_{{\rm s}}^2 } \simeq v_{{\rm K}}$|⁠, where v_K is the NS's Keplerian velocity.

We use the red giant's profile from Taam et al. (1978) with a mass of M_g = 16 M_⊙, a radius of R_g = 535 R_⊙, a core radius of R_core = 2.07 × 10¹⁰ cm and a core mass of |$M_{\rm core}=7\times 10^{33} \,\rm {g}\simeq 3.5\,\mathrm{M}_{\odot }$|⁠. A power-law fit of the density profile in the giant's envelope gives

\begin{equation} \rho _{{\rm e}} \simeq Ar^\beta = 0.68 \left( \frac{r}{\mathrm{R}_{\odot }} \right)^{-2.7} \,\rm {g}\,\rm {cm}^{-3}, \end{equation}

(2)

where r is the radial coordinate of the star. The BHL accretion rate can then be written as

\begin{eqnarray} \dot{M}_{\rm BHL} &\cong & \pi \left(\frac{2GM_{\rm NS}}{v_{{\rm K}}^2}\right)^2\rho _{{\rm e}}v_{{\rm K}}=4\pi a^2\left(\frac{M_{{\rm NS}}}{M(a)}\right)^2\rho _{{\rm e}}v_{{\rm K}} \nonumber \\ &\simeq & 3 \times 10^3 \left( \frac{a}{1\,\mathrm{R}_{\odot }} \right)^{-1.2} \left( \frac{M(a)}{7\,\mathrm{M}_{\odot }} \right)^{-3/2}\,\mathrm{M}_{\odot }\,\,\rm {yr}^{-1}, \end{eqnarray}

(3)

where a is the distance between the NS and the core's centre, M_g(r) = M_core + M_env(r/R_g)^0.3 is the giant's mass enclosed inside radius r, M(r) = M_g(r) + M_NS, and we take M_NS = 1.4 M_⊙ in the rest of the paper. We take the mass accretion rate to be a fraction f_a of the BHL accretion rate, and we take a fraction η ≃ 0.1 of the accreted mass to be launched in the two jets:

\begin{equation} \dot{M}_{2\rm j}=\eta \dot{M}{\rm acc}= \eta f_{\rm a} \dot{M}_{\rm BHL}. \end{equation}

(4)

Around the NS an accretion disc is easily formed as the ratio of orbital separation to the NS radius is very large, such that the specific angular momentum of the accreted gas is more than an order of magnitude above what is required to form an accretion disc (equation 7 of Soker 2004). Such an accretion disc can launch two bipolar jets inside the envelope as shown schematically in Fig. 1. As a result of the NS motion, the jets will encounter different parts of the envelope during their propagation and form a hot bubble on each side of the orbital plane (Soker et al. 2013).

Figure 1.

A schematic drawing (not to scale) of the spiral-in process while the jets release energy. As the NS spirals-in, the jets’ heads encounter different parts of the envelope and release their energy at different regions. A continuous hot bubble is formed in each side of the equatorial plane (Soker et al. 2013).

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To examine the fate of the jets, we compare the propagation time-scale of the jets inside the envelope τ_j with the time-scale it takes for a jet's head to cross its width τ_c. τ_j can be estimate as follows. The jets’ head velocity v_h is determined by the pressure balance on the two sides of the jets’ head |$\rho _{{\rm e}} v_{{\rm h}}^{2}\simeq \rho _{{\rm j}}(v_{{\rm j}}-v_{{\rm h}})^{2} \simeq \rho _{\rm j} v_{\rm j}^2$|⁠, as v_h ≪ v_j; v_j is the initial velocity of the gas in the jet, about the escape speed from the NS and ρ_e is the envelope density encountered by the jet. We take the jet to have a half opening angle of θ ≈ 0.2 (the exact value of θ is not important, it can be any value less than about 0.5), and a mass outflow rate into each jet of |$\frac{1}{2} \eta \dot{M}_{\rm acc}$|⁠. The jets’ head velocity is then

\begin{equation} v_{\rm h}(z) \simeq v_{\rm j}\sqrt{\frac{\rho _{j}}{\rho _{{\rm e}}(z)}} = \sqrt{\frac{\frac{1}{2} \eta \dot{M}_{\rm acc}v_{\rm j}}{\pi z^{2} \theta ^{2}A(a^{2}+z^{2})^{\beta /2}}}, \end{equation}

(5)

where we take the jets’ density to be

\begin{equation} \rho _{{\rm j}}=\frac{\frac{1}{2}\eta \dot{M}_{\rm acc}}{\pi z^{2} \theta ^{2} v_{{\rm j}}}, \end{equation}

(6)

as θ ≪ 1. The propagation time of the jets to a distance |$z=\int ^{\tau _{\rm j}}_0 v_{\rm h} {\rm {d}} t$| can then be solved analytically:

\begin{equation} \tau _{\rm j} = \frac{a^{2+\beta /2}}{2+\beta /2}\theta \sqrt{\frac{2A\pi }{\eta \dot{M}_{\rm acc}v_{\rm j}}}\left[ \left(1 +\frac{z^2}{a^2}\right)^{1+\beta /4}-1\right]. \end{equation}

(7)

We substitute |$\dot{M}_{\rm acc}$| from equation (4), take β = −2.7, define |$v_{{\rm j}5} \equiv v_{\rm j}/10^5\,\rm {km}\,\rm {s}^{-1}$|⁠, and scale quantities for the inner part of the envelope to get:

\begin{eqnarray} \tau _{\rm j} &\simeq & 3 \times 10^3 v_{{\rm j}5}^{-1/2} \left( \frac{a}{\mathrm{R}_{\odot }}\right)^2 \left( \frac{\theta }{10^\circ }\right) \left( \frac{\eta }{0.1}\right)^{-1/2} \nonumber \\ &&\times \left( \frac{M_{\rm NS}}{1.4 \,\mathrm{M}_{\odot }} \right) \left( \frac{M(a)}{7 \,\mathrm{M}_{\odot }} \right)^{5/4} \left[ \left(1 +\frac{z^2}{a^2}\right)^{1+\beta /4}-1\right]\,\rm {s}. \end{eqnarray}

(8)

For the crossing time, we take (Soker 2004)

\begin{equation} \tau _{\rm c}=\frac{2 z\theta }{v_{{\rm K}}} \simeq 200 \left( \frac{\theta }{10^\circ }\right)\, \left( \frac{z}{\mathrm{R}_{\odot }}\right) \,\left( \frac{a}{\mathrm{R}_{\odot }}\right)^{1/2} \left( \frac{M(a)}{7 \,\mathrm{M}_{\odot }}\right)\,\rm {s}. \end{equation}

(9)

The ratio between these times is given by (note that θ cancels out)

\begin{eqnarray} \frac{\tau _{\rm j}}{\tau _{\rm c}} &\simeq & 15 v_{{\rm j}5}^{-1/2} \left( \frac{a}{\mathrm{R}_{\odot }}\right)^{1/2} \left( \frac{a}{z}\right)\, \left( \frac{\eta }{0.1}\right)^{-1/2} \nonumber \\ &&\times \left( \frac{M_{\rm NS}}{1.4 \,\mathrm{M}_{\odot }} \right) \,\left( \frac{M(a)}{7 \,\mathrm{M}_{\odot }} \right)^{1/4} \left[ \left(1 +\frac{z^2}{a^2}\right)^{1+\beta /4}-1\right]. \end{eqnarray}

(10)

The jets are unlikely to penetrate through the envelope when τ_c < τ_j. The reason is as follows. The moment a fresh supply of jet material ceases along a particular direction, the propagation of the jet's head stops along that direction. The inequality τ_c < τ_j implies that before the jet's head manages to exit the star along any direction, a fresh supply of jet material has ceased; the jet cone has crossed that direction and moved to other directions. This process was simulated in a very simple preliminary setting (Soker et al. 2013), but it requires detail numerical simulations to determine the exact outcome, and under what conditions the jets dissipate in the envelope. From simulations of active galactic nuclei jets, we know that a relative motion of the jets’ source and the interstellar medium leads to dissipation and bubble inflation (Soker et al. 2013).

For z ≈ a, β = −2.7 and η = 0.1 the ratio is

\begin{equation} \frac{\tau _{\rm j}}{\tau _{\rm c}} \simeq 4 \left( \frac{a}{\mathrm{R}_{\odot }}\right)^{1/2}. \end{equation}

(11)

We find that the condition τ_c < τ_j is satisfied. We conclude that the jets may not be able to penetrate through the envelope and will deposit their energy inside the envelope.

The total energy deposited by the jets inside the envelope is

\begin{equation} E_{{\rm j}} =\int \dot{E}_{{\rm j}} {\rm d}t = \int \frac{1}{2} \eta \dot{M}_{\rm acc} v_{\rm j}^2 \ \mathrm{d}t, \end{equation}

(12)

where integration is over the lifetime of the jets. |$\dot{M}_{\rm acc}$| can be eliminated with an expression that equates the power of the interaction of the NS with the envelope, i.e. the work of the drag force, with the releasing rate of orbital energy (Iben & Livio 1993):

\begin{equation} -\frac{GM_{\rm g}(a)M_{\rm NS}}{2a^2} \dot{a}= \xi \dot{M}_{\rm BHL} v_{{\rm K}}^2, \end{equation}

(13)

where ξ ≃ 1 is a parameter characterizing the drag force (accretion + gravitational interaction with the rest of the envelope). Equations (12) and (13) give

\begin{equation} \int \mathrm{d}E_{\rm j} = -\int _{R_{\rm g}} ^{a} \frac{1}{4a^\prime } \frac{\eta f_{\rm a}}{\xi } \frac{M_{\rm g}(a^\prime )M_{\rm NS}}{M(a^\prime )} v_{\rm j}^2 \mathrm{d}a^\prime , \end{equation}

(14)

where R_g is the giant radius, and a is the final location of the NS. Approximating the reduced mass by M_g(a)M_NS/M(a) ≃ M_NS allows us to perform the integration analytically to obtain

\begin{equation} E_{\rm j} \simeq \frac{1}{4} \frac{\eta f_{\rm a}}{\xi } v_{\rm j}^2 M_{\rm NS} \left[ \ln \left(\frac{R_{\rm g}}{a}\right) \right]. \end{equation}

(15)

As the jets are unlikely to penetrate the envelope, we assume that there is a self-regulation process, i.e. a negative feedback process (Soker et al. 2013), such that the jets from the NS prevent the accretion rate on to the NS from being too high.

2.2 Jets inside a CE

Few words on the nature of the jet launching setting are in place here. First, we note that some recent numerical simulations of CE evolution have showed that there is an initial rapid phase of evolution in which the orbit is shrunk significantly while the outer parts of the CE are inflated (e.g. De Marco et al. 2012; Passy et al. 2012; Ricker & Taam 2012). Even in that phase the accretion rate by the companion can be quite high, despite being below the BHL rate. In the simulation of Ricker & Taam (2012), the rapid plunge-in phase lasts for about 20 d, and the accreted mass during that period is M_acc ≃ 0.0003 M_⊙, giving an accretion rate of |$\dot{M}_{\rm acc} \simeq 0.005 \,\mathrm{M}_{\odot } \,\rm {yr}^{-1}$|⁠. This is more than what is required for neutrino cooling to allow high accretion rate (Chevalier 1993). So the NS can accrete at a very high rate along the entire CE evolution of the cases studied here.

Another point to emphasize is that the accretion energy can in principle be channelled to neutrinos, jets and electromagnetic (EM) radiation. We take the view that at very high accretion rates, both on to NS and main-sequence stars, a large fraction of the energy is carried by jets rather than by EM radiation (Soker 2015 and references therein). The neutrino cooling in the present setting allows a very high accretion rate, but we assume that the jets’ power is much above the Eddington luminosity limit. The jets are collimated, such that accretion can proceed from directions perpendicular to the jets’ axis. In this process, most of the energy in the disc that is not carried by neutrinos is transferred to magnetic fields that by violent reconnection eject mass. Namely, energy is channelled to magnetic fields and outflows much more than to thermal energy and EM radiation (Shiber, Schreier, & Soker, in preparation). The jets are not only a byproduct of the high accretion rate allowed by neutrino cooling, but by themselves allow an even higher accretion rate.

Thirdly, we point out that part of the evolution might take place in a grazing envelope evolution (GEE) rather than a CE evolution. In the GEE, a stellar companion (NS or a main-sequence star) grazes the envelope of a giant star while both the orbital separation and the giant radius shrink simultaneously (Soker 2015). The orbital decay itself is caused by the gravitational interaction of the secondary star with the envelope inwards to its orbit, i.e. dynamical friction (gravitational tide). The binary system might be viewed as evolving in a constant state of ‘just entering a CE phase’. The GEE is made possible only if the companion manages to accreted mass at a high rate and launch jets that remove the outskirts of the giant envelope, hence preventing the formation of a CE. This might occur when the NS is in the low-density parts of the envelope. Eventually, it enters the dense part of the core (see below), and a CE phase commences. Hence, the occurrence of a GEE in the outer parts of the envelope does not change our conclusions.

2.3 Inside the envelope

Let the removal of the envelope by the jets have an efficiency of χ, such that

\begin{equation} \chi E_{\rm j} \lesssim E_{\rm e/bind}. \end{equation}

(16)

The removal energy supplied by the jets is smaller than the binding energy of the envelope since in addition to the energy deposited by the jets there is the orbital energy of the spiralling-in binary system. In the traditional CE calculation, only the orbital energy is considered. The binding energy of the envelope of the model described in Section 2.1 is

\begin{equation} E_{\rm e/bind} \simeq \frac{ G M_{\rm env}^2 }{R_{\rm core}} \left[ \frac{3}{7} \frac{M_{\rm core}}{M_{\rm env}} \left( \frac{R_{\rm core}}{R_{\rm g}} \right)^{0.3} + \frac{3}{4} \left( \frac{R_{\rm core}}{R_{\rm g}} \right)^{0.6} \right]. \end{equation}

(17)

For R_core ≃ 0.3 R_⊙, M_core = 3.5 M_⊙ and M_env = 12.5 M_⊙ we obtain E_e/bind ≃ 4 × 10⁴⁹ erg. Substituting equations (15) and (17) in equation (16) gives

\begin{equation} f_{\rm a} \lesssim 0.01 \ \xi \left(\frac{\eta }{0.1}\right)^{-1} \left(\frac{\chi }{0.01}\right)^{-1}. \end{equation}

(18)

Substituting typical values in equation (3) with χ ≃ 0.01, we find the accretion rate of the NS for a ≈ 1 R_⊙ to be |${\approx } 30\,\mathrm{M}_{\odot }\,\,\rm {yr}^{-1}$|⁠. In this regime, neutrino-cooled accretion occurs as |$\dot{M}_{\rm acc} \gtrsim 10^{-3}\,\mathrm{M}_{\odot }\,\,\rm {yr}^{-1}$| (Chevalier 1993), and so high accretion rate can take place. The Keplerian orbital time is P_K ≃ 1(a/R_⊙)^3/2 h. If evolution proceed over a time of 10 P_K ≃ 0.5 d, the total accreted mass is less than about 0.04 M_⊙.

The total accreted mass in the jet-feedback scenario is calculated from

\begin{equation} \frac{E_{\rm e/bind}}{\chi } \simeq E_{\rm j} \simeq \frac{\eta }{2} M_{\rm acc} v_{\rm j}^2. \end{equation}

(19)

This gives an upper limit on the accreted mass as the orbital gravitational energy released by the NS-core system reduces the required energy from the jets. Substituting typical values used here we derive

\begin{equation} M_{\rm acc} \lesssim 0.04 v_{{\rm j}5}^{-2} \left(\frac{E_{\rm bind}}{4\times 10^{49} \,\rm {erg}} \right) \left(\frac{\eta }{0.1}\right)^{-1} \left(\frac{\chi }{0.1}\right)^{-1} \,\mathrm{M}_{\odot }. \end{equation}

(20)

This is the same as the value estimated above, showing that the final stage of the CE inside the envelope lasts for about t_f–CE ≃ 1 day. Hence, most of the accretion takes place during the few hours to few days of the final stage of the CE, when evolution is rapid. In the outer regions of the envelope, that have very small binding energy and where the spiralling-in time is of the order of years, the accretion rate is very small in the feedback scenario.

We emphasize again that although most of the accretion energy is taken by neutrinos, in the proposed scenario a non-negligible fraction of the energy is carried by jets launched from the accretion disc around the NS. When accretion rate is high, we have L_ν ≫ L_jets ≫ L_Edd, where L_ν is the neutrino luminosity, L_jets is the jets’ power and L_Edd is the critical Eddington luminosity from the NS.

We conclude that within the frame of the jet-feedback mechanism an NS ends the spiralling-in inside the envelope of a giant after accreting only a small amount of mass, that most likely leaves it as an NS rather than forming a BH.

2.4 Inside the core

We can repeat the calculations of Section 2.3 to the phase when the NS is inside the core. The binding energy of the core is larger than 10⁵⁰ erg. The ejected mass by the jets in the frame of the jet-feedback mechanism is

\begin{equation} M_{2\rm j} = \eta M_{\rm acc} \lesssim 0.01 v_{{\rm j}5}^{-2} \left(\frac{E_{\rm bind}}{10^{50} \,\rm {erg}} \right) \left(\frac{\chi }{0.1}\right)^{-1} \,\mathrm{M}_{\odot }. \end{equation}

(21)

The Keplerian orbital period for the core and the NS is approximately 10 min. During that time the NS can explode the core with the jets. The explosion will last a few minutes, but since the entire system is optically thick due to the ejected envelope, the explosion will last days, as in a typical supernova (SN). By explosion, we refer here to the case where the jets expel the envelope or the core within a time period much shorter than the dynamical time of the giant, and the ejected mass has energy above its binding energy. This occurs when the NS is deep in the envelope or inside the core.

During the NS merger with the core the Bondi–Hoyle accertion rate can get as high as |$1\,\mathrm{M}_{\odot }\,\rm {s}^{-1}$| (Fryer & Woosley 1998). In this regime, neutrino-cooled accretion can take place as |$\dot{M}_{\rm acc} \gtrsim 10^{-3}\,\mathrm{M}_{\odot }\,\,\rm {yr}^{-1}$| (Chevalier 1993), and the accretion rate can get near the Bondi–Hoyle rate. Simulations by Ricker & Taam (2012) show that the actual rate can be much lower than the Bondi–Hoyle rate. In addition, Chevalier (1996) argued that angular momentum considerations can prevent neutrino cooling from occurring.

Here, we take a different approach, we assume that jets are lunched during the NS-core merger process. These jets move relative to the core material as the NS spirals-in and deposit part of their energy inside the core. This limits the accretion rate by a feedback mechanism; higher accretion rate results in higher energy deposition in the core and so suppresses the accretion process.

The NS spirals inside the core within about 5–10 orbits, summing up to a total interaction time of t_j ≈ 1 h. The interaction of the jets with the core takes place within a radius of R_i ≈ 0.1 R_⊙. This accretion rate is well below the Bondi–Hoyle rate and is comparable with the results of Ricker & Taam (2012). The result of the process will be probably observed as a Type IIn SN (Chevalier 2012).

Finally, when the NS is well inside the core, such that the core mass that is left is about equal to the NS mass, the rest of the core forms an accretion disc around the NS. This accretion disc of mass M_disc ≈ 1 M_⊙ launches jets that interact with gas at a larger distances of r ≈ 1 R_⊙. This distance comes from the distance the mass expelled from the core at the escape speed of |$v_{\rm esc} \approx 1000\,\rm {km}\,\rm {s}^{-1}$| reaches within a fraction of an hour. Gamma-ray burst (GRB) are observed in Type Ic SN (Woosley & Bloom 2006) and hence we do not claim this system will be a GRB, since likely the jets do not penetrate the entire envelope.

3 IMPLICATIONS

If our claim that jets from NS can indeed remove the envelope and part of the core of RSG stars holds, we can think of two implications. Both of which require further study.

3.1 The RSG star HV2112

Levesque et al. (2014) attributed the peculiar abundances of some isotopes of the RSG star HV2112 in the Small Magellanic Cloud to the star being a TZO. However, some features, such as the high calcium abundance, are not accounted for by processes occurring in TZO. Tout et al. (2014) examined whether HV2112 can be a superasymptotic giant branch (SAGB) star, a star with an oxygen/neon core supported by electron degeneracy and undergoing thermal pulses with a third dredge up. The initial mass range of SAGB progenitors is thought to be 7 ≲ M_SAGB ≲ 11 M_⊙ (Eldridge & Tout 2004; Siess 2006; Doherty et al. 2015), depending on the manner convective overshooting is treated (Eldridge & Tout 2004) and on metallicity (Doherty et al. 2015). RSG stars originate from more massive stars than the progenitors of SAGB stars. At the evolutionary stage of HV2112, SAGB and RSG stars occupy more or less the same region in the HR diagram. In the TZO scenario, the star HV2112 is an RSG star, while in the scenario proposed here it is an SAGB star, hence of a lower mass.

Tout et al. (2014) argued that an SAGB star can synthesize most of the elements that were used to claim HV2112 to be a TZO, e.g. molybdenum, rubidium and lithium. But they found no way for an SAGB star to synthesize calcium. They still preferred a TZO interpretation for HV2112, and attributed the enriched calcium envelope to the formation process of a TZO. The calcium, they argued, can be synthesized when the degenerate electron core of a giant star is tidally disrupted by an NS and forms a disc around the NS, as in the calculations of Metzger (2012) for a WD merger with an NS. The high temperatures in such accretion disc leads to calcium production. Interestingly, they found that the kinetic energy of the outflow from the accretion disc that is required to spread calcium in the giant, has enough energy to unbind the envelope. They postulated that the outflow is collimated, hence most of it escapes from the star. We find in Section 2 that the jets from the NS are formed while it is still in a Keplerian orbit, hence the jets are not well collimated, and the envelope and a large part of the core are ejected.

The peculiar abundances of some isotopes (e.g. lithium) might be related to the presence of a binary companion. The post-AGB star HD172481, with a metallicity of [Fe/H] = −0.55, is in a binary system and has a very high lithium abundance (Reyniers & Van Winckel 2001). Tout et al. (2014) also noted that an SAGB star can synthesize all elements, besides calcium. They argued against the calcium enrichment scenario by a CCSN because the fraction of intercepted ejecta by HV2112, while still on the main sequence, is small.

Based on our calculations in Section 2, we argue that a TZO cannot be formed in the process where an NS spirals inside an RSG star. The jets launched by the accreting NS will expel the entire envelope. We instead speculate that HV2112 had a companion just slightly more massive than HV2112 when both were on the main sequence. In such massive binary systems, the lighter star expands to become a giant before the more massive star explodes (Sabach & Soker 2014). By the influence of the companion, the CCSN could have been a Type Ib SN. At explosion, the radius of HV2112, R₂, could have been a sizable fraction of the orbital separation, a. It intercepted a fraction of f ≃ 0.04(R₂/0.4a)² of the SN ejecta. We use this ratio to replace equation (4) of Tout et al. (2014) where the factor is scaled to f ≃ 4 × 10⁻⁴. If, for example, the companion's initial mass was about 12 M_⊙, it could have ejected ≈0.01 M_⊙ of calcium (Woosley & Weaver 1995). As the mass of calcium in HV2112 is estimated by Tout et al. (2014) to be ≈10⁻⁴ M_⊙, it requires about a quarter of the SN ejecta to hit HV2112 during the explosion and stays bound to it, for such an orbital separation (for more detail see Sabach & Soker 2014). After the explosion, the NS was kicked out of the binary system.

The main question for the proposed scenario is whether indeed such a large amount of calcium can be accreted to the companion. While some other works suggested this possibility for other systems, e.g. for the hyper-runaway star HD271791 (Schaffenroth et al. 2014), recent numerical simulations by Hirai, Sawai & Yamada (2014) suggested that this is not possible. The SN ejecta that encounter the companion induce a shock that runs through the companion. The shock heats the companion and the excess energy leads to mass removal. In their numerical simulations they found that up to 25 per cent of the companion mass can be removed; this is the case when the companion is as close as possible, as the scaling we used above of R₂ ≃ 0.4a. If this is indeed the case, then our proposed scenario cannot work.

However, there are some processes that might change the outcome, in particular non-spherical SN ejecta of calcium (and other newly synthesized elements). A non-spherical ejection of synthesized elements is expected in the jittering-jets model for core collapse SN explosion (Papish & Soker 2014a,b). One possibility is that the amount of calcium produced in the SN explosion is larger, or at least the calcium distribution is non-spherical, with calcium-rich gas ejected towards the companion. Another process that can overcome the difficulties posed by the results of Hirai et al. (2014) and allows large quantities of calcium and other heavy elements to be accreted on to the companion is if the newly synthesized elements from the core of the SN expand in dense clumps. Such clumps can penetrate deeper to the star, and stay bound. We consider the question of whether SN ejecta can enriched a companion as not settled yet. This is the weak point of the speculative scenario proposed here.

3.2 The r-process

Our analysis in Section 2 points to three types of interactions of the NS jets inside a CE, CE-SN jets, with a star that could in principle take place. (i) Small amounts of jets’ mass interact with the low-density envelope during the final stages of the inspiral inside the envelope. (ii) Next a jets’ mass of about 0.01 M_⊙ interacts with the dense core when the NS enters the core. Interaction occurs within a distance of about 0.1 R_⊙. The amount of mass carried by the jets and their typical distance of interaction with stellar mater in the above two types of jets, is determined by the assumptions of the jet-feedback mechanism. One has to bear in mind the large uncertainties. (iii) Finally, the central leftover of the core is destructed by the NS gravity and an accretion disc of about 1 M_⊙ is formed around the NS. This disc is expected to launch jets with a total mass of about 0.1 M_⊙, that catch-up with previously ejected core material at ≈1 R_⊙. The last two stages occur within a few minutes, and the last launching episode, the most massive one, lasts for tens to hundreds of seconds.

The r-process can generally occur both in the jets (Cameron 2001; Winteler et al. 2012) and in the post-shock jets’ material (Papish & Soker 2012). In the type (i) jet interaction listed above the amount of jet material is small and its contribution to the r-process can be neglected. For the latter phases, the post-shock temperature can be estimated from the post-shock-radiation-dominated pressure, |$P = \frac{6}{7}\frac{\dot{M}_{\rm j} v_{\rm j}}{4\pi \delta r^2}$|

\begin{eqnarray} T &\simeq & 2\times 10^8 \left( \frac{\dot{M}_{\rm j}}{10^{-3} \,\mathrm{M}_{\odot }/ \,\rm {s}}\right)^{1/4} \left( \frac{v_{\rm j}}{10^5 \,\rm {km}\,\rm {s}^{-1}}\right)^{1/4} \left( \frac{r}{\mathrm{R}_{\odot }}\right)^{-1/2} \nonumber \\ &&\times \left( \frac{\delta }{0.1}\right)^{-1/4} \,\rm {K}. \end{eqnarray}

(22)

Here, δ is the solid opening angle of the jet and r is the radius where the jet is shocked. This is much too low for r-process to occur in the post-shock jets’ material at a distance of r ≈ 0.1–1 R_⊙. In these cases, r-process will occur inside the jets.

The flow structure studied here is different in key ingredients from two other types of jet launching models in CCSNe. In the jittering-jets model (Papish & Soker 2014a), listed in the second column of Table 1, jets are launched by a newly formed NS. However, each launching episode lasts for a short time of less than 0.1 s, and the disc formed at each launching episode is short lived. It is not clear that the neutron fraction in the ejecta will be as high as in the case studied here, where the magnetic fields lift material from very close to the NS (Winteler et al. 2012). Another difference is that the high neutrino luminosity from the newly formed NS in the jittering-jets model is likely to bring the ejecta closer to equilibrium, e.g. lower the neutron fraction. A third difference is that the jittering jets are expected to explode the star, and so they are shocked relatively close to the centre at r_sh ≈ 0.001–0.01 R_⊙ (Papish & Soker 2012). Even if strong r-process elements have been synthesize in the jets, they will be disintegrated in the shock. In the flow studied in this paper, the shock is expected to take place much further out, and the core of the primary star has been already destroyed and formed the massive accretion disc now circling the NS.

Table 1.

Open in new tab

Summery of the differences between CCNS jets, CE-NS jets and GRBs jets that provide possible sites for r-process nucleosynthesis. The properties of the jets in CCSNe are based on the jittering-jets model (Papish & Soker 2011), or the magnetic-jets studied by Winteler et al. (2012). The number of CE-NS mergers relative to all CCSNe is taken from Chevalier (2012). Data for GRBs are taken from Popham, Woosley & Fryer (1999) and Pruet et al. (2005). Only in the flow structure of CCSN MHD jets and the NS-CE jets the accretion disc is both steady and bounded from inside, by the NS surface. These lead to low-entropy neutron-rich outflow that facilitate the nucleosynthesis of strong r-process (third peak) elements.

	CCSN jittering jets	CCSN MHD jets	NS common-envelope jets	GRB jets
Source	Papish & Soker (2012)	Winteler et al. (2012)	This paper	Popham et al. (1999); Pruet et al. (2005)
Activity duration (s)	≈1	<1	≈100	≈1–1000
Ejected mass (M_⊙)	≈0.01	≈0.01	≈0.01–0.1	≈10⁻⁵–10⁻⁶
Shock distance (R_⊙)	≈0.001–0.01	–	≈0.1–1	–
\|$L_{\nu } (\,\rm {erg}\,\rm {s}^{-1})$\|	≈5 × 10⁵²	≈5 × 10⁵²	≲ 10⁵⁰	≈0.01–1000 × 10⁵¹
Compact object	NS	NS	NS	BH
Y_e	≈0.15	≈0.15	Assumed to be as in Winteler et al. (2012)	≈0.5 for low accretion rate
Frequency and r-process nucleosynthesis.	Weak r-process in most CCSNe.	Rapid core rotation in 1 per cent of CCSNe. Strong r-process takes place.	1 per cent relative to all CCSNe. Strong r-process takes place.

	CCSN jittering jets	CCSN MHD jets	NS common-envelope jets	GRB jets
Source	Papish & Soker (2012)	Winteler et al. (2012)	This paper	Popham et al. (1999); Pruet et al. (2005)
Activity duration (s)	≈1	<1	≈100	≈1–1000
Ejected mass (M_⊙)	≈0.01	≈0.01	≈0.01–0.1	≈10⁻⁵–10⁻⁶
Shock distance (R_⊙)	≈0.001–0.01	–	≈0.1–1	–
\|$L_{\nu } (\,\rm {erg}\,\rm {s}^{-1})$\|	≈5 × 10⁵²	≈5 × 10⁵²	≲ 10⁵⁰	≈0.01–1000 × 10⁵¹
Compact object	NS	NS	NS	BH
Y_e	≈0.15	≈0.15	Assumed to be as in Winteler et al. (2012)	≈0.5 for low accretion rate
Frequency and r-process nucleosynthesis.	Weak r-process in most CCSNe.	Rapid core rotation in 1 per cent of CCSNe. Strong r-process takes place.	1 per cent relative to all CCSNe. Strong r-process takes place.

Table 1.

Open in new tab

	CCSN jittering jets	CCSN MHD jets	NS common-envelope jets	GRB jets
Source	Papish & Soker (2012)	Winteler et al. (2012)	This paper	Popham et al. (1999); Pruet et al. (2005)
Activity duration (s)	≈1	<1	≈100	≈1–1000
Ejected mass (M_⊙)	≈0.01	≈0.01	≈0.01–0.1	≈10⁻⁵–10⁻⁶
Shock distance (R_⊙)	≈0.001–0.01	–	≈0.1–1	–
\|$L_{\nu } (\,\rm {erg}\,\rm {s}^{-1})$\|	≈5 × 10⁵²	≈5 × 10⁵²	≲ 10⁵⁰	≈0.01–1000 × 10⁵¹
Compact object	NS	NS	NS	BH
Y_e	≈0.15	≈0.15	Assumed to be as in Winteler et al. (2012)	≈0.5 for low accretion rate
Frequency and r-process nucleosynthesis.	Weak r-process in most CCSNe.	Rapid core rotation in 1 per cent of CCSNe. Strong r-process takes place.	1 per cent relative to all CCSNe. Strong r-process takes place.

	CCSN jittering jets	CCSN MHD jets	NS common-envelope jets	GRB jets
Source	Papish & Soker (2012)	Winteler et al. (2012)	This paper	Popham et al. (1999); Pruet et al. (2005)
Activity duration (s)	≈1	<1	≈100	≈1–1000
Ejected mass (M_⊙)	≈0.01	≈0.01	≈0.01–0.1	≈10⁻⁵–10⁻⁶
Shock distance (R_⊙)	≈0.001–0.01	–	≈0.1–1	–
\|$L_{\nu } (\,\rm {erg}\,\rm {s}^{-1})$\|	≈5 × 10⁵²	≈5 × 10⁵²	≲ 10⁵⁰	≈0.01–1000 × 10⁵¹
Compact object	NS	NS	NS	BH
Y_e	≈0.15	≈0.15	Assumed to be as in Winteler et al. (2012)	≈0.5 for low accretion rate
Frequency and r-process nucleosynthesis.	Weak r-process in most CCSNe.	Rapid core rotation in 1 per cent of CCSNe. Strong r-process takes place.	1 per cent relative to all CCSNe. Strong r-process takes place.

Our flow structure is markedly different from the jets launched in GRB that are formed around BH. In the flow studied by Surman, McLaughlin & Hix (2006), for example, the jets are launched at r = 100 and 250 km from the centre, compared with r ≈ 15 km in the present study, and the entropy considered is s/k = 10–50, higher than in the study of Winteler et al. (2012). The same holds for the neutrino wind in the study of Pruet et al. (2005), that within a very short time reaches an entropy per baryon of s/k = 50–80. In both Surman et al. (2006) and Pruet et al. (2005), the outflow starts as neutron-rich, Y_e ≈ 0.2, but the high entropy implies that positron convert neutrons to protons.

In CCNSe, the high neutrino luminosity of |$L_\nu \approx 5\times 10^{52} \,\rm {erg}\,\rm {s}^{-1}$| can suppress the r-process by raising the electron fraction (reducing the neutron fraction) through weak interactions (e.g. Pruet et al. 2006; Fischer et al. 2010). This has a large effect on the formation of r-process elements in neutrino driven winds and could affect to some degree the r-process in CCNSe jets (Winteler et al. 2012). In particular, high neutrino luminosity can suppresses the third peak of the r-process. The synthesis of the third peak, the strong r-process, is a rare process relative to the synthesis process of the first two peaks, as evident from the large abundance variations of Eu/Fe found in old stars (Cowan et al. 2011). Winteler et al. (2012) found that in magnetic-jet simulation strong r-process with mass of about 6 × 10⁻³ M_⊙ is synthesized. To account for the third peak abundance, they required that one in about 100 CCSNe has the strong r-process.

Fryer et al. (2006) studied the ejection of matter from an SN fallback as a site for the r-process. They found that the conditions in the ejecta are compatible with the production of the ‘strong’ r-process for accretion rate similar to those in our proposed scenario,|$\dot{M}_{\rm acc} \approx 3\times 10^{-4}\,\mathrm{M}_{\odot }\,\rm {s}^{-1}$| and have an initial electron fraction of Y_e = 0.5. In their calculations, the ejecta is driven by energy released during the accretion on to the surface of the NS, but not in a jet like driven outflow.

The CE-NS jets can have the required properties to account for the strong r-process. First, based on Podsiadlowski, Cannon & Rees (1995), Chevalier (2012) estimated that about 1 per cent of observed CCSNe are from an NS-core merger. The ejected mass in the jets in our proposed CE-NS scenario is 0.01–0.1 M_⊙, which can lead to a synthesis of approximately 0.001–0.01 M_⊙ of heavy elements. This ratio is based on the simulations of jets in CCSNe performed by Nishimura et al. (2006) who found that the total amount of r-process elements is approximately 10 per cent of the total jets ejected mass. This mass is similar to what Winteler et al. (2012) have found.

4 SUMMARY

We studied the CE evolution of an NS inside an RSG (Section 2), and found that the NS is very likely to launch energetic jets that might expel the entire envelope and most of the core of the giant star. Based on this, we proposed that TZO are unlikely to be formed by this channel if accretion on to the NS can exceed the Eddington rate with much of the accretion energy directed into jets that subsequently dissipate within the giant envelope. We then discussed the implications of our results to the recent claim that the evolved star HV2112 is a TZO (Levesque et al. 2014; Tout et al. 2014), and to r-process nucleosynthesis inside the jets.

In the TZO model for HV2112 (Levesque et al. 2014; Tout et al. 2014), the star is an RSG star originated from a main-sequence star with an initial mass of |$M_{\rm MS}(\rm TZO)\approx 15 \,\mathrm{M}_{\odot }$|⁠. In Section 3.1, we proposed an alternative scenario for the peculiar abundances of HV2112. In the proposed rare scenario, HV2112 is presently an SAGB star that originated from a main-sequence star with an initial mass of |$M_{\rm MS}(\rm SAGB)\approx 8.5{\rm -}11 \,\mathrm{M}_{\odot }$|⁠. Beside calcium, SAGB can synthesize all elements with high abundances (Tout et al. 2014). We suggest that HV2112 had a companion slightly more massive than the initial mass of HV2112. The companion evolved first, but it exploded when HV2112 was already a giant (Sabach & Soker 2014). This implies that HV2112 intercepted a large fraction of the SN ejecta, including a sufficient mass of calcium. We also point out some weak points in our proposed scenario. In particular, the question of whether a giant companion can accrete a large enough fraction from the SN ejecta that hits it. It seems that our proposed scenario might work only if the newly synthesized elements are ejected from the core of the SN in non-spherical structures, i.e. clumps or jets towards the companion.

In Section 3.2, we discussed the possibility that jets launched by the NS as it merges with the giant's core could be a rare site for the strong r-process. Although most ingredients of the proposed scenario were studied in the past, they were never put together to yield the scenario we have proposed in this study. For example, the NS-core merger was studied in the past as a possible candidate for SNe events where strong interaction with a dense environment takes place (Chevalier 2012). As the NS accretes mass from the giant at a very high rate due to neutrino cooling, an accretion disc is formed around the NS and two opposite jets are launched during the spiral-in process (Armitage & Livio 2000). We estimated the total energy deposited by the jets inside the envelope (equation 15) using the jet-feedback mechanism (Soker et al. 2013), where energy deposit by the jets regulates the accretion rate. A small amount of accreted mass is sufficient to launch jets that expel the envelope (Section 2.3).

In many cases, the NS merges with the core. We termed the jets launched by the NS during its interaction with the core ‘CE-NS jets’. In these cases, we have found that much stronger jets are launched (Section 2.4), unbind, and expel the outer parts of the core. The total mass launched by the jets in the outer part of the core is about 0.01 M_⊙. The jets in this phase interact with the surrounding core matter at a distance of r ≈ 0.1 R_⊙. This distance is too large for the r-process to occur inside the post-shock jets’ material due to low post-shock temperature (eqaution 22). However, the r-process can take place inside the jets close to the centre before they are shocked, much as in the MHD jets studied by Winteler et al. (2012).

In the third and final phase, when the NS is well inside the core an accretion disc with a mass of about 1 M_⊙ is form around the NS from the destructed core. This accretion disc launches two opposite jets with a total mass of approximately 0.1 M_⊙. We find that in total 0.01–0.1 M_⊙ of jets’ material is ejected by the NS as it interacts with the core (see Table 1). Nucleosynthesis of r-process elements can take place inside these jets (Cameron 2001) with a total r-process material that can be as high as about 0.01 M_⊙.

We compared the properties of the CE-SN jets with jets launched in CCSNe and found that the flow studied here is similar to that of MHD jets launched by newly formed NS when the pre-collapse core is rapidly rotating (Winteler et al. 2012). Winteler et al. (2012) showed that under these conditions of low-entropy neutron-rich outflow the third r-process peak elements can be synthesized (the strong r-process). Lower neutrino luminosity of the NS in the NS-core merger (Table 1) favours the production of strong r-process in the CE-NS jets compared to CCSNe jets. The rareness of this process of approximately 1 per cent of the CCSNe rate (Chevalier 2012) can explain the large scattering of r-process elements in the early chemical evolution of the galaxy (Argast et al. 2004; Winteler et al. 2012).

We thank Christopher Tout, the referee, for very valuable and detail comments. OP thanks Friedrich-Karl Thielemann for his hospitality and discussions of the r-process.

REFERENCES

Argast

Samland

Thielemann

F.-K.

Qian

Y.-Z.

A&A

2004

, vol.

416

pg.

997

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Article Contents

Abstract

1 INTRODUCTION

2 JETS INSIDE A CE

2.1 General derivation

2.2 Jets inside a CE

2.3 Inside the envelope

2.4 Inside the core

3 IMPLICATIONS

3.1 The RSG star HV2112

3.2 The r-process

4 SUMMARY

REFERENCES

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