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Soft X-ray Emission and Lithium Production in Cen X-4 during Shin-ichiro Fujimoto,1 Ryuichi Matsuba,2 and Kenzo Arai,3 1 Department of Electronic Control, Kumamoto National College of Technology, 2659-2 Suya, Koshi, Kumamoto 861-1102, Japan 2 Institute for e-Learning Development, Kumamoto University, Kumamoto 860-8555, Japan 3 Department of Physics, Kumamoto University, Kumamoto 860-8555, Japan E-mail(SF): fujimoto@ec.knct.ac.jp We investigate emission mechanism of soft X-ray radiation from a neutron star soft X-ray transient (NSSXT), Cen X-4 and unusually high abundances of Li on a low-mass secondary in Cen X-4 during aquiescent state. An accretion flow in NSSXTs in quiescence is though to be an advection-dominated oneand truncated by magneto-centrifugal forces due to the magnetic field of a neutron star. The advectiondominated accretion flow (ADAF) is very hot (> 1 MeV) enough to synthesize abundant neutrons throughthe spallation of 4He via protons in the flow. Although almost all charged nuclei in the ADAF are outflowedby the magneto-centrifugal forces, the neutrons accrete onto the neutron star because of no influence ofthe magnetic field on the neutrons. Consequently, the accretion flow is composed of neutrons near theneutron star. The accretion energy of the neutrons liberated on the surface of the star is a possible energybudget for soft X-ray radiation in a NSSXT in quiescence. Moreover, Li is abundantly synthesized in theADAF through α−α reactions and is transfered to the surface of the secondary by the magneto-centrifugalforces. We find that for reasonable values of the mass accretion rate and the magnetic field of the neutronstar, the estimated soft X-ray luminosity and abundance of Li on the secondary are comparable to thoseobserved in Cen X-4.
Key words: Accretion, accretion disks — neutron stars — nuclear reactions, nucleosynthesis, abun- fields and fast rotation of the neutron star, accreting ma- X-ray emission from neutron star soft X-ray transients terial is expelled through propeller effects, which cause (NSSXTs) in quiescence is phenomenologically fitted winds driven via magneto-centrifugal forces when a mass with two components, a blackbody-like soft component accretion rate is sufficiently low. Even when the pro- and power-law hard component. Although the origin peller effects operate, accretion through the polar region of the hard component is still unclear, there are two of the star is possible because of weak centrifugal forces scenarios for the soft X-ray component. The energy in the region. The fraction of the mass accretion rate source for the blackbody-like, soft X-ray is interpreted that reached the neutron star surface has been estimated as deep crustal heating (Brown et al., 1998; Rutledge et to be ∼ 10−3 for reasonable values of the mass accretion al., 2001a,b). However, the quiescent state of Cen X-4 rate and magnetic field of the star (Menou et al., 1999).
is variable on timescales (at a factor of ∼ 0.4, ∼ 3, and However, the fraction could be much lower if the accre- ∼ 0.45 in 5 yr (Rutledge et al., 2001a), a few days (Cam- tion flow has a toroidal morphology with empty funnels pana et al., 1997), and down to ∼ 100 s (Campana et al., along the rotational axis (Menou et al., 1999). We note 2004), respectively). This could rule out the scenario of that the MHD simulation of an ADAF show that the the energy source due to the deep crustal heating.
flow has funnels with densities lower than that at the The other energy budget for the soft X-ray radia- equatorial plane (Machida et al., 2004).
tion is residual polar accretion onto a neutron star from ADAF has very low density, so that ions interact in- a quasi spherical advection dominated accretion flow efficiently with electrons. As a result of the inefficient (ADAF) (Zhang et al., 1998; Menou et al., 1999), which interaction between the ions and the electrons, which are possibly exists around the neutron star during quies- main coolant in ADAF, the ions have high temperatures cence (Narayan et al., 1996, 1997). Due to magnetic due to viscous heating and attain to ∼ 30 MeV near an inner edge of ADAF (Narayan & Yi, 1994, 1995a,b). Due for a neutron star with mass M = 1.4M . We note to such high temperatures, helium breaks via the spal- that rin becomes much greater during the operation of lation with protons to produce neutrons in ADAF. Due the propeller effects, which will be discussed later. The to magneto-centrifugal forces, almost all charged parti- cles are ejected from an inner region of the ADAF. How- ever, neutrons continues to accrete onto the neutron star, n = 1.7 × 1018α−1m−1 ˙ since neutrons are not affected by the magnetic field of the neutron star. As the neutrons liberate almost all where α is the viscous parameter, m = M/M , and its gravitational binding energy onto the surface of the m is the mass accretion rate in units of the Edding- neutron star, the liberated energy is a possible energy budget for the blackbody-like, soft X-ray radiation.
Edd = 1.4 × 1017 m g s−1 = 2.1 × 10−9m M yr−1.
Moreover, Li produced in ADAFs by α-α reactions Once the temperatures, densities and drift timescales transports to a secondary star through the propeller are specified, we can follow the abundance evolution in effects (Yi & Narayan, 1997). The transportation en- an ADAF from the outer boundary rout to rin, using a hances the Li abundance on the low-mass secondary, nuclear reaction network. We set rout to be 100 rg. It is and causes a high abundance of Li observed on the low- likely that rout becomes much larger during the quiescent mass secondary in a NSSXT, Cen X-4 (Martin et al., state (Narayan et al., 1997), but the abundance distri- 1994). We note that Li is destroyed in the deep con- bution in the ADAF is independent from the choice of vective envelope of usual late-type stars, and that high larger rout because of low temperatures (< 1 MeV) in the abundances of Li have been detected in late-type secon- outer region (Guessoum & Kazanas, 1999). We have de- daries of black hole soft X-ray transients (BHSXTs) in veloped a nuclear reaction network, in which four α − α quiescence (Wallerstein, 1992; Martin et al., 1992, 1994, reactions to synthesize 6He,6Li,7Li, and 7Be are taken 1996), and have been examined by Fujimoto et al. (2008) into account, based on a network in FMA08. Our net- (hereafter FMA08). As we can see later, the estimated work contains 21 species of nuclei; n, p, D, T, 3He, 4He, soft X-ray luminosity and abundance of Li on the sec- 6He, 6Li, 7Li, 7Be, 9B, 11C, 12C, 13N, 14N, 15O, 16O, 17F, ondary are comparable to those observed in Cen X-4, 20Ne, 21Na, and 24Mg, and 18 reactions, whose rates are for reasonable values of the mass accretion rate and mag- taken from Table 1 in (Guessoum & Gould, 1989) or ther- mally averaged with experimental cross sections (Read In the present study, we propose a new mechanism & Viola, 1984) for α − α reactions. It should be empha- to produce a soft X-ray radiation from NSSXTs, that sized that photodisintegration reactions are not impor- is the liberation of the gravitational energy of neutrons tant for abundance evolution inside ADAFs, since the on the surface of the star accreting through a neutron- ADAF is optically thin and photons have no chance to ADAF. We also examine production of Li through the interact with nuclei due to low gas densities (Eq. (2)).
transportation of Li from the ADAF to the secondary.
Initial abundance at rout is set to be the solar composi- The paper is organized as follows: in §2, we examine tion (Anders & Grevesse, 1989) without Li.
an abundance distribution in an accretion flow around Figure 1 shows the abundance distribution of neu- a neutron star. We estimate the soft X-ray luminosity, trons, 4He, 6Li, 7Li, and 7Be inside ADAFs for α = 0.3, which is interpreted as the energy liberation of neutrons m = 0.01 and 0.1. Neutrons are produced accreted through a neutron accretion flow in §3. In §4, significantly via the breakup of 4He at an inner region we examine Li production on a secondary in NSSXTs.
(r < 20rg). The distribution of neutrons is similar to Finally we summarize our results in §5.
that in Figure 1 of (Jean & Guessoum, 2001). Lithium isappreciably synthesized at the inner region of the ADAF.
2. Abundance distribution in an advection dominated ac- 7Be is comparable to and slightly lower than 7Li, while 6He is much lower than 6Li. We note that the number We assume that an accretion flow around a neutron star fraction of neutrons Yn and Li abundances depends not is an ADAF in quiescence in the present study. The on m solely, but on the combination ˙ temperature of ions in ADAFs is comparable to virial fix α = 0.3 in the present paper (Narayan et al., 1997).
temperature, and is given at radius r by (Narayan & Yi,1994, 1995a,b); 3. New interpretation of soft X-ray emission in terms of T = 3.7 × 1012 rin K = 31.9 in MeV. The very low mass accretion rates on to a neutron star Here rin is the radius at the inner edge of the ADAF, been suggested the termination of mass accretion via and is set to be 3rg, where rg is the Schwarzschild radius the propeller effects, which can explain a sudden spectral =0.3,m=1.4,m=0.01 α=0.3,m=1.4,m=0.1 Fig. 1. Abundance distribution in ADAFs for α = 0.3, m = 1.4, and ˙ m = 0.01 (left panel) and 0.1 (right panel). The solid, dashed, short-dashed, dotted, and dash-dotted lines indicate the mass fractions of n, 4He, 6Li, 7Li, and 7Be, respectively.
state transition observed in X-ray from three NSSXTs, Aql X-1 (Campana et al., 1998; Zhang et al., 1998), SAX J1808.4-3658 (Gilfanov et al., 1998), and 4U 1608- 52 (Chen et al., 2006). Through the propeller effects, the material is ejected from ADAF around the ejection if rej is larger than the corotation radius (Yi & Narayan,1997), otherwise the propeller effects do not work. Here, B Fig. 2. Radius where the mass fraction of 7Li equals to 10−7 in the ADAF, r(Li), and ejection (Alfv´en) radius r NS are the magnetic field and the rotational period rates. Solid, dashed, and dotted lines indicate r(Li), rej for the of the neutron star, respectively. Figure 2 shows rej for magnetic field of the neutron star BNS = 108G, and rej for BNS = 108G (dashed line) and 109G (dotted line) as a BNS = 109G, respectively, in units of rg. We also present radii m. We also show the radius where the mass where a mass accretion rate of neutrons ˙ mn equals to 1 × 10−6 (thin dash-dotted line) or 5 × 10−6 (dash-dotted line).
fraction of 7Li equals to 10−7 in the ADAF (solid line).
The propeller effects operating in NSSXTs during qui- escence have important meaning to an accretion flowaround the neutron star. As shown in Figure 1, appre- surface of the neutron star. The liberated energy is a ciable fractions of neutrons are produced in the ADAF possible candidate for a energy budget of the blackbody- like, soft X-ray radiation. If we interpret the soft X-ray ej, which is smaller than 20 rg for a reasonable set of parameters (Figure 2). Although almost all charged par- radiation of ∼ 1032 erg s−1 as the energy liberation onto ticles are ejected due to magneto-centrifugal forces near the neutron star through the neutron-ADAF, a mass accretion rate of neutrons through the neutron-ADAF ej, neutrons are not affected by the magnetic field of the neutron star because of the charge-less of neutrons.
mn ∼ 10−6 is required in units of the Eddington accre- Consequently, even after the operation of the propeller tion rate. We note that the quiescent soft X-ray lumi- effects, accretion of neutrons continues to take place onto nosity in Cen X-4 is 2 − 3 × 1032 erg s−1 (Asai et al., the neutron star, and a neutron-ADAF is formed around mXn,ADAF, assuming rej > As the neutron-ADAF emits little radiation during ac- rc, where Xn,ADAF is the mass fraction of neutrons at cretion, the neutrons accreting onto the neutron star lib- m, higher BNS means larger rej and thus erate almost all its gravitational binding energy onto the mn because of smaller Xn,ADAF. The blackbody- like, soft X-ray emission with an order of 1032 erg s−1 transfer rate predicted by binary evolution models (King m ≥ 7 × 10−3 for a neutron star with BNS ≥ et al., 1996; Menou et al., 1999) for a secondary mass of mn equals to 1 × 10−6 (thin dash- 0.23M and the orbital period of 0.629 day (Casares et dotted line) or 5 × 10−6 (dash-dotted line) are shown in al., 2007) and is consistent with an averaged rate es- timated by Heinke et al. (2007) based on an outburstluminosity and a quiescent duration. We note that the 4. Transportation of Li to the secondary through the pro- magnetic field of the neutron star has been estimated as ∼ 2 × 109 G by Zhang et al. (1998), although in their The material in an ADAF is outflowed via the propeller evaluation they adopted a state change luminosity and effects, so that a fraction of Li produced in the ADAF a spin period of the star, which are uncertain.
can be transfered to the secondary and enhance Li abun-dances on the secondary. A fraction of the Li on the sec- ondary is returned to the ADAF through mass accretion.
We have proposed the emission mechanism of soft X-ray We can estimate an equilibrium abundances of Li. For radiation from NSSXTs and have examined unusually isotropic ejection of Li from the ADAF, the production high abundances of Li on a low-mass secondary in Cen X-4 during a quiescent state. Inside the hot (> 1 MeV) ADAF around a neutron star, neutrons are abundantly synthesized through the spallation of 4He via protons in the flow. We find that the neutron-ADAF is formed around the neutron star after the operation of the pro- Li,ADAF, R∗ and a are the mass fraction of Li (6Li and 7Li) at an ejection radius of the ADAF, r peller effects. The accretion energy of the neutrons lib- the radius of the secondary, and the binary separation, erated on the surface of the star is a possible energy bud- respectively. While the mass transfer rate of Li from get for soft X-ray radiation in a NSSXT in quiescence.
the surface to the ADAF is expressed as ˙ Moreover, Li is abundantly synthesized in the ADAF through α − α reactions and is transfered to the surface Li is the mass fraction of Li on the secondary.
For equilibrium between the production and loss rates of the secondary by the magneto-centrifugal forces. We M −, one can obtain an equilibrium Li abundance find that the estimated soft X-ray luminosity and abun- dance of Li on the secondary are comparable to observed values in Cen X-4 for reasonable values of the mass ac- cretion rate and the magnetic field of the neutron star, or 2 − 4 × 10−11M yr−1 and 1 − 2 × 108 G, respectively.
7, because of larger fractions of 7Li compared with 6Li, We also find that the isotopic ratio of lithium 6Li/ 7Li is found to be comparable to an observed ratio in Cen X-4.
We find that YLi, eq is comparable to the observed Li abundances in Cen X-4 (6.67 × 10−10(Yp/0.9) (Casareset al., 2007)) for XLi,ADAF = 0.817 × 10−7, which isrealized at ∼ 14r Anders, E., & Grevesse, N. 1989, Geochim. Cosmochim.
g and ∼ 18rg in the ADAF for ˙ 0.01 and 0.1, respectively (Figure 1). We note that Li isotopic ratios 6Li/7Li in the ADAF at the above radii are 0.19, which is comparable to the observed ratio in Asai, K., Dotani, T., Hoshi, R., Tanaka, Y., Robinson, −0.05) (Casares et al., 2007). Moreover, we C. R., & Terada, K. 1998, PASJ, 50, 611 m ∼ 0.01−0.02 and BNS = 2−3×108 G, the Brown, E. F., Bildsten, L., & Rutledge, R. E. 1998, ApJ, estimated values for the Li abundance as well as the soft X-ray luminosity are comparable to the observed values.
We note that the estimate for Li abundance is largely Campana, S., Mereghetti, S., Stella, L., & Colpi, M.
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