FINAL PRODUCTS OF THE rp-process ON ACCRETING NEUTRON STARS

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1 The Astrophysical Journal, 603: , 2004 March 1 # The American Astronomical Society. All rights reserved. Printed in U.S.A. FINAL PRODUCTS OF THE rp-process ON ACCRETING NEUTRON STARS Osamu Koike, Masa-aki Hashimoto, and Reiko Kuromizu Department of Physics, School of Sciences, Kyushu University, Fukuoka , Japan; koike@gemini.rc.kyushu-u.ac.jp, hashi@gemini.rc.kyushu-u.ac.jp, kuromizu@gemini.rc.kyushu-u.ac.jp and Shin-ichirou Fujimoto Kumamoto National College of Technology, Kumamoto , Japan; fujimoto@ec.knct.ac.jp Received 2002 November 12; accepted 2003 November 13 ABSTRACT Using both shell-flash and realistic models on accreting neutron stars with the full nuclear reaction network up to Bi, we investigate the detailed relation between the final products of the rp-process and the ignition pressure. We find that nuclear fuels of H and 4 He are almost burned out after the flash and that the mass number of synthesized nuclei reaches to 100 in the pressure range from to dyn cm 2 foraneutronstarof1.4m and10km radius. Furthermore, p-nuclei up to 126 Xe are found to be produced after the flash, thanks to our large network. The postprocess nucleosynthesis for accretion rates of ,3 10 9, and 10 8 M yr 1, which corresponds to an ignition pressure from 10 22:7 to 10 22:9 dyn cm 2, reveals that H is exhausted completely during the burst. This is because H decreases significantly as a result of the steady burning before the burst and convective mixing at the initial stage; we find that 64 Zn is the most abundant element after the burst. Subject headings: accretion, accretion disks nuclear reactions, nucleosynthesis, abundances stars: neutron X-rays: bursts 1. INTRODUCTION Thermonuclear runaway on accreting neutron stars has been widely accepted as a model for type I X-ray bursts (XRBs; Lewin, van Paradijs, & Taam 1993; Strohmayer & Bildsten 2004). If the accreting matter is mainly composed of H and He, explosive burning in the H-rich mixture leads to the production of proton-rich heavy nuclei during the burst ( s) via either rapid proton captures on seed nuclei or -decays (rp-process; Wallace & Woosley 1981). It had been believed that this rp-process terminated around the Fe group nuclei; in particular, 56 Ni was considered to be the most abundant final product. On the other hand, the endpoint of the rp-process plays an important role in the construction of an XRB model, because the thermal structure and composition of the accreting layers depend on the final products. The products would further our understanding of soft X-ray transients (Brown, Bildsten, & Rutledge 1998; Brown, Bildsten, & Chang 2002) and superbursts (SBs). In particular, SBs characterized by a duration of 10 4 s and an energy of ergs are detected in six low-mass X-ray binaries (summarized in Kuulkers et al. 2002). It is advocated that some amount of carbon accumulates below the accretion layer and triggers SBs (Cumming & Bildsten 2001; Strohmayer & Brown 2002). Considering the importance of the final products after the burst, detailed calculations using a shell-flash model of constant pressure were carried out; the abundance flow was found to proceed beyond 56 Ni (Hanawa, Sugimoto, & Hashimoto 1983), and the final product was concluded to be 68 Se (Koike et al. 1999). However, the endpoint of the rp-process was not clear, because the network of Koike et al. (1999) was insufficient to examine the heavy nuclei of A > 70. Schatz et al. (1998) found that nuclei of A 100 were produced under a 242 constant and T, using a reaction network up to Sn. For neutron stars with Eddington accretion rates or higher, the rp-process results in the synthesis of nuclei far beyond Fe (Schatz et al. 1999). Recently, the rp-process was found to terminate at A 100 because of the block of the SnSbTe cycle (Schatz et al. 2001). Furthermore, accreting neutron stars were proposed to be the possible production sites of p-nuclei such as Mo and Ru (Schatz et al. 1998) and Ru, Pd, and Cd (Schatz et al. 2001). However, both the ejection mechanism from the neutron star and the contribution to the cosmic abundance are unknown. Although the most promising site of the origin of p-nuclei is a Type II supernova explosion (Rayet et al. 1995), some p-nuclei, such as Mo, Ru, and La isotopes, were found to be underproduced. As another possibility, nucleosynthesis of p-nuclei inside supernova-driven supercritical accretion disks, formed after a Type II supernova explosion, has been investigated (Fujimoto et al. 2001): it is still an open question whether enough p-nuclei can be produced. Because of the large gravitational potential of a neutron star, the accretion layers are well approximated as having a flat configuration during the flash, and the pressure of the burning layer is determined by the weight of the accumulated layers unless the luminosity exceeds the Eddington limit (ṁ Edd ¼ 8: gcm 2 s 1 ; Fujimoto, Hanawa, & Miyaji 1981, hereafter FHM). Moreover, the relation between the accretion rate and nuclear burning has been investigated, where the nuclear burning is related to the ignition pressure (FHM; Hanawa & Fujimoto 1982; Fushiki & Lamb 1987). Adopting the steady state model, FHM classified the shell flashes into three cases according to the accretion rate Ṁ: High Ṁ. Unstable He ignition causes mixed H/He burning. Intermediate Ṁ. A pure He flash occurs after H depletion through the hot CNO cycle.

2 FINAL PRODUCTS OF rp-process ON ACCRETING NSs 243 Low Ṁ. Unstable H burning grows to an H/He combined flash. Modes in nuclear burning related to the ignition pressure are discussed by Bildsten (1998). We note that the classification of cases 1 3 by FHM has not always been definite in a realistic situation, since multizone effects, such as the convection during the burning, should be very important. As mentioned above, the ignition pressure is a critical parameter for the XRB model. Nevertheless, a detailed relation between the rp-process and the pressures has not been discussed thus far. Furthermore, the shell-flash model must be connected to a realistic model of an accreting neutron star, because the final products of the rp-process are determined from an evolutionary calculation with complete nucleosynthesis. In the present paper, using the shell-flash model and the full nuclear reaction network (FNRN), we investigate the relation between the ignition pressure and the final products, including p-nuclei. Then we deduce the nuclear fuels after the burst, which become the critical quantities for determining the character of the following burst. In x 2 we explain the adopted model and show the computational results. In x 3 the results are discussed in connection with accreting neutron star models within the framework of stellar evolution. Our results are summarized in x MODEL COMPUTATIONS 2.1. Nuclear Reaction Network The previous version of our network has not always traced abundance flows, since the isotopes contained were limited to Kr (Hashimoto & Arai 1985; Koike et al. 1999). It has been demonstrated that the flow proceeds significantly beyond Kr (Schatz et al. 1998); we should note that the abundance flows of Schatz et al. (1998) are not always adequate for XRB, because they calculated nucleosynthesis under a constant and T. Recent studies of the rp-process used a network up to Xe (Schatz et al. 2001), which may be insufficient to discuss the endpoint, as shown in x 3.2. To investigate the final products of the rp-process, we need the FNRN, which includes all the possible flows of the abundances beyond Xe. Therefore, we have developed a nuclear reaction network up to Bi, as seen in Table 1. Included channels are ( p, ), (, ), (, p), (3, ), (n, ), (n, p), and (n, ), with their inverse reactions, and weak interactions ( decays and electron captures); delayed particle emissions are included if available. The nuclear data are taken from the following references: Rauscher & Thielemann (2000, 2001; REACLIB). Experimental and theoretical data (reaction rates, mass excesses, and partition functions). Angulo et al. (1999; NACRE). Experimental reaction rates from H to Si. Iliadis et al. (2001). With (p, ), (p, ) reaction rates from Ne to Ca. Horiguchi, Tachibana, & Katakura (1996; Chart of the Nuclides). -decays and particle emissions. Fuller, Fowler, & Newman (1980, 1982). Weak interaction rates. Audi & Wapstra (1995). Mass excesses. We use in most cases REACLIB data, with supplementation by the other above compilations if available. Rates of 56 Nið p; Þ 57 Cuð p; Þ 58 Zn are taken from Forstner et al. (2001). It has been suggested that two-proton captures at waiting points, such as 68 Seð2p; Þ 70 Kr, are important during the burst (Schatz et al. 1998). Considering the uncertain reaction rate of (2p, ), we use the data of REACLIB for ( p, ), where the waiting points heavier than 64 Ge have negative Q-values. In the present calculations, the abundance flows proceed beyond the waiting points through the successive ( p, ) reactions and/or + decays after ( p, ). Therefore, although the path along the production of heavy elements may be altered, the inclusion of (2p, ) reactions does not change our results significantly. The inverse reaction rates by Iliadis et al. (2001) and Forstner et al. (2001) are calculated from the forward reaction rates using the principle of detailed balance. TABLE 1 Elements Included in the Full Nuclear Reaction Network Elements A Elements A Elements A Elements A H Ti Tc Gd He V Ru Tb Li Cr Rh Dy Be Mn Pd Ho B Fe Ag Er C Co Cd Tm N Ni In Yb O Cu Sn Lu F Zn Sb Hf Ne Ga Te Ta Na Ge I W Mg As Xe Re Al Se Cs Os Si Br Ba Ir P Kr La Pt S Rb Ce Au Cl Sr Pr Hg Ar Y Nd Tl K Zr Pm Pb Ca Nb Sm Bi Sc Mo Eu

3 244 KOIKE ET AL. Vol. 603 If we couple directly a large reaction network as shown in Table 1 with a stellar evolution code, it takes a very long computational time to carry out the evolutionary calculation during the accretion. Thus, to save computing time in XRB simulations, the approximation reaction network (APRN) has been devised (Wallace & Woosley 1981; Hanawa et al. 1983; Rembges et al. 1997). We use an APRN that includes 16 nuclides: 1 H, 4 He, 12 C, 14 O, 15 O, 17 F, 22 Mg, 30 S, 56 Ni, 60 Ni, 60 Zn, 64 Zn, 64 Ge, 68 Ge, and 68 Se (Hanawa et al. 1983). This small network was constructed to reproduce approximately the nuclear energy generation rate, which was calculated with a large network up to Kr in the framework of the shell-flash model. The same method has been used in the evolutionary calculations for massive stars (Woosley & Weaver 1995; Hashimoto 1995). In the following computations, we compare the results of the FNRN calculation with those of APRN in connection with the stellar evolutionary calculation (x 3.1). The electron screening factors (Graboske et al. 1973; Itoh et al. 1979) are included in both networks Shell-Flash Model and Physical Inputs To investigate the rp-process using FNRN and APRN, we adopt the shell-flash model in the spirit of the one-zone picture (Hanawa et al. 1983; Koike et al. 1999). This model approximately reproduces the structure of accretion layers during the flash. Therefore, it is possible to examine the effects of uncertainties in the nuclear reaction rates on the rp-process (Koike et al. 1999). The ignition pressure P, whichremains constant during the flash, is expressed as the integrated form of the hydrostatic equation: P ¼ g s ; g s ¼ GM t R 2 1 2GM 1=2 t Rc 2 ; ð1þ where g s and are the gravitational acceleration of the neutron star and the column depth, respectively. The general relativistic effect is taken into consideration in g s ; G is the gravitational constant, c the speed of light, M t the gravitational mass, and R the radius of the neutron star. For example, we have log g s ¼ 14:38 for M t ¼ 1:4 M and R ¼ 10 km, and log g s ¼ 14:75 for M t ¼ 2:0 M and R ¼ 9:0 km. The former set of (M t, R) is typical and is deduced from the observation of XRBs (Lewin et al. 1993). The latter is derived from the observation of (and theory regarding) the quasi-periodic oscillations in 4U (Kaaret, Ford, & Chen 1997). We note that the burning layer stays hydrostatic in the pressure ranges in our investigation (FHM). The energy equation is written as dt c p dt ¼ n rad ; rad ¼ 4acT : ð2þ Here T and c p are the temperature of the shell and the specific heat capacity under constant pressure, respectively, n is the nuclear energy generation rate, rad is the radiative energy loss rate, where a is the radiation constant, and is the opacity. The neutrino loss rate ( ) associated with -decays is also taken into account. Although data for values of proton-rich nuclei are very uncertain, they are estimated to be less than 20% of the nuclear energy generation rate around the peak of the flash. Therefore, the peak temperature (T p ) is affected to some extent. However, these effects are not important as far as final abundances are concerned, since the decrease in T p is small. The conduction opacity is negligible for the major part of the nuclear burning during the flash, although it is important to the thermal condition in the XRB before the ignition. Then we adopt an opacity that includes the Compton effect: ¼ T =ð1 þ 2:2T 9 Þ,where T and T 9 are the Thomson scattering opacity and the temperature in 10 9 K, respectively. We take two quantities, P and g s, as the parameters of the shellflash model. These parameters and the initial mass fractions are listed in Table 2. The ratio of the H and He mass fractions, X =Y, enables us to estimate the number of protons per seed nucleus. Using equations (1) and (2), we follow the rp-process through the evolution of density and temperature until the temperature decreases to K, at which nuclear burning is inactive. The density can be computed with the aid of the equation of state Computational Results Let us discuss the selected parameters of P and X =Y in Table2.First,forZ CNO ¼ 0:02 of the accreting matter, the column depth needed to initiate the shell flash, which is proportional to Z 1=2 CNO,isð1:2 2:5Þ108 gcm 2 (Fujimoto et al. 1987). Assuming log g s ¼ 14:38, the ignition pressures become and dyn cm 2 for Z CNO ¼ 0:02 and 10 3, respectively. Ignitions of the nuclear fuels occur at higher pressures ( log P k 23) according to the accretion rate and thermal state of the neutron star core (Hanawa & Fujimoto 1986). Second, the composition of the fuels changes as follows: H burns stably into He via the hot CNO cycle in the accretion phase; the convection mixes material in the early stage of the flash so that X =Y ranges from nearly 1 to 3, as seen in Table 8. In addition, after the convection has ceased, fuels are processed into heavier elements. Thus, the parameters P and X =Y in our shell-flash calculation cover those of the previous calculations (Hanawa & Fujimoto 1984, 1986). The final products and the residual fuels after the flash are tabulated for the shell-flash calculation in Tables 3 6, in which the flash is assumed to be quenched at T 9 0:2: As is shown in Table 3, the mass number of synthesized nuclei has reached the maximum A 100 in the narrow range of the ignition pressure: log P ¼ with log g s ¼ 14:38. In addition, most of the nuclear fuel is found to be consumed if log P k 23 for the given range of X =Y and g s. On the other hand, if we use APRN, the remaining H after the flash is overestimated (Table 7). Our qualitative results are not different from one another if we change g s, so we discuss the computational results of log g s ¼ 14:38 in x 3. To compare the results of the shell-flash calculations with those of the evolutionary calculations, we have performed postprocess calculations (PPCs); small abundances can be followed with FNRN using the density and temperature, which are obtained from the evolutionary calculation of an TABLE 2 Physical Inputs for the Shell-Flash Calculation Network log g s (cm s 2 ) log P (dyn cm 2 ) Full , 2, Approximation Notes. Here X =Y is the ratio of H to He in the initial mass fraction, where we assume X þ Y ¼ 0:98, X ð 14 OÞ¼0:007, and X ð 15 OÞ¼0:013. The initial temperature is set to be K for all cases. X/Y

4 No. 1, 2004 FINAL PRODUCTS OF rp-process ON ACCRETING NSs 245 TABLE 3 Mass Fractions of Abundant Nuclei after the Flash for log g s ¼ 14:38 and X =Y ¼ 3 (logp, E 18, T 9p ) (22.60, 5.31, 1.34) (22.75, 5.27, 1.49) (23.00, 5.63, 1.81) (23.25, 6.08, 2.13) (23.50, 6.10, 2.38) (23.75, 6.25, 2.62) Case Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Ge 1.53E 01 1 H 1.07E Cd 2.38E Cd 3.17E Ag 2.02E Zn 4.21E Zn 1.02E Se 6.26E Ag 9.96E Cd 2.15E Pd 1.80E Ge 1.63E H 1.02E Sr 6.18E 02 1 H 5.73E Ag 9.08E Cd 1.42E Ni 9.08E Se 9.00E Sr 6.03E Cd 5.46E Cd 9.04E Ag 1.27E Kr 5.71E As 6.80E Ge 5.76E Cd 3.94E Ag 4.98E Pd 6.08E Se 5.15E Ga 6.18E Kr 4.54E Ag 3.80E Ag 2.46E Zn 5.87E Co 4.04E He 4.34E Zr 2.54E Cd 3.38E Zn 2.05E Cd 4.87E Sr 2.86E Kr 4.05E 02 4 He 2.48E Ag 2.97E In 1.98E Cd 3.89E Kr 2.26E As 2.63E Rh 2.41E Pd 2.30E In 1.40E Ag 3.30E Fe 2.14E Ga 2.23E Y 2.16E Pd 2.06E Pd 1.24E Rb 1.76E Ni 2.05E Ge 2.13E Mo 2.15E Sr 1.84E Pd 9.85E Ge 1.44E Sr 1.15E Sr 2.09E Zr 2.07E Pd 1.77E Ge 9.65E Se 1.19E Br 1.10E Sr 1.67E Zn 1.97E In 1.74E Cd 8.33E Kr 7.81E As 6.98E Se 1.50E Tc 1.90E Ag 1.68E Se 7.89E Tc 7.07E Ge 6.57E Kr 1.34E Ru 1.79E Ru 1.33E Rb 7.33E Pd 5.00E Zn 3.85E 03 Note. Here T 9 0:2 is set to be the end of the flash, T 9p is the peak temperature in 10 9 K, and E 18 is the total released nuclear energy in ergs g 1. accreting neutron star. For example, Iliadis et al. (1999) carried out a PPC for an XRB assuming the initial compositions to be proportional to the solar abundances. Realistic neutron star models have been constructed from a spherically symmetric evolutionary code (Hanawa & Fujimoto 1984; Fujimoto et al. 1984), which has been developed to simulate an XRB initiated by accretion onto a neutron star of M t ¼ 1:3 M and R ¼ 8:1 km(logg s ¼ 14:56) using an n by APRN. The star is divided into 266 mesh points in mass coordinates. The neutron star interior is defined as the region from the center to the 120th mesh point, outside of which is the envelope (10 m in thickness). As for the convection that occurs in the early stage of the burst, we adopt the Schwarzschild criterion and assume the instantaneous mixing of compositions. We have performed the XRB calculation for three cases, Ṁ ¼ 1:0 10 8,3:0 10 9,and3: M yr 1, whichcorrespondto1.0ṁ Edd,0.3ṁ Edd, and 0.03ṁ Edd, respectively. These rates approximately correspond to case 1 in FHM. Initial models are constructed as follows: accretion continues onto a cold neutron star until a steady state is achieved, in which the nonhomologous part of the gravitational energy release vanishes (Fujimoto et al. 1984). During the accretion, we change accreted materials composed of H and He into 56 Fe without nuclear burning. It takes yr for the steady state to be attained. The accretion rates adopted in the present paper pertain to XRBs from H/He mixed burning, which have been continuously observed to the present day (Lewin et al. 1993); for example, an XRB profile TABLE 4 Mass Fractions of Abundant Nuclei after the Flash for log g s ¼ 14:38 and X =Y ¼ 2 (logp, E 18, T 9p ) (22.60, 5.43, 1.38) (22.75, 5.46, 1.55) (23.00, 5.61, 1.89) (23.25, 5.59, 2.18) (23.50, 5.61, 2.43) (23.75, 5.76, 2.64) Case Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Ga 1.93E Ge 1.42E Cd 9.73E Cd 3.07E Ag 1.91E Zn 4.27E Zn 1.85E Se 1.12E Sr 9.12E Ag 9.39E Pd 1.64E Ge 1.66E Ge 1.25E Zn 1.07E Ag 6.14E Cd 9.26E Cd 1.38E Ni 9.11E As 9.99E Sr 6.90E Se 4.92E Ag 8.93E Ag 1.09E Se 5.24E Se 6.26E Kr 6.65E Kr 4.75E Cd 7.30E Pd 6.67E Kr 5.09E He 4.46E Sr 4.33E Cd 3.60E Ag 2.73E Zn 6.21E Co 4.00E Ge 3.81E Ga 2.78E Rb 3.50E Rb 2.61E Cd 4.34E Sr 2.85E Ga 2.71E As 2.60E Ag 3.11E Sr 2.23E Ag 3.78E Kr 2.32E H 2.58E 02 1 H 2.47E Sr 2.72E Pd 1.92E Rb 2.94E Ni 2.21E Kr 2.46E 02 4 He 2.44E Tc 2.70E Tc 1.92E Cd 2.87E Fe 1.93E As 1.85E Kr 2.17E Ag 2.40E Pd 1.73E Ge 1.71E Br 1.07E Ge 1.84E Se 1.68E Pd 2.30E Zn 1.71E Se 1.45E Sr 1.05E Br 1.31E Sr 1.68E Pd 1.90E Pd 1.38E Tc 1.28E As 7.13E Sr 9.52E As 1.62E Ru 1.86E Pd 1.37E Pd 1.07E Ge 6.46E Ge 8.25E Rb 1.47E Zn 1.80E Cd 1.10E Kr 9.85E Zn 3.89E 03 Note. Here T 9 0:2 is set to be the end of the flash, T 9p is the peak temperature in 10 9 K, and E 18 is the total released nuclear energy in ergs g 1.

5 246 KOIKE ET AL. Vol. 603 TABLE 5 Mass Fractions of Abundant Nuclei after the Flash for log g s ¼ 14:38 and X =Y ¼ 1 (logp, E 18, T 9p ) (22.60, 4.53, 1.45) (22.75, 4.61, 1.64) (23.00, 4.66, 1.98) (23.25, 4.61, 2.26) (23.50, 4.60, 2.49) (23.75, 4.71, 2.67) Case Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Zn 4.17E Zn 4.91E Zn 3.64E Zn 1.46E Zn 1.12E Zn 4.38E Ga 2.36E Ga 2.60E Ge 2.05E Rb 1.13E Cd 1.01E Ge 1.68E He 8.76E Ge 5.32E Se 1.59E Sr 1.09E Ag 1.01E Ni 9.52E Ni 3.48E 02 4 He 4.60E Kr 7.63E Se 1.05E Rb 8.67E Se 5.29E Ni 3.11E Ge 2.46E Sr 4.06E Kr 1.04E Pd 5.60E Co 4.09E Ge 2.45E As 2.10E Ga 1.92E Tc 5.95E Pd 5.05E Kr 3.95E Ge 2.34E Ni 1.91E Rb 1.78E Cd 3.63E Ag 4.76E Sr 2.63E S 1.31E Ni 1.76E 02 4 He 1.27E Ag 3.52E Tc 4.76E Ni 2.61E C 1.27E C 8.82E Sr 1.04E Ge 3.34E Ge 4.66E Kr 2.35E Si 1.21E Se 7.54E Kr 7.93E Pd 1.71E Se 4.22E Fe 1.74E Cu 1.21E Cu 5.45E As 7.35E Zr 1.70E Ag 3.11E Br 9.83E Co 1.21E Co 4.83E Se 4.91E Pd 1.58E Kr 3.06E Sr 8.45E As 9.95E S 4.43E Sr 4.69E Sr 1.50E Pd 2.46E As 7.18E K 9.91E K 4.32E Sr 3.40E Mo 1.50E Cd 2.10E Ge 6.02E Ar 6.86E Si 3.94E C 3.02E Y 1.46E Mo 1.88E Kr 3.99E 03 Note. Here T 9 0:2 is set to be the end of the flash, T 9p is the peak temperature in 10 9 K, and E 18 is the total released nuclear energy in ergs g 1. from GS with Ṁ 1: M yr 1 (Ubertini et al. 1999) shows evidence of the rp-process (Bildsten 2000). We note that low accretion rates, Ṁ < M yr 1,are also suggested from observations (Strohmayer & Bildsten 2004; Migliari et al. 2003). Figure 1 shows the surface luminosity and the temperature of the burning layer with Ṁ ¼ 3: M yr 1. We perform PPCs as follows: During the XRB calculation, we store and T as a function of time at the hottest zone of the flash. Then we start PPCs from the seeds and fuels obtained just after the cessation of convection (Fig. 2), when the energy transfer is radiative, as shown by the dotted line in Figure 3. Therefore, detailed nucleosynthesis is computed until the end of the burst using ðtþ and TðtÞ. We do not calculate the change in composition during convection with FNRN, since the main products from APRN in the evolutionary code should not be wrong from the ignition to the peak of the burst. We stress again that PPCs use the initial seeds and fuels synthesized in the convective region and the realistic profile of ðtþ and TðtÞ during the burst. In these calculations, H is found to be exhausted. The most abundant nucleus is 64 Zn for the three accretion rates models shown in Table DISCUSSION 3.1. Final Products and Fuel Consumption Proton capture is generally hindered by the Coulomb barrier for low temperatures and by photodisintegration for high TABLE 6 Mass Fractions of Abundant Nuclei after the Flash for log g s ¼ 14:75 and X =Y ¼ 3 (logp, E 18, T 9p ) (23.00, 4.78, 1.49) (23.25, 5.01, 1.84) (23.50, 5.88, 2.21) (23.75, 6.08, 2.48) (24.00, 6.27, 2.77) Case Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction H 1.69E Cd 1.64E Cd 2.94E Cd 3.71E Zn 5.41E Se 1.12E 01 1 H 1.37E Cd 2.70E Ag 1.78E Ni 1.48E Kr 9.03E Ag 9.17E Ag 7.23E Ag 9.21E Ge 1.17E Sr 6.69E Cd 8.06E Cd 5.73E Cd 8.09E Ni 5.24E Sr 5.63E Ag 4.77E Ag 4.34E Ag 4.25E Co 4.85E Ge 4.90E Ag 3.69E In 3.55E Pd 4.24E Se 3.03E As 3.06E Cd 2.86E 02 1 H 2.53E Pd 3.51E Sr 1.54E Y 2.54E Pd 2.45E In 2.27E Cd 2.82E Fe 1.14E Sr 2.21E Pd 1.99E Ag 1.30E Zn 2.45E Kr 1.07E He 2.19E Pd 1.75E Cd 1.12E Rb 1.86E Kr 5.40E Zr 1.96E Pd 1.71E Pd 8.41E Kr 9.45E Sr 2.04E Zr 1.77E Sr 1.51E Cd 8.18E Se 8.96E Kr 1.97E Kr 1.74E Ag 1.48E Sr 7.77E Sr 8.30E Ge 1.33E Br 1.65E Kr 1.39E Pd 7.15E Tc 6.80E Zn 1.22E Rb 1.49E Sr 1.36E Sr 4.52E Pd 6.08E Cu 1.15E 03 Note. Here T 9 0:2 is set to be the end of the flash, T 9p is the peak temperature in 10 9 K, and E 18 is the total released nuclear energy in ergs g 1.

6 No. 1, 2004 FINAL PRODUCTS OF rp-process ON ACCRETING NSs 247 TABLE 7 Remaining Mass Fractions of Fuel after the Flash for APRN under the Shell-Flash Model (logp, E 18, T 9p ) Nuclide (22.75, 4.16, 1.38) (23.00, 3.90, 1.72) (23.25, 3.32, 2.08) (23.50, 2.20, 2.37) (23.75, 2.06, 2.63) 1 H E E E E E 01 4 He E E E E E Se E E E E E Ge E E E E E Zn E E E E E 12 Note. Here T 9 0:2 is set to be the end of the flash, T 9p is the peak temperature in 10 9 K, and E 18 is the total released nuclear energy in ergs g 1. temperatures. However, there are temperature windows in which the lifetime of the target nucleus for proton capture becomes several orders of magnitude shorter than the burst timescale (Schatz et al. 1998; Wiescher & Schatz 2000). The window of 56 Ni, a representative waiting point, is T 9 ¼ 1: Around the temperature of this window, the rp-process proceeds efficiently beyond the waiting point. Therefore, passing across the point, there exists a maximum in the mass number of synthesized nuclei, as seen in Figure 4, where A ash ¼ ð P X i =A i Þ 1 with P X i ¼ 1 and the summation is taken over nuclei heavier than oxygen. When log g s ¼ 14:38 and X =Y ¼ 3, nuclei of A 100 are produced for log P ¼ because of the operation of the SnSbTe cycle, which is consistent with the results of Schatz et al. (2001). They found that the SnSbTe cycle limits production to nuclei of A 100 during the flash in an accumulated layer of 4: g, assuming log g s ¼ 14:28, ṁ ¼ 8: gcm 2 s 1, and a metallicity of On the other hand, we find that the final products consist of A ¼ and80for logp ¼ 23:75. The former products are due to the reverse reactions to the waiting points: 65 As(, p) 64 Ge, 69 Br(, p) 68 Se, and 73 Rb(, p) 72 Kr. The latter are due to the ZrNb cycle (Schatz et al. 1998), which becomes active at T 9 k 2:0. We note that the case of X =Y ¼ 0 results in a pure He flash, as investigated by Hashimoto, Hanawa, & Sugimoto (1983): the synthesized nuclei remain an Fe group (A P 60). If g s is obtained and the burst simply shows the behavior of a limit cycle, the final products can be inferred from observational data using P ¼ g s ṁ rec,where rec is the recurrence time of the bursts. As shown in Figure 5, the APRN nearly reproduces the T p computed by the FNRN, because T p is mainly determined from the He consumption (Fig. 6). For log g s ¼ 14:38 and X =Y ¼ 3, however, Figure 5 shows that the nuclear energy release by the APRN deviates from that by the FNRN by more than 40% if log P > 23. Thus, the APRN can be safely used to get the nuclear energy generation and peak temperature as long as log P < 23. In addition, in the calculation by Koike et al. (1999), who used a network up to Kr, the most abundant final product is 68 Se, because the abundance flow was artificially stopped. This indicates that the remaining H fuel is overestimated if log P 23, since the abundance flow cannot proceed beyond Kr during the decay phase of the burst. As for the remaining He fuel, the consumed amount is evaluated just before the peak of the burst; the amounts are almost the same if the network contains nuclei up to 56 Ni. The total nuclear energy released during the flash is controlled by the degree of H consumption (Figs. 5 and 7); it can be estimated from E tot ¼ E H X þ E He Y,whereE H ¼ 8: ergs g 1 and E He ¼ 1: ergs g 1 are the nuclear energies released in the conversion of H and He to 56 Fe, respectively; X and Y are the amounts of H and He consumption. It should be noted that accurate computation of the fuels would be crucial to simulating an XRB under various Fig. 1. Change in the surface luminosity (solid line) and temperature (dashed line) of the burning layer for the evolutionary calculation with Ṁ ¼ M yr 1. The abscissa denotes the time elapsed from the beginning of the burst. Fig. 2. Abundance distribution when the selected zone in the PPC becomes radiative. Note that the region of 20:7 < log P < 22:8 is still convective. The accretion rate is M yr 1. The composition is assumed to be 56 Fe at the bottom of the burning layer for the evolutionary calculations.

7 248 KOIKE ET AL. Vol. 603 Fig. 3. Evolutionary profile of (, T) usedintheppcwithṁ¼ M yr 1. The solid and dotted curves show the loci where the convective and radiative energy transfers are dominant, respectively. The quantities X i and Y i are the input mass fractions for the PPC shown in Fig. 2, and X f and Y f are the remaining fuels in the evolutionary calculation. conditions, e.g., accretion rate, composition of accreting matter, and thermal state of the neutron star. Therefore, we must extend APRN to include enough endpoints for log P k 23. In addition, to carry out a precise simulation, it is required that nuclear data, such as the Q-values and reaction rates of protonrich nuclei, be determined with enough accuracy from experiments and/or theories. Calculation with the FNRN could result in a longer duration of the burst than in previous studies (Hanawa & Fujimoto 1986). Fig. 4. Averaged mass number of the rp-process ashes as a function of the ignition pressure. As for the consumed fuels, Y obtained from PPC is consistent with that from FNRN, as inferred in Figure 6. However, H is consumed completely. For Ṁ ¼ 3: M yr 1, H decreases from X ¼ 0:73 to 0.13 during the steady burning before the burst, increases to X ¼ 0:53 at a maximum due to the convective mixing, and finally becomes X ¼ 0:48 because of the nuclear burning at the end of convection. This leads to an increase in heavier elements, which become seeds of the rp-process. The decrease in H yields the most abundant nucleus, 64 Zn, which decays from 64 Ge since there is no time to supply the H fuel before the end of the burst. PPC insists TABLE 8 Final Products Obtained from PPCs Model 1 a Model 2 b Model 3 c Case Nuclide Mass Fraction Nuclide Mass Fraction Nuclide Mass Fraction Zn 3.47E Zn 2.65E Se 1.25E Ni 1.85E Ge 1.69E Zn 1.22E Ga 8.23E Se 1.37E Ge 9.95E Ni 6.39E Kr 7.79E Kr 8.72E C 3.65E Sr 7.42E Sr 8.43E Co 3.44E Ga 4.08E Rb 6.95E S 3.43E Rb 2.01E Tc 2.09E K 3.18E As 1.83E Sr 1.97E He 2.24E Sr 1.14E Sr 1.73E Ar 2.19E 02 4 He 1.10E Mo 1.69E Fe 1.42E Sr 1.01E Ru 1.65E Ge 1.37E Kr 1.01E Ru 1.53E Cl 1.30E Tc 7.81E Kr 1.45E Ar 1.29E C 7.65E Ru 1.41E Cr 1.22E Mo 7.11E Zr 1.36E 02 Note. Here Ṁ is the mass accretion rate, log P is the pressure at the selected mass shell, T 9p is the peak temperature in 10 9 K, X i, Y i,andz i are the initial mass fractions for H, He, and 56 Ni, respectively, and X f and Y f are the residual fuels in the evolutionary calculations. a In this model, Ṁ is 3: M yr 1, logp is 22.71, T 9p is 1.34, X i, Y i,andz i are 2: , 3: ,and1: , respectively, X i =Y i is 0.783, X f and Y f are 2: and 3: , respectively, and 1 H and 4 He have mass fractions of 1: and 2: , respectively. b In this model, Ṁ is 3: M yr 1,logPis 22.91, T 9p is 1.36, X i, Y i,andz i are 4: ,2: , and 1: , respectively, X i =Y i is 2.28, X f and Y f are 4: and 1: , respectively, and 1 H and 4 He have mass fractions of 9: and 1: , respectively. c In this model, Ṁ is 1: M yr 1,logPis 22.94, T 9p is 1.38, X i, Y i,andz i are 5: ,1: , and 1: , respectively, X i =Y i is 2.70, X f and Y f are 8: and 1: , respectively, and 1 Hand 4 He have mass fractions of 3: and 8: , respectively.

8 No. 1, 2004 FINAL PRODUCTS OF rp-process ON ACCRETING NSs 249 Fig. 5. Total released nuclear energy (solid lines) and peak temperature (dotted lines) during the flash. The filled circles, squares, and triangles and open squares indicate the peak temperatures attained for X =Y ¼ 3, 2, and 1 with FNRN and X =Y ¼ 3 with APRN, respectively. that although quantitative understanding of realistic situations requires evolutionary calculations with FNRN, one can reduce the problems to shell-flash calculations with the proper choices of initial X =Y and metallicity, as far as the final products are concerned. This is understood from Figure 4 because the line of PPC for log g s ¼ 14:56 increases with increasing P for a fixed X =Y and lies between the results of the shell-flash calculations for log g s ¼ 14:38 and Comparing the results in Table 8 with those in Tables 3 5, we can limit the applicability of APRN in a realistic evolutionary calculation. Our evolutionary calculation with APRN can be legitimized with the condition that both log P < 23 and X =Y < 3, except for the H consumption, which is underestimated by 10% 20% (Fig. 7). In the meantime, the FNRN calculations indicate that the heating of the accretion layers by electron capture on residual H (Fushiki et al. 1992; Taam, Woosley, & Lamb 1996) is not effective for log P 23. Thus, the very long tailed burst would be ascribed to other scenarios. Cumming & Bildsten (2001) have supposed that the carbon flash in the ocean of the rp-process ashes is the cause of the SB, where carbon is assumedtobe 0.1 in mass fraction. Figure 8 shows that the Fig. 7. Same as Fig. 6 but for H remaining carbon mass fraction is less than 0.02, which may not be sufficient to trigger the carbon flash. However, some amounts of He and/or C would survive if the He-rich burst (X =Y < 1) took place after the continuous stable H burning Production of p-nuclei To compare the final products regarding the p-nuclei in the solar abundances (Anders & Grevesse 1989), we define the overproduction factor f p ¼ð P0 X i Þ=X, where the summation is taken over the mass fractions of nuclei on the isobaric chain that decay to a given p-nucleus and X is the mass fraction of the corresponding daughter p-nucleus. We find that p-nuclei up to 126 Xe, 120 Te, and 114 Sn have been overproduced by the same f p for X =Y ¼ 3, 2, and 1 with log g s ¼ 14:38, as shown in Figure 9. This figure gives the relation between the ignition pressure and the overproduction factor, which also depends considerably on X =Y. As seen from Figure 10, our results of p-nuclei production would be consistent with those of Schatz et al. (2001), in which the abundance flows reach to Te isotopes. On the other hand, we find that the rp-process connected with an XRB proceeds to synthesis up to 126 Xe through small abundance flows beyond the SnSbTe cycle insensitive to the size of the neutron star if log P 23. This difference is ascribed to the size of the network adopted. Fig. 6. Fraction of consumed He as a function of the ignition pressure Fig. 8. Total mass fraction of CNO elements remaining after the flash

9 250 KOIKE ET AL. Vol. 603 Fig. 9. Overproduction factor vs. ignition pressure for 114 Sn For an XRB to contribute to p-nuclei, the produced nuclei must escape the gravitational potential of the neutron star. According to a study on mass loss (Ebisuzaki, Hanawa, & Sugimoto 1983; Kato 1983) with super-eddington surface luminosity, the gas of the envelope absorbs the surplus radiation flux, and some amount of gas could be ejected. As a consequence, the surface luminosity becomes quite close to the Eddington luminosity. Therefore, plausible candidates for mass loss may be indicated by bursts with Eddington luminosity, which show photospheric radius expansion (PRE), or even SBs. It has been suggested that bursts with PRE take place on cold neutron stars that might observationally be soft X-ray transients (Hanawa & Fujimoto 1986). Although the steady state approximation was assumed, Kato (1986) obtained mass-loss solutions for an envelope of H or He and suggested that the H envelope is blown off because of the super-eddington luminosity. In the present study we assume the stars to be in hydrostatic equilibrium and spherically symmetric; during the bursts for the three cases of accretion rates investigated, a convective zone extends to 5 matmost from the bottom of the burning layer, whose height is approximately half that of the accumulated layer. The relation between the convection and mass loss has been an open question because of the multidimensional effects coupled to the thermal instability. Therefore, whether the synthesized p-nuclei are ejected or not should be examined by hydrodynamic calculations that include mass loss from the neutron star. In particular, regarding the investigation of p-nuclei, we need to clarify the detailed conditions of PRE: the ignition pressure, X =Y at the beginning of the burst, and the extension of convective layers where the products should be transported to the outer shell. For instance, while the envelopes remain around 10 m during the burst for the three cases with H/He burning, the burst of pure He accretion (X =Y ¼ 0; Ṁ ¼ M yr 1 ) lifts the accumulated layer from 15 to 40 m because of PRE; although Zingale et al. (2001) performed two-dimensional calculations of the flash from helium detonations on neutron stars, they expected very little matter to be ejected. Considering a probable configuration of the mass loss, rapidly rotating neutron stars could eject the accreting gas because of the deformation of the surface layers. In particular, it has been shown that rotating neutron stars with meson condensates would have a discontinuity in density due to a phase transition; the density near the surface is so small and thermally unstable that mass loss could occur during the burst (Nozawa et al. 1996). In this connection, a strange star with an envelope could also become a site of mass ejection, because observations of an XRB from the strange-star candidate 4U show PREs in both the usual XRBs and SBs (Strohmayer & Brown 2002). 4. SUMMARY In the present research, our results are summarized as follows: 1. In the framework of the shell flash, the mass number of produced nuclei reaches to 100, and almost all H and He are exhausted in a narrow range of ignition pressure, log P ¼ for X =Y k 2, with the value of the neutron star at log g s ¼ 14:38. When log P 23:5, the final products remain around A ¼ For log P ¼ 22: with X =Y P 1, H and He fuels are burned out, and the final product is 64 Zn. 2. The validity of the APRN is clarified for the remaining H and He fuels; the APRN can be used safely if log P < 23, but residual H is overestimated. Fig. 10. Overproduction factor of p-nuclei from 92 Mo to 108 Cd vs. ignition pressure for X =Y ¼ 3 and log g s ¼ 14:38

10 No. 1, 2004 FINAL PRODUCTS OF rp-process ON ACCRETING NSs From the postprocess calculations of Ṁ ¼ to 10 8 M yr 1, the final product with log P < 23 is found to be 64 Zn because of the steady burning before the burst and the convective mixing during the early epoch of the bursts. 4. The remaining carbon mass fraction after the burst is less than 0.02, which is insufficient to trigger an SB. 5. Thanks to the use of a large network up to Bi, p-nuclei such as 126 Xe, 120 Te, and 114 Sn have been produced over an extent of X =Y ¼ 1 3, indifferent to the size of the neutron stars. Our results concerning both the final products and the residual fuels should help to construct a realistic thermal structure and composition for the accretion layers in XRBs through either the opacities or the electron captures of the rp-process ashes. We would like to thank to Kenzo Arai for reading the manuscript and for valuable comments. One of the authors (O. K.) would like to thank Takashi Yoshida for processing the numerous nuclear data. Anders, E., & Grevesse, N. 1989, Geochim. Cosmochim. Acta, 53, 197 Angulo, C., et al. 1999, Nucl. Phys. A, 656, 3 Audi, G., & Wapstra, A. H. 1995, Nucl. Phys. A, 595, 409 Bildsten, L. 1998, in The Many Faces of Neutron Stars, ed. R. Buccheri, J. van Paradijs, & M. A. Alpar (NATO ASI Ser. C, 515; Dordrecht: Kluwer), , in AIP Conf. Ser. 522, Cosmic Explosions, ed. S. S. Holt & W. W. Zhang (New York: AIP), 359 Brown, E. F., Bildsten, L., & Chang, P. 2002, ApJ, 574, 920 Brown, E. F., Bildsten, L., & Rutledge, R. E. 1998, ApJ, 504, L95 Cumming, A., & Bildsten, L. 2001, ApJ, 559, L127 Ebisuzaki, T., Hanawa, T., & Sugimoto, D. 1983, PASJ, 35, 17 Forstner, O., Herndl, H., Oberhummer, H., Schatz, H., & Brown, B. A. 2001, Phys. Rev. C, 64, 5801 Fujimoto, M. Y., Hanawa, T., Iben, I., Jr., & Richardson, M. B. 1984, ApJ, 278, 813 Fujimoto, M. Y., Hanawa, T., & Miyaji, S. 1981, ApJ, 247, 267 (FHM) Fujimoto, M. Y., Sztajno, M., Lewin, W. H. G., & van Paradijs, J. 1987, ApJ, 319, 902 Fujimoto, S., Arai, K., Matsuba, R., Hashimoto, M., Koike, O., & Mineshige, S. 2001, PASJ, 53, 509 Fuller, G. M., Fowler, W. A., & Newman, M. 1980, ApJS, 42, , ApJS, 48, 279 Fushiki, I., & Lamb, D. Q. 1987, ApJ, 323, L55 Fushiki, I., Taam, R. E., Woosley, S. E., & Lamb, D. Q. 1992, ApJ, 390, 634 Graboske, H. C., DeWitt, H. E., Grossman, A. S., & Cooper, M. S. 1973, ApJ, 181, 457 Hanawa, T., & Fujimoto, M. Y. 1982, PASJ, 34, , PASJ, 36, , PASJ, 38, 13 Hanawa, T., Sugimoto, D., & Hashimoto, H. 1983, PASJ, 35, 491 Hashimoto, M. 1995, Prog. Theor. Phys., 94, 663 Hashimoto, M., & Arai, K. 1985, Phys. Rep. Kumamoto Univ., 7, 47 Hashimoto, M., Hanawa, T., & Sugimoto, D. 1983, PASJ, 35, 1 Horiguchi, T., Tachibana, T., & Katakura, J. 1996, Chart of the Nuclides (Ibaraki: Nucl. Data Center) REFERENCES Iliadis, C., D Auria, J. M., Starrfield, S., Thompson, W. J., & Wiescher, M. 2001, ApJS, 134, 151 Iliadis, C., Endt, P. M., Prantzos, N., & Thompson, W. J. 1999, ApJ, 524, 434 Itoh, N., Totsuji, H., Ichimaru, S., & DeWitt, H. E. 1979, ApJ, 234, 1079 Kaaret, P., Ford, E. C., & Chen, K. 1997, ApJ, 480, L27 Kato, M. 1983, PASJ, 35, , PASJ, 38, 29 Koike, O., Hashimoto, M., Arai, K., & Wanajo, S. 1999, A&A, 342, 464 Kuulkers, E., et al. 2002, A&A, 382, 503 Lewin, W. H. G., van Paradijs, J., & Taam, R. E. 1993, Space Sci. Rev., 62, 223 Migliari, S., et al. 2003, MNRAS, 342, 909 Nozawa, T., Hashimoto, M., Oyamatsu, K., & Eriguchi, Y. 1996, Phys. Rev. D, 53, 1845 Rauscher, T., & Thielemann, F.-K. 2000, At. Data Nucl. Data Tables, 75, , At. Data Nucl. Data Tables, 79, 47 Rayet, M., Arnould, M., Hashimoto, M., Prantzos, N., & Nomoto, K. 1995, A&A, 298, 517 Rembges, F., Freiburghaus, C., Rauscher, T., Thielemann, F.-K., Schatz, H., & Wiescher, M. 1997, ApJ, 484, 412 Schatz, H., Bildsten, L., Cumming, A., & Wiescher, M. 1999, ApJ, 524, 1014 Schatz, H., et al. 1998, Phys. Rep., 294, , Phys. Rev. Lett., 86, 3471 Strohmayer, T., & Bildsten, L. 2004, in Compact Stellar X-Ray Sources, ed. W. H. G. Lewin & M. van der Klis (Cambridge: Cambridge Univ. Press), in press (astro-ph/ ) Strohmayer, T. E., & Brown, E. F. 2002, ApJ, 566, 1045 Taam, R. E., Woosley, S. E., & Lamb, D. Q. 1996, ApJ, 459, 271 Ubertini, P., Bazzano, A., Cocchi, M., Natalucci, L., Heise, J., Muller, J. M., & in t Zand, J. J. M. 1999, ApJ, 514, L27 Wallace, R. K., & Woosley, S. E. 1981, ApJS, 45, 389 Wiescher, M., & Schatz, H. 2000, Prog. Theor. Phys. Suppl., 140, 11 Woosley, S. E., & Weaver, T. A. 1995, ApJS, 101, 181 Zingale, M., et al. 2001, ApJS, 133, 195