{'fraction_non_alphanumeric': 0.05399390137043917, 'fraction_numerical': 0.032648697907539166, 'mean_word_length': 4.021825222212444, 'pattern_counts': {'":': 0, '<': 15, '<?xml version=': 0, '>': 23, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The r-process in the neutrino-driven wind from a black-hole torus

We examine r-process nucleosynthesis in the neutrino-driven wind from the thick accretion disk (or"torus") around a black hole. Such systems are expected as emnants of binary neutron star or neutron star -- black hole mergers. We consider a simplified, analytic, time-dependent evolution model of a 3M_sun central black hole surrounded by a neutrino emitting accretion torus with 90km radius, which serves as basis for computing spherically symmetric neutrino-driven wind solutions. We find that ejecta with modest entropies (~30 per nucleon in units of the Boltzmann constant) and moderate expansion timescales (~100ms) dominate in the mass outflow. The mass-integrated nucleosynthetic abundances are in good agreement with the solar system r-process abundance distribution if a minimal value of the electron fraction at the charged-particle freezeout, Ye,min~0.2, is achieved. In the case of Ye,min~0.3, the production of r-elements beyond A~130 does not reach to the third peak but could be still important for an explanation of the abundance signatures in r-process deficient stars in the early Galaxy. The total mass of the ejected r-process nuclei is estimated to be ~1x10^-3 M_sun. If our model was representative, this demands a Galactic event rate of ~2x10^-4 yr^-1 for black-hole-torus winds from merger remnants to be the dominant source of the r-process elements. Our result thus suggests that black-hole-torus winds from compact binary mergers have the potential to be a major but probably not the dominant production site of r-process elements.


INTRODUCTION
In the past decades, core-collapse supernovae (CC-SNe) have been considered to be the most promising astrophysical site for providing physical conditions suitable for the r(rapid neutron capture)-process (see, e.g., Thielemann et al. 2011, for a recent review). The scenarios include the neutrino-driven wind of CCSNe (Woosley et al. 1994;Takahashi et al. 1994;Qian & Woosley 1996;Otsuki et al. 2000;Wanajo et al. 2001; Thompson et al. 2001;Farouqi et al. 2010), prompt explosions of CCSNe (Sumiyoshi et al. 2001) or of electron-capture supernovae (ECSNe; a subset of CCSNe arising from collapsing oxygen-neon-magnesium cores, Hillebrandt et al. 1984;Wanajo et al. 2003), and the shocked surface layers of the stellar core in collapsing ECSNe (Ning et al. 2007).
However, recent hydrodynamical simulations of CC-SNe (e.g., Buras et al. 2006;) and of ECSNe (Kitaura et al. 2006;Janka et al. 2008) do not support the prompt explosion or the shocked surface layer scenarios. The nucleosynthesis calculations with one-dimensional hydrodynamical results of EC-SNe do not confirm the production of elements beyond A ∼ 90, either (Hoffman et al. 2008;Wanajo et al. 2009). Furthermore, recent long-term simulations of CCSNe and ECSNe show that the neutrino-driven outflows are proton-rich all the way (Fischer et al. 2010;Hüdepohl et al. 2010), which poses a severe difficulty to the scenario that has been favored for a long time, 1 Technische Universität München, Excellence Cluster Universe, Boltzmannstr.
Merger scenarios have been disfavored compared to those of CCSNe partly due to discrepancies between Galactic chemical evolution models and the spectroscopic analyses of Galactic halo stars. The low Galactic event rate (7 × 10 −6 -3 × 10 −4 yr −1 , Belczynski et al. 2002) of mergers and the long lifetimes of binary systems (∼ 1 Myr or 100-1000 Myr, Belczynski et al. 2002) are expected to lead to the delayed appearance of r-elements in the Galactic history with too large star-to-star scattering of their abundances (Qian 2000;Argast et al. 2004). These facts seem to be in conflict with the observational results of Galactic halo stars (Honda et al. 2004;François et al. 2007). Banerjee et al. (2011) suggested that the early enrichment of r-elements might be due to neutrino-induced r-processing in the compact heliumshells of CCSNe of low-metallicity stars, and the contribution from mergers could follow only at a higher metallicity. However, recent studies of Galactic chemical evolution based on the hierarchical clustering of subhalos (Prantzos 2006, also Y. Ishimaru 2011 or with various binary population synthesis models (De Donder & Vanbeveren 2004) do not exclude NS-NS and BH-NS mergers as the dominant astrophysical site of the r-process in the early Galaxy. The reason of observed star-to-star scattering only found in relements (but not in α and iron-group elements) has not been fully understood, either (Ishimaru & Wanajo 1999;Tsujimoto et al. 1999;Argast et al. 2000;Arnone et al. 2005;Karlsson & Gustafsson 2005;Cescutti 2008). For these reasons, NS-NS and BH-NS mergers cannot be excluded as the primary source of r-elements in the Galaxy. More studies of nucleosynthesis are highly desired.
In this paper, we examine r-process nucleosynthesis in BH-torus winds, which are expected to be common to both NS-NS and BH-NS mergers. There exist few previous studies of nucleosynthesis relevant to these conditions (Surman et al. 2008;Metzger et al. 2009;Caballero et al. 2011), which are based on parametrized outflow conditions. While Metzger et al. (2009) discuss viscously driven mass ejecta, Surman et al. (2008) and Caballero et al. (2011) examined some phenomenologically chosen trajectories leading to at least a weak rprocess, but did neither discuss time-dependences nor did provide the integrated abundance distribution or the ejected amount of r-process nuclei. Currently, multidimensional simulations of the wind phase after the formation of a stable accretion torus are not yet available. Hence, we adapt a semi-analytic, spherically symmetric, general relativistic steady-state wind model for nucleosynthesis calculations of BH-torus winds. The model has originally been developed for the studies of the r-process in neutrino-driven winds of CCSNe (Wanajo et al. 2001).
Our paper is organized as follows. In § 2, we describe our model of stationary BH-torus winds and discuss basic outcomes derived from the wind solutions. In § 3, a phenomenological, time-evolutionary model of the neutrino luminosities of the torus is introduced, which is needed to determine the initial composition for nucleosynthesis and to calculate the mass-integrated yields as well as the ejecta mass. The results of nucleosynthesis calculations with the wind solutions are then presented in § 4, along with the mass-integrated abundances ejected from the BH torus. In § 5, we discuss the potential role of BH- -Sketch of our model design for BH-torus winds. A rotating BH with the mass M BH = 3M ⊙ is located in the center of an accretion torus ("neutrino surface") that lies between 2R S and 10R S from the center, where R S is the Schwarzschild radius (= 8.86 km). The wind is assumed to be radial. Thus we replace the complex neutrino-surface geometry by a spherical outflow model considering a neutrinosphere with radius Rν = D around the gravity center (e.g., the asterisks on the dotted circle).
torus winds as the origin of r-elements in the Galaxy. A summary of the paper follows in § 6.

MODELING BH-TORUS WINDS
Our treatment of BH-torus winds is based on the semi-analytic, spherically symmetric, general relativistic model of PNS winds that has been developed for studies of r-process nucleosynthesis by Wanajo et al. (2001). The mass of the central BH is taken to be M BH = 3M ⊙ , which can be considered as representative of NS-NS mergers (or BH-NS mergers with a low-mass BH, Belczynski et al. 2008). As illustrated in Figure 1, the rotating accretion torus around a spinning BH is defined as the "neutrino surface" and is assumed to lie between 2R S (= 17.7 km) and 10R S (= 88.6 km) from the center (where R S = 8.86 km is the Schwarzschild radius) as suggested by detailed hydrodynamical simulations of NS-NS and BH-NS merging (e.g., Janka et al. 1999;Setiawan et al. 2006) In order to connect the aspherical configuration of the BH-torus system to our spherical model for the wind outflows, an arbitrary point on the torus is replaced by a point on a hypothetical neutrinosphere with the same distance from the center, R ν = D (dotted circle in Figure 1). The wind trajectory reaching away from the neutrinosphere, which yields a description of the dynamical and thermodynamical outflow properties, is then derived in the same manner as for spherical PNS winds by solving the general relativistic stationary equations of mass, momentum, and energy conservation (Eqs. (1)-(3) in Wanajo et al. 2001). The Schwarzschild geometry due to the central BH is included here, but the gravitational ef- Lν is assumed to increase linearly from L ν,0 /100 to L ν,0 (denoted in the legend in units of 10 51 erg s −1 ) between 2R S (= 17.7 km) and 5R S (= 44.3 km; dotted line) and adopt a constant value at larger distances D.
fects of the torus and wind masses are very small and thus neglected. Rotation of the mass-losing object is neglected as well. The equation of state for ions (ideal gas) and arbitrarily degenerate, arbitrarily relativistic electrons and positrons is taken from Timmes & Swesty (2000). The average neutrino energies are taken to be 15, 20, and 30 MeV, for electron neutrino, electron antineutrino, and heavy-lepton neutrinos, respectively Setiawan et al. 2006). The neutrino luminosities of all the flavors are assumed to have the same value L ν in our wind model. The electron fraction (number of protons per nucleon), Y e , is assumed to be 0.5 (for a justification, see 4 ). At the inner boundary, the density is taken to be ρ = 10 10 g cm −3 (a different choice has no big impact 5 ), and the temperature, T , is taken such that neutrino heating and cooling balance each other (∼ a few MeV). The velocity (or equivalently, mass ejection rate,Ṁ ) at the neutrinosphere is determined such that the wind becomes supersonic through a sonic point.
As anticipated from Figure 1, the neutrino flux from the outer regions of the torus is shielded in the vicinity of the BH by the presence of the torus itself. In order to mimic this effect in our spherical models, we simply assume that L ν increases linearly from L ν,0 /100 to L ν,0 between 2R S (= 17.7 km) and 5R S (= 44.3 km) and adopts a constant value on the outer side. Figure 2 shows the assumed profiles for selected L ν,0 in units of 10 51 erg s −1 . We define the outflows from R ν < 5R S and R ν > 5R S as the "inner" and "outer" winds, respectively. The calculated radial profiles of velocity u, density ρ, and temperature T for the cases with R ν = 2R S (solid 4 As described in § 3, Lν µ,τ ≪ Lν e < Lν e and Ye ≪ 0.5 are expected in the early phase of BH-torus outflows. However, assuming Lν ≡ 1 2 (Lν e + Lν e ) for all neutrino kinds and Ye = 0.5 is reasonably good for computing the dynamics of BH-torus winds because the wind-driving energy deposition by νe andνe is very similar while that of heavy-lepton ν's is small. Note that these assumptions for Lν and Ye are applied only in this section. 5 The wind profile hardly depends on the boundary density for 10 10 g cm −3 . Tests show that the wind profiles remain essentially unchanged when the inner boundary density is varied between values somewhat above 10 9 g cm −3 (where the density gradient of the wind changes; Fig. 3, left-middle panel) and below the neutrinospheric value (around 10 11 g cm −3 or higher). lines), 5R S (dashed lines), and 10R S (long-dashed lines) are shown in Fig. 3 (left panels) in dependence on the distance r from the center. L ν,0 is taken to be 10 53 erg s −1 . Right panels in Fig. 3 display the temporal evolution of r, ρ, and T of selected ejected mass elements, where the time coordinate t = 0 is set at the inner boundary (ρ = 10 10 g cm −3 ).
The above assumption of the neutrino luminosity profiles ( Fig. 2) implies fundamental differences in the neutrino heating properties between the inner and outer winds. In Figure 4, the neutrino heating and cooling rates,q (in units of erg g −1 s −1 ), for the cases with R ν = 2R S (solid lines), 5R S (dotted lines), and 10R S (dashed lines) are displayed as functions of the radial distance from the center, r. L ν,0 is taken to be 10 53 erg s −1 .
Heating is due to ν e andν e captures on free nucleons (νN ), neutrino scattering by e − and e + (νe), and νν pair annihilation to e − e + pairs (νν). Cooling is caused by e − and e + captures on free nucleons (eN ) and e − e + pair annihilation to νν pairs (ee). All the rates are taken from Otsuki et al. (2000, see their Eqs.(8)-(16)), where the gravitational redshift of neutrino energies and the bending of trajectories due to general relativistic effects are fully taken into account.
As can be seen in Figure 4,q νN dominates the heating rates in the outer winds (dotted and dashed lines). The rateq νe plays only a secondary role, andq νν is negligible. This can also be found in the studies of PNS winds (Qian & Woosley 1996;Otsuki et al. 2000;Thompson et al. 2001). In contrast, in the innermost winds (solid lines),q νν plays the dominant role for heating. This is a consequence of the substantially smaller mass ejection rate,Ṁ ( Fig. 5; defined as that from the corresponding neutrinosphere), driven by the small L ν from the innermost region of the torus (Fig. 2). This leads to very small values of ρ and also of T in the vicinity of the torus (cf. Wanajo 2006b, for a PNS case). For a given radius r, the heating rates scale with L ν , ρ, and T according toq νN ∝ L ν ,q νe ∝ L ν ρ −1 T 4 , anḋ q νν ∝ L ν 2 ρ −1 . As a result, the reduction of ρ and T at small r boostsq νν due to radially increasing L ν (as given in Fig. 2) to much higher values than the other rates (see a similar discussion for anisotropic PNS winds, Wanajo 2006b). Indeed, this has been discussed as a promising mechanism to power short GRB jets presumably arising from NS-NS or BH-NS merging Janka et al. 1999, and references therein).
The greaterq νν in the inner winds leads to substantially faster (terminal) radial velocities, u, higher asymptotic entropies per nucleon, S, and short expansion timescales, τ (defined as the e-folding time of T below 0.5 MeV). As shown in Figure 6, the innermost winds become relativistic, achieving u ∼ (0.3-1) c (where c is the velocity of light). Figures 7 and 8 also show that the innermost winds obtain extremely high S (∼ 1000 in units of the Boltzmann constant, k B ) and short τ (∼ 1 ms). In contrast, the outer winds have modest u (∼ 0.1c), S (∼ a few 10 k B ) and τ (∼ a few 100 ms). For a given D, a larger L ν,0 leads to higher u and shorter τ because of the greater neutrino energy deposition. However, the resulting largerṀ reduces the neutrino heating per mass, leading to slightly smaller S.
Note that the three-dimensional simulations of BH ac- , and temperature (bottom) for the cases with Rν = 2R S (solid lines), 5R S (dashed lines), and 10R S (long-dashed lines) versus distance r from the center. L ν,0 is taken to be 10 53 erg s −1 . Asterisks mark the sonic points. Right: Temporal evolution of radius (top), density (middle), and temperature (bottom) of ejected mass elements for the same cases. Time is set to t = 0 at the inner boundary (ρ = 10 10 g cm −3 ). cretion tori by Setiawan et al. (2006) indicate that the matter in the inner region moves quickly towards the central BH with short accretion timescales of ∼ 1-10 ms (with the radial velocities of ∼ (0.01-0.1)c). Moreover, the lifetime of an accretion torus is estimated to be of the order of ∼ 100 ms. This is substantially shorter than the period of a PNS wind phase (∼ 10 s). It is important, therefore, to test the applicability of our steady-state wind solutions to the BH-torus case. More specifically, the matter should escape from the BH-torus surface region within a sufficiently short period of time (≪ 100 ms).
To test this, we introduce the "injection timescale" τ inj for each wind, during which the matter moves from the inner boundary to the heating region whereq peaks (Fig. 4). Once the matter reaches this maximal-heating region, where the density is already significantly lower, the subsequent matter motion would not be substantially disturbed by the time-evolving torus conditions. We thus regard our steady-state model applicable if τ inj ≪ 100 ms is satisfied. Figure 9 shows the injection distances, defined as d inj = r(q =q max ) − D, as functions of D for selected L ν,0 . The inner (except for innermost) winds have relatively small d inj (∼ 10 km), while the outer winds have greater d inj increasing with D (from 10 km to 30-40 km). Note that d inj is relatively insensitive to L ν,0 as also found in the PNS case (see Fig. 4 in Thompson et al. 2001). Figure  -Neutrino heating and cooling rates,q, for the cases with Rν = 2R S (solid lines), 5R S (dotted lines), and 10R S (dashed lines) as functions of radius from the center, r. L ν,0 is taken to be 10 53 erg s −1 . Heating is due to νe andνe captures on free nucleons (νN ), neutrino scattering by e − and e + (νe), and νν pair annihilation to e − e + pairs (νν). Cooling is due to e − and e + captures on free nucleons (eN ) and e − e + pair annihilation to νν pairs (ee). The net total rates are indicated in black. The vertical dashed line indicates D = 5R S . Note that Lν increases with r as in Fig. 2 for the Rν = 2R S case and that the steep drop ofq νN for this case is due to the decreasing free nucleon abundance by α-particle formation.   (solid lines) as functions of D for selected L ν,0 . We find particularly large τ inj for the innermost winds (see also right panels in Fig. 3). It should be noted, however, that the injection timescales could be overestimated owing to the ambiguity of the boundary density (see footnote 5) and thus of the boundary velocity (cf.,Ṁ = 4πr 2 ρu). To avoid this, the elapsed times from r = D + 1 km to r = D + d inj are also drawn in Fig. 10 (dotted lines). This indicates that the large τ inj for the innermost winds is largely due to the small initial velocities (see Fig. 3, top-left panel) arising from our choice of the boundary density (ρ = 10 10 g cm −3 for all the cases).
Considering the condition τ inj ≪ 100 ms, we find that our steady-state treatment can be (at least marginally) applicable for the winds with L ν,0 > 50 (in units of 10 51 erg s −1 ). Note that, once the matter reaches r = r(q max ), the outflow becomes supersonic within a short period of time. The supersonic outflows are sonically disconnected from the surface and are not affected by the time-evolving BH-torus any more. Dashed lines in Fig. 10 indicate the elapsed times from r = D + 1 km to the sonic points, which are ∼ 2τ inj except for the innermost region. The total ejecta mass might be somewhat overestimated owing to the longer τ inj for lower L ν,0 . As we find in Fig. 5, however,Ṁ for L ν,0 < 50 (in units of 10 51 erg s −1 ) is substantially smaller and its contribution to the total mass will be sub-dominant. The ejecta mass from the inner region might be also overestimated because of the fast accretion timescales estimated from hydrodynamical studies (∼ 1-10 ms, Setiawan et al. 2006). As we will see below, however, the ejecta from the outer region dominate the total amount (∼ 90%; § 3). It is also important to note, taking our injection timescale condition seriously, that the outer-torus region beyond ∼ 100 km is not expected to contribute significantly to the total ejecta mass because of long injection timescales.
It should be noted that the work by Setiawan et al. (2006) was based on a neutrino trapping/leakage scheme and employed a simple α-model for the gas viscosity. The dynamics of outflows from BH tori will be highly dependent on neutrino transport as well as magnetic fields, which are to be explored in future studies of hyperaccreting BHs. This did not allow Setiawan et al. (2006) to describe mass loss from the tori by energy transfer and deposition associated with neutrino transport, nor did their models adequately account for magnetically-driven mass loss. Outflows and winds were previously discussed by Pruet et al. (2006);Metzger et al. (2008aMetzger et al. ( ,b, 2009Surman et al. (2008); Caballero et al. (2011);Rosswog (2011), although all of those works did not employ selfconsistent hydrodynamical models of this phenomenon.

TIME EVOLUTION OF THE BH-TORUS
3.1. Why is the BH-torus wind neutron-rich? As mentioned in § 1, recent hydrodynamical simulations of CCSNe predict that the PNS wind is protonrich (Fischer et al. 2010;Hüdepohl et al. 2010). The BHtorus wind from "collapsars" (MacFadyen & Woosley 1999) resulting from collapsing rapidly rotating stellar cores is also suggested to be proton-rich (e.g., Kizivat et al. 2010). The BH-torus from NS-NS and BH-NS mergers, originating from decompressed, very neutron-rich NS matter, is different from the collapsar case. The initially neutron-rich torus leads to more production ofν e by e + captures on neutrons, than ν e production by e − captures on protons, and thus one obtains Lν e > L νe . This allows the BHtorus wind (outside of the torus at lower densities) to remain neutron-rich owing to moreν e captures on free protons,ν than ν e captures on free neutrons, However, despite the fact that the neutrinospheric layers in a PNS are also neutron-rich, the simulations cited above show that PNSs produce essentially equal luminosities of ν e andν e , resulting in the proton-richness of the ejecta because of the neutron-proton mass difference, which reducesν e captures compared to ν e captures. So what exactly is the difference between the PNS and merger BH-torus cases? This can be explained as follows. For PNSs, the main point is the fact that the PNS is in a phase of neutronization. It evolves from more protonrich (symmetric) initial conditions to more neutron-rich final conditions. In course of this transition, its core radiates more ν e thanν e (see Eqs. (1) and (2)). On their radial way out of the PNS through highly neutrinoopaque layers this initial ν e flux is converted into equal ν e andν e fluxes by multiple absorption and reemission processes (and µ and τ fluxes of similar size). The escaping ν e andν e luminosities are roughly equal because the neutrinospheric layers with their typical densities (∼ 10 11 g cm −3 initially and up to ∼ 10 13 g cm −3 at very late times) reach their so-called "β-equilibrium" state (defined by equal number production of ν e andν e and Y e = const. in time) within some tens of milliseconds up to about ∼ 100 ms. This is much shorter than the PNS cooling timescale of seconds. On the long PNS evolution timescale the emission is therefore mostly characterized by essentially equal L νe and Lν e (with a small difference making sure that there is a net ν e -flux out of the still neutronizing high-density PNS core).
In contrast, the hot post-merger torus is composed of decompressed neutron star matter. It starts out from a very neutron rich initial state and (on its way to a new βequilibrium condition) protonizes gradually (Eq. (1)) because of overall lower densities than it had initially. Since the density and temperature of the torus (on average some 10 11 -10 12 g cm −3 and about 3-10 MeV) are very similar to the neutrinospheric conditions of a PNS, the protonization of the torus proceeds on the same timescale as the neutronization of the neutrinospheric region in the PNS case. As mentioned above, this typical timescale is tens of milliseconds at the given densities, presumably up to ∼ 100 ms. This is exactly a major fraction of the accretion timescale of most of the torus mass into the BH (and is the timescale for the protonization assumed in our simple model described in § 3.2). Because of the protonization, Lν e is higher than L νe , in inverse analogy to the fact that L νe is higher in the case of a collapsing stellar core during the early times when the postshock layer is still on its way to reach the β-equilibrium condition, starting out from a nearly symmetric initial state. For this reason, the neutrino-driven ejecta from the BHtorus are expected to be neutron-rich (see Eqs. (3) and (5)) for a significant duration of the wind phase.
Note that a direct consequence of the fact that the torus conditions in density and temperature are roughly similar to the neutrinospheric conditions in a PNS is the finding that the µ and τ neutrino luminosities are 5-10 times lower than the ν e andν e luminosities in the case of the tori (see Janka et al. 1999;. In a PNS the µ and τ neutrinos are produced at much higher densities than ν e andν e . Such densities are not reached by the accretion tori.

Time Evolution of Neutrino Luminosities
In order to calculate the nucleosynthesis for each wind trajectory, the Y e value of the torus, which defines the initial composition, should be specified. In addition, the ejecta mass for each wind trajectory should be determined to calculate the mass-integrated nucleosynthetic abundances. For this purpose, we assume that the time evolution of L νe and Lν e can be written as where L ν,i = 10 53 erg s −1 is chosen as a representative value of the initial neutrino luminosity at t = t i = 10 ms (e.g., Janka et al. 1999;Setiawan et al. 2006). The power exponent β is taken to be 1.3 (Metzger et al. 2008b;Lee et al. 2009). The value of α is uncertain and for simplicity assumed to be a modest number, α = 1, because Lν e > L νe is expected during a significant time of the torus evolution ( § 3.1). These relations give Lν e /L νe = 3 at t = t i , being in agreement with hydrodynamical results Setiawan et al. 2006), and Lν e = L νe for t ≫ t i (Metzger et al. 2008b). Eqs. (5) and (6) yield an approximative time evolution of (the torus-averaged value of) Y e in the protonizing torus ( § 3.1; Eqs. (1) and (2)), where N b and ǫ ν are the total baryon number of the torus and the mean neutrino energy (∼ 18 MeV, Janka et al. 1999;Setiawan et al. 2006) averaged for ν e andν e . This can be integrated to yield where Y e,i = 0.05 is assumed for the initial electron fraction (e.g., . Further assuming that Y e asymptotes to Y e,f = 0.50 for t ≫ t i (e.g., Metzger et al. 2008b), we get This simplifies Eq. (8) to become Eq. (10) provides Y e of the torus at a given evolutionary time, t. Note that the value of N b (not made use of in this study) can be estimated from Eq. (9) and leads to the approximate torus mass, which is consistent with hydrodynamical results of compact binary mergers (e.g., Janka et al. 1999;).

Connecting Steady Wind and BH-Torus Evolution Models
Our description of BH-torus winds in § 2 is based on steady-state solutions for constant L ν,0 and Y e . In order to connect the computed wind trajectories to the timeevolving torus model described in § 3.2, we assume This is a reasonable assumption because the wind from the outer torus is driven predominantly by ν e andν e captures on free nucleons (Fig. 4), whose heating effect is nearly symmetric between ν e andν e . This is not true for the innermost torus, which however does not significantly contribute to the mass-integrated nucleosynthetic abundances as we will see later. Eq. (12) gives, with Eqs. (5), (6) and (10), L νe , Lν e , t, ∆t, and Y e (as the initial value for nucleosynthesis) for a given L ν,0 in our steady-state model of BH-torus winds. These values are listed in Table 1 for L ν,0 = 200, 190, · · · , 10 (in units of 10 51 erg s −1 ). Here, ∆t are the time intervals ∆t j = t j+1 − t j between the j-th and (j + 1)-th wind trajectories. For the 20th wind trajectory (last line in Table 1), ∆t is determined such that the total evolutionary time becomes t = 100 ms. The mass ejection rate for the j-th value of L ν,0 from the torus region D i ≤ D ≤ D i+1 is calculated as where the torus is imagined to be a disk, ejecting matter perpendicularly toward the north and south directions.
Here,Ṁ i,j is the mass ejection rate from the corresponding neutrinosphere with R ν = D i (Fig. 5) for the j-th value of L ν,0 , and the mass flux density (Ṁ i,j /4πD 2 i ) of the spherical wind calculation is weighted by the effective torus surface element in Eq. (13). The mass ejection rate during time interval ∆t j from the entire torus with L ν,0 = (L ν,0 ) j is then given aṡ Eq. (13) with the ∆t from Table 1 gives the ejecta mass for the wind at D = D i and with L ν,0 = (L ν,0 ) j . From Eq. (15) the total ejecta mass in the BH-torus outflow during the first 100 ms is calculated as where the inner region (D ≤ 5R S ) contributes only ∼ 10% (= 2.40 × 10 −4 M ⊙ ). The total ejecta mass in Eq. (16) is only a few percent of our assumed (initial) BH-torus mass (∼ 0.1M ⊙ ; Eq. (11)). This may justify our assumption of steady-state neutrino-driven outflows, provided that the lifetime of the BH-torus is > 100 ms, which can be expected to be the case, considering typical mass-accretion rates of BH-tori in hydrodynamical models (see, e.g., Fig. 4 in Setiawan et al. 2006). Note that the initial high mass-loss phase (withṀ 0.1M ⊙ s −1 ; Fig. 5) for the outer winds lasts for only a short period of time (a few ms; Table 1).
From Eq. (15) and with the numbers of Table 1, the ejecta mass ∆m ej (normalized by m ej ) as a function of u can be constructed in a binned form as histogram (Fig. 11). We find that the sub-relativistic winds with u ∼ 0.1c dominate the ejecta. The relativistic ejecta from  the innermost torus are essentially unimportant. While the entropies are high, S ∼ 100-1000 k B , in the innermost winds (Fig. 7), the ejecta with modest entropies, S ∼ 30k B , dominate (Fig. 12). Moreover, the winds with modest τ ∼ 100 ms dominate, and those with short τ ∼ 1-10 ms make a very small contribution (Fig. 13).
Note that L ν,i as well as β in Eqs. (5) and (6) would strongly depend on the mass of the torus as well as the viscous parameter ( Fig. 10 in Setiawan et al. 2006), whose values are highly uncertain. A higher value of L ν,i will increase the ejecta mass m ej in Eq. (16) as anticipated from Fig. 5. A smaller β increases the ejecta mass as well (e.g., by about a factor of two when β = 0.7, roughly half of the original value, is chosen) because of a higher L ν,0 for a longer time (leading to a higher mass ejection rate; Fig. 5). However, the nucleosynthetic abundance distributions would not be significantly changed. This is due to the fact that Eq. (10) can be written as Y e (t) = Y e,f − (Y e,f − Y e,i )L νe /L ν,i , i.e., as a function of L νe only (for α = 1), being independent of β. Because the change of L νe is similar to that of L ν,0 (Table 1), the Y e value at a given L ν,0 is quite similar, e.g., ∆Y e < 0.02 for β = 0.7 is associated with the somewhat shallower decline of the neutrino luminosities. Accordingly, the integrated abundance distribution will be mostly independent of β.

NUCLEOSYNTHESIS IN BH-TORUS WINDS
The nucleosynthetic yields in each wind trajectory are computed by solving an extensive nuclear reaction network code. The network consists of 6300 species between the proton and neutron drip lines, all the way from single neutrons and protons up to the Z = 110 isotopes (for more detail, see Wanajo et al. 2011b). Neutrino interactions on free nucleons and α-particles are also taken into account, but fission reactions are not included. As will be described in § 4.3, the effect of (neutron-induced) fission during the r-process is expected to be of minor importance in our explored cases. Our fiducial case ("case 1") is defined by initiating each nucleosynthesis calculation when the temperature decreases to T 9 = 10 (where T 9 is the temperature in units of 10 9 K), at which nuclear statistical equilibrium (NSE) is immediately recovered from arbitrary initial compositions. The initial composition we adopt is Y e and 1 − Y e for free protons and free neutrons, respectively, using the Y e value of the torus for a given L ν,0 (see Table 1). The calculations are carried out for wind solutions with L ν,0 = 10-200 in steps of 10 (in units of 10 51 erg s −1 ; Table 1) and D = (2-10) R S = 17.7-88.6 km with intervals of 0.1R S = 0.886 km, i.e., for 1620 trajectories in total. Figure 14 shows the variation of Y e and of the mass fraction of α-particles, X α , as functions of (decreasing) temperature for L ν,0 = 2 × 10 53 erg s −1 and D = 5R S (case 1; solid lines). This wind trajectory has the lowest initial (torus) Y e of 0.05 (indicated by a horizontal solid line) of our considered models. As can be seen in Fig. 14, Y e increases during the early wind expansion phase from its initial value (at T 9 = 10; vertical solid line) to Y e,2.5 (at T 9 = 2.5, considered as corresponding to the onset of the r-process phase; vertical dashed line). This is caused by several effects. The first effect is that, as soon as the nucleosynthesis calculation starts, Y e relaxes toward the equilibrium value, Y e,a (e.g., Eq. (77) in Qian & Woosley 1996), due to ν e andν e captures on free nucleons (Eqs. (3) and (4)). The asymptotic value for this wind trajectory is Y e,a = 0.21. The second effect is associated with the continuous α-particle formation (peaking at T 9 ≈ 7 in Fig. 14) from recombination of free protons and free neutrons produced by neutrino capture reactions (Eqs. (3) and (4)). This drives Y e toward 0.5 ("α-effect"; Meyer et al. 1998a). As a result of -Evolution of the electron fraction (Ye; red) and of the mass fraction of α-particles (Xα; blue) as functions of (decreasing) temperature for case 1 (solid lines; only for T 9 < 10) and case 2 (dotted lines). L ν,0 = 2 × 10 53 erg s −1 and D = 5R S are taken for both cases. For case 2, three cases of the Ye evolution are shown (for T 9 > 10), in which all four reactions (Eqs. (1)-(4)), only νe andνe captures on free nucleons (Eqs. (3) and (4)), and only e − and e + captures on free nucleons (Eqs. (1) and (2)) are included (indicated by "all", "ν", and "e", respectively). The horizontal and vertical solid lines indicate, respectively, the initial (torus) Ye (= 0.05) and T 9 = 10 (at which the computation is switched to making use of the full reaction network). The vertical dashed line at T 9 = 2.5 indicates where r-processing begins.

Electron Fractions
these combined effects, Y e,2.5 (= 0.18) is sizably higher than the initial value of 0.05.
It is important to note that ν e andν e captures on free nucleons (Eqs. (3) and (4)) and also e − and e + captures on free nucleons (Eqs. (1) and (2)) will also operate before the temperature decreases to T 9 = 10. We therefore consider another case ("case 2"), in which each nucleosynthesis calculation is started from closer to the neutrinosphere (at R ν = D = 5R S and T 9 = 60 in this case) including the four reactions of Eqs. (1)-(4) (labelled "all" in Fig. 14; dotted lines). The computation is then switched to making use of the full reaction network at T 9 = 10. Fig. 14 also shows the results when including only ν e andν e captures ("ν"; Eqs. (3) and (4)) and e − and e + captures ("e"; Eqs. (1) and (2)) for T 9 > 10. We find that the Y e immediately jumps to ∼ 0.15 mostly by neutrino captures, continues to gradually increase to 0.26 by competition of all four reactions of Eqs. (1)-(4), and decreases slightly toward Y e,a (but still Y e = 0.23 > Y e,a = 0.21 at T 9 = 10). The increase of Y e for T 9 < 10 is solely due to the α-effect. As a result, Y e = 0.29 at T 9 = 2.5, which is ∼ 0.1 higher than that in our fiducial case 1. Figure 15 shows the Y e values when the temperature has decreased to T 9 = 2.5, Y e,2.5 , over the entire D range for selected L ν,0 cases (denoted in the legend). The shifts of Y e from the initial values (see Table 1) are particularly prominent in the inner winds, where the matter experiences a strong α-rich freezeout owing to the high S and short τ (Figs. 7 and 8; cf. Fig. 17). As described above, the Y e,2.5 values are significantly different between cases 1 and 2, in particular for the high L ν,0 (i.e., low Y e ) winds.
We emphasize, however, that this is based on our simplified wind models and the exact Y e evolution for T 9 > 10 would be highly dependent on the detailed density structure as well as the highly uncertain neutrino field in the vicinity of the torus, where only transport calculations can give an appropriate description of the energy and direction distribution of the neutrinos. We therefore consider the Y e,2.5 differences between cases 1 and 2 as possible uncertainties of Y e in this study. As can be seen in Fig. 15, the range of Y e,2.5 for case 2 is well bracketed by that for case 1 between L ν,0 = 10 and 100 (in units of 10 51 erg s −1 ). For this reason, we take case 1 as our fiducial model (and as an optimum case for strong r-processing) in the following sections.

Neutron-to-seed Ratios
The neutron-to-seed ratios at the onset of the r-process (defined at T 9 = 2.5), (Y n /Y h ) 2.5 , are shown in Figure 16. We find sizable (Y n /Y h ) 2.5 > 1000 (up to ∼ 10 8 ; not displayed in Fig. 16) in the innermost region. Except for the inner winds, however, (Y n /Y h ) 2.5 is nearly constant with D for L ν,0 ≥ 100 (in units of 10 51 erg s −1 ), being (Y n /Y h ) 2.5 ∼ 120 at most. This is large enough to expect the formation of the third r-process peak (A = 195) and beyond, but not fission cycling. A high neutron excess (Y e,2.5 0.2) is needed for a strong r-process at the modest S (< 100k B ; Figure 7) and τ (> 10 ms; Figure 8 Figure 17 shows the mass fractions of α-particles in the final nucleosynthetic abundances (solid lines). In the inner winds, the α concentration is significant owing to the high S and short τ . The r-process thus starts from the seed abundances formed in neutron-rich quasi nuclear equilibrium (QSE; A ∼ 90, Meyer et al. 1998b). Note that the α-abundances do not change after chargedparticle freezeout (T 9 ∼ 4; Fig. 14). In the innermost winds, the extremely high S and short τ lead to neutronrich freezeout. This is the reason why Y e,2.5 decreases as D approaches the inner tip of the torus (Fig. 15). The low mass fraction of α-particles in the outer winds indicates that the r-process starts from seed abundances formed in conditions close to neutron-rich NSE (A ∼ 80, Hartmann et al. 1985;Wanajo et al. 2011a). The nucleosynthetic abundances are thus dominated by heavy elements, not by α-particles, in the outer winds. Figure 18 shows the atomic mass numbers of the final products, A h , mass-averaged over heavy nuclei with Z > 2. We find that A h is a flat function of D in the outer winds for all L ν,0 , similar to (Y n /Y h ) 2.5 in Fig. 16. This suggests that in the outer winds the torus-Y e (assumed to be constant over the entire range of D) pre- dominantly determines A h , rather than the modest S or τ , which both exhibit gradients with distance D (Figs. 7  and 8). In the innermost winds (D < 3R S ), however, the high S and short τ play crucial roles. Except for the innermost winds, A h ranges from 60 to 220, encompassing nuclei from the trans-iron to the actinide region, but well below the neutron-induced fissioning point (A ∼ 290, e.g., Fig. 3 in Goriely & Clerbaux 1999). This is a consequence of Y e,2.5 ≥ 0.17 in the outer winds (Fig. 15), which is still too high to expect fission cycling at the modest values of S and τ .

Mass-integrated Abundances
In order to evaluate the net abundances for each L ν,0 , the nucleosynthetic yields are mass-integrated over the entire torus range between D = 2R S and 10R S . For the j-th L ν,0 , the abundance of nuclide A is calculated with Eqs. (13) and (14) as Figure 19 shows the mass-integrated nucleosynthetic abundances for selected L ν,0 cases. As noted in § 4.3, the effect of neutron-induced fission is expected to be negligible. In order to roughly include the effect of spontaneous and β-delayed fissions, we simply added the abundances with A ≥ 256 (all expected to decay by fission) such as  The calculated abundances for case 1 are in good agreement with the solar r-process distribution (circles; scaled to match the 3rd and 2nd peak heights for case 1 and case 2, respectively). The contributions from the inner (D < 5R S ; green lines) as well as innermost (D < 3R S ; light-blue lines) winds are sub-dominant for case 1, but important for case 2.
Actual abundances will depend on the (highly uncertain) decay chains and the abundance distribution of fission fragments. The sharp abundance peak at A ∼ 140 for L ν,0 = 2 × 10 53 erg s −1 (case 1; solid red line in Fig. 19) is formed by fission fragments. The effect of fission for the other cases are however unimportant.
The time-integrated yield of nuclei of atomic mass number A for the entire torus region is calculated as making use of Eqs. (15) and (16). In Fig. 20, the resulting yields are compared with the solar system rprocess abundances (circles; vertically shifted to match the height of the third and second r-process peaks for cases 1 and 2, respectively). For case 1, we find good agreement of the calculated abundances with the solar r-process distribution over the entire range of the rprocess, A = 90 − 210. No overproduction of the N = 50 (A ≈ 90) nuclei can be seen, which were problematic in the wind from PNSs born in SNe (Woosley et al. 1994;Wanajo et al. 2001). This can be understood from the fact that the r-processing in the outer winds of BH-tori starts from NSE (or α-deficient QSE) seeds (A ∼ 80), rather than from (α-rich) QSE seeds (A ∼ 90). For case 2, however, the production of heavy r-process el-ements beyond A = 130 drops steeply. Figure 20 also shows the time-integrated abundances from the inner (D ≤ 5R S ) and innermost (D ≤ 3R S ) torus. For case 1, we find similar abundance curves for both regions, but with sizably smaller amounts than the total production (10 and 100 times smaller, respectively). This indicates that the low mass ejection rates (Fig. 5) from the inner and innermost torus diminish the role of their nucleosynthetic contributions, regardless of their high S and short τ . For case 2, on the other hand, the contributions from inner and innermost regions dominate the abundances heavier than A ∼ 140.
Note that, for case 1, the deficient Pb (A = 206-208) and Bi (A = 209) abundances relative to the other relements for D < 5R S (Fig. 20) are due to a fundamental difference in r-processing between the inner and outer winds. The modest τ of an outer wind trajectory leads to an r-process at high temperature (T 9 ∼ 1), in which case the nucleosynthetic flow approximately follows the path determined by the (n, γ)-(γ, n) equilibrium. In the inner region, however, a shorter τ results in an rprocess at substantially lower temperature (T 9 < 0.5), in which the flow is determined by the competition between (n, γ) reactions and β-decays ("cold r-process", Wanajo 2007; also Blake & Schramm 1976;Panov & Janka 2009). Wanajo (2007) shows that this non-equilibrium process leads to underabundant Pb.
The ejected mass of r-processed nuclei, defined as those with A ≥ 100, is derived as showing a dominance of r-processed material (66% and 59% for cases 1 and 2, respectively) in the total ejecta (Eq. (16)). This is a consequence of the fact that the rprocess starts from the NSE (or α-deficient QSE) seeds in most cases ( § 4.3). The mass of fission products in the ejecta can be calculated as well, accounting for only 3% and 0.01% of the total r-process material for cases 1 and 2, respectively. The mass of Eu in the ejecta, the element taken as representative of r-elements in Galactic chemical evolution studies (e.g., Ishimaru & Wanajo 1999), is estimated to be m Eu,ej = m ej A=151,153 AY A = 6.77 × 10 −6 M ⊙ (case 1), 3.98 × 10 −7 M ⊙ (case 2). Figure 21 shows the ejecta-mass histogram as a function of Y e,2.5 for case 1 (solid lines) and case 2 (dotted lines). The color coding in Fig. 21 discriminates all abundances, those with all yields having A > 100 (all r-abundances), and those with all yields having A > 180 (the third peak abundances and heavier). We find that, for case 1, all Y e,2.5 values contribute with similar weights to the total abundances. For case 2, the values of Y e,2.5 ≈ 0.3-0.4 dominate the total ejecta. Wind trajectories with low Y e are, however, crucial for the production of the r-nuclei with A > 100 (Y e,2.5 0.35), and in particular with A > 180 (Y e,2.5 0.20). This -Histogram of the ejecta-mass distribution ∆m ej (normalized by the total ejecta mass, m ej ) for case 1 (solid lines) and for case 2 (dotted lines) as functions of Y e,2.5 . Different colors correspond to all ejecta and those with all yields having A > 100 and those with all yields having A > 180, respectively (slightly shifted in the horizontal direction for visibility).
is due to the presence of modest S and τ in the ejecta (Figs. 12 and 13), which demands relatively low Y e values for strong r-processing. Figure 21 also shows that the later wind outflow with L ν < 10 52 erg s −1 (t 100 ms and Y e ∼ 0.5), not included in our calculations, would make no relevant contribution to the r-abundances.

BH-TORUS WINDS AS THE ORIGIN OF r-ELEMENTS
In § 4, we found that our fiducial model (case 1) of BH-torus winds leads to the full r-process with the solarlike r-pattern for A = 90-210. The ejecta mass of the r-processed matter (A ≥ 100), m r,ej = 1.30 × 10 −3 M ⊙ (Eq. (20); case 1), is more than a factor of 10 larger than that needed for CCSNe to be the dominant source of the r-process elements in the Galaxy (Mathews & Cowan 1990). More specifically, the ejected mass of Eu (a nearly pure r-process element), m Eu,ej = 6.77 × 10 −6 M ⊙ (Eq. (22); case 1), is a factor of 60 greater than that needed for CCSNe to be the major source of the Galactic Eu . Provided that our fiducial model (case 1) with M BH = 3M ⊙ and a torus mass of M torus ∼ 0.1M ⊙ (Eq. (11)) is representative of NS-NS (or BH-NS) mergers, the canonical CCSN event rate of ∼ 10 −2 yr −1 implies that a time-averaged Galactic merger rate of ∼ 2×10 −4 yr −1 would be needed. This is consistent with the upper bound of a merger event rate between 7 × 10 −6 and 3 × 10 −4 yr −1 derived by population synthesis methods for NS-NS and BH-NS binaries (at solar-metallicity conditions, Belczynski et al. 2002) and of statistical results based on binary pulsar surveys (2×10 −5 -3×10 −4 yr −1 , Kalogera et al. 2004). For case 2 (with inclusion of reactions of Eqs. (1)-(4) at T 9 > 10), we find inefficient production of r-elements beyond A ∼ 130. However, a similar constraint to the Galactic merger rate may be applied for this case, owing to the similar r-processed ejecta mass of m r,ej = 1.16 × 10 −3 M ⊙ (Eq. (20); case 2).
It is important to note that the actual ejecta mass of r-abundances could be higher than that we obtained on the basis of our simplified BH-torus wind model. The total ejecta mass, m ej ≈ 2 × 10 −3 M ⊙ (Eq. (16)), can be even 10 times smaller than that expected from hydrodynamical simulations of compact object mergers  Roederer et al. (2010) and the Ge value is from Cowan et al. (2005). For both stars, the abundances are vertically shifted to match the calculated Eu abundances.
(but not of the subsequent BH-torus accretion with its neutrino-driven outflow; Janka et al. 1999). There will be additional contributions from the early mass loss due to the tidal ejection of neutron-rich matter during the merger event (Freiburghaus et al. 1999;Goriely et al. 2005) and neutrino-driven outflows from HMNSs (for the NS-NS case, Dessart et al. 2009) or/and magnetically driven outflows from HMNSs (Rezzolla et al. 2011;Shibata et al. 2011). Moreover, the centrifugal force due to rapid rotation, which we do not take into account, effectively reduces the gravity from the central BH. This could lead to larger mass ejection rates than those obtained here (see Otsuki et al. 2000;Wanajo et al. 2001, for PNS winds). Magnetic fields, which are not considered in our models either, could play a significant role for the mass ejection, producing viscously driven or MHDdriven outflows in addition to the considered neutrinodriven ejecta (Metzger et al. 2009). It should also be noted that the production of heavy r-process elements beyond A ∼ 130 is marginal if we consider our case 2 to be representative of NS-NS and BH-NS mergers. Case 2 takes into account ν e ,ν e , e − , and e + captures on free nucleons also for T 9 > 10, resulting in significantly higher minimal Y e,2.5 (∼ 0.3) than that in case 1 (∼ 0.2). However, the detailed evolution of Y e will be highly dependent on the density structure and the uncertain neutrino field in the vicinity of the BH-torus, while we consider a simplified spherical wind model and do not have neutrino transport results for BH-tori at bound. Effects of magnetic fields noted above would also modify the evolution of Y e . General relativistic effects (which we consider only in the framework of spherically symmetric configurations) can also be important for determining the exact Y e evolution (Caballero et al. 2011). For all these reasons, the nucleosynthetic outcome of this study should be regarded only as suggestive. Future detailed multidimensional simulations of NS-NS (or BH-NS) merging, including the later BH-torus wind phase, are required for more quantitative results.
Nevertheless, the good agreement of our nucleosynthesis result for case 1 with the solar r-pattern is en-couraging. Such an agreement is also important when one considers compact binary mergers as the origin of early Galactic r-elements in metal-deficient stars with their uniform (solar-like) r-patterns (Sneden et al. 2008). In Figure 22, the nucleosynthetic abundances for case 1 (solid line; as a function of atomic number) are compared with an r-process enhanced star CS 22892-052 with [Fe/H] ≈ −3.1 (filled circles; scaled to match the calculated Eu abundance, Sneden et al. 2003). We find quite a good agreement of our result with the stellar abundances distribution of CS 22892-052. The good agreement of model and observed abundances is obtained if our BH-torus wind model represents typical NS-NS (or BH-NS) merger events, if the minimal Y e,2.5 (at the onset of r-processing) is as low as in case 1 ( 0.2), and if the evolution of L νe and Lν e evolutions in Eqs. (5) and (6) is appropriate (e.g., α in Eq. (6) is not very different from unity and β = 1.3 and the factor of 2 within the bracket of Eq. (6) are good choices). These should be tested by future long-time hydrodynamical simulations of NS-NS and BH-NS merging events and of the evolution of their remnants. Note that, even if the production of r-elements heavier than A ∼ 130 is marginal as found in case 2, our model could be a possible explanation for the abundance distribution found in an rprocess deficient star HD 122563 with [Fe/H] ≈ −2.7 (open circles; scaled to match the calculated Eu abundance, Honda et al. 2006). This suggests that NS-NS and BH-NS mergers could at least be the origin of some trans-iron elements up to Z ∼ 50 (A ∼ 120).
For an observational support, future modeling of the Galactic r-element evolution that is not in conflict with spectroscopic results of metal-deficient stars will be important (e.g. Prantzos 2006). In addition, radioactive decays of r-processed ejecta can lead to faint SN-like transients (Li & Paczyński 1998;Metzger et al. 2010;Roberts et al. 2011). Future detections of such signals, possibly as accompanying events of short GRBs, will be a direct support for the occurrence of r-processing in NS-NS and BH-NS mergers. According to the estimates by Metzger et al. (2010), a peak luminosity of ∼ 3 × 10 41 erg s −1 could be expected from the BH-wind ejecta with m r,ej ∼ 1 × 10 −3 M ⊙ (Roberts et al. (2011), however, obtained only slightly higher R-band luminosities for considerably higher ejecta masses). It will be difficult to distinguish the wind component from the early, tidally ejected counterpart. Both could contain similar amounts of radioactive matter. However, the velocities as well as the geometry of the r-processed ejecta might be distinctive between them. Our result implies that the r-processed BH-wind ejecta reach out widely from the torus with velocities of ∼ 0.1c (except for the innermost region, Figs. 6 and 11). In contrast, tidal ejecta come from the tips of (one or two) spiral arms, and are expected to achieve larger outgoing velocities ( 0.2c, Roberts et al. 2011). These could lead to some different features in the light curves (e.g., line profiles or the time of the peak), potentially distinguishable by observations.

SUMMARY
We investigated r-process nucleosynthesis in the neutrino-driven outflows from a BH accretion torus (BH-torus winds) formed in NS-NS (or BH-NS) mergers. Different from previous works (Surman et al. 2008;Metzger et al. 2010) we investigated a time-and spacedependent semi-analytic model setup. The BH-torus wind models were constructed by considering spherically symmetric, general relativistic neutrino-driven wind solutions (Wanajo et al. 2001) with the gravitational potential of a central BH of M BH = 3M ⊙ . The BH accretion torus (around a rotating BH) was assumed to lie between D = 2R S and 10R S (R S = 8.86 km) from the center. Each wind trajectory reaching away from the torus was obtained by assuming a hypothetical neutrinosphere in the spherical wind model with the radius R ν = D.
In the innermost wind region (D ∼ 2R S ), the efficient energy deposition due to νν pair annihilation to e − e + pairs leads to very high entropies (S 100-1000k B per nucleon) and short expansion timescales (τ 1-10 ms). This allows for a strong r-process regardless of Y e (even with Y e > 0.5 when τ < 1 ms, Meyer 2002) or no production of heavy elements (in the relativistic winds with S ≫ 1000k B , Lemoine 2002;Beloborodov 2003). However, the small mass ejection from the innermost torus makes this contribution to the total nucleosynthetic abundances essentially negligible. In the outer wind regions (D > 5R S ), on the other hand, the dominant heating is due to ν e andν e captures on free nucleons as in the case of PNS winds, resulting in modest entropies (S ∼ 30k B ) and expansion timescales (τ ∼ 100 ms). Low Y e values ( 0.2 at T 9 = 2.5) are thus essential for a strong r-process. The contribution from outer wind regions dominates the total nucleosynthetic abundances because of their greater mass ejection rates. Note that our BH-torus model does not predict a νpprocess (Fröhlich et al. 2006;Pruet et al. 2006;Wanajo 2006a) as suggested in the case of (proton-rich) collapsar disk winds (Kizivat et al. 2010).
The mass-integrated nucleosynthetic abundances, obtained with a phenomenological time evolution of neutrino luminosities, are in good agreement with the solar r-pattern over the entire r-process range of A = 90−210, when the neutrino-matter interactions are considered only for T 9 < 10 (case 1). This can be taken as the optimal case for strong r-processing in our models. However, when ν e ,ν e , e − , and e + captures on free nucleons are taken into account also for T 9 > 10 (case 2), the production of heavy r-elements beyond A ∼ 130 drops off steeply. The total ejecta mass of the BHtorus wind of our simplified model is calculated to be m ej ≈ 2 × 10 −3 M ⊙ , in which the r-processed matter dominates (m r,ej 1 × 10 −3 M ⊙ ). Provided that our BH-torus wind model is representative, NS-NS and BH-NS mergers can produce all (or at least a significant part of) the Galactic r-abundances if the event rate (averaged over the Galactic history) was ∼ 2 × 10 −4 yr −1 , which is consistent with the upper bound of present (solar-metallicity) population synthesis results (7×10 −6 -3 × 10 −4 yr −1 , Belczynski et al. 2002) and of statistical results based on binary pulsar surveys (2 × 10 −5 -3 × 10 −4 yr −1 , Kalogera et al. 2004). This implies that BH-torus winds from NS-NS and/or BH-NS mergers could be major (or partial) production sites of the rprocess elements in the Galaxy. It should be noted that the actual ejecta mass of r-abundances could be substantially higher than the estimate based on our BHtorus wind model, in which we do not consider any other effects than neutrino-driven outflows, namely, centrifugal force, magnetic fields, or tidally ejected neutron-rich matter from NS disruption.
Obviously, more elaborate hydrodynamical studies of the considered astrophysical site are needed to obtain information of the neutrino field that controls the dynamics as well as the neutron-richness in the BH-torus winds. Note that NS-NS and BH-NS mergers are also suggested to be the sources of short GRBs. An interesting possibility in this context is that the radioactive neutron-rich nuclei ejected during and after mergers might lead to detectable transient electromagnetic signals (Li & Paczyński 1998;Kulkarni 2005;Metzger et al. 2010;Roberts et al. 2011). Studies of Galactic chemical evolution will also be important to test the contributions of NS-NS and BH-NS mergers to the enrichment history of the r-process elements, in particular their role in the early Galaxy.