CHEMICAL ABUNDANCES OF THE SECONDARY STAR IN THE BLACK HOLE X-RAY BINARY V404 CYGNI

The merged and normalized spectrum of the secondary star in V404 Cygni may show apparently weaker stellar lines due to the veiling introduced by the accretion disk. This veiling is found to be ∼13% ± 2% in the range 6400–6600 Å in a set of observations taken during the period 1990–1993 (Casares & Charles 1994). This veiling was estimated by performing standard optimal subtraction techniques with a K0 IV template star.

The high quality and resolution of the Keck/HIRES spectrum enable us to infer the stellar parameters, (T_eff, log g, and the metallicity [Fe/H]) of the companion star, taking into account any possible veiling from the accretion disk as in previous studies of other LMXBs (see, e.g., González Hernández et al. 2004, 2008b). For simplicity, the veiling was defined as a linear function of wavelength and thus described with two additional parameters, the veiling at 4500 Å, f₄₅₀₀ = F⁴⁵⁰⁰_disk/F⁴⁵⁰⁰_sec, and the slope, m₀. We note that the total flux is defined as F_total = F_disk + F_sec, where F_disk and F_sec are the flux contributions of the disk and the continuum of the secondary star, respectively.

The most recent version of this code (see also González Hernández et al. 2009) allows us to compare, via a χ²-minimization procedure, up to 50 small spectral regions of the stellar spectrum with a grid of synthetic spectra computed using the local thermodynamical equilibrium (LTE) code MOOG (Sneden 1973). We used a grid of LTE model atmospheres (Kurucz 1993) and the atomic line data from the Vienna Atomic Line Database (VALD; Piskunov et al. 1995). The oscillator strengths of relevant lines were adjusted until they reproduced the solar atlas (Kurucz et al. 1984) with solar abundances (Grevesse et al. 1996). The corrections applied to the log gf values taken from the VALD database were smaller than ∼0.2 dex.

We inspected the high-quality HIRES spectrum of V404 Cygni, trying to search for Fe i–Fe ii lines. We finally selected 16 spectral features containing more than 50 Fe lines with excitation potentials between 1 and 5 eV. We emphasize that these Fe lines have a range of log gf values and are spread over the whole spectral range 5100–6750 Å, and we try to find the best-fit model for different veiling factors and various veiling slopes. Therefore, the strength of a given spectral feature depends not only on the stellar parameters and metallicity of the star but also on the veiling factor appropriate for that feature at the corresponding wavelength. In addition, due to the relatively high rotation velocity of the secondary star, these Fe lines were blended with stellar lines of other elements such as Ti and Ni. However, the main contributors to the selected features were always the Fe lines, and the abundances of other elements were in any case scaled with the metallicity of the model.

The five free parameters were varied in the ranges given in Table 1. The rotation velocity of the companion star was measured to be 36.4 km s⁻¹ using the HIRES spectrum (for further details, see J. I. González Hernández et al. 2011, in preparation), and a limb darkening of = 0.65 was adopted. The microturbulence, ξ, was computed using an experimental expression as a function of effective temperature and surface gravity (Allende Prieto et al. 2004). The value for the best-fit model given below is ξ = 1.117 km s⁻¹.

We obtain as most likely values T_eff = 4800 ± 100 K, log [g/(cm s²)] = 3.50 ± 0.15, [Fe/H] = 0.20 ± 0.17, f₄₅₀₀ = 0.15 ± 0.05, and m₀ = −0.00013 ± 0.00002. The 1σ uncertainties of the five free parameters were determined using 1000 realizations whose corresponding histograms are displayed in Figure 2. Thus, we find a very small veiling, with f₅₁₇₀ ≈ 0.05 for the spectral region of the Mg i b triplet at 5167–5183 Å and almost zero for longer wavelengths. This veiling is lower than that measured during early phases of quiescence (Casares et al. 1993). We emphasize that the linear function adopted to model the behavior of the veiling is strictly valid only in the spectral range 5000–6800 Å, and therefore should not be extrapolated beyond that wavelength range. On the other hand, we have analyzed several spectral ranges around 7750 Å, 8450 Å, and 8750 Å by assuming a veiling f_NIR = 0 for all of them, and the Fe i lines in these regions seem to be well reproduced by the spectral synthesis. However, a veiling of 0 throughout the infrared might not be correct, and one would have to analyze spectral lines in the infrared to check if this veiling, derived in the optical, holds for longer wavelengths.

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The stellar parameters of secondary stars in LMXBs are particularly relevant for the determination of orbital inclinations, which are typically derived from the modeling of ellipsoidal variations using optical and NIR light curves at quiescence (see, e.g., Gelino et al. 2006). Shahbaz et al. (1994) derived T_eff ≈ 4360 K for the companion star in their modeling of the K-band light curve of V404 Cygni. Hynes et al. (2009) suggest that its most likely spectral is K0 III, which implies T_eff ≈ 4570 K using the temperature scale of giants in van Belle et al. (1999). Khargharia et al. (2010), however, propose a spectral type of K3 III as the best template that matches their NIR broadband spectra with little contribution from the accretion disk, providing a veiling of ∼2% and ∼3% for their H- and K-band spectroscopy. This spectral type lends to a T_eff ∼ 4300 K, according to their model. However, our spectroscopic value (T_eff ≈ 4800 K) may require more contribution of the flux from the accretion disk in the NIR bands (see, e.g., Hynes et al. 2005), which may also imply a different orbital inclination, and therefore a different black hole mass.

We have collected the most updated information on orbital parameters for several X-ray binaries from the literature to derive the expected size of the Roche lobe and thus the corresponding surface gravity. We compare these values with our spectroscopic determinations in Table 3. Using Kepler's third law, we have estimated the current orbital separation, a_{c, f}, from the orbital period, P_orb, and the reported masses of the compact object, M_{CO, f}, and the companion star, M_{2, f}. The ratio of the radius of the Roche lobe, R_L, and the orbital separation can be estimated using Eggleton's expression (Eggleton 1983) as

$$\begin{equation*} R_L/a_{c,f}=0.49q^{2/3}\!/[0.6q^{2/3}+\ln\! {(1+q^{1/3})}]. \end{equation*}$$

Assuming that the star is filling its Roche lobe, R_L = R_{2, f}, and using the mass of the secondary star, we derive the expected surface gravity.

From Table 3 one can see that in general, the spectroscopic determinations are close to values derived from the size of the Roche lobe of the secondary star. In particular, for Centaurus X-4, A0620-00, and XTE J1118+480, the values are consistent within the 1σ uncertainties, and for Nova Sco 94 at 1.2σ. However, for V404 Cygni, the surface gravity is only compatible at the 5σ level, given the relatively small uncertainty in the spectroscopic surface gravity. On the other hand, we note that surface gravities derived from the size of the Roche lobe strongly depend on the current masses of the compact object and the secondary star, and thus depend on the estimated, sometimes uncertain, orbital inclination. We note, for instance, the case of A0620-00, whose black hole mass estimate has changed over the last 10 years from 11.0 ± 1.9 M_☉ (Gelino et al. 2001), to 9.7 ± 0.6 M_☉ (Froning et al. 2007), and finally to 6.61 ± 0.25  M_☉ (Cantrell et al. 2010). However, for the case of V404 Cygni, the mass ratio and the orbital period have been determined with high precision (see Table 3), leaving little room to increase the value of the surface gravity obtained from the secondary's mass and the size of the Roche lobe. Thus, adopting larger masses (Shahbaz et al. 1994) for the compact object, M_{CO, f} = 12 M_☉, and the companion star, M_{2, f} = 0.7 M_☉, the result does not change significantly; the estimated surface gravity would be $\log g_{R_L} = 2.72\pm 0.13$. Therefore, a possible uncertain orbital inclination does not seem to be the reason for this disagreement.

We inspected several regions in the observed Keck/HIRES spectrum of the secondary star, searching for suitable lines for a detailed chemical analysis. Using the derived stellar parameters, we first determined the Fe abundance by comparing synthetic spectra with each individual feature in the HIRES spectrum (see Table 2). The kinematical and dynamical properties, the stellar and veiling parameters, and the element abundances in LMXBs are summarized in Tables 3, 4, and 5. In Figure 3 we display one of the spectral regions analyzed to obtain the Fe abundance, also showing the best synthetic spectral fit to the observed spectrum of a template star (HIP 64797 with T_eff=4970 K, log  g=4.33, and [Fe/H] =−0.24 dex). We only use as abundance indicators those features which are well reproduced in the template star. The chemical analysis is summarized in Table 2. The errors in the element abundances show their sensitivity to the uncertainties in the effective temperature ($\Delta _{T_{\mathrm{eff}}}$), gravity (Δ_log g), veiling (Δ_vel), microturbulence (Δ_ξ), and the dispersion of the measurements from different spectral features (Δ_σ). In Table 2, we also state the number of features analyzed for each element. The uncertainties Δ_σ were estimated as $\Delta _\sigma =\sigma /\sqrt{N}$, where σ is the standard deviation of the N measurements. The uncertainties $\Delta _{T_{\mathrm{eff}}}$, Δ_ξ, Δ_log g, and Δ_vel were determined in the same way as, for instance, in the T_eff case: $\Delta _{T_{\rm eff}} = (\sum _{i=1}^N\;\Delta _{T_{\rm eff},i})/N$. The total uncertainty given in Table 2 was derived using the following expression: $\Delta \mathrm{[X/H]} = \sqrt{\vphantom{A^A}\smash{\hbox{${\Delta _{\sigma }^2 + \Delta _{T_{\mathrm{eff}}}^2 + \Delta _{\log g}^2 + \Delta _{\xi }^2 + \Delta _{\rm vel}^2}$}}}$.

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Table 2. Chemical Abundances of the Secondary Star in V404 Cygni

Element	log (X)☉a	[X/H]	[X/Fe]	σ	Δσb	$\Delta _{T_{\rm eff}}$	Δlog g	Δξ	Δvel	Δ[X/H]	Δ[X/Fe]	nc
Fe	7.50	0.23	...	0.12	0.02	0.05	0.00	−0.16	0.08	0.19	...	51
Od	8.74	0.60	0.37	0.07	0.05	−0.16	0.06	−0.06	0.06	0.20	0.24	2
Na	6.33	0.30	0.07	0.20	0.12	0.10	−0.03	−0.13	0.10	0.23	0.14	3
Mg	7.58	0.00	−0.23	0.09	0.03	0.06	−0.03	−0.09	0.08	0.15	0.09	8
Al	6.47	0.38	0.15	0.07	0.05	0.05	0.00	−0.08	0.05	0.11	0.11	2
Si	7.55	0.36	0.13	0.22	0.06	−0.06	0.04	−0.10	0.06	0.15	0.15	14
Ca	6.36	0.20	−0.03	0.16	0.05	0.11	−0.04	−0.24	0.10	0.29	0.12	11
Ti	5.02	0.42	0.19	0.24	0.06	0.15	0.02	−0.28	0.12	0.34	0.17	15
Cr	5.67	0.31	0.08	0.15	0.07	0.15	−0.05	−0.07	0.07	0.20	0.16	5
Ni	6.25	0.21	−0.02	0.32	0.11	0.06	−0.00	−0.25	0.14	0.31	0.15	9

Notes. Chemical abundances and uncertainties due to the uncertainties $\Delta _{T_{\rm eff}} = +100$ K, Δ_log g = +0.15 dex, Δ_ξ = +0.5 km s⁻¹, and Δ_vel = 0.05. ^aThe solar element abundances were adopted from Grevesse et al. (1996) for all elements except oxygen which was taken from Ecuvillon et al. (2006). ^bThe uncertainties from the dispersion of the best fits to different features, Δ_σ, are estimated using the following formula: $\Delta _\sigma =\sigma /\sqrt{N}$, where σ is the standard deviation of the measurements. ^cNumber of spectral features of this element analyzed in the star, or if there is only one, its wavelength. ^dThe oxygen abundance has been corrected for NLTE effects, Δ_NLTE = −0.2, using the NLTE computations in Ecuvillon et al. (2006).

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In Figure 4 we show the spectral region 5910–5955 Å, where there are some Ti and Si lines used to derive their abundances. In this region there are also some telluric lines, with equivalent widths of ∼30 mÅ, which are significantly weaker than the stellar features, whose equivalent widths are ∼250 mÅ, and we do not think these lines have caused any problem in the abundance determination. This spectral region contains two Fe features at ∼5914.2 and ∼5916.3 Å which are sensitive to surface gravity variations. One can easily notice the relative different strengths of both Fe features in the template spectra (with log  g ≈4.3) and in the secondary star in V404 Cygni (with log  g ≈3.5).

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The oxygen abundance was derived from the O i triplet at 7771–5 Å, which for the relatively high rotation velocity of the secondary star in V404 Cygni produces two well-resolved features that we have analyzed independently. In Figure 5 we show the 7755–7820 Å range, where the O i features in the secondary star appear to be apparently enhanced when compared with those in the template star having similar effective temperature. The best fit in LTE gives an oxygen abundance of $\mathrm{[O/H]_{\rm LTE}} \approx 0.8$. We note that the atomic data for O i lines were adopted from Ecuvillon et al. (2006). These authors slightly modified the oscillator strengths in order to obtain a solar oxygen abundance of log (O)_☉ = 8.74. For other elements we assumed as solar abundances those given by Grevesse et al. (1996).

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The O i λ7771–5 triplet suffers from appreciable non-LTE (NLTE) effects (see, e.g., Ecuvillon et al. 2006). For the stellar parameters and oxygen abundance of the secondary star, NLTE corrections⁶ are estimated to be ∼−0.20 dex for the NIR O i λ7771–5 triplet. Table 2 provides the oxygen abundance properly corrected for NLTE effects.

In principle, one could argue that the relatively "high" value for the spectroscopic surface gravity found in this work (see Section 3.1) for V404 Cygni may affect the derived abundances. We note that the spectroscopic values were derived for the secondary star at nearly inferior conjunction, which means that we are looking at the "spherical" side of the Roche-lobe-like star. Therefore, the derived T_eff and log  g values should be larger than the mean T_eff and log  g values of the star (see Table 3), although this would only account for 100 K and 0.1 dex, respectively.

In Table 2, one can see that the NIR O i lines are sensitive to the surface gravity, with a change of 0.06 dex in derived abundance for a change of +0.15 dex in log g. This means that for a surface gravity as low as log g = 2.7, one would obtain a 0.32 dex lower oxygen abundance. On the other hand, the Fe abundance would not be sensitive to this change in surface gravity, and therefore we would get [O/Fe]_NLTE = 0.05 dex.⁷ We also note that, for instance, a 300 K lower T_eff would result in a substantial increase in the derived oxygen abundance, ∼0.48 dex (see Table 2), and a smaller decrease in the Fe abundance, ∼ − 0.15 dex, yielding [O/Fe]_NLTE = 1 dex with [Fe/H] = 0.08. These values have been estimated without taking into account the possibly smaller NLTE correction at the lower value of T_eff.

The magnesium abundance was derived from eight Mg i features, including the four optical lines of the Mg i b λ5167–83 Å triplet and Mg i λ5528 Å. These Mg i lines are known to be sensitive to NLTE effects (see, e.g., Zhao et al. 1998), although with NLTE corrections of only ∼+0.05 in the Sun and probably smaller ones at these cooler temperatures (Zhao & Gehren 2000).

We note here that we are applying an automatic 1.5σ abundance rejection over the initial set of lines, slightly affecting the Mg abundance. This discards two Mg i features, lowering the Mg abundance by 0.06 dex and decreasing the standard deviation of the measurements from 0.15 to 0.09 dex. For other elements like Si and Ti, the 1.5σ rejection yields 0.04 lower and 0.03 higher abundance, respectively, with a decrease of the standard deviation by only 0.02 dex.

Finally, possible differences in the stellar parameters also have an impact on the Mg abundance (see Table 2). The Mg i lines are sensitive to the effective temperature and surface gravity, with a change of 0.06 and −0.03 dex in derived abundance for changes of 100 K in T_eff and +0.15 dex in log  g, respectively. In this case, 300 K lower T_eff would result in 0.18 dex lower Mg abundance, whereas a decrease of 0.8 dex in log  g would give rise to a 0.16 dex higher Mg abundance.

The secondary star in V404 Cygni may have lost a significant amount of its initial mass through a mass-transfer mechanism onto the compact object, during the binary evolution. Its post-SN evolution has been studied in detail by Miller-Jones et al. (2009b). These authors suggest that from 0.5 to 1.5 M_☉ may have been accreted from the companion star. We estimated the current mass of the secondary star at M_{2, f} = 0.54 ± 0.08 M_☉ (see Table 3), from the current black hole mass M_{BH, f} = 9.0 ± 0.6 M_☉ (Khargharia et al. 2010) and mass ratio q_f = 0.060 ± 0.005 (Casares & Charles 1994). Following Miller-Jones et al. (2009b), we assume an initial mass for the secondary star of M_{2, i} ≈ 2 M_☉ and an initial black hole mass of M_{BH, i} ≈ 8 M_☉. Therefore, the final mass of the black hole would be M_{BH, f} ≈ 9.5 M_☉ which is consistent with the current estimate of the black hole mass (Khargharia et al. 2010).

The high O content in this companion star may not suggest any strong CNO processing within the star itself during its evolution, since this would increase the N abundance (see, e.g., Haswell et al. 2002). Oxygen, however, is not expected to decrease too much compared with C (Clayton 1983). Therefore, the CNO-processed material is C underabundant and N overabundant. Unfortunately, in the Keck/HIRES optical spectrum of the secondary star there are no sufficiently strong and unblended stellar lines to provide an accurate and reliable C abundance. Khargharia et al. (2010) argued that their NIR spectrum of V404 Cygni suggests that CO molecules seem to fit well with a solar-abundance K3 III template spectrum for which they adopt T_eff ≈ 4300 K. We note here that CO molecular bands are more sensitive to the C abundance than to the O abundance and are stronger at lower effective temperatures. Thus, their arguments do not necessarily contradict our determination of the O abundance.

The present orbital distance is a_{c, f} ≈ 31 R_☉ (see Table 3). We will assume that the post-SN orbital separation after tidal circularization of the orbit was a_{c, i} ≈ 15 R_☉, since the secondary must have experienced mass and angular momentum losses during the binary evolution until it reached its present configuration. Similarly to the case of XTE J1118+480 (González Hernández et al. 2008b), we can estimate the maximum ejected mass in the SN/HN explosion. A binary system such as V404 Cygni will survive a spherical SN explosion if the ejected mass ΔM = M_He − M_{BH, i} ⩽ (M_He + M_{2, i})/2 (Hills 1983). This implies a mass of the He core before the SN explosion of M_He ⩽ 18 M_☉. We therefore adopt He core masses of M_He ≈ 15–16 M_☉, so we infer an He core radius of R_He ≈ 3 R_☉ from the expression in Portegies Zwart et al. (1997, and references therein).

Assuming a pre-SN circular orbit and an instantaneous spherically symmetric ejection (that is, shorter than the orbital period), one can estimate the pre-SN orbital separation, a₀, using the relation given by van den Heuvel & Habets (1984): a₀ = a_{c, i} μ_f, where μ_f = (M_{BH, i} + M_{2, i})/(M_He + M_{2, i}). We find a₀ ≈ 9, for the adopted values of M_He = 15 M_☉ and a_{c, i} = 15 R_☉. At the time of the SN explosion (∼5–6 Myr; Brunish & Truran 1982), a 2 M_☉ secondary star, still in its pre-main-sequence evolution, has a radius R_{2, i} ≈ 3.3 R_☉. The material possibly captured by the secondary star in the SN/HN event has a much larger mean molecular weight than the pre-explosion gas of the secondary star, so it has probably been well mixed within the star by thermohaline mixing in a relatively short timescale (Podsiadlowski et al. 2002, and references therein). Therefore, the subsequent lost of material from the secondary star onto the compact object should not affect the chemical composition of its atmosphere. The amount of mass deposited on the secondary can be estimated as m_cap = ΔM(πR²_{2, i}/4πa²₀)f_cap M_☉, where f_cap is the fraction of mass, ejected within the solid angle subtended by the secondary star, that is eventually captured. We assume that the captured mass, m_cap, is completely mixed with the rest of the companion star.

We compute the expected abundances in the atmosphere of the secondary star after the pollution from the progenitor of the compact object as in González Hernández et al. (2004) and González Hernández et al. (2008b). We use 40 M_☉ spherically symmetric core-collapse explosion models (M_He ≈ 15.1 M_☉) at solar metallicity (Z = 0.02) and for two different explosion energies (Umeda & Nomoto 2002, 2005; Tominaga et al. 2007). These models imply ΔM ≈ 7 M_☉ and need small capture efficiencies of f_cap ≲ 0.1 (i.e., 10%) to increase significantly the metal content of the secondary star. In order to fix the f_cap parameter, we have tried to get an expected Al abundance, [Al/H] ≈ 0.45, consistent with the observed Al abundance within the error bars. These model computations are shown in Table 7. These models would also provide a different mass fraction of each element at each value of the mass cut (defined as the mass that initially collapsed to form the compact remnant). For more details of the models, see Tominaga et al. (2007).

The assumptions regarding the initial mass and the post-SN orbital distance of the secondary star are not so relevant due to the free parameter f_cap. A different value for the initial mass of the secondary star, as small as (say) 1 M_☉ with an initial radius of R_{2, i} ≈ 1.3 R_☉at the time of the SN explosion, and for the post-SN orbital separation, say a_{c, i} = 25 R_☉, would require a larger capture efficiency factor of f_cap ≈ 0.45 (i.e., 45%).

The explosion energy is E_K = 1 × 10⁵¹ erg and E_K = 30 × 10⁵¹ erg for the SN and HN models, respectively. This energy is deposited instantaneously in the central region of the progenitor core to generate a strong shock wave. The subsequent propagation of the shock wave is followed through a hydrodynamic code (Umeda & Nomoto 2002, and references therein). As in González Hernández et al. (2008b), our model computations assume different mass cuts and fallback masses, and a mixing factor of one which assumes that all fallback matter is well mixed with the ejecta. The amount of fallback, M_fall, is the difference between the final remnant mass, M_{BH, i}, and the initial remnant mass of the explosion, M_cut. We should recall here the ejected mass, ΔM, which is equal to M_He − M_{BH, i}, where M_He is the mass of the He core.

We use SN/HN models to provide us with the yields of the explosion before radiative decay of element species. We then compute the integrated, decayed yields of the ejecta by adopting a mass cut and by mixing all of the material above the mass cut. Finally, we calculate the composition of the matter captured by the secondary star, and we mix it with the material of its convective envelope. It has been suggested that the black hole in the LMXB Nova Sco 1994 could have formed in a two-stage process where the initial collapse led to the formation of a neutron star accompanied by a substantial kick and the final mass of the compact remnant was achieved by matter that fell back after the initial collapse (Podsiadlowski et al. 2002). However, the black hole mass in that system has been estimated at ∼5.4 M_☉ (Beer & Podsiadlowski 2002) or ∼6.6 M_☉ (Shahbaz 2003; see Table 3), while the black hole in V404 Cygni may have an initial mass of ∼8 M_☉ which would require a fallback mass of ∼6.6 M_☉ if we assume ∼1.4 M_☉ for a canonical neutron star. MacFadyen et al. (2001) proposed a scenario where collapsar models harbor black holes that could form in a mild explosion with substantial fallback (up to ∼5 M_☉).

In Figure 8, we show the expected abundances of the secondary star after contamination from the nucleosynthetic products of the SN explosion (E_K = 1 × 10⁵¹ erg) of an M_He ≈ 15 M_☉ progenitor star. The initial abundances of the secondary star have been estimated from the average abundances of thin-disk solar-type stars with [Fe/H] ≈0.23 (González Hernández et al. 2010), which are provided in Table 7. Note that for a given model, the Al abundance in the secondary star hardly depends on the mass cut, since Al forms in the outer layers of the explosion. Thus, once the capture efficiency is fixed, the Al abundance in Figure 8 is almost constant.

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The expected abundances of O, Mg, and Al in the secondary star after contamination from the SN ejecta remain mostly independent of the adopted mass cut, whereas other elements like Si, Ca, Ti, Fe, and Ni are quite sensitive to the mass cut of the model. This appears to be more clear in the HN model, where the higher explosion energy enhances the amounts of the α-process elements Si, Ca, and Ti. The Fe-group elements like Cr, Fe, and Ni are also sensitive to the mass cut, especially in the HN model.

For both the SN model (left panel in Figure 8) and the HN model (right panel in Figure 8), the predicted abundances agree with the observed abundances in the secondary star relatively well, except for those of O and Mg. The expected Mg abundance is too high in comparison with the observed value since the adopted initial Mg abundance is already higher than the observed abundance (see Table 7). The case of O is just the contrary; the initial abundance is so low that it is not possible to reach the observed O abundance when fitting other element abundances (see Figure 8).

For mass cuts above ∼3 M_☉, very little Si, Ca, Ti, Fe, Cr, and Ni is ejected; thus, the expected abundances of the model essentially reflect the initial abundances of the secondary star. In contrast, O, Na, Mg, and Al are hardly sensitive to the mass cut, and all are enhanced due to the capture of enriched material in the SN/HN explosion.

We could have also investigated a model with solar initial abundances for the secondary star ([X/H]₀ = 0) and the same explosion model of solar metallicity (Z = 0.02), although it is unlikely that a significant amount of elements formed in the inner layers of the explosion (such as Ti, Ni, and Fe) would be present in the ejecta. In such models, only the HN explosion with a mass cut as low as M_cut ≈ 2 M_☉ would fit the relatively enhanced observed abundances of Si, Ti, Cr, Fe, and Ni, but we would still not be able to fit the O and Mg abundances. This low mass cut would require very efficient mixing processes and the model would also need a small capture efficiency of f_cap ≈ 0.15 (i.e., only 15% of the matter ejected within the solid angle subtended by the secondary star).

Miller-Jones et al. (2009a) pointed out that due to the relatively small peculiar velocity of the system, V404 Cygni does not require an asymmetric kick. However, here we explore this possibility using explosion models from Maeda et al. (2002) that are not spherically symmetric. An aspherical SN explosion produces chemical inhomogeneities in the ejecta which are dependent on direction. Thus, if the jet in the aspherical SN explosion is collimated perpendicular to the orbital plane of the binary (for more details, see González Hernández et al. 2005a), where the secondary star is located, elements such as Ti, Fe, and Ni are ejected mainly in the jet direction, while O, Mg, Al, Si, and S are preferentially ejected near the equatorial plane of the helium star (Maeda et al. 2002).

In Figure 9, we compare the predicted abundances in the atmosphere of the secondary star after pollution from an aspherical explosion model of a metal-rich progenitor having a 16 M_☉ He core (see also Table 7). The initial abundances of the secondary were, as in the spherical case, equally extracted from the average values of solar-type stars of the solar neighborhood with similar iron content (see Table 7). The left panel of Figure 9 reflects the composition of the material ejected in the equatorial plane, which should be rich in O, Na, Mg, Al, and Si—the only elements significantly enhanced with respect to the initial abundances. We see that the choice of the mass cut does not make a significant difference, and as in the spherical case, this model fits all of the element abundances within their error bars except for O and Mg.

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In the right panel of Figure 9 we have considered complete lateral mixing (Podsiadlowski et al. 2002)—that is, the ejected matter is completely mixed within each velocity bin (for more details, see González Hernández et al. 2008b). The observed abundances might be better reproduced if complete lateral mixing is adopted, since this process tends to enhance the Si, Ca, Ti, Cr, Fe, and Ni element abundances at all mass cuts. A model with solar initial abundances for the secondary star (i.e., [X/H]₀ = 0) and the same explosion model of solar metallicity (Z = 0.02) was also inspected, providing the same result except for the equatorial model, which produces too low abundances of Ti, Fe, and Ni in comparison with the observations.