Issue 
A&A
Volume 658, February 2022



Article Number  A70  
Number of page(s)  7  
Section  Stellar structure and evolution  
DOI  https://doi.org/10.1051/00046361/202142464  
Published online  03 February 2022 
New nickel opacities and their impact on stellar models
^{1}
IRAP, Université de Toulouse, CNRS, UPS, CNES, Toulouse, France
email: alain.huibonhoa@irap.omp.eu
^{2}
CEA, DAM, DIF, 91297 Arpajon, France
^{3}
Université ParisSaclay, CEA, Laboratoire Matière sous Conditions Extrêmes, 91680 BruyèresleChâtel, France
^{4}
Laboratoire Univers et Particules de Montpellier, Université de Montpellier, CNRS, Place Eugène Bataillon, 34095 Montpellier, France
Received:
16
October
2021
Accepted:
18
November
2021
Context. The chemical element nickel is of particular interest in stellar physics. In the layers in which the Fepeak elements dominate the mean opacity (the socalled Zbump), Ni is the second contributor to the Rosseland opacity after iron, according to the Opacity Project data. Reliable nickel cross sections are therefore mandatory for building realistic stellar models, especially for mainsequence pulsators such as β Cep and slowly pulsating B stars, whose oscillations are triggered by the κmechanism of the Fepeak elements. Unfortunately, the Opacity Project data for Ni were extrapolated from those of Fe, and previous studies have shown that they were underestimated in comparison to detailed calculations.
Aims. We investigate the impact of newly computed monochromatic cross sections on the Rosseland mean opacity of Ni and on the structure of mainsequence massive pulsators. We compare our results with the widely used Opacity Project and OPAL data.
Methods. Monochromatic cross sections for Ni were obtained with the SCORCG code. The ToulouseGeneva evolution code was used to build the stellar models.
Results. With the new data, the Rosseland opacities of Ni are roughly the same as those of the Opacity Project or OPAL at high temperatures (log T > 6). At lower temperatures, significant departures are observed; the ratios are up to six times higher with SCORCG. These discrepancies span a wider temperature range in the comparison with OPAL than in comparison with the Opacity Project. For massive star models, the results of the comparison with a structure computed with Opacity Project data show that the Rosseland mean of the global stellar mixture is only marginally altered in the Zbump. The maximum opacity is shifted towards slightly more superficial layers. A new maximum appears in the temperature derivative of the mean opacity, and the driving of the pulsations should be affected.
Key words: atomic data / opacity / atomic processes / stars: interiors
© A. HuiBonHoa et al. 2022
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1. Introduction
Opacities describe the interactions between radiation and matter. In stellar physics, they are used to evaluate the amount of energy that is carried by the radiation field. They are therefore of prime importance for building stellar models. In stellar interiors, the medium is optically thick so that the transfer equation can be expressed by an analytical function that involves the Rosseland mean opacity (RMO). In most parts of mainsequence stars, which are in the hydrogenburning phase, the most important elements that contribute to the RMO are hydrogen and helium. One noticeable exception is the layer around log T = 5.3, where the iron peak elements are the main contributors (this is often referred to as the Zbump).
In addition to structural effects, the domination of the RMO by the Fepeak elements enables them to trigger oscillations through the κmechanism for stars in the upper part of the main sequence. This mechanism is invoked to explain the pulsations of the slowly pulsating B (SPB) stars (Dziembowski et al. 1993), which are the coolest pulsators of the upper main sequence and exhibit highovertone gravity modes (Waelkens 1991). In turn, in the β Cep pulsators (e.g., Stankov & Handler 2005, and references therein), this process excites loworder p and gmodes (Dziembowski & Pamyatnykh 1993). In the overlapping zone between the instability strips of the SPB and βCep (around 10 M_{⊙}), some objects show oscillations of both types of stars (the socalled hybrid pulsators; Balona et al. 2011, and references therein), which are also excited by the Zbump κmechanism (Pamyatnykh 1999). Outside the main sequence, some Btype subdwarfs (sdB, 22 000 ≲ T_{eff} ≲ 35 000) also show pulsations. Their effective temperature range is similar to that of the β Cep and the hottest SPBs. Charpinet et al. (1996, 1997) and Fontaine et al. (2003) showed that the driving mechanism for the pmode and for the gmode oscillations in sdBs, respectively, is the κmechanism of the Fepeak elements.
The need for sufficiently complete and accurate opacities to calculate realistic stellar models led to the computations of theoretical opacity dataset starting in the mid1990s. Of the different groups involved in this effort, the Opacity Project (OP) is the only one to have made the monochromatic cross sections for each chemical element publicly available (Seaton 2005). The mean opacities can then be computed consistently with respect to the local mixture in each part of the star. The monochromatic opacities of Cr, Mn, and Ni were not computed in detail, however, and come from an extrapolation of the data for iron (Seaton et al. 1994). TurckChièze et al. (2016) showed that this method could lead to discrepant values of the RMO especially for Ni compared to detailed computations, so that a caveat was attached to the reliability of the RMO computed with the OP opacities in the Zbump. In addition, nickel is of prime importance in the excitation of the pulsations, especially for highovertone gmodes in upper mainsequence stars (e.g., DaszyńskaDaszkiewicz et al. 2017) or in sdBs (Jeffery & Saio 2006).
Monochromatic data have also been produced by the OPAL group (Iglesias & Rogers 1996) and were used in the Montréal (Turcotte et al. 1998) and Montréal/Montpellier (Deal et al. 2021) stellar evolution codes, but they are not publicly available. HuiBonHoa & Vauclair (2018a) found that the radiative accelerations for nickel in the Zbump are of similar strength between OP and OPAL, which poses the question whether the OPAL opacities might also be underestimated there.
Accurate data for this element are therefore needed to build realistic models. Rosseland means with detailed calculation of the Ni opacities are available in the OPLIB database (Colgan et al. 2016), which is suitable for models with homogeneous content in their envelope. Models in which atomic diffusion is considered exhibit inhomogeneous chemical compositions (HuiBonHoa & Vauclair 2018a,b) and require monochromatic cross sections in order to consider the feedback of the local abundances on the opacities. We therefore present new monochromatic data computed with the SCORCG code (Pain & Gilleron 2015).
After a description of the SCORCG code in Sect. 2, we present the new data and compare their RMOs with those of OP and OPAL (Sect. 3). We then explain how we processed our data to use them in stellar evolution codes (Sect. 4). Finally, we discuss the impact of the new data on a stellar structure computed with the ToulouseGeneva evolution code (TGEC) in Sect. 5.
2. SCORCG code
In this section, we outline the main features of the SCORCG code, which is described in detail in Pain & Gilleron (2015). SCORCG is an opacity computation code consisting of two parts: the building of the atomic structure that consistently takes plasma effects into account (and assumes local thermodynamical equilibrium) is devoted to the superconfiguration code for opacity (SCO) part (Blenski et al. 2000), thus avoiding the isolatedatom approximation. A selfconsistent calculation is performed for each superconfiguration, which in this way has its own potential and set of wave functions. That density effects on the wave functions are considered is one of the strengths of SCORCG compared to other codes. The data required to calculate the detailed transition arrays (i.e. direct and exchange Slater, spinorbit, and dipolar integrals) are calculated by the SCO part within a plasma model accounting for the density and screening effects on the wave functions, and given as inputs to the RCG part (Cowan 1981), performing the detailedline computation of the transition array (detailedline accounting, DLA). The selection of transition arrays for which a detailed linebyline treatment is possible and relevant is made according to some userdefined criteria involving the mean energy spacing between neighbouring lines and the mean line width in the transition array. DLA calculations are performed only for pairs of configurations giving rise to fewer than 800 000 lines (the maximum size of a Jblock inside a configuration is 4000). In other cases, transition arrays are represented statistically by Gaussian profiles in the unresolved transition arrays (UTA; BaucheArnoult et al. 1979) or spinorbit split arrays (SOSA; BaucheArnoult 1985) formalisms. If the Rydberg supershell contains at least one electron, then transitions starting from the superconfiguration are treated within the supertransition array model (STA; BarShalom et al. 1989).
This hybrid design allows us to consider many highly excited states that can have a significant contribution to the opacity in spite of their low probabilities. The number of detailed calculations in SCORCG is now largely dominant, and subsequently the computed spectrum is less sensitive to the modelling of the remaining statistical contributions (UTA, SOSA, and STA).
3. Data for nickel
3.1. Rosseland mean opacities
Among the different types of mainsequence stars, seismic observations are the most stringent for the hybrid pulsators, which simultaneously exhibit acoustic and gravity waves (p and gmodes, respectively). Therefore, we computed the cross sections for Ni in the temperatureelectron density (T, N_{e}) domain involved in the mainsequence evolution of such a star. In practice, we chose a mass of 9.5 M_{⊙}, which is the mass of the wellstudied hybrid pulsator ν Eri (e.g., Handler et al. 2004; Pamyatnykh et al. 2004; DaszyńskaDaszkiewicz et al. 2017). This domain appears as a strip in this plane. The new data were calculated at the same 371 grid points as the OP cross sections since they are meant to be combined together to compute the RMO for the actual chemical mixture of a stellar model. The computations were successful at the 274 grid points shown in Fig. 1. They failed for 97 points, especially at low temperatures and electron densities (log T < 4.7, log N_{e} < 17), and for log N_{e} = 17, only the points with log T ∈ [4.8; 5.15] could be computed. For all these points, the FermiDirac distribution function tends to a Heaviside function due to the low densities, leading to numerical issues. In addition, five other points ((log T, log N_{e}) = (6, 21), (6.75, 24), (6.9, 24.5), (6.95, 24.5), and (7.45,25.5)), scattered among the successful calculations, could not be computed for a reason still under investigation, yielding the gaps in Fig. 1. We show in the next subsection, however, that the effect on the stellar structure should be small. The highest values are in the Zbump, around log T = 5.4.
Fig. 1. Rosseland mean opacities κ_{R} of nickel computed with SCORCG in the (T, N_{e}) plane. The dots represent the grid points where the computations are made. The highest values are met in the area around log T = 5.4, i.e., in the socalled Zbump. 
We recall that the Rosseland opacity κ_{R} is a harmonic mean of the monochromatic opacities κ_{ν} weighted by the temperature derivative of the Planck function ,
which can also be expressed as
where F(u) is the normalised temperature derivative of the Planck function in terms of (the expression of F(u) is given by Eq. (8) of Badnell et al. 2005). In this study, all the values of Rosseland means are computed with a trapezoidal rule.
The total monochromatic opacity κ_{ν} or κ(u) is the sum of the cross sections of four physical processes: absorption through spectral lines (boundbound transitions), photoionisation (boundfree transitions), reverse bremsstrahlung (freefree interactions), and electron scattering. Figure 2 shows the contribution of each process to the RMO. A contribution is defined as (κ_{tot} − κ_{tot − P})/κ_{tot}, where κ_{tot} is the Rosseland mean considering all the absorption processes and κ_{tot − P} the RMO with process P ignored. If process P has a significant role in the RMO, then κ_{tot − P} is small compared to κ_{tot} and its contribution tends to 1. Conversely, if its role is negligible, κ_{tot − P} is close to κ_{tot} and the contribution is then close to zero. We conclude from Fig. 2 that the RMOs are mostly due to line absorptions and to photoionisation, the freefree process contributing marginally at low temperatures. Boundbound absorption is no longer a dominant process above log T ≃ 6.7, where the number of electrons per atom is higher than 24, in other words, fewer than four electrons are left on average. Scattering is the less important process everywhere in the computed domain.
Fig. 2. Logarithm of the contributions to the Rosseland mean opacities (see text) in the (T, N_{e}) plane, plotted according to the same scale. Its lower limit is set to −2.5, and the smallest scattering contributions are upper limits. κ_{tot} is the RMO considering all the absorption processes, κ_{tot − P} is the RMO without process P, P being one of the opacity sources (lines bb, photoionisation bf, reverse bremsstrahlung ff, or scattering, scatt). 
Figure 3 shows the spectra of the different absorption processes for two sets of (T, N_{e}): the set shown in the upper panel is in the Zbump, more specifically, in a region in which line absorption dominates the RMO and where the contribution of photoionisation is the smallest. The lower panel refers to conditions where photoionisation is the main absorption process and where the boundbound opacity is close to its lowest contribution. The effect of the weighting by the temperature derivative of the Planck function is evident: any absorption process that has significant cross sections around the maximum of F(u) will be a main contributor to the RMO. Scattering is not shown not only because of its negligible contribution, but mostly because it is not considered in the rest of this work. Its actual effect is to be computed after the mixture of the medium defined, so that the number of free electrons per atom and the ionisation fractions for the different elements in the stellar conditions are known.
Fig. 3. Spectra with the logarithm of the spectral lines (red lines), photoionisation (blue lines), and reversebremsstrahlung (green lines) cross sections (left scale) vs. photon energy expressed in for two different temperatureelectron density sets. The conditions for which they have been computed and the resulting Rosseland mean are detailed in each panel. The dashed lines denote the normalised temperature derivative of the Planck function in logarithm, log F(u) (right scale). 
3.2. Comparison with other data
3.2.1. Opacity Project
The Ni cross sections of OP come from an extrapolation of those of iron (Seaton et al. 1994). TurckChièze et al. (2016) showed that the RMOs computed with these values could be very different from that of detailed calculations. The upper panel of Fig. 4 presents the logarithms of the ratios of the RMOs computed with our new data (κ_{R, SR}) and those from OP (κ_{R, OP}) in the (T, N_{e}) plane. The values of κ_{R, OP} were computed from the monochromatic cross sections using a trapezoidal scheme.
Fig. 4. Ratios of the SCORCG Rosseland means and those of OP or OPAL in the (T, N_{e}) plane. κ_{R, SR} is the RMO from the new data and κ_{R, OP, OPAL} that of the comparison dataset. Top panel: comparison with OP. The SCORCG RMOs can be up to six times larger than those of OP in a narrow band in the Zbump, around log T = 5.3. Bottom panel: same plot with OPAL. The OPAL temperature step is larger for log T > 6. The area in which the SCORCG RMOs are higher than those of OPAL is larger than for OP. 
The ratios of the SCORCG and the OP RMOs can be as high as 6 in the Zbump, that is, of the same order of magnitude as the value stated by TurckChièze et al. (2016). Outside the Zbump, the RMOs are roughly similar, except for several grid points at which the RMO from the new data can be as low as onetenth of that of OP. Because Ni is no longer a main contributor to the RMO outside the Zbump, however, we expect that the effect on the stellar structure should be small compared to the use of OP data. The case of layers whose temperature is in the Zbump, but whose electronic density is lower than the lower limit of the computed domain is more questionable. Further calculations towards lower densities are needed to determine to which extent the RMOs are underestimated with the OP cross sections in these conditions.
3.2.2. OPAL
Although the cross sections of ironpeak elements were recently updated (Iglesias 2015), they are not available to us. We therefore show the results from previous computations here (Iglesias & Rogers 1996). Nevertheless, the impact of the new OPAL calculations should be negligible according to Fig. 1 of Iglesias (2015). The OPAL opacities were computed in detail for all the elements of their set, at grid points defined by the temperature and R = ρ/T6, where ρ is the density and T6 is the temperature divided by 10^{6}. The temperature values are the same as those of OP up to log T = 6, above which the step is twice that of OP in log T. Since the spacing is constant in log R, the electronic densities at the OPAL grid points are different from those of our grid. We obtained the Rosseland means at our N_{e} values by interpolating the OPAL RMOs using a cubic spline. To be consistent with the comparison with OP, the RMOs were also computed from the monochromatic cross sections.
The logarithms of the ratios of the SCORCG RMOs and those from OPAL (κ_{R, OPAL}) are plotted in the lower panel of Fig. 4. As for OP, the new data yield higher Rosseland means in the Zbump, but the area covered by these enhancements is larger. At the same location as in the comparison with OP, several values are lower than those from OPAL, with likely little influence on the stellar structure as they lie outside the Zbump. These discrepancies could arise from the number of atomic configurations involved in the calculations. A more thorough investigation of the impact of the difference between SCORCG and OPAL would require computing the SCORCG cross sections at the same grid points as OPAL.
4. Implementation in stellar codes
For stellar evolution codes to benefit from the new data, we aim to use them in lieu of the existent data (OP or OPAL). We also wished to reach this goal without changing the routine that computes the Rosseland mean, so that we have to replace the existent data by those obtained with the new calculations whenever available. The physical quantities to change are obviously the cross sections, but also the mean number of electrons per atom and the ionisation fractions for the various elements that are needed to compute the scattering. Since the SCORCG cross sections are computed at present on the same grid points as the OP data, we focused on introducing the new data in the OP files. Further efforts are needed to merge the new opacities with OPAL data.
The cross sections of SCORCG were computed for a photon energy grid comprising 299 999 points equally spaced in u in the interval between 0 and 40. In turn, the OP mesh contained 10 000 points with a spacing keeping F(u)Δu roughly constant, with Δu the step between consecutive grid points. u itself is between 0 and 20. We tested two methods to reduce the number of mesh points, one with a sampling of the SCORCG data on the OP grid points, the other by considering the average between the middle of the two intervals surrounding each OP grid point, which could provide a more representative value where the spectra have complex features. Furthermore, Eq. (2) suggests that the inverses of the cross sections shoud be used to calculate the RMOs, rather than the cross sections themselves. In addition to these two calculations, we applied both methods to the cross sections themselves to determine the relevance of using their inverses. We defined the relative change of the RMO as (κ_{R, orig.} − κ_{R, 10k})/κ_{R, orig.} where κ_{R, orig.} is the RMO obtained with the original energy grid and κ_{R, 10k} with that of OP. These differences are plotted in the (T, N_{e}) plane in Fig. 5 for each combination. The mean of the inverses of the cross sections definitely provides the best results, whereas the mean of the cross sections yields the largest differences. We note that these cross sections do not include the contribution of electron scattering.
Fig. 5. Relative difference between the original SCORCG RMO (κ_{R, orig.}) and the calculation with the OP frequency mesh (κ_{R, 10k}) in the (T, N_{e}) plane, plotted according to the same scale. Its upper limit is set to 5%. The dark red parts are to be considered as lower limits. From left to right, the panels show the results with the mean of the inverses of the cross sections, the mean of the cross sections, the sampling of the inverses, and the sampling of the cross sections. 
The last step of the implementation consists of replacing the original OP cross sections, number of electrons per atoms, and ionisation fractions in the OP files. For this, the new cross sections were converted into atomic units, which is the unit used in the OP files.
5. Impact on stellar models
TGEC was used as testbed. TGEC is a 1D stellar evolution code (HuiBonHoa 2008) that implements the latest physics. The RMOs were computed onthefly with the method described in HuiBonHoa (2021). This ensures full consistency between the mean opacity and the chemical composition in any layer of the model. We used the monochromatic opacities from the Opacity Project OPCD v.3.3 data (Seaton 2005) for all the chemicals but nickel, for which the new data were considered whenever available. The computations were performed for a 9.5 M_{⊙} model without atomic diffusion, so that the chemical composition is homogeneous outside the stellar core, where nucleosynthesis takes place. We used the Grevesse & Noels (1993) metal content, as in HuiBonHoa & Vauclair (2018a,b). Using other solar compositions such as that of Asplund et al. (2009) should not affect the bulk of our results because the ratios of the different Fepeak elements and H differ from those of Grevesse & Noels (1993) by less than 0.1 dex.
We first compared the impact of the new Ni opacities on the Rosseland mean of the whole chemical mixture of the star. The upper panel of Fig. 6 shows the RMOs of a stellar structure computed with the new Ni data along with those of a structure calculated with the original OP data as a function of temperature. The new data shift the maximum opacity of the Zbump towards a slightly lower temperature, and the width of the peak is reduced. In his comparison of OP and OPAL, Iglesias (2015) suspected that the greater width of the Zbump obtained with the OP cross sections could be due to Ni, which is consistent with our results. The value of the maximum is marginally enhanced (by about 2 × 10^{−3}). No significant difference can be seen outside the Zbump, as expected. With the same abscissae, we plot in the lower panel the ratio of the RMOs for the whole stellar mixture computed with the new data and those from the OP data (thick line). The same ratio for Ni alone is also shown (thin line). The dip of the global RMO ratio around log T = 5.5 accounts for the change in shape of the Zbump. The ratio for nickel alone has a maximum close to 5 around log T = 5.3, to be related to the high ratios present in Fig. 4 at similar temperatures. No clear correlation appears between the RMO ratio for Ni and the global ratio, however. In particular, in some layers of the Zbump around log T = 5.4, the new Ni RMO can even be higher along with a lower global RMO.
Fig. 6. Comparison of the mean opacities of a stellar model computed with the new Ni data and one with the OP data. Upper panel: Rosseland mean (κ_{R}) of the stellar mixture with the new Ni data (solid line) and that with OP (dashed line) vs. log T. Lower panel: ratio of the SCORCG (κ_{R, SR}) and OP (κ_{R, OP}) Rosseland means vs. log T for the stellar mixture (thick line) and for Ni alone (thin line). The dotted line represents a ratio of one. 
This lack of correlation is due to the details of the crosssection spectrum of each chemical element of the stellar mixture. As an illustration, we detail the case in which the conditions in temperature and electron density yield a higher RMO for Ni alone, whereas that of the global mixture is reduced when the new data are used (log T = 5.4, log N_{e} = 18.0). Figure 7 shows the logarithm of the ratios of the cross sections of the global mixture with the new data and those with the OP values (thick line), and the same ratio for Ni alone (thin line). Plotting the logarithm of the ratios instead of the ratios themselves has the advantage of being meaningful in terms of cross sections, but also in terms of their inverses, as involved in the expression of the Rosseland mean, by considering the opposite. The ratio of the cross sections for the global mixture changes significantly in the interval 3 < u < 5.5, whereas that of Ni departs from unity in the whole photon energy domain. We can therefore deduce that nickel contributes significantly to the cross sections of the global mixture only for u in the interval [3, 5.5]. The ratio of the global cross section more or less follows that of Ni in this range. Around the maximum of the F(u) function, the ratio for nickel is above unity over a wider range in u than the one for which this ratio is below one, yielding an increase in the Ni Rosseland mean. In contrast, the interval for which the ratio of the global mixture is above one is smaller than the one where it is below one, along with deficiencies in opacity more important than their increase. The global RMO is thus smaller with the new data.
Fig. 7. Logarithm of the ratio of the monochromatic cross sections for the stellar mixture with the new Ni data (κ_{SR}) and those with the OP Ni data (κ_{OP}) vs. u, and the same quantity for Ni alone (thick and thin solid lines, respectively, left scale). The dashed line shows the F(u) function (right scale). The dotted line represents a ratio of one. For the sake of legibility, the spectra have been convolved with a Gaussian kernel with a standard deviation of 0.05. 
Since the shape of the Zbump is modified with the new data, we expect that the contribution of the various elements to the RMO changes. The definition of this contribution is similar to that of the different absorption processes mentioned in Sect. 3.1: for a given chemical element A, its contribution writes (κ_{tot} − κ_{tot − A})/κ_{tot}, where κ_{tot} is the Rosseland mean of the whole stellar mixture and κ_{tot − A} is the RMO without element A. Figure 8 focuses around the Zbump and includes the four most important contributors there, namely H, He, Fe, and Ni. With the new data, a change is expected for Ni, whose location of its maximum contribution is displaced at log T = 5.4 instead of log T = 5.46. In addition, its contribution is reduced compared to the OP data. The other elements are also affected by the new Ni cross sections because of the change in the Ni spectrum. With the new data, the interval in which the nickel opacity is strong around the maximum of the F function overlaps more strongly in terms of photons energy with the interval in which iron has strong absorption features as well. That the photons are shared with iron in this energy range explains the reduced nickel contribution. For the same reason, the contribution of Fe is slightly reduced. The contributions of H and He, whose cross sections do not have any strong dependence versus photon energy near the maximum of the F function, are enhanced because of the decrease of those of some other elements, mainly Fe.
Fig. 8. Contributions to the Rosseland mean opacities around the Zbump as a function of log T. Only the four most important contributors in these layers (H, He, Fe, and Ni) are represented. The solid lines correspond to the new data, and the dashed lines show the OP values. 
Figure 9 compares the adiabatic and real gradients for the models with the new data and the model with OP. The new data change the actual gradient in the whole Zbump, whereas the adiabatic gradient is only affected around log T = 5.6. The new data yield a slightly larger convective zone in the Zbump compared to the OP model. The subsequent changes in the stellar structure and fundamental parameters are summarised in Table 1.
Fig. 9. Adiabatic (thin lines), and real gradients (thick lines) as a function of log T. The solid and dashed lines correspond to a model computed with the new Ni data and to a model calculated with Ni cross sections from OP, respectively. 
Relative changes in the stellar structure and fundamental parameters between the SCORCG model and the OP model.
6. Discussion and conclusions
With Ni cross sections computed with SCORCG, the shape of the RMO versus T in the Zbump is only slightly altered. It has a narrower peak and a shallower maximum in temperature. The value of the maximum is almost unchanged. The temperature derivative of the Rosseland opacity is plotted in Fig. 10. This derivative is related to the driving of pulsation modes (Pamyatnykh 1999) and reads κ_{T} + κ_{ρ}/(Γ_{3} − 1), where , , and . It shows an additional maximum around log T = 5.5 with the new data, and the stability of certain pulsation modes are likely to be affected. The shape of this derivative is close to that obtained with OPAL or OPLIB by Walczak et al. (2015) for their 10 M_{⊙} model. The details of a stability analysis are beyond the scope of the present paper, but we can already state that the new data for Ni are not able to reconcile the models with the observed pulsation modes of mainsequence massive pulsators because the RMOs we obtain in the Zbump are too small compared to the values needed to reproduce individual objects (Walczak et al. 2019, and references therein) as well as the instability strips (Moravveji 2016). This missing opacity could be produced by an accumulation of ironpeak elements, as suggested by Pamyatnykh et al. (2004) and computed with selfconsistent models by HuiBonHoa & Vauclair (2018a,b). Forthcoming studies are planned to use the new Ni data to compute radiative accelerations and revisit their results. A stability analysis would then be worth performing to confirm the agreement of observed modes and those obtained with these models.
Fig. 10. Temperature derivative of the Rosseland opacity vs. temperature. The solid line corresponds to the new data, and the dashed line shows the OP computation. 
Acknowledgments
This work was supported by the “Programme National de Physique Stellaire” (PNPS) of CNRS/INSU cofunded by CEA and CNES.
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All Tables
Relative changes in the stellar structure and fundamental parameters between the SCORCG model and the OP model.
All Figures
Fig. 1. Rosseland mean opacities κ_{R} of nickel computed with SCORCG in the (T, N_{e}) plane. The dots represent the grid points where the computations are made. The highest values are met in the area around log T = 5.4, i.e., in the socalled Zbump. 

In the text 
Fig. 2. Logarithm of the contributions to the Rosseland mean opacities (see text) in the (T, N_{e}) plane, plotted according to the same scale. Its lower limit is set to −2.5, and the smallest scattering contributions are upper limits. κ_{tot} is the RMO considering all the absorption processes, κ_{tot − P} is the RMO without process P, P being one of the opacity sources (lines bb, photoionisation bf, reverse bremsstrahlung ff, or scattering, scatt). 

In the text 
Fig. 3. Spectra with the logarithm of the spectral lines (red lines), photoionisation (blue lines), and reversebremsstrahlung (green lines) cross sections (left scale) vs. photon energy expressed in for two different temperatureelectron density sets. The conditions for which they have been computed and the resulting Rosseland mean are detailed in each panel. The dashed lines denote the normalised temperature derivative of the Planck function in logarithm, log F(u) (right scale). 

In the text 
Fig. 4. Ratios of the SCORCG Rosseland means and those of OP or OPAL in the (T, N_{e}) plane. κ_{R, SR} is the RMO from the new data and κ_{R, OP, OPAL} that of the comparison dataset. Top panel: comparison with OP. The SCORCG RMOs can be up to six times larger than those of OP in a narrow band in the Zbump, around log T = 5.3. Bottom panel: same plot with OPAL. The OPAL temperature step is larger for log T > 6. The area in which the SCORCG RMOs are higher than those of OPAL is larger than for OP. 

In the text 
Fig. 5. Relative difference between the original SCORCG RMO (κ_{R, orig.}) and the calculation with the OP frequency mesh (κ_{R, 10k}) in the (T, N_{e}) plane, plotted according to the same scale. Its upper limit is set to 5%. The dark red parts are to be considered as lower limits. From left to right, the panels show the results with the mean of the inverses of the cross sections, the mean of the cross sections, the sampling of the inverses, and the sampling of the cross sections. 

In the text 
Fig. 6. Comparison of the mean opacities of a stellar model computed with the new Ni data and one with the OP data. Upper panel: Rosseland mean (κ_{R}) of the stellar mixture with the new Ni data (solid line) and that with OP (dashed line) vs. log T. Lower panel: ratio of the SCORCG (κ_{R, SR}) and OP (κ_{R, OP}) Rosseland means vs. log T for the stellar mixture (thick line) and for Ni alone (thin line). The dotted line represents a ratio of one. 

In the text 
Fig. 7. Logarithm of the ratio of the monochromatic cross sections for the stellar mixture with the new Ni data (κ_{SR}) and those with the OP Ni data (κ_{OP}) vs. u, and the same quantity for Ni alone (thick and thin solid lines, respectively, left scale). The dashed line shows the F(u) function (right scale). The dotted line represents a ratio of one. For the sake of legibility, the spectra have been convolved with a Gaussian kernel with a standard deviation of 0.05. 

In the text 
Fig. 8. Contributions to the Rosseland mean opacities around the Zbump as a function of log T. Only the four most important contributors in these layers (H, He, Fe, and Ni) are represented. The solid lines correspond to the new data, and the dashed lines show the OP values. 

In the text 
Fig. 9. Adiabatic (thin lines), and real gradients (thick lines) as a function of log T. The solid and dashed lines correspond to a model computed with the new Ni data and to a model calculated with Ni cross sections from OP, respectively. 

In the text 
Fig. 10. Temperature derivative of the Rosseland opacity vs. temperature. The solid line corresponds to the new data, and the dashed line shows the OP computation. 

In the text 
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