Solar Metallicity Research Articles

Does the i-process operate at nearly solar metallicity?

Context. A sample of 895 s-process-rich candidates has been found among the 454 180 giant stars surveyed by LAMOST at low spectral resolution (R ~ 1800). In a previous study, taking advantage of the higher resolution (R ~ 86 000) offered by the HERMES-Mercator spectrograph, we performed a reanalysis of 15 of the brightest stars of this sample. Among these 15 programme stars, which have close-to-solar metallicities, 11 showed mild to strong heavy-element overabundances. However, we did not investigate the nucleosynthetic process(es) at the origin of these overabundances in our former study. Aims. We derive the abundances in s- and r-process elements of the 15 targets in order to investigate whether some stars also show an i-process signature, as sometimes found in their lower-metallicity counterparts (namely, the carbon-enhanced metal-poor (CEMP)-rs stars). Methods. Abundances are derived from the high-resolution HERMES spectra for Pr, Nd, Sm, and Eu using the TURBOSPECTRUM radiative-transfer local thermodynamic equilibrium code with MARCS model atmospheres. Results. Using the new classification scheme proposed in our recent study, we find that two stars show overabundances in both sand r-process elements that are well above the level expected from Galactic chemical evolution (GCE), an analogous situation to that of CEMP-rs stars at lower metallicities. We compare the abundances of the most enriched stars with the nucleosynthetic predictions from the STAREVOL stellar evolutionary code and find abundances compatible with an i-process occurring in asymptotic giant branch stars. Conclusions. Despite there being a larger number of heavy elements with which to characterize the enrichment pattern, the limit between CEMP-s and CEMP-rs stars remains indistinct. Nevertheless, it is interesting to note that an increasing number of extrinsic stars are found to have abundances better reproduced by an i-process pattern even at close-to-solar metallicities.

Revisiting the properties of GW190814 and its formation history

ABSTRACT GW190814 was reported during LIGO’s and Virgo’s third observing run with the most asymmetric component masses (an ∼23 M⊙ black hole and an ∼2.6 M⊙ compact object). Under the assumption that this event is a binary black hole (BBH) merger formed through the isolated binary evolution channel, we reanalyse the publicly released data of GW190814 with the modified astrophysical priors on the effective spin χeff, and further explore its formation history using detailed binary modelling. We show that GW190814 is likely to have been formed through the classical common envelope channel. Our findings show that the properties inferred using the modified astrophysical priors are consistent with those inferred by the uniform priors. With the newly inferred properties of GW190814, we perform detailed binary evolution of the immediate progenitor of the BBH (namely a close binary system composed of a BH and a helium star) in a large parameter space, taking into account mass-loss, internal differential rotation, supernova kicks, and tidal interactions between the helium star and the BH companion. Our findings show that GW190814-like events could be formed in limited initial conditions just after the common envelope phase: an ∼23 M⊙ BH and a helium star of MZamsHe ∼ 8.5 M⊙ at solar metallicity (∼ 7.5 M⊙ at 10 per cent solar metallicity) with an initial orbital period at around 1.0 d. Additionally, the inferred low spin of the secondary indicates that the required metallicity for reproducing GW190814-like events should not be too low (e.g. Z ≳ 0.1 Z⊙).

Stellar wind yields of very massive stars

ABSTRACT The most massive stars provide an essential source of recycled material for young clusters and galaxies. While very massive stars (VMSs, M>100 $\rm {\rm M}_{\odot }$) are relatively rare compared to O stars, they lose disproportionately large amounts of mass already from the onset of core H-burning. VMS have optically thick winds with elevated mass-loss rates in comparison to optically thin standard O-star winds. We compute wind yields and ejected masses on the main sequence, and we compare enhanced mass-loss rates to standard ones. We calculate solar metallicity wind yields from MESA stellar evolution models in the range 50–500 $\rm {\rm M}_{\odot }$, including a large nuclear network of 92 isotopes, investigating not only the CNO-cycle, but also the Ne–Na and Mg–Al cycles. VMS with enhanced winds eject 5–10 times more H-processed elements (N, Ne, Na, Al) on the main sequence in comparison to standard winds, with possible consequences for observed anticorrelations, such as C–N and Na–O, in globular clusters. We find that for VMS 95 per cent of the total wind yields is produced on the main sequence, while only ∼ 5 per cent is supplied by the post-main sequence. This implies that VMS with enhanced winds are the primary source of 26Al, contrasting previous works where classical Wolf–Rayet winds had been suggested to be responsible for galactic 26Al enrichment. Finally, 200 $\rm {\rm M}_{\odot }$ stars eject 100 times more of each heavy element in their winds than 50 $\rm {\rm M}_{\odot }$ stars, and even when weighted by an IMF their wind contribution is still an order of magnitude higher than that of 50 $\rm {\rm M}_{\odot }$ stars.

The γ-process nucleosynthesis in core-collapse supernovae

Context. The γ-process nucleosynthesis in core-collapse supernovae is generally accepted as a feasible process for the synthesis of neutron-deficient isotopes beyond iron. However, crucial discrepancies between theory and observations still exist: the average yields of γ-process nucleosynthesis from massive stars are still insufficient to reproduce the solar distribution in galactic chemical evolution calculations, and the yields of the Mo and Ru isotopes are a factor of ten lower than the yields of the other γ-process nuclei. Aims. We investigate the γ-process in five sets of core-collapse supernova models published in the literature with initial masses of 15, 20, and 25 M⊙ at solar metallicity. Methods. We compared the γ-process overproduction factors from the different models. To highlight the possible effect of nuclear physics input, we also considered 23 ratios of two isotopes close to each other in mass relative to their solar values. Further, we investigated the contribution of C–O shell mergers in the supernova progenitors as an additional site of the γ-process. Results. Our analysis shows that a large scatter among the different models exists for both the γ-process integrated yields and the isotopic ratios. We find only ten ratios that agree with their solar values, all the others differ by at least a factor of three from the solar values in all the considered sets of models. The γ-process within C–O shell mergers mostly influences the isotopic ratios that involve intermediate and heavy proton-rich isotopes with A > 100. Conclusions. We conclude that there are large discrepancies both among the different data sets and between the model predictions and the solar abundance distribution. More calculations are needed; particularly updating the nuclear network, because the majority of the models considered in this work do not use the latest reaction rates for the γ-process nucleosynthesis. Moreover, the role of C–O shell mergers requires further investigation.

Bridging the gap between intermediate and massive stars II: Mmas for the most metal-rich stars and implications for Fe CCSNe rates

ABSTRACT The minimum initial mass required for a star to explode as an Fe core collapse supernova, typically denoted Mmas, is an important quantity in stellar evolution because it defines the border between intermediate mass and massive stellar evolutionary paths. The precise value of Mmas carries implications for models of galactic chemical evolution and the calculation of star formation rates. Despite the fact that stars with super-solar metallicities are commonplace within spiral and some giant elliptical galaxies, there are currently no studies of this mass threshold in super metal-rich models with Z > 0.05. Here, we study the minimum mass necessary for a star to undergo an Fe core collapse supernova when its initial metal content falls in the range 2.5 × 10−3 ≤ Z ≤ 0.10. Although an increase in initial Z corresponds to an increase in the Fe ignition threshold for Z ≈ 1 × 10−3 to Z ≈ 0.04, we find that there is a steady reversal in trend that occurs for Z > 0.05. Our super metal-rich models thus undergo Fe core collapse at lower initial masses than those required at solar metallicity. Our results indicate that metallicity-dependent curves extending to Z = 0.10 for the minimum Fe ignition mass should be utilized in galactic chemical evolution simulations to accurately model supernovae rates as a function of metallicity, particularly for simulations of metal-rich spiral and elliptical galaxies.

Photometric metallicities of fundamental-mode RR Lyr stars from Gaia G band photometry of globular-cluster variables

ABSTRACT Photometric metallicity formulae of fundamental-mode RR Lyr (RRab) stars are presented using globular-cluster data exclusively. The aim is to check whether this selection may help increasing the overall accuracy of the fits and eliminating the systematic bias of the photometric results, namely that they tend to overestimate [Fe/H] of the most metal-poor variables. The G band time-series data available in the Gaia DR3 archive and a new compilation of the published spectroscopic globular cluster [Fe/H] values on a uniform solar reference metallicity scale are utilized. We have derived a new [Fe/H]phot − P, φ31 formula, and have diagnosed that no significant increase in the accuracy of the fit can be achieved using non-linear or multiparameter formulae. The best result is obtained when different formulae are applied for variables with Oosterhoff (Oo)-type I and II properties. However, even this solution cannot eliminate the systematic bias of the results completely. This separation of the variables has also led to the conclusion that the photometric estimates of the [Fe/H] are less reliable for the Oo-type II variables than for the Oo-type I sample. Published [Fe/H]phot values and the results of the available photometric formulae in the Gaia G band are compared with the present results. It is found that each of the solutions yields very similar results, with similar accuracy and systematic biases. Major differences are detected only in the zero-points of the [Fe/H] scales, and these offsets are larger than differences in the accepted solar reference values would explain.

The Mass–Temperature Relation for B and Early A Stars Based on International Ultraviolet Explorer Spectra of Detached Eclipsing Binaries

Ultraviolet spectra were taken of 25 detached eclipsing binaries (DEBs) with spectral types O, B, and early A with the International Ultraviolet Explorer satellite in the 1150–1900 Å region. The spectra were compared with BOSZ model atmospheres. The composite spectra of the DEBs were modeled by a combination of models representing the hot and cool components, and the temperatures of the hottest components of the systems were determined. From these temperatures a direct mass–temperature relation was obtained for stars close to the main sequence with solar metallicity for B and early A stars: log M/M ⊙ = −5.90 ± 0.27 + (1.56 ± 0.07) × log T. This relation allows a mass to be inferred for comparable stars from an ultraviolet spectrum. The five chemically peculiar Am stars in the sample have larger radii than normal A stars of the same mass.

Frequency of the dark matter subhalo collisions and bifurcation sequence arising formation of dwarf galaxies

ABSTRACT The cold dark matter model predicts galaxies have 100 times more dark matter mass than stars. Nevertheless, recent observations report the existence of dark-matter-deficient galaxies with less dark matter than expected. To solve this problem, we investigate the physical processes of galaxy formation in head-on collisions between gas-containing dark matter subhaloes (DMSHs). Analytical estimation of the collision frequency between DMSHs associated with a massive host halo indicates that collisions frequently occur within one-tenth of the virial radius of the host halo, with a collision time-scale of about $10\, \mathrm{Myr}$, and the most frequent relative velocity increases with increasing radius. Using analytical models and numerical simulations, we show the bifurcation channel of the formation of dark-matter-dominated and dark-matter-deficient galaxies. In the case of low-velocity collisions, a dark-matter-dominated galaxy is formed by the merging of two DMSHs. In the case of moderate-velocity collisions, the two DMSHs penetrate each other. However, the gas medium collides, and star formation begins as the gas density increases, forming a dwarf galaxy without dark matter at the collision surface. In the case of high-velocity collisions, shock-breakout occurs due to the shock waves generated at the collision surface reaching the gas surface, and no galaxy forms. For example, the simulation demonstrates that a pair of DMSHs with a mass of $10^9\, \mathrm{M_\odot }$ containing gas of 0.1 solar metallicity forms a dark-matter-deficient galaxy with a stellar mass of $10^7\, \mathrm{M_\odot }$ for a relative velocity of $200\, \mathrm{km\, s^{-1}}$.

Effectiveness of the front and rear grids as a result of silicon solar cell metallization patterns: A study using Griddler simulator

The objective of this investigation is to evaluate the effect of metallization patterns on the front and rear grids on the efficiency of the silicon heterojunction (SHJ) cells. Griddler 2.5 PRO simulator was utilized to analyze the effects of various front grid metallization designs and geometries on open circuit voltage (VOC), short circuit density (JSC), fill factor (FF), and efficiency (ƞ) of silicon-based PV cells. Griddler 2.5 PRO is designed to assess different cell types, and gain a better understanding of the limiting factors that influence solar cell characteristics in laboratory and field settings. The finite-element method (FEM) is applied in solar cell modeling to approximate the cell plane as a network of resistors and diodes. It also features an interface for generating H-patterns and back metal grids. The simulations varied the number of busbars used on the front side metal grids of solar cells from 1 to 5 and the number of metal fingers used for grid pattern optimization from 80 to 130, with finger widths ranging from 10 to 60 µm. For optimization of efficiency and fill factor, various styles (straight, rectangular pad tapered, round pad, digital, two split, and three split) and shapes (straight, pointed, digital, apollo, and wine bottle) were explored. The front and rear contact resistances were kept constant during these simulations to obtain the best fill factor and efficiency. In this model, with 110 fingers (the finger sheet resistance of front and rear sides is kept at 3 mΩ/□) and four busbars, with two split style and straight shapes and a finger width of 25 µm, was designed to achieve maximum performance of the solar cell. Various recombination loss factors in the cells are also analyzed. The results indicate that this is one of the most efficient silicon solar cells modeled, with a fill factor and efficiency of 80 % and 19.55 %, respectively, which is noteworthy for a planar solar cell.

Computational investigation of the effect ZnS buffer layer on the hole transport of polymer solar cell

Semiconductor organic solar absorber exhibits poor charge transport process because of exciton short diffusion length, short life time, and poor carrier mobilities in the medium. Such transport properties have negatively impacted the performance of organic solar cells (OSC). This article is designed to investigate the effect of solar absorber thickness and metal plasmonic nanoparticles using the most popular polymer blend (P3HT:PCBM) via SCAPS device simulation program. Bulk hetero-junction (BHJ) design of OSC has partially addressed the challenges by increasing inter-facial area of the acceptor/donor (A/D) molecules, which boosts the generation of free charges. However, the collection of these charges hindered due to low carrier mobilities in polymer medium. Significant influence of the Zinc Sulfide (ZnS) metal nanoparticles (NPs) have been observed on the performance of OSC at various concentrations. Thus, we are reporting here the effect of absorber layer thickness and ZnS NPs on the charge transport process in OSC.

Paste Development for an Optimized Filament Stretching Effect during Parallel Dispensing on Transparent Conductive Oxide Layers for Solar Cell Metallization

The availability of silver as an electrically conductive filler material in printing pastes for solar cell metallization is becoming a more crucial issue for multiterawatt‐scale production due to its global constraints. Therefore, the silver consumption for solar cell production needs to be reduced drastically by substituting silver with alternative conductive filler materials or utilizing process‐specific phenomena. The phenomenon of filament stretching during microextrusion allows significantly lower paste laydowns. The magnitude of filament stretching is paste‐dependent and therefore further knowledge of the pastes’ impact to the filament stretching is required. This study presents nine low‐temperature curing pastes differing in the particle system and binder resin. The rheological and thermal behavior of these suspensions are investigated and printing tests onto silicon heterojunction (SHJ) precursors are carried out. Additionally, scanning electron microscopy (SEM)‐based microstructure analyses of printed electrodes are performed. Based on these experimental results, the impact of paste compositions regarding the paste behavior during microextrusion and the SHJ solar cell performances are analyzed. The developed paste formulations exhibit a strong filament stretching, leading to a reduced silver laydown of down to ΔmAg = −60%rel. and an absolute efficiency gain of up to Δη = +0.75%abs. due to less shading losses.

Astrophysical Parameters of the Open Cluster NGC 2509

This study presents structural and fundamental astrophysical parameters of poorly studied open cluster NGC 2509. We used the third photometric and astrometric data release of the Gaia (Gaia DR3) to perform analyses. By taking into account the Gaia DR3 astrometric data, we calculated the membership probabilities of the stars in the region of NGC 2509. As a result of the membership analysis, 244 stars with membership probabilities P  50% were determined as the physical members of the cluster. The colour excess, distance and age were obtained simultaneously by fitting solar metallicity PARSEC isochrones to G×GBP-GRP colour-magnitude diagram. We considered the most likely cluster member stars during the fitting procedure and calculated the colour excess, distance and age of the NGC 2509 as E(GBP-GRP) = 0.100±0.184 mag, d = 2518±667 pc and t = 1.5±0.1 Gyr, respectively.

Boosting interfacial solar steam generation by three-dimensional bilayer cellulose aerogels

Interfacial solar steam generation (ISSG) provides a sustainable approach of clean water production through desalination and water purification. It is still needed to pursue a fast evaporation rate, high-quality freshwater production, and low-cost evaporators. Herein, a three-dimensional (3D) bilayer aerogel was fabricated using cellulose nanofiber (CNF) as a skeleton filled with polyvinyl alcohol phosphate ester (PVAP), and carbon nanotubes (CNT) as a light absorbing material in the top layer. The CNF/PVAP/CNT aerogel (CPC) had broadband light absorption ability and exhibited an ultrafast water transfer rate. The lower thermal conductivity of CPC effectively confined the convert heat in the top surface and minimized heat loss. Additionally, a large amount of intermediate water caused by water activation decreased the evaporation enthalpy. Under 1 sun irradiation, the CPC-3 (3.0 cm height of CPC) achieved a high evaporation rate of 4.02 kg m−2 h−1 with an energy conversion efficiency of 125.1%. The additional convective flow and environmental energy made CPC achieve an ultrahigh evaporation rate of 11.37 kg m−2 h−1, surpassing 673% of the solar input energy. More importantly, the continuous solar desalination and higher evaporation rate (10.70 kg m−2 h−1) in seawater revealed that CPC was a promising candidate for practical desalination. Outdoor cumulative evaporation was up to 73.2 kg m−2 d−1 in weak sunlight and lower temperature, which would meet the daily drinking water demands of 20 people. The excellent cost-effectiveness of 1.085 L h−1 $−1 presented its potential for a wide range of practical applications, such as solar desalination, wastewater treatment, and metal extractions.

The formation of merging black holes with masses beyond 30 M⊙ at solar metallicity

The formation of merging black holes with masses beyond 30 M⊙ at solar metallicity

Astrophysical Parameters of the Open Cluster Berkeley 6

In this study, the structural and basic astrophysical parameters of poorly studied open cluster Berkeley 6 is calculated. Analyses of the cluster are carried out using the third photometric, spectroscopic and astrometric data release of Gaia (Gaia DR3). The membership probabilities of stars located through the cluster region are calculated by considering their astrometric data. Thus, we identified 119 physical members for Berkeley 6. The colour excess, distance and age of the cluster are determined simultaneously on the colour-magnitude diagram. We fitted solar metallicity PARSEC isochrones to the colour-magnitude diagram by considering the most probable member stars and obtained E(GBP-GRP) colour excess as 0.918±0.145 mag. Distance and age of the cluster are determined as d=2625±337 pc and t=350±50 Myr, respectively.

Understanding the progenitor formation galaxies of merging binary black holes

ABSTRACT With nearly a hundred gravitational wave detections, the origin of black hole mergers has become a key question. Here, we focus on understanding the typical galactic environment in which binary black hole (BBH) mergers arise. To this end, we synthesize progenitors of BBH mergers as a function of the redshift of progenitor formation, present-day formation galaxy mass, and progenitor stellar metallicity for 240 star formation and binary evolution models. We provide guidelines to infer the formation galaxy properties and time of formation, highlighting the interplay between the star formation rate and the efficiency of forming merging BBHs from binary stars, both of which strongly depend on metallicity. We find that across models, over 50 per cent of BBH mergers have a progenitor metallicity of a few tenths of Solar metallicity, however, inferring formation galaxy properties strongly depends on both the binary evolution model and global metallicity evolution. The numerous, low-mass black holes (≲ 15 M⊙) trace the bulk of the star formation in galaxies heavier than the Milky Way (MGal ≳ 1010.5 M⊙). In contrast, heavier BBH mergers typically stem from larger black holes forming in lower metallicity dwarf galaxies (MGal ≲ 109 M⊙). We find that the progenitors of detectable BBHs tend to arise from dwarf galaxies at a lower formation redshift (≲1). We also produce a posterior probability of the progenitor environment for any detected gravitational wave signal. For the massive GW150914 merger, we show that it likely came from a very low-metallicity (Z ≲ 0.025 Z⊙) environment.

Rapid population synthesis of black hole high-mass X-ray binaries: implications for binary stellar evolution

ABSTRACT We conduct binary population synthesis to investigate the formation of wind-fed high-mass X-ray binaries containing black holes (BH-HMXBs). We evolve multiple populations of high-mass binary stars and consider BH-HMXB formation rates, masses, spins, and separations. We find that systems similar to Cygnus X-1 likely form after stable Case A mass transfer (MT) from the main-sequence progenitors of BHs, provided such MT is characterized by low accretion efficiency, β ≲ 0.1, with modest orbital angular momentum losses from the non-accreted material. Additionally, efficient BH-HMXB formation relies on a new simple treatment for Case A MT that allows donors to retain larger core masses compared to traditional rapid population-synthesis assumptions. At solar metallicity, our Preferred model yields $\mathcal {O}(1)$ observable BH-HMXBs in the Galaxy today, consistent with observations. In this simulation, 8 per cent of BH-HMXBs go on to merge as binary black holes or neutron star-black hole binaries within a Hubble time; however, none of the merging binaries have BH-HMXB progenitors with properties similar to Cygnus X-1. With our preferred settings for core mass growth, mass transfer efficiency, and angular momentum loss, accounting for an evolving metallicity, and integrating over the metallicity-specific star formation history of the Universe, we find that BH-HMXBs may have contributed ≈2–5 BBH merger signals to detections reported in the third gravitational-wave transient catalogue of the LIGO–Virgo–KAGRA Collaboration. We also suggest MT efficiency should be higher during stable Case B MT than during Case A MT.

TOI-5678b: A 48-day transiting Neptune-mass planet characterized with CHEOPS and HARPS

Context. A large sample of long-period giant planets has been discovered thanks to long-term radial velocity surveys, but only a few dozen of these planets have a precise radius measurement. Transiting gas giants are crucial targets for the study of atmospheric composition across a wide range of equilibrium temperatures and, more importantly, for shedding light on the formation and evolution of planetary systems. Indeed, compared to hot Jupiters, the atmospheric properties and orbital parameters of cooler gas giants are unaltered by intense stellar irradiation and tidal effects. Aims. We aim to identify long-period planets in the Transiting Exoplanet Survey Satellite (TESS) data as single or duo-transit events. Our goal is to solve the orbital periods of TESS duo-transit candidates with the use of additional space-based photometric observations and to collect follow-up spectroscopic observations in order to confirm the planetary nature and measure the mass of the candidates. Methods. We use the CHaracterising ExOPlanet Satellite (CHEOPS) to observe the highest-probability period aliases in order to discard or confirm a transit event at a given period. Once a period is confirmed, we jointly model the TESS and CHEOPS light curves along with the radial velocity datasets to measure the orbital parameters of the system and obtain precise mass and radius measurements. Results. We report the discovery of a long-period transiting Neptune-mass planet orbiting the G7-type star TOI-5678. Our spectroscopic analysis shows that TOI-5678 is a star with a solar metallicity. The TESS light curve of TOI-5678 presents two transit events separated by almost two years. In addition, CHEOPS observed the target as part of its Guaranteed Time Observation program. After four non-detections corresponding to possible periods, CHEOPS detected a transit event matching a unique period alias. Follow-up radial velocity observations were carried out with the ground-based high-resolution spectrographs CORALIE and HARPS. Joint modeling reveals that TOI-5678 hosts a 47.73 day period planet, and we measure an orbital eccentricity consistent with zero at 2σ. The planet TOI-5678 b has a mass of 20 ± 4 Earth masses (M⊕) and a radius of 4.91 ± 0.08 R⊕ Using interior structure modeling, we find that TOI-5678 b is composed of a low-mass core surrounded by a large H/He layer with a mass of 3.2±1.7−1.3 M⊕. Conclusions. TOI-5678 b is part of a growing sample of well-characterized transiting gas giants receiving moderate amounts of stellar insolation (11 S⊕). Precise density measurement gives us insight into their interior composition, and the objects orbiting bright stars are suitable targets to study the atmospheric composition of cooler gas giants.

An evolutionary model for the V404 Cyg system

V404 Cyg is a low mass X-Ray binary (LMXB) system that has undergone outbursts in 1938, 1989, and 2015. During these events, it has been possible to make determinations for the relevant data of the system. This data include the mass of the compact object (i.e., a black hole; BH) and its companion, the orbital period, the companion spectral type, and luminosity class. Remarkably, the companion star has a metallicity value that is appreciably higher than solar. All these data allow for the construction of theoretical models to account for its structure, determine its initial configuration, and predict its fate. Assuming that the BH is already formed when the primary star reaches the zero age main sequence, we used our binary evolution code for this purpose. We find that the current characteristics of the system are nicely accounted for by a model with initial masses of 9 M⊙ for the BH, 1.5 M⊙ for the companion star and an initial orbital period of 1.5 d, while also considering that at most 30% of the mass transferred by the donor is accreted by the BH. The metallicity of the donor for our best fit is Z = 0.028 (twice solar metallicity). We also studied the evolution of the BH spin parameter, assuming that is not rotating initially. Remarkably, the spin of the BHs in our models is far from reaching the available observational determination. This may indicate that the BH in V404 Cyg was initially spinning, a result that may be relevant for understanding the formation BHs in the context of LMXB systems.

Power-2 limb-darkening coefficients for the uvby, UBVRIJHK, SDSS ugriz, Gaia, Kepler, TESS, and CHEOPS photometric systems

Context. The phenomenon of limb-darkening is relevant to many topics in astrophysics, including the analysis of light curves of eclipsing binaries, optical interferometry, measurement of stellar diameters, line profiles of rotating stars, gravitational microlensing, and transits of extrasolar planets Aims. Multiple parametric limb-darkening laws have been presented, and there are many available sources of theoretical limb-darkening coefficients (LDCs) calculated using stellar model atmospheres. The power-2 limb-darkening law allows a very good representation of theoretically predicted intensity profiles, but few LDCs are available for this law from spherically symmetric model atmospheres. We therefore present such coefficients in this work. Methods. We computed LDCs for the space missions Gαiα, Kepler, TESS, and CHEOPS and for the passbands uυby, UBVRIJHK, and SDSS ugriz, using the PHOENIX-COND spherical models. We adopted two methods to characterise the truncation point, which sets the limb of the star: the first (M1) uses the point where the derivative dI(r)/dr is at its maximum – where I(r) is the specific intensity as a function of the normalised radius r – corresponding to µcri, and the second (M2) uses the midpoint between the point µcri and the point located at µcri–1. The LDCs were computed adopting the Levenberg–Marquardt least-squares minimisation method, with a resolution of 900 equally spaced µ points, and covering 823 model atmospheres for a solar metallicity, effective temperatures of 2300–12000 K, log g values from 0.0 to 6.0, and microturbulent velocities of 2 km s−1. As our previous calculations of LDCs using spherical models included only 100 µ points, we also updated the calculations for the four-parameter law for the passbands listed above, and compared them with those from the power-2 law. Results. Comparisons between the quality of the fits provided by the power-2 and four-parameter laws show that the latter presents a lower merit function, χ2, than the former for both cases (M1 and M2). This is important when choosing the best approach for a particular science goal.