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A Grid of Synthetic Spectra for Subdwarfs: Non-LTE Line-blanketed Atmosphere Models

A Grid of Synthetic Spectra for Subdwarfs: Non-LTE Line-blanketed Atmosphere Models A new grid of detailed atmosphere model spectra for hot and moderately cool subdwarf stars is presented. High- resolution spectra and synthetic photometry are calculated in the range from 1000–10,000 Å using non-LTE fully line-blanketed atmosphere structures. Our grid covers eight temperatures within 10,000 „ T [K] „ 65,000, three eff surface gravities in the range 4.5 „ log g [cgs] „ 6.5, two helium abundances matching two extreme helium-rich and helium-poor scenarios, and two limiting metallicity boundaries regarding both solar ([Fe/H] = 0) and Galactic halos ([Fe/H] = −1.5 and [α/Fe]=+0.4). Besides its application in the determination of fundamental parameters of subdwarfs in isolation and in binaries, the resulting database is also of interest for population synthesis procedures in a wide variety of stellar systems. Unified Astronomy Thesaurus concepts: Stellar atmospheres (1584); Spectral energy distribution (2129); Stellar spectral lines (1630); Subdwarf stars (2054) 1. Introduction day (45%). (iii) Those showing additional spectral lines from a cool FGK main-sequence or subgiant companion that have slowly The evolutionary scenario of subdwarfs is still emerging. Hot varying or nearly constant velocities, indicating periods of many subdwarf stars evolve from low- to intermediate-mass progenitors months to years. and reach far beyond the main sequence, at the blue end of the There is observational evidence indicating that subdwarfs are horizontal branch (HB) or mixed with post-HB stars (Heber 2009). the most likely candidates to account for the ultraviolet (UV) Even though they lie mostly between the main sequence and the upturn observed on spectroscopic and photometric analyses of white dwarf (WD) cooling sequence in the Hertzsprung–Russell globular clusters and elliptical galaxies (Yi et al. 1999; Busso diagram, they are contaminated with WDs. et al. 2005; Green et al. 2008). The most accepted formation scenario is of an extreme HB star Analysis from asteroseismology (Charpinet et al. 2005), that lost its envelope after the He-burning phase, evolving directly spectroscopy (Wade et al. 2005; Dorsch et al. 2018, 2019), and to the WD-cooling sequence by avoiding the asymptotic giant photometry (Johnson et al. 2014) of field subdwarf stars found branch (AGB)(Wade et al. 2005;Heber 2009;Fontaineetal. nonsolar He abundances. He-rich and He-poor sequences, as a 2012). These objects experienced mass transfer followed by function of effective temperature, were proposed by Edelmann common envelope ejection in a binary system leaving the stellar et al. (2003) and updated by Németh et al. (2012) and Lei et al. core exposed (Green et al. 2008; Geier et al. 2010). More recent (2019). Those sequences also support the evidence that He- investigations support this scenario, such as the observational enriched sdOs are more common than the He-deficient ones evidence of hot O- and B-type subdwarf formation (sdO and sdB, (Heber 2009). respectively) from the product of binary interactions (Pelisoli et al. It is ideal to have homogeneous and widely available model 2020). Also, the expected evolutionary path suggests that sdOs spectra for these elusive systems, in order to improve our evolve from sdBs (Heber 2009). An alternative evolutionary knowledge of their fundamental physical parameters and scenario suggests that the merger of two low-mass He-core WDs evolution. Such models should be computed as fully as might form isolated H-rich B-type hot subdwarfs (Hall & Jeffery possible regarding the radiative transfer, considering nonlocal 2016;Schwab 2018). thermodynamic equilibrium (NLTE), fully blanketed atmos- A small fraction of sdBs in close binaries (Wade et al. 2005) phere structures (Lanz & Hubeny 1995; Lanz et al. 1997). fall out of the red giant branch before He ignition, perhaps Considerable improvements in NLTE atmosphere models have because they are low-mass stars that do not support the burning been achieved over the last five decades. The first NLTE spectra of He in their cores (Heber 2009). of hot atmospheres in the early 1970s (Mihalas & Hummer 1974) The hot subdwarfs can be separated into three main groups were built based on pure H atmosphere structures, and the metal according to Saffer et al. (2001). (i) Those nonbinaries that have lines were considered only in the spectral synthesis. Analysis by no detectable spectral lines from a cool companion, and show Lanz & Hubeny (1995) took H, C, and Fe into account for the only small or insignificant velocity variations (35%). (ii) Those opacity of hot and high-gravity NLTE atmosphere models. They single-lined spectroscopic binaries which have significant or large found critical differences in effective temperature determinations velocity variations and probable orbital periods on the order of a and line profiles arising from the inclusion of explicit atomic species (i.e., with the kinetic equilibrium equation solved) in the Original content from this work may be used under the terms atmospheric structure. The subdwarfs’ atmospheres have more of the Creative Commons Attribution 4.0 licence. Any further evident NLTE effects due to their lower surface gravities (when distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. compared to WDs; Lanz et al. 1997). They built spectra 1 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. considering full line blanketing with H/He,CNO,Si, Fe,and Ni equilibrium, therefore level populations in NLTE were as implicit ions and concluded that this approach significantly calculated. Departures from LTE may be specially significant improved the line profile analysis. Hubeny et al. (1998) showed for high-temperature subdwarf atmospheres (Hubeny & Lanz that NLTE metal-line-blanketing effects produce a conspicuous 1995; Lanz & Hubeny 1995; Lanz et al. 1997) as also found in difference (typically 20%) in the line profiles seen in the UV DA-type WD atmospheres (Levenhagen et al. 2017). spectra of hot WDs. By considering explicit metal ions such as H/ The starting point was to compute an LTE gray structure He, CNO, Si, and Fe in the atmosphere structure a better emergent model, which is then used as an input to build the NLTE line- flux match was achieved. blanketed models (Hubeny 1988; Hubeny et al. 1994).We Overall, the subdwarfs’ spectra are built for specific targets considered H, He, C, N, O, Ne, Mg, Al, Si, S, and Fe as explicit and studies. We have hundreds of hot subdwarf stars cataloged ions (see Table 1) contributing to the opacity. The set of (Geier et al. 2017; Heber et al. 2017; Geier & Raddi 2019; ionization states for the selected atomic species were chosen on Geier 2020), with their spectral analysis focused on classifica- the basis of ionization energies, model-effective temperatures, tion and/or kinematic properties (Luo et al. 2019). A lot of and candidate-permitted transitions from Willians & Livio work was done to analyze the He-abundance (Fontaine et al. (1995). The atomic data of each ion included as an explicit 2019) sequences (Lei et al. 2019). The sequences also show species in the NLTE atmosphere models are summarized in differences between field subdwarfs and extreme HB sub- Table 1 (see details in Lanz & Hubeny 2003, 2007). dwarfs in globular clusters (Lei et al. 2020). As describedbyLanz&Hubeny (2007),the LTE fluxes are NLTE structures and subdwarf spectra were calculated by about 10% higher than the NLTE predictions, and this is most Nemeth et al. (2014), covering specific temperature and gravity noticeable in the near-UV. Lanz & Hubeny (2007) also mentioned ranges. The opacities of H, He, and a few metal ions were that the lower NLTE fluxes result from the overpopulation of the included to compute the atmosphere structure in these models. H I (n= 2) level at the depth of formation of the continuum flux, However, only a small and nonhomogeneous collection of hence implying a larger Balmer continuum opacity. detailed subdwarf model spectra is currently available. High- The adopted abundances are expressed as solar ([Fe/H]= 0.0; temperature spectral grids may be also calculated by other Asplund et al. 2009) or Galactic halo ([Fe/H]=−1.5 and [α/ codes e.g., the Tübingen NLTE Model Atmosphere package Fe]=+0.4) as well as He-rich (Edelmann et al. 2003) and He- (Rauch et al. 2018). poor abundances (Németh et al. 2012; Lei et al. 2019). Our choice In this work we present an extensive high-spectral-resolution of usingsolar andhalometallicity is notintendedtodescribe grid of NLTE synthetic spectra for subdwarfs in the optical and subdwarf typical abundances. Instead, these solar and halo points UV. The models are fully line blanketed with H, He, C, N, O, Ne, just set a broad Z range, probing its effect on the continuum and Mg,Al, Si,S,and Fe as opacity sources (see Table 1).Wealso line profiles. It is well established that atmospheric subdwarf metal consider nonsolar chemical abundances to better sample the abundances have little or virtually no memory of their parent subdwarf parameter space. Low-temperature convective atmo- main-sequence abundances (e.g., Moehler 2001;Némethetal. spheres were also included in the square grid. The complete grid is 2012; Byrne et al. 2018). Metals at the subdwarf surface vary by available our SpecModels website as well as on the Spanish large amounts depending on previous binary evolution and Virtual Observatory’s Theoretical Spectra Web Server and the diffusion processes, leading to diverse abundance patterns (e.g., Vizier database. O’Toole & Heber 2006) with loose observational constraints. He- Section 2 describes the atmosphere structure models, in rich and He-poor abundance variations were chosen based on particular the differences between the LTE and NLTE assump- linear fits as a function of temperature based on Lei et al. (2019) tions made. Section 3 describes the synthetic spectra, comparing (see Table 2). Note that TLUSTY (Hubeny 1988;Hubeny& the results with observational data. Section 4 describes the Lanz 2011a) uses the solar chemical abundances as defined by construction of the synthetic magnitudes and their application in Grevesse & Sauval (1998) as default values, and we rearranged all color–color diagrams. Section 5 presents the concluding remarks. the chemical species to the solar abundance as definedbyAsplund et al. (2009). The atmosphere structures (available upon request to the authors) may be interpolated in metallicity and specific 2. Atmosphere Structure modified metal abundances used in custom spectral synthesis. The atmosphere structure models were computed by The time spent on computational work increases and the TLUSTY code v205 and v208 (for convective 10,000 K convergence is more difficult when the complexity of the heavy models; Hubeny 1988; Hubeny & Lanz 2011a). It calculates a elements is included in the TLUSTY atmosphere code (Hubeny self-consistent solution of the equations describing the radiative 1988;Hubeny&Lanz 2011a). As a reference, each one of the 96 (or radiative plus convective) transfer and physical state of the structures were computed and analyzed in a typical timescale of atmosphere. The geometry of the model is plane-parallel with aday. homogeneous chemical abundances (Hubeny & Lanz 1995). The grid of subdwarf-structure models is composed of eight The most popular subdwarf models available have been built effective temperatures (T : 10,000, 15,000, 20,000, 25,000, eff in LTE. In LTE all energy partitioning such as atomic, ionic, 30,000, 35,000, 45,000, and 65,000 K), each one computed in and molecular level populations is given by Saha–Boltzmann three surface gravities (log g [cgs]: 4.5, 5.5, and 6.5) and four equations, being defined by the local temperature. The LTE different chemical abundances: solar and He-rich, solar and He- conditions may differ from those derived in actual statistical poor, halo and He-rich, halo and He-poor. The broadening of lines was treated carefully considering the http://dc.zah.uni-heidelberg.de/theossa/q/web/form Lyman and Balmer line profile tables from Tremblay & Bergeron Spectral Models of Stars and Stellar Populations, http://specmodels.iag. (2009). The high-frequency limit for lines that are taken into usp.br/. http://svo2.cab.inta-csic.es/theory//newov2/ account in the opacity sampling was set to 6 × 10 × T or the eff https://vizier.u-strasbg.fr/viz-bin/VizieR highest bound-free edge frequency, if greater. Opacity-sampling 2 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. Table 1 Atomic Data of the Explicit Species Included in the NLTE Atmosphere Models Atomic Data Explicit Ions Included in NLTE Ion Super(level) Lines Reference 10 kK 15 kK 20 kK 25 kK 30 kK 35 kK 45 kK 65 kK H 11 1 ✓✓ ✓ H 9 172 1 ✓✓ ✓✓✓✓ ✓✓ He 24 784 2 ✓✓ ✓✓✓✓ ✓✓ He II 20 190 1 ✓✓ ✓✓✓✓ ✓✓ C 40 3201 3 ✓✓ ✓✓ C II 22 238 4 ✓✓ ✓✓✓✓ ✓✓ C III 46 738 5 ✓✓ ✓✓✓✓ ✓✓ C IV 25 330 6 ✓✓✓ ✓✓ N 34 785 1 ✓✓ ✓✓ N II 42 3396 3 ✓✓ ✓✓✓✓ ✓✓ N III 32 549 4 ✓✓ ✓✓✓✓ ✓✓ N IV 48 1093 5 ✓✓✓ ✓✓ N V 16 330 6 ✓✓✓ ✓✓ O 33 418 1 ✓✓ ✓✓ O II 48 3484 1 ✓✓ ✓✓✓✓ ✓✓ O III 41 3855 3 ✓ ✓✓✓✓ ✓✓ O IV 39 922 4 ✓✓✓ ✓✓ O V 64 4 ✓✓✓ ✓✓ Ne 35 2715 7 ✓✓ ✓✓ Ne II 32 2301 1 ✓✓ ✓✓✓✓ ✓✓ Ne III 34 1354 1 ✓✓✓ ✓✓ Ne IV 12 38 1 ✓✓✓ ✓✓ Mg II 25 306 1 ✓✓ ✓✓✓✓ ✓✓ Al II 29 536 8 ✓✓ ✓✓✓✓ ✓✓ Al III 23 306 1 ✓✓ ✓✓✓✓ ✓✓ Si II 40 392 9 ✓✓ ✓✓ Si III 30 747 8 ✓✓ ✓✓✓✓ ✓✓ Si IV 23 306 1 ✓ ✓✓✓✓ ✓✓ S II 33 4166 1 ✓✓ ✓✓ S III 41 3452 10 ✓✓ ✓✓✓✓ ✓✓ S IV 38 909 9 ✓ ✓✓✓✓ ✓✓ S V 25 1171 8 ✓✓✓ ✓✓ S VI 16 398 1 ✓✓ Fe II 36 1,264,969 12, 13 ✓✓ ✓✓ Fe III 50 1,604,934 11, 13 ✓✓ ✓✓✓✓ ✓✓ Fe IV 43 1,776,984 11, 14 ✓ ✓✓✓✓ ✓✓ Fe V 42 1,008,835 11, 15 ✓✓✓ ✓✓ Fe VI 32 40,298 11, 15 ✓✓ ✓✓ References: (1) Lanz & Hubeny (2003, 2007); (2) http://physics.nist.gov/PhysRefData/ASD/index.html; (3) Luo & Pradhan (1989); (4) Fernley et al. (1999); (5) Tully et al. (1990); (6) Peach et al. (1988); (7) Hibbert & Scott (1994); (8) Butler et al. (1993); (9) Mendoza et al. (1995); (10) Nahar & Pradhan (1993); (11) Kurucz (1994); (12) Nahar (1997); (13) Nahar (1996); (14) Bautista & Pradhan (1997); (15) Bautista (1996). steps smaller than the thermal broadening were set. The structure model was computed in LTE without a microturbulent −1 microturbulent velocity was set to 10 km s . The opacity- velocity. Most models were computed using the hybrid complete- sampling approach was used to compute the superline cross linearization and accelerated lambda-iteration (CL/ALI) method sections with better accuracy, also, the iron peak lines were treated (Hubeny & Lanz 1995;Hubeny 2003), which is the default in a line-blanketed model. The only exception to the description above was the cooler procedure for computing fully consistent, NLTE metal-line- atmosphere models with 10,000 K, which require a convective blanketed atmosphere models in TLUSTY (Hubeny 1988).When treatment (Fontaine et al. 1981; Bergeron et al. 1992);a the convergence was not achieved directly from CL/ALI we mixing-length theory parameter equal to the pressure-scale computed the atmosphere structure models using the Rybicki height (α = 1.0) was used. For the 10,000 K case, the final scheme (Hubeny & Mihalas 2014), which is also suitable for MLT 3 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. −2 Figure 1. Structure models of the temperature [K] as function of mass depth [gcm ] in a logarithmic scale computed using LTE (dotted lines) and NLTE (dashed lines) assumptions. The effective temperatures are shown in the colored scale from bottom (10,000 K) to top (65,000 K). (a) These models have solar and He-rich abundances and log g [cgs] = 4.5. (b) These models have halo and He-rich abundances and log g [cgs] = 6.5. The explicit atoms and ions included to compose the level and Table 2 superlevels are the most important ingredients to compute Numerical He Abundances detailed NLTE structure models. They have an impact on the cross section computation, justifying the careful choice of the T [K] log(n /n ) log(n /n ) eff He H poor He H rich most important ions for each model. 10,000 −4.98 −3.81 The electron density and the mass density are shown in 15,000 −4.35 −3.13 Figure 2, having a similar profile as a function of the mass 20,000 −3.72 −2.46 depth. The effects of the surface gravity in the atmosphere 25,000 −3.09 −1.78 height are evident as already mentioned above. The coolest 30,000 −2.46 −1.11 35,000 −1.83 −0.43 structure models such as the example of 10,000 K in 45,000 −0.57 0.92 Figures 2(a) and (b) have an inversion on the density profiles 65,000 1.95 3.62 near log [Depth (mass)] = −1, this is due to the effect of convection that was considered for these specific temperatures. The hot structure models as the example of 65,000 K in treating high-temperature and high-gravity atmospheres, with Figures 2(c) and (d) have densities with a linear dependency of better convergence behavior in some cases. the mass depth. The effective temperature as function of the mass depth is An Inglis–Teller diagram for the grid was produced, which is shown in Figure 1. The outermost mass depth corresponds to the a classical tool for evaluating model sequences’ behavior over a −7 Rosseland optical depth τ= 10 while the innermost depth has gravity range. It involves the electron density and the τ= 100, logarithmically sampled in 70 layers. The color-bar scale maximum n level that originates a distinguishable Balmer indicates the effective temperature from bottom 10,000 K in absorption line, which is useful for diagnosing our model’s yellow to top 65,000 K in purple. The hottest structures are more quality. We interpolated the model electron density to a specific extended toward the inner thick region compared to the coolest optical depth τ = 0.1, counting the highest visible term in the model. The structure models in Figure 1(a) have a surface gravity final synthetic spectra. A linear least-squares fit of the electron (log g) equal to 4.5, so they are more extended if we compare density, and the maximum number of the absorption lines near them to the structures in Figure 1(b), which represent more the Balmer’s discontinuity, is shown in Figure 3. compact objects with log g equal to 6.5. The dotted lines represent We also performed convergence analyses for all the 96 the starting model computed using LTE assumptions, where we subdwarf-structure models computed. The most critical conv- can see the almost isothermal behavior in the external region for ergence criterion is the magnitude of the relative changes of the models with different effective temperatures. On the other hand, components of the state vector, which is defined as a set of all the dashed lines represent the structure computed using the NLTE structural parameters (e.g., temperature, particle number densities, assumptions and line blanketing of the explicit species. In the and the mean radiation intensities in discretized frequency points) latter, a small temperature inversion on their outer regions can be in a given discretized depth point (Hubeny & Lanz 2011a).The seen in some cases, which is important to the line-core profile necessary condition for convergence is that the maximum relative change of all state vector components in all the 70 depths is formation. The inner region converges to the solution with minor −3 differences if we compare the LTE and NLTE structures. Note smaller than 10 . However, a supplementary condition is the that mass depths are shown, if we look at a specific line optical conservation of the total flux concerning the total theoretical flux, depth the differences between LTE and NLTE structure models sT . The output parameters such as the number of depths, eff aremuchmoresignificant. column mass, temperature, and densities in each depth and The structure models are highly sensitive to the chemical relative changes between iterations are used in the convergence abundances via opacities, electron density, and mass density. analysis, as well as in the emergent flux in all frequency points 4 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. −2 Figure 2. Structure models of the electron density (top) and mass density (bottom) as function of mass depth [gcm ] in a logarithmic scale. We are comparing different surface gravity models computed using NLTE assumptions. These models have halo and He-rich abundances. (a), (b) T = 10,000 K; (c), (d) eff T = 65,000 K. eff describedinSection 2. We considered NLTE assumptions for the evaluation of the level and superlevel populations. The line profiles were carefully treated in a special computation for H and He (Lanz & Hubeny 2003, 2007). The reference atomic line list is Coelho (2014), based on Coelho et al. (2005) and line lists from 7 8 R. Kurucz and F. Castelli (see, e.g., Kurucz 2017; Castelli & Hubrig 2004). The hydrogen and hydrogenic lines are treated as a part of the continuum and their profiles are computed using tables from Tremblay & Bergeron (2009). The quasi-molecular satellites of Lα,Lβ,and Hα (λ= 1215.67, 1025.18, and 6562.79 Å, respectively), are considered. In that case, additional input files containing the corresponding data were used (Allard et al. 2009). The four He I triplet lines, (λ = 4026, 4387, 4471, and 4921 Å) were treated using special line-broadening tables (Barnard et al. 1974; Shamey 1969). The He II lines are treated as the approximate hydrogenic ion by analytical values of the Stark + Doppler profile (Hubeny et al. 1994), which improves Figure 3. An Inglis–Teller diagram of models with halo and He-rich the accuracy of the line profile for T > 10,000 K, and the line eff abundances. profiles are given by the Stark-broadening tables of Schöning & Butler (1989). We are also considering Stark broadening used by the SYNSPEC code (Hubeny & Lanz 2011b) to build computed by Tremblay & Bergeron (2009). synthetic spectra. The spectral grid coverage is between 1000–10,000 Å with steps of 0.01 Å. The resulting spectrum was subsequently 3. Synthetic Spectra processed with the ROTIN code (Hubeny & Lanz 2011b),which resamples the original synthetic spectrum but considering that no We computed the grid of synthetic spectra with the SYNSPEC code designed to synthesize the emergent spectra from atmos- phere model structures. We used the NLTE atmosphere structure http://kurucz.harvard.edu/linelists.html from TLUSTY models (Hubeny 1988; Hubeny & Lanz 2011a) http://wwwuser.oats.inaf.it/castelli/linelists.html 5 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. Figure 4. Sample spectra with coverage from 1000–9000 Å without instrumental broadening for different temperatures from top (65,000 K) to bottom (10,000 K), log g [cgs] = 5.5 with halo and He-rich abundances. rotational velocity and no instrumental degradation have been interpolation in the grid was performed as the intent is not to taken into account. determine exact abundances or stellar parameters, but rather to We show the normalized emergent flux (in arbitrary units) exhibit the grid potentialities. The targets were selected from the given as a function of wavelength for the spectral coverage subdwarf catalog in Lei et al. (2019) and Hubble Space from 1000 to 9000 Å in Figure 4. A forest of lines is seen at Telescope’s (HST)/Space Telescope Imaging Spectrograph (STIS) this particular sampling, where no instrumental degradation is Legacy Archive data. They are located in the solar neighborhood. included. They are synthetic spectra with T equal to 65,000, According to Lei et al. (2019), the target Lamost 442708048 eff 45,000, 35,000, 30,000, 25,000, 20,000, 15,000. and 10,000 K has T = 26,620 ± 70 K, log g = 5.53 ± 0.01 [cgs], log (n / eff He (from top to bottom) and log g [cgs] = 5.5 with halo and He- n ) = −2.78 ± 0.05, E(B − V ) = 0.018 and, from the Gaia rich abundances. Collaboration et al. (2018) parallax, its distance is 317 ± 5 pc. In Figure 5 we can compare the different spectral types in the We performed a comparison with models near to these values, near-UV region between 1000 and 2000 Å, where for visual within the boundaries of our grid, as T = 25,000 K, log g = eff effect it is degraded to a Gaussian instrumental profile with 5.5 [cgs], [Fe/H]= 0, and log (n /n )=−3.09 (see Figure 7 (a)). He H FWHM equal to 5 Å. The hotter spectra have a bluer Lamost 183405148 has, according to Lei et al. (2019), continuum and the He lines are dominant. The Stark broad- T = 46,270 ± 330 K, log g = 5.88 ± 0.04, log (n /n ) = eff He H ening is more evident on the coolest spectra, where a stronger 0.29 ± 0.01, E(B − V ) = 0.021, and from its parallax (Gaia Lyman series is present, besides its quasi-molecular absorption Collaboration et al. 2018) the distance is 333±9pc. The closest features. model spectrum adopted corresponds to T = 45,000 K, eff In Figure 6 we can compare the different spectral types on log g= 5.5 [cgs], [Fe/H]= 0, and log (n /n )= 0.92 (see He H the Balmer break region between 3500–6750 Å, where for Figure 7 (b)). visual effect the resolution is degraded by a Gaussian HST/STIS Legacy Archive data on the bright subdwarf HD instrumental profile with FWHM equal to 5 Å. As expected, 4539 were used to illustrate the models in the FUV. Parameters the H is mostly ionized and the Balmer series is weaker in the for this sdB are as follows: T = 26,000± 500 K, log g= 5.2± eff hotter spectra. The coolest models are not favorable to the 0.1, log (n /n )=−2.32± 0.05, E(B− V )= 0.04± 0.01 (Sale He H formation of strong He lines. Moreover, the spectra presented et al. 2008) and d= 171.6± 2.1 pc (Gaia EDR3; Gaia in Figure 6 follow the He-abundance sequence from Németh Collaboration et al. 2021). The models were scaled to match the et al. (2012), which shows low He abundance even for the He- continuum flux in the middle of each spectral range. He-poor rich sequence of cool subdwarfs. branch and halo low-Z abundances were assumed here while T eff With the purpose of illustrating the grid, we present a simple and log g were linearly interpolated from model nodes to the comparison of model spectra with the spectra of the Lamost literature values (see Figure 8). Rotation, instrumental resolution, 442708048, Lamost 183405148, and HD 4539 subdwarfs. No and exact chemical composition were neglected, which would 6 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. Figure 5. Sample spectra in the UV region (1000–2000 Å) with an FWHM Figure 6. Sample spectra in the optical region (3500–6750 Å) with FWHM resolution = 5 Å for different temperatures: from top (65,000 K) to bottom resolution = 5 Å for different temperatures: from top (65,000 K) to bottom (10,000 K), and log g [cgs] = 5.5 with halo and He-rich abundances. (10,000 K), and log g [cgs] = 5.5 with halo and He-rich abundances. explain the significant differences found in the lines and continua previously evaluated from Calspec’s standard spectrum (Bohlin offsets. By using the Gaia distances and reddening values above, et al. 2014). stellar radii compatible with typical values for subdwarfs in Figure 9 illustrate our models in two color–color panels: panel eclipsing binaries (e.g., Rebassa-Mansergas et al. (2019) could be (a) was chosen to trace the overall continuum inclination, and found. A line and/or continuum fitting of spectra can be panel (b) traces the behavior of the Balmer jump. In panel (a) we performed with the XTGRID facility (Nemeth 2019). show F469N—F673N versus FQ757N—FQ750N colors of the HST/Wide Field Camera 3 (WFC3) photometric system. The 4. Synthetic Magnitudes dependence on effective temperature is clear. Those indices measure how lower-temperature synthetic models have a flatter Synthetic magnitudes have been computed for several standard continuum in the optical region. The point-size scale represents photometric bands to trend the grid’s behavior in the color indices the surface gravity, where larger symbols relate to lower gravity space and provide a comparison with photometry data. We used (log g= 4.5), and smaller symbols stand for higher gravity the filter response functions available on the Filter Profile Service (log g= 6.5), which also reveal a linear dependence in the color at the Spanish Virtual Observatory to convolve our synthetic integrated fluxes in the AB and Vega systems. The filters were space. Finally, the circles represent solar abundance and down- interpolated in the spectra wavelength steps within the pointing triangles represent low halo metallicity, which has no Shannon–Whittaker scheme. Photon-counting integrated fluxes clear separation on the diagram. were assumed (Bessell et al. 1998). Vega’s zero-points were In Figure 9(b) the Strömgren photometric system indices were used. Zero-points were derived from Vega ubvy magnitudes (Hauck & Mermilliod 1998) and its calibrated spectrum from the http://svo.cab.inta-csic.es/main/index.php STScI CALSPEC database (Bohlin et al. 2014).The color–color 7 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. Figure 10. Color–color diagram (g–r vs. u–g) composed of observational data on subdwarfs from SDSS (see text) with a hue scale representing determined effective temperatures, while the gray crosses show an undetermined effective temperature. The synthetic colors from our grid are plotted with the same hue, style, and size scales as in Figure 9. diagram of Figure 9(b) was constructed with u (349.6 nm) – v Figure 7. Top: comparison between the observed spectrum of subdwarf (410.3 nm) and v–b (466.6nm) colors. It shows a temperature Lamost 4427080 (dashed purple) and the model spectrum with T = 25,000 K eff dependence of the Balmer break, which is more evident and also and log g = 5.5 (solid green). Bottom: comparison between the observed gravity-dependent for cooler atmospheres. spectrum of Lamost 183405148 (dashed purple) and the model spectrum with T = 45,000 K and log g = 5.5 (solid blue). eff The study of the 5874 hot subdwarf stars with Gaia Data Release 2 by Geier (2020) is the most complete sample of subdwarfs. From this catalog we selected data from 3450 targets (1482 with determined effective temperature and colors) observed by the Sloan Digital Sky Survey (SDSS) photometric system to compare with the grid synthetic magnitudes. The color–color diagram in Figure 10 is composed of g–r and u–g colors without any color cutoff. Observational data with a determined effective temperature are shown as dots scaled by hue, while those with an undetermined effective temperature are gray crosses. Our synthetic colors are displayed in the same hue, style, and size scales as in Figure 9, matching the sdO, sdB, and sdOB previously classified by Geier (2020). The upper data sequence represents the subdwarf composite binaries with main-sequence star companions. Figure 8. Comparison between the observed HST/STIS UV spectrum of HD 4539 (dashed purple) and an interpolated model spectrum with T 26,000 K eff and log g = 5.2 (solid green). 5. Summary We presented a grid of NLTE, fully blanketed theoretical spectra and synthetic photometry for hot and moderately cool subdwarf stars. The atmosphere models were computed considering line blanketing of H, He, C, N, O, Ne, Mg, Al, Si, S, and Fe. The effective temperatures are T = 10,000, eff 15,000, 20,000, 25,000, 30,000, 35,000, 45,000, and 65,000 K, while the surface gravities are log g [cgs] = 4.5, 5.5, and 6.5. The two representative chemical abundances are solar and Galactic halos, each one with two extreme scenarios for He- rich and He-poor stellar atmospheres. The main differences between LTE and NLTE atmosphere structures are shown for these objects. They have significant differences in the outermost atmospheres, leading to distinct line-core profile formation. Figure 9. Color–color diagrams with the scale showing the effective temperatures, while the point-size scale shows the surface gravities (larger to lower gravity (4.5) The complete high-resolution spectral synthesis is performed and smaller to the higher gravity (6.5)); the circles indicate solar abundances and from the UV to near-IR (1000 to 10,000 Å) in 0.01 Å steps. We down-pointing triangles the low halo metallicity. (a) Color–color diagram for provided an illustrative analysis for the UV and the optical HST/WFC3 indices F469N—F673N and FQ757N—FQ750N. (b) Color–color regions by comparing our models with observed spectra from diagram for classical Strömgren u (349.6 nm) – v (410.3 nm) and v–b (466.6 nm) indices, aiming to probe the Balmer discontinuity. LAMOST and HST/STIS Legacy Archive data. 8 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. The behavior of the color indices were analyzed using the Coelho, P. R. T. 2014, MNRAS, 440, 1027 Dorsch, M., Latour, M., & Heber, U. 2018, OAst, 27, 19 HST/WFC3 and the Strömgren photometric systems. A clear Dorsch, M., Latour, M., & Heber, U. 2019, A&A, 630, A130 separation in effective temperature can be seen, as well as Edelmann, H., Heber, U., Hagen, H. J., et al. 2003, A&A, 400, 939 gravity for lower-temperature models, as provided by the Fernley, J. A., Hibbert, A., Kingston, A. E., & Seaton, M. J. 1999, JPhB, Balmer discontinuity. We also matched our synthetic magni- 32, 5507 Fontaine, G., Bergeron, P., Brassard, P., et al. 2019, ApJ, 880, 79 tudes against SDSS subdwarf data with fair agreement. Fontaine, G., Brassard, P., Charpinet, S., et al. 2012, A&A, 539, A12 These results pave the way for both spectroscopic and Fontaine, G., Villeneuve, B., & Wilson, J. 1981, ApJ, 243, 550 photometric analyses of fundamental parameters in isolated or Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1 binary objects which, in turn, may provide a more detailed Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, insight into the atmosphere models themselves. In addition, 649, A1 Geier, S. 2020, A&A, 635, A193 classical stellar population synthesis analysis can make use of Geier, S., Heber, U., Podsiadlowski, P., et al. 2010, A&A, 519, A25 the homogeneous spectral grid to better understand the blue Geier, S., Raddi, R., Gentile Fusillo, N. P., & Marsh, T. R. 2019, A&A, and UV properties of old stellar populations. The full spectral 621, A38 grid and synthetic indices are available in the IAG-USP, Geier, S., Østensen, R. H., Nemeth, P., et al. 2017, OAst, 26, 164 5 6 Green, E. M., Fontaine, G., Hyde, E. A., For, B.-Q., & Chayer, P. 2008, in ASP SVO, and Vizier databases. Conf. Ser. 392, Hot Subdwarf Stars and Related Objects, ed. U. Heber et al. (San Francisco, CA: ASP), 75 We thank Ivan Hubeny who kindly released the new versions Grevesse, N., & Sauval, A. J. 1998, SSRv, 85, 161 of TLUSTY 208 and SYNSPEC 54 and boosted the discussions Hall, P. D., & Jeffery, C. S. 2016, MNRAS, 463, 2756 about the convective models. We thank the anonymous referee Hauck, B., & Mermilliod, M. 1998, A&AS, 129, 431 Heber, U. 2009, ARA&A, 47, 211 for refereeing this paper and for the suggestions that improved Heber, U., Irrgang, A., & Schaffenroth, J. 2017, OAst, 27, 35 the work. Hibbert, A., & Scott, M. P. 1994, JPhB, 27, 1315 This study was financed in part by the Coordenação de Hubeny, I. 1988, CoPhC, 52, 103 Aperfeiçoamento de Pessoal de Nível Superior—Brasil Hubeny, I. 2003, in ASP Conf. Ser. 288, Stellar Atmosphere Modeling, ed. I. Hubeny, D. Mihalas, & K. Werner (San Francisco, CA: ASP), 17 (CAPES), Finance Code 001. M.P.D. acknowledges support Hubeny, I., Heap, S. R., & Lanz, T. 1998, in ASP Conf. Ser. 131, Properties of from CNPq under grant #305033. P.C. acknowledges support Hot Luminous Stars, ed. I. Howarth (San Francisco, CA: ASP), 108 from Conselho Nacional de Desenvolvimento Científico e Hubeny, I., Hummer, D. G., & Lanz, T. 1994, A&A, 282, 151 Tecnológico (CNPq) under grant #310041/2018-0 and from Hubeny, I., & Lanz, T. 1995, ApJ, 439, 875 Fundação de Amparo à Pesquisa do Estado de São Paulo Hubeny, I., & Lanz, T. 2011a, TLUSTY: Stellar Atmospheres, Accretion Disks, and Spectroscopic Diagnostics, Astrophysics Source Code Library, (FAPESP) process #2018/05392-8. ascl:1109.021 This research has made use of the SVO Filter Profile Service Hubeny, I., & Lanz, T. 2011b, Synspec: General Spectrum Synthesis Program, (http://svo2.cab.inta-csic.es/theory/fps/) supported from the Astrophysics Source Code Library, ascl:1109.022 Spanish MINECO through grant AYA2017-84089. This work Hubeny, I., & Mihalas, D. 2014, Theory of Stellar Atmospheres (Princeton, NJ: Princeton Univ. 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A Grid of Synthetic Spectra for Subdwarfs: Non-LTE Line-blanketed Atmosphere Models

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Abstract

A new grid of detailed atmosphere model spectra for hot and moderately cool subdwarf stars is presented. High- resolution spectra and synthetic photometry are calculated in the range from 1000–10,000 Å using non-LTE fully line-blanketed atmosphere structures. Our grid covers eight temperatures within 10,000 „ T [K] „ 65,000, three eff surface gravities in the range 4.5 „ log g [cgs] „ 6.5, two helium abundances matching two extreme helium-rich and helium-poor scenarios, and two limiting metallicity boundaries regarding both solar ([Fe/H] = 0) and Galactic halos ([Fe/H] = −1.5 and [α/Fe]=+0.4). Besides its application in the determination of fundamental parameters of subdwarfs in isolation and in binaries, the resulting database is also of interest for population synthesis procedures in a wide variety of stellar systems. Unified Astronomy Thesaurus concepts: Stellar atmospheres (1584); Spectral energy distribution (2129); Stellar spectral lines (1630); Subdwarf stars (2054) 1. Introduction day (45%). (iii) Those showing additional spectral lines from a cool FGK main-sequence or subgiant companion that have slowly The evolutionary scenario of subdwarfs is still emerging. Hot varying or nearly constant velocities, indicating periods of many subdwarf stars evolve from low- to intermediate-mass progenitors months to years. and reach far beyond the main sequence, at the blue end of the There is observational evidence indicating that subdwarfs are horizontal branch (HB) or mixed with post-HB stars (Heber 2009). the most likely candidates to account for the ultraviolet (UV) Even though they lie mostly between the main sequence and the upturn observed on spectroscopic and photometric analyses of white dwarf (WD) cooling sequence in the Hertzsprung–Russell globular clusters and elliptical galaxies (Yi et al. 1999; Busso diagram, they are contaminated with WDs. et al. 2005; Green et al. 2008). The most accepted formation scenario is of an extreme HB star Analysis from asteroseismology (Charpinet et al. 2005), that lost its envelope after the He-burning phase, evolving directly spectroscopy (Wade et al. 2005; Dorsch et al. 2018, 2019), and to the WD-cooling sequence by avoiding the asymptotic giant photometry (Johnson et al. 2014) of field subdwarf stars found branch (AGB)(Wade et al. 2005;Heber 2009;Fontaineetal. nonsolar He abundances. He-rich and He-poor sequences, as a 2012). These objects experienced mass transfer followed by function of effective temperature, were proposed by Edelmann common envelope ejection in a binary system leaving the stellar et al. (2003) and updated by Németh et al. (2012) and Lei et al. core exposed (Green et al. 2008; Geier et al. 2010). More recent (2019). Those sequences also support the evidence that He- investigations support this scenario, such as the observational enriched sdOs are more common than the He-deficient ones evidence of hot O- and B-type subdwarf formation (sdO and sdB, (Heber 2009). respectively) from the product of binary interactions (Pelisoli et al. It is ideal to have homogeneous and widely available model 2020). Also, the expected evolutionary path suggests that sdOs spectra for these elusive systems, in order to improve our evolve from sdBs (Heber 2009). An alternative evolutionary knowledge of their fundamental physical parameters and scenario suggests that the merger of two low-mass He-core WDs evolution. Such models should be computed as fully as might form isolated H-rich B-type hot subdwarfs (Hall & Jeffery possible regarding the radiative transfer, considering nonlocal 2016;Schwab 2018). thermodynamic equilibrium (NLTE), fully blanketed atmos- A small fraction of sdBs in close binaries (Wade et al. 2005) phere structures (Lanz & Hubeny 1995; Lanz et al. 1997). fall out of the red giant branch before He ignition, perhaps Considerable improvements in NLTE atmosphere models have because they are low-mass stars that do not support the burning been achieved over the last five decades. The first NLTE spectra of He in their cores (Heber 2009). of hot atmospheres in the early 1970s (Mihalas & Hummer 1974) The hot subdwarfs can be separated into three main groups were built based on pure H atmosphere structures, and the metal according to Saffer et al. (2001). (i) Those nonbinaries that have lines were considered only in the spectral synthesis. Analysis by no detectable spectral lines from a cool companion, and show Lanz & Hubeny (1995) took H, C, and Fe into account for the only small or insignificant velocity variations (35%). (ii) Those opacity of hot and high-gravity NLTE atmosphere models. They single-lined spectroscopic binaries which have significant or large found critical differences in effective temperature determinations velocity variations and probable orbital periods on the order of a and line profiles arising from the inclusion of explicit atomic species (i.e., with the kinetic equilibrium equation solved) in the Original content from this work may be used under the terms atmospheric structure. The subdwarfs’ atmospheres have more of the Creative Commons Attribution 4.0 licence. Any further evident NLTE effects due to their lower surface gravities (when distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. compared to WDs; Lanz et al. 1997). They built spectra 1 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. considering full line blanketing with H/He,CNO,Si, Fe,and Ni equilibrium, therefore level populations in NLTE were as implicit ions and concluded that this approach significantly calculated. Departures from LTE may be specially significant improved the line profile analysis. Hubeny et al. (1998) showed for high-temperature subdwarf atmospheres (Hubeny & Lanz that NLTE metal-line-blanketing effects produce a conspicuous 1995; Lanz & Hubeny 1995; Lanz et al. 1997) as also found in difference (typically 20%) in the line profiles seen in the UV DA-type WD atmospheres (Levenhagen et al. 2017). spectra of hot WDs. By considering explicit metal ions such as H/ The starting point was to compute an LTE gray structure He, CNO, Si, and Fe in the atmosphere structure a better emergent model, which is then used as an input to build the NLTE line- flux match was achieved. blanketed models (Hubeny 1988; Hubeny et al. 1994).We Overall, the subdwarfs’ spectra are built for specific targets considered H, He, C, N, O, Ne, Mg, Al, Si, S, and Fe as explicit and studies. We have hundreds of hot subdwarf stars cataloged ions (see Table 1) contributing to the opacity. The set of (Geier et al. 2017; Heber et al. 2017; Geier & Raddi 2019; ionization states for the selected atomic species were chosen on Geier 2020), with their spectral analysis focused on classifica- the basis of ionization energies, model-effective temperatures, tion and/or kinematic properties (Luo et al. 2019). A lot of and candidate-permitted transitions from Willians & Livio work was done to analyze the He-abundance (Fontaine et al. (1995). The atomic data of each ion included as an explicit 2019) sequences (Lei et al. 2019). The sequences also show species in the NLTE atmosphere models are summarized in differences between field subdwarfs and extreme HB sub- Table 1 (see details in Lanz & Hubeny 2003, 2007). dwarfs in globular clusters (Lei et al. 2020). As describedbyLanz&Hubeny (2007),the LTE fluxes are NLTE structures and subdwarf spectra were calculated by about 10% higher than the NLTE predictions, and this is most Nemeth et al. (2014), covering specific temperature and gravity noticeable in the near-UV. Lanz & Hubeny (2007) also mentioned ranges. The opacities of H, He, and a few metal ions were that the lower NLTE fluxes result from the overpopulation of the included to compute the atmosphere structure in these models. H I (n= 2) level at the depth of formation of the continuum flux, However, only a small and nonhomogeneous collection of hence implying a larger Balmer continuum opacity. detailed subdwarf model spectra is currently available. High- The adopted abundances are expressed as solar ([Fe/H]= 0.0; temperature spectral grids may be also calculated by other Asplund et al. 2009) or Galactic halo ([Fe/H]=−1.5 and [α/ codes e.g., the Tübingen NLTE Model Atmosphere package Fe]=+0.4) as well as He-rich (Edelmann et al. 2003) and He- (Rauch et al. 2018). poor abundances (Németh et al. 2012; Lei et al. 2019). Our choice In this work we present an extensive high-spectral-resolution of usingsolar andhalometallicity is notintendedtodescribe grid of NLTE synthetic spectra for subdwarfs in the optical and subdwarf typical abundances. Instead, these solar and halo points UV. The models are fully line blanketed with H, He, C, N, O, Ne, just set a broad Z range, probing its effect on the continuum and Mg,Al, Si,S,and Fe as opacity sources (see Table 1).Wealso line profiles. It is well established that atmospheric subdwarf metal consider nonsolar chemical abundances to better sample the abundances have little or virtually no memory of their parent subdwarf parameter space. Low-temperature convective atmo- main-sequence abundances (e.g., Moehler 2001;Némethetal. spheres were also included in the square grid. The complete grid is 2012; Byrne et al. 2018). Metals at the subdwarf surface vary by available our SpecModels website as well as on the Spanish large amounts depending on previous binary evolution and Virtual Observatory’s Theoretical Spectra Web Server and the diffusion processes, leading to diverse abundance patterns (e.g., Vizier database. O’Toole & Heber 2006) with loose observational constraints. He- Section 2 describes the atmosphere structure models, in rich and He-poor abundance variations were chosen based on particular the differences between the LTE and NLTE assump- linear fits as a function of temperature based on Lei et al. (2019) tions made. Section 3 describes the synthetic spectra, comparing (see Table 2). Note that TLUSTY (Hubeny 1988;Hubeny& the results with observational data. Section 4 describes the Lanz 2011a) uses the solar chemical abundances as defined by construction of the synthetic magnitudes and their application in Grevesse & Sauval (1998) as default values, and we rearranged all color–color diagrams. Section 5 presents the concluding remarks. the chemical species to the solar abundance as definedbyAsplund et al. (2009). The atmosphere structures (available upon request to the authors) may be interpolated in metallicity and specific 2. Atmosphere Structure modified metal abundances used in custom spectral synthesis. The atmosphere structure models were computed by The time spent on computational work increases and the TLUSTY code v205 and v208 (for convective 10,000 K convergence is more difficult when the complexity of the heavy models; Hubeny 1988; Hubeny & Lanz 2011a). It calculates a elements is included in the TLUSTY atmosphere code (Hubeny self-consistent solution of the equations describing the radiative 1988;Hubeny&Lanz 2011a). As a reference, each one of the 96 (or radiative plus convective) transfer and physical state of the structures were computed and analyzed in a typical timescale of atmosphere. The geometry of the model is plane-parallel with aday. homogeneous chemical abundances (Hubeny & Lanz 1995). The grid of subdwarf-structure models is composed of eight The most popular subdwarf models available have been built effective temperatures (T : 10,000, 15,000, 20,000, 25,000, eff in LTE. In LTE all energy partitioning such as atomic, ionic, 30,000, 35,000, 45,000, and 65,000 K), each one computed in and molecular level populations is given by Saha–Boltzmann three surface gravities (log g [cgs]: 4.5, 5.5, and 6.5) and four equations, being defined by the local temperature. The LTE different chemical abundances: solar and He-rich, solar and He- conditions may differ from those derived in actual statistical poor, halo and He-rich, halo and He-poor. The broadening of lines was treated carefully considering the http://dc.zah.uni-heidelberg.de/theossa/q/web/form Lyman and Balmer line profile tables from Tremblay & Bergeron Spectral Models of Stars and Stellar Populations, http://specmodels.iag. (2009). The high-frequency limit for lines that are taken into usp.br/. http://svo2.cab.inta-csic.es/theory//newov2/ account in the opacity sampling was set to 6 × 10 × T or the eff https://vizier.u-strasbg.fr/viz-bin/VizieR highest bound-free edge frequency, if greater. Opacity-sampling 2 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. Table 1 Atomic Data of the Explicit Species Included in the NLTE Atmosphere Models Atomic Data Explicit Ions Included in NLTE Ion Super(level) Lines Reference 10 kK 15 kK 20 kK 25 kK 30 kK 35 kK 45 kK 65 kK H 11 1 ✓✓ ✓ H 9 172 1 ✓✓ ✓✓✓✓ ✓✓ He 24 784 2 ✓✓ ✓✓✓✓ ✓✓ He II 20 190 1 ✓✓ ✓✓✓✓ ✓✓ C 40 3201 3 ✓✓ ✓✓ C II 22 238 4 ✓✓ ✓✓✓✓ ✓✓ C III 46 738 5 ✓✓ ✓✓✓✓ ✓✓ C IV 25 330 6 ✓✓✓ ✓✓ N 34 785 1 ✓✓ ✓✓ N II 42 3396 3 ✓✓ ✓✓✓✓ ✓✓ N III 32 549 4 ✓✓ ✓✓✓✓ ✓✓ N IV 48 1093 5 ✓✓✓ ✓✓ N V 16 330 6 ✓✓✓ ✓✓ O 33 418 1 ✓✓ ✓✓ O II 48 3484 1 ✓✓ ✓✓✓✓ ✓✓ O III 41 3855 3 ✓ ✓✓✓✓ ✓✓ O IV 39 922 4 ✓✓✓ ✓✓ O V 64 4 ✓✓✓ ✓✓ Ne 35 2715 7 ✓✓ ✓✓ Ne II 32 2301 1 ✓✓ ✓✓✓✓ ✓✓ Ne III 34 1354 1 ✓✓✓ ✓✓ Ne IV 12 38 1 ✓✓✓ ✓✓ Mg II 25 306 1 ✓✓ ✓✓✓✓ ✓✓ Al II 29 536 8 ✓✓ ✓✓✓✓ ✓✓ Al III 23 306 1 ✓✓ ✓✓✓✓ ✓✓ Si II 40 392 9 ✓✓ ✓✓ Si III 30 747 8 ✓✓ ✓✓✓✓ ✓✓ Si IV 23 306 1 ✓ ✓✓✓✓ ✓✓ S II 33 4166 1 ✓✓ ✓✓ S III 41 3452 10 ✓✓ ✓✓✓✓ ✓✓ S IV 38 909 9 ✓ ✓✓✓✓ ✓✓ S V 25 1171 8 ✓✓✓ ✓✓ S VI 16 398 1 ✓✓ Fe II 36 1,264,969 12, 13 ✓✓ ✓✓ Fe III 50 1,604,934 11, 13 ✓✓ ✓✓✓✓ ✓✓ Fe IV 43 1,776,984 11, 14 ✓ ✓✓✓✓ ✓✓ Fe V 42 1,008,835 11, 15 ✓✓✓ ✓✓ Fe VI 32 40,298 11, 15 ✓✓ ✓✓ References: (1) Lanz & Hubeny (2003, 2007); (2) http://physics.nist.gov/PhysRefData/ASD/index.html; (3) Luo & Pradhan (1989); (4) Fernley et al. (1999); (5) Tully et al. (1990); (6) Peach et al. (1988); (7) Hibbert & Scott (1994); (8) Butler et al. (1993); (9) Mendoza et al. (1995); (10) Nahar & Pradhan (1993); (11) Kurucz (1994); (12) Nahar (1997); (13) Nahar (1996); (14) Bautista & Pradhan (1997); (15) Bautista (1996). steps smaller than the thermal broadening were set. The structure model was computed in LTE without a microturbulent −1 microturbulent velocity was set to 10 km s . The opacity- velocity. Most models were computed using the hybrid complete- sampling approach was used to compute the superline cross linearization and accelerated lambda-iteration (CL/ALI) method sections with better accuracy, also, the iron peak lines were treated (Hubeny & Lanz 1995;Hubeny 2003), which is the default in a line-blanketed model. The only exception to the description above was the cooler procedure for computing fully consistent, NLTE metal-line- atmosphere models with 10,000 K, which require a convective blanketed atmosphere models in TLUSTY (Hubeny 1988).When treatment (Fontaine et al. 1981; Bergeron et al. 1992);a the convergence was not achieved directly from CL/ALI we mixing-length theory parameter equal to the pressure-scale computed the atmosphere structure models using the Rybicki height (α = 1.0) was used. For the 10,000 K case, the final scheme (Hubeny & Mihalas 2014), which is also suitable for MLT 3 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. −2 Figure 1. Structure models of the temperature [K] as function of mass depth [gcm ] in a logarithmic scale computed using LTE (dotted lines) and NLTE (dashed lines) assumptions. The effective temperatures are shown in the colored scale from bottom (10,000 K) to top (65,000 K). (a) These models have solar and He-rich abundances and log g [cgs] = 4.5. (b) These models have halo and He-rich abundances and log g [cgs] = 6.5. The explicit atoms and ions included to compose the level and Table 2 superlevels are the most important ingredients to compute Numerical He Abundances detailed NLTE structure models. They have an impact on the cross section computation, justifying the careful choice of the T [K] log(n /n ) log(n /n ) eff He H poor He H rich most important ions for each model. 10,000 −4.98 −3.81 The electron density and the mass density are shown in 15,000 −4.35 −3.13 Figure 2, having a similar profile as a function of the mass 20,000 −3.72 −2.46 depth. The effects of the surface gravity in the atmosphere 25,000 −3.09 −1.78 height are evident as already mentioned above. The coolest 30,000 −2.46 −1.11 35,000 −1.83 −0.43 structure models such as the example of 10,000 K in 45,000 −0.57 0.92 Figures 2(a) and (b) have an inversion on the density profiles 65,000 1.95 3.62 near log [Depth (mass)] = −1, this is due to the effect of convection that was considered for these specific temperatures. The hot structure models as the example of 65,000 K in treating high-temperature and high-gravity atmospheres, with Figures 2(c) and (d) have densities with a linear dependency of better convergence behavior in some cases. the mass depth. The effective temperature as function of the mass depth is An Inglis–Teller diagram for the grid was produced, which is shown in Figure 1. The outermost mass depth corresponds to the a classical tool for evaluating model sequences’ behavior over a −7 Rosseland optical depth τ= 10 while the innermost depth has gravity range. It involves the electron density and the τ= 100, logarithmically sampled in 70 layers. The color-bar scale maximum n level that originates a distinguishable Balmer indicates the effective temperature from bottom 10,000 K in absorption line, which is useful for diagnosing our model’s yellow to top 65,000 K in purple. The hottest structures are more quality. We interpolated the model electron density to a specific extended toward the inner thick region compared to the coolest optical depth τ = 0.1, counting the highest visible term in the model. The structure models in Figure 1(a) have a surface gravity final synthetic spectra. A linear least-squares fit of the electron (log g) equal to 4.5, so they are more extended if we compare density, and the maximum number of the absorption lines near them to the structures in Figure 1(b), which represent more the Balmer’s discontinuity, is shown in Figure 3. compact objects with log g equal to 6.5. The dotted lines represent We also performed convergence analyses for all the 96 the starting model computed using LTE assumptions, where we subdwarf-structure models computed. The most critical conv- can see the almost isothermal behavior in the external region for ergence criterion is the magnitude of the relative changes of the models with different effective temperatures. On the other hand, components of the state vector, which is defined as a set of all the dashed lines represent the structure computed using the NLTE structural parameters (e.g., temperature, particle number densities, assumptions and line blanketing of the explicit species. In the and the mean radiation intensities in discretized frequency points) latter, a small temperature inversion on their outer regions can be in a given discretized depth point (Hubeny & Lanz 2011a).The seen in some cases, which is important to the line-core profile necessary condition for convergence is that the maximum relative change of all state vector components in all the 70 depths is formation. The inner region converges to the solution with minor −3 differences if we compare the LTE and NLTE structures. Note smaller than 10 . However, a supplementary condition is the that mass depths are shown, if we look at a specific line optical conservation of the total flux concerning the total theoretical flux, depth the differences between LTE and NLTE structure models sT . The output parameters such as the number of depths, eff aremuchmoresignificant. column mass, temperature, and densities in each depth and The structure models are highly sensitive to the chemical relative changes between iterations are used in the convergence abundances via opacities, electron density, and mass density. analysis, as well as in the emergent flux in all frequency points 4 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. −2 Figure 2. Structure models of the electron density (top) and mass density (bottom) as function of mass depth [gcm ] in a logarithmic scale. We are comparing different surface gravity models computed using NLTE assumptions. These models have halo and He-rich abundances. (a), (b) T = 10,000 K; (c), (d) eff T = 65,000 K. eff describedinSection 2. We considered NLTE assumptions for the evaluation of the level and superlevel populations. The line profiles were carefully treated in a special computation for H and He (Lanz & Hubeny 2003, 2007). The reference atomic line list is Coelho (2014), based on Coelho et al. (2005) and line lists from 7 8 R. Kurucz and F. Castelli (see, e.g., Kurucz 2017; Castelli & Hubrig 2004). The hydrogen and hydrogenic lines are treated as a part of the continuum and their profiles are computed using tables from Tremblay & Bergeron (2009). The quasi-molecular satellites of Lα,Lβ,and Hα (λ= 1215.67, 1025.18, and 6562.79 Å, respectively), are considered. In that case, additional input files containing the corresponding data were used (Allard et al. 2009). The four He I triplet lines, (λ = 4026, 4387, 4471, and 4921 Å) were treated using special line-broadening tables (Barnard et al. 1974; Shamey 1969). The He II lines are treated as the approximate hydrogenic ion by analytical values of the Stark + Doppler profile (Hubeny et al. 1994), which improves Figure 3. An Inglis–Teller diagram of models with halo and He-rich the accuracy of the line profile for T > 10,000 K, and the line eff abundances. profiles are given by the Stark-broadening tables of Schöning & Butler (1989). We are also considering Stark broadening used by the SYNSPEC code (Hubeny & Lanz 2011b) to build computed by Tremblay & Bergeron (2009). synthetic spectra. The spectral grid coverage is between 1000–10,000 Å with steps of 0.01 Å. The resulting spectrum was subsequently 3. Synthetic Spectra processed with the ROTIN code (Hubeny & Lanz 2011b),which resamples the original synthetic spectrum but considering that no We computed the grid of synthetic spectra with the SYNSPEC code designed to synthesize the emergent spectra from atmos- phere model structures. We used the NLTE atmosphere structure http://kurucz.harvard.edu/linelists.html from TLUSTY models (Hubeny 1988; Hubeny & Lanz 2011a) http://wwwuser.oats.inaf.it/castelli/linelists.html 5 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. Figure 4. Sample spectra with coverage from 1000–9000 Å without instrumental broadening for different temperatures from top (65,000 K) to bottom (10,000 K), log g [cgs] = 5.5 with halo and He-rich abundances. rotational velocity and no instrumental degradation have been interpolation in the grid was performed as the intent is not to taken into account. determine exact abundances or stellar parameters, but rather to We show the normalized emergent flux (in arbitrary units) exhibit the grid potentialities. The targets were selected from the given as a function of wavelength for the spectral coverage subdwarf catalog in Lei et al. (2019) and Hubble Space from 1000 to 9000 Å in Figure 4. A forest of lines is seen at Telescope’s (HST)/Space Telescope Imaging Spectrograph (STIS) this particular sampling, where no instrumental degradation is Legacy Archive data. They are located in the solar neighborhood. included. They are synthetic spectra with T equal to 65,000, According to Lei et al. (2019), the target Lamost 442708048 eff 45,000, 35,000, 30,000, 25,000, 20,000, 15,000. and 10,000 K has T = 26,620 ± 70 K, log g = 5.53 ± 0.01 [cgs], log (n / eff He (from top to bottom) and log g [cgs] = 5.5 with halo and He- n ) = −2.78 ± 0.05, E(B − V ) = 0.018 and, from the Gaia rich abundances. Collaboration et al. (2018) parallax, its distance is 317 ± 5 pc. In Figure 5 we can compare the different spectral types in the We performed a comparison with models near to these values, near-UV region between 1000 and 2000 Å, where for visual within the boundaries of our grid, as T = 25,000 K, log g = eff effect it is degraded to a Gaussian instrumental profile with 5.5 [cgs], [Fe/H]= 0, and log (n /n )=−3.09 (see Figure 7 (a)). He H FWHM equal to 5 Å. The hotter spectra have a bluer Lamost 183405148 has, according to Lei et al. (2019), continuum and the He lines are dominant. The Stark broad- T = 46,270 ± 330 K, log g = 5.88 ± 0.04, log (n /n ) = eff He H ening is more evident on the coolest spectra, where a stronger 0.29 ± 0.01, E(B − V ) = 0.021, and from its parallax (Gaia Lyman series is present, besides its quasi-molecular absorption Collaboration et al. 2018) the distance is 333±9pc. The closest features. model spectrum adopted corresponds to T = 45,000 K, eff In Figure 6 we can compare the different spectral types on log g= 5.5 [cgs], [Fe/H]= 0, and log (n /n )= 0.92 (see He H the Balmer break region between 3500–6750 Å, where for Figure 7 (b)). visual effect the resolution is degraded by a Gaussian HST/STIS Legacy Archive data on the bright subdwarf HD instrumental profile with FWHM equal to 5 Å. As expected, 4539 were used to illustrate the models in the FUV. Parameters the H is mostly ionized and the Balmer series is weaker in the for this sdB are as follows: T = 26,000± 500 K, log g= 5.2± eff hotter spectra. The coolest models are not favorable to the 0.1, log (n /n )=−2.32± 0.05, E(B− V )= 0.04± 0.01 (Sale He H formation of strong He lines. Moreover, the spectra presented et al. 2008) and d= 171.6± 2.1 pc (Gaia EDR3; Gaia in Figure 6 follow the He-abundance sequence from Németh Collaboration et al. 2021). The models were scaled to match the et al. (2012), which shows low He abundance even for the He- continuum flux in the middle of each spectral range. He-poor rich sequence of cool subdwarfs. branch and halo low-Z abundances were assumed here while T eff With the purpose of illustrating the grid, we present a simple and log g were linearly interpolated from model nodes to the comparison of model spectra with the spectra of the Lamost literature values (see Figure 8). Rotation, instrumental resolution, 442708048, Lamost 183405148, and HD 4539 subdwarfs. No and exact chemical composition were neglected, which would 6 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. Figure 5. Sample spectra in the UV region (1000–2000 Å) with an FWHM Figure 6. Sample spectra in the optical region (3500–6750 Å) with FWHM resolution = 5 Å for different temperatures: from top (65,000 K) to bottom resolution = 5 Å for different temperatures: from top (65,000 K) to bottom (10,000 K), and log g [cgs] = 5.5 with halo and He-rich abundances. (10,000 K), and log g [cgs] = 5.5 with halo and He-rich abundances. explain the significant differences found in the lines and continua previously evaluated from Calspec’s standard spectrum (Bohlin offsets. By using the Gaia distances and reddening values above, et al. 2014). stellar radii compatible with typical values for subdwarfs in Figure 9 illustrate our models in two color–color panels: panel eclipsing binaries (e.g., Rebassa-Mansergas et al. (2019) could be (a) was chosen to trace the overall continuum inclination, and found. A line and/or continuum fitting of spectra can be panel (b) traces the behavior of the Balmer jump. In panel (a) we performed with the XTGRID facility (Nemeth 2019). show F469N—F673N versus FQ757N—FQ750N colors of the HST/Wide Field Camera 3 (WFC3) photometric system. The 4. Synthetic Magnitudes dependence on effective temperature is clear. Those indices measure how lower-temperature synthetic models have a flatter Synthetic magnitudes have been computed for several standard continuum in the optical region. The point-size scale represents photometric bands to trend the grid’s behavior in the color indices the surface gravity, where larger symbols relate to lower gravity space and provide a comparison with photometry data. We used (log g= 4.5), and smaller symbols stand for higher gravity the filter response functions available on the Filter Profile Service (log g= 6.5), which also reveal a linear dependence in the color at the Spanish Virtual Observatory to convolve our synthetic integrated fluxes in the AB and Vega systems. The filters were space. Finally, the circles represent solar abundance and down- interpolated in the spectra wavelength steps within the pointing triangles represent low halo metallicity, which has no Shannon–Whittaker scheme. Photon-counting integrated fluxes clear separation on the diagram. were assumed (Bessell et al. 1998). Vega’s zero-points were In Figure 9(b) the Strömgren photometric system indices were used. Zero-points were derived from Vega ubvy magnitudes (Hauck & Mermilliod 1998) and its calibrated spectrum from the http://svo.cab.inta-csic.es/main/index.php STScI CALSPEC database (Bohlin et al. 2014).The color–color 7 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. Figure 10. Color–color diagram (g–r vs. u–g) composed of observational data on subdwarfs from SDSS (see text) with a hue scale representing determined effective temperatures, while the gray crosses show an undetermined effective temperature. The synthetic colors from our grid are plotted with the same hue, style, and size scales as in Figure 9. diagram of Figure 9(b) was constructed with u (349.6 nm) – v Figure 7. Top: comparison between the observed spectrum of subdwarf (410.3 nm) and v–b (466.6nm) colors. It shows a temperature Lamost 4427080 (dashed purple) and the model spectrum with T = 25,000 K eff dependence of the Balmer break, which is more evident and also and log g = 5.5 (solid green). Bottom: comparison between the observed gravity-dependent for cooler atmospheres. spectrum of Lamost 183405148 (dashed purple) and the model spectrum with T = 45,000 K and log g = 5.5 (solid blue). eff The study of the 5874 hot subdwarf stars with Gaia Data Release 2 by Geier (2020) is the most complete sample of subdwarfs. From this catalog we selected data from 3450 targets (1482 with determined effective temperature and colors) observed by the Sloan Digital Sky Survey (SDSS) photometric system to compare with the grid synthetic magnitudes. The color–color diagram in Figure 10 is composed of g–r and u–g colors without any color cutoff. Observational data with a determined effective temperature are shown as dots scaled by hue, while those with an undetermined effective temperature are gray crosses. Our synthetic colors are displayed in the same hue, style, and size scales as in Figure 9, matching the sdO, sdB, and sdOB previously classified by Geier (2020). The upper data sequence represents the subdwarf composite binaries with main-sequence star companions. Figure 8. Comparison between the observed HST/STIS UV spectrum of HD 4539 (dashed purple) and an interpolated model spectrum with T 26,000 K eff and log g = 5.2 (solid green). 5. Summary We presented a grid of NLTE, fully blanketed theoretical spectra and synthetic photometry for hot and moderately cool subdwarf stars. The atmosphere models were computed considering line blanketing of H, He, C, N, O, Ne, Mg, Al, Si, S, and Fe. The effective temperatures are T = 10,000, eff 15,000, 20,000, 25,000, 30,000, 35,000, 45,000, and 65,000 K, while the surface gravities are log g [cgs] = 4.5, 5.5, and 6.5. The two representative chemical abundances are solar and Galactic halos, each one with two extreme scenarios for He- rich and He-poor stellar atmospheres. The main differences between LTE and NLTE atmosphere structures are shown for these objects. They have significant differences in the outermost atmospheres, leading to distinct line-core profile formation. Figure 9. Color–color diagrams with the scale showing the effective temperatures, while the point-size scale shows the surface gravities (larger to lower gravity (4.5) The complete high-resolution spectral synthesis is performed and smaller to the higher gravity (6.5)); the circles indicate solar abundances and from the UV to near-IR (1000 to 10,000 Å) in 0.01 Å steps. We down-pointing triangles the low halo metallicity. (a) Color–color diagram for provided an illustrative analysis for the UV and the optical HST/WFC3 indices F469N—F673N and FQ757N—FQ750N. (b) Color–color regions by comparing our models with observed spectra from diagram for classical Strömgren u (349.6 nm) – v (410.3 nm) and v–b (466.6 nm) indices, aiming to probe the Balmer discontinuity. LAMOST and HST/STIS Legacy Archive data. 8 The Astrophysical Journal Supplement Series, 256:41 (10pp), 2021 October Pacheco et al. The behavior of the color indices were analyzed using the Coelho, P. R. T. 2014, MNRAS, 440, 1027 Dorsch, M., Latour, M., & Heber, U. 2018, OAst, 27, 19 HST/WFC3 and the Strömgren photometric systems. A clear Dorsch, M., Latour, M., & Heber, U. 2019, A&A, 630, A130 separation in effective temperature can be seen, as well as Edelmann, H., Heber, U., Hagen, H. J., et al. 2003, A&A, 400, 939 gravity for lower-temperature models, as provided by the Fernley, J. A., Hibbert, A., Kingston, A. E., & Seaton, M. J. 1999, JPhB, Balmer discontinuity. We also matched our synthetic magni- 32, 5507 Fontaine, G., Bergeron, P., Brassard, P., et al. 2019, ApJ, 880, 79 tudes against SDSS subdwarf data with fair agreement. Fontaine, G., Brassard, P., Charpinet, S., et al. 2012, A&A, 539, A12 These results pave the way for both spectroscopic and Fontaine, G., Villeneuve, B., & Wilson, J. 1981, ApJ, 243, 550 photometric analyses of fundamental parameters in isolated or Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1 binary objects which, in turn, may provide a more detailed Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, insight into the atmosphere models themselves. In addition, 649, A1 Geier, S. 2020, A&A, 635, A193 classical stellar population synthesis analysis can make use of Geier, S., Heber, U., Podsiadlowski, P., et al. 2010, A&A, 519, A25 the homogeneous spectral grid to better understand the blue Geier, S., Raddi, R., Gentile Fusillo, N. P., & Marsh, T. R. 2019, A&A, and UV properties of old stellar populations. The full spectral 621, A38 grid and synthetic indices are available in the IAG-USP, Geier, S., Østensen, R. H., Nemeth, P., et al. 2017, OAst, 26, 164 5 6 Green, E. M., Fontaine, G., Hyde, E. A., For, B.-Q., & Chayer, P. 2008, in ASP SVO, and Vizier databases. Conf. Ser. 392, Hot Subdwarf Stars and Related Objects, ed. U. Heber et al. 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